diff --git a/CNAME b/CNAME
index 309da1f..6990feb 100644
--- a/CNAME
+++ b/CNAME
@@ -1 +1 @@
-theread.me
+mahdi.blog
diff --git a/_art/iran-yeylaq.md b/_art/2018-07-18-iran-yeylaq.md
similarity index 89%
rename from _art/iran-yeylaq.md
rename to _art/2018-07-18-iran-yeylaq.md
index b63bfe7..94aa644 100644
--- a/_art/iran-yeylaq.md
+++ b/_art/2018-07-18-iran-yeylaq.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "iran-yeylaq"
-date:   2021-03-12
+date:   2018-07-18
 categories: art
 author: Mahdi
 ---
diff --git a/_art/ox-bathing.md b/_art/2018-09-10-ox-bathing.md
similarity index 89%
rename from _art/ox-bathing.md
rename to _art/2018-09-10-ox-bathing.md
index c956b6f..2444eb1 100644
--- a/_art/ox-bathing.md
+++ b/_art/2018-09-10-ox-bathing.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "ox-bathing"
-date:   2021-02-01
+date:   2018-09-10
 categories: art
 author: Mahdi
 ---
diff --git a/_art/shepherd.md b/_art/2018-09-21-shepherd.md
similarity index 90%
rename from _art/shepherd.md
rename to _art/2018-09-21-shepherd.md
index b29d26b..2190525 100644
--- a/_art/shepherd.md
+++ b/_art/2018-09-21-shepherd.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "shepherd"
-date:   2021-03-12
+date:   2018-09-21
 categories: art
 author: Mahdi
 ---
diff --git a/_art/dog-and-puppy.md b/_art/2018-09-23-dog-and-puppy.md
similarity index 94%
rename from _art/dog-and-puppy.md
rename to _art/2018-09-23-dog-and-puppy.md
index e3c1b07..811f759 100644
--- a/_art/dog-and-puppy.md
+++ b/_art/2018-09-23-dog-and-puppy.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "dog-and-puppy"
-date:   2021-03-12
+date:   2018-09-23
 categories: art
 author: Mahdi
 ---
diff --git a/_art/tabatabaei-house.md b/_art/2019-02-22-tabatabaei-house.md
similarity index 91%
rename from _art/tabatabaei-house.md
rename to _art/2019-02-22-tabatabaei-house.md
index 88716dc..636f104 100644
--- a/_art/tabatabaei-house.md
+++ b/_art/2019-02-22-tabatabaei-house.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "tabatabaei-house"
-date:   2021-03-12
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 categories: art
 author: Mahdi
 ---
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similarity index 89%
rename from _art/jebir.md
rename to _art/2019-09-10-jebir.md
index 8dfac21..fef60a1 100644
--- a/_art/jebir.md
+++ b/_art/2019-09-10-jebir.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "jebir"
-date:   2021-02-01
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 categories: art
 author: Mahdi
 ---
diff --git a/_art/birds-sunrise-sea-iran.md b/_art/2019-10-29-birds-sunrise-sea-iran.md
similarity index 91%
rename from _art/birds-sunrise-sea-iran.md
rename to _art/2019-10-29-birds-sunrise-sea-iran.md
index 5514663..535b6cf 100644
--- a/_art/birds-sunrise-sea-iran.md
+++ b/_art/2019-10-29-birds-sunrise-sea-iran.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "birds-sunrise-sea-iran"
-date:   2021-03-12
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 categories: art
 author: Mahdi
 ---
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similarity index 91%
rename from _art/darak-2.md
rename to _art/2019-10-30-darak-2.md
index 6d8763e..993c46b 100644
--- a/_art/darak-2.md
+++ b/_art/2019-10-30-darak-2.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "darak-2"
-date:   2021-03-12
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 categories: art
 author: Mahdi
 ---
diff --git a/_art/darak.md b/_art/2019-10-30-darak.md
similarity index 91%
rename from _art/darak.md
rename to _art/2019-10-30-darak.md
index 99a9c32..9d3e825 100644
--- a/_art/darak.md
+++ b/_art/2019-10-30-darak.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "darak"
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 categories: art
 author: Mahdi
 ---
diff --git a/_art/windcatcher.md b/_art/2019-10-31-windcatcher.md
similarity index 96%
rename from _art/windcatcher.md
rename to _art/2019-10-31-windcatcher.md
index 4be64a9..0da47d9 100644
--- a/_art/windcatcher.md
+++ b/_art/2019-10-31-windcatcher.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "windcatcher"
-date:   2021-02-01
+date:   2019-10-31
 categories: art
 author: Mahdi
 ---
diff --git a/_art/flamingos-iran.md b/_art/2019-11-03-flamingos-iran.md
similarity index 91%
rename from _art/flamingos-iran.md
rename to _art/2019-11-03-flamingos-iran.md
index 00d42aa..c57f376 100644
--- a/_art/flamingos-iran.md
+++ b/_art/2019-11-03-flamingos-iran.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "flamingos-iran"
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 categories: art
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 ---
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similarity index 93%
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index e1b6b97..c86aacd 100644
--- a/_art/christmas-day-homeless-man-church.md
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@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "christmas-day-homeless-man-church"
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 categories: art
 author: Mahdi
 ---
diff --git a/_art/cemetery.md b/_art/2020-03-15-cemetery.md
similarity index 93%
rename from _art/cemetery.md
rename to _art/2020-03-15-cemetery.md
index 49e9153..573ce77 100644
--- a/_art/cemetery.md
+++ b/_art/2020-03-15-cemetery.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "cemetery"
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 categories: art
 author: Mahdi
 ---
diff --git a/_art/dublin-chimneys.md b/_art/2020-05-06-dublin-chimneys.md
similarity index 90%
rename from _art/dublin-chimneys.md
rename to _art/2020-05-06-dublin-chimneys.md
index 17bd52e..9f7c001 100644
--- a/_art/dublin-chimneys.md
+++ b/_art/2020-05-06-dublin-chimneys.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "dublin-chimneys"
-date:   2021-03-12
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 categories: art
 author: Mahdi
 ---
diff --git a/_art/grey-heron-bushy-park.md b/_art/2020-05-16-grey-heron-bushy-park.md
similarity index 91%
rename from _art/grey-heron-bushy-park.md
rename to _art/2020-05-16-grey-heron-bushy-park.md
index 3e7fc37..f26b1d5 100644
--- a/_art/grey-heron-bushy-park.md
+++ b/_art/2020-05-16-grey-heron-bushy-park.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "grey-heron-bushy-park"
-date:   2021-03-12
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 categories: art
 author: Mahdi
 ---
diff --git a/_art/not-silent.md b/_art/2020-10-18-not-silent.md
similarity index 90%
rename from _art/not-silent.md
rename to _art/2020-10-18-not-silent.md
index 97935c8..22f7c51 100644
--- a/_art/not-silent.md
+++ b/_art/2020-10-18-not-silent.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "not-silent"
-date:   2021-03-12
+date:   2020-10-18
 categories: art
 author: Mahdi
 ---
diff --git a/_art/drummer-vanishing.md b/_art/2020-10-21-drummer-vanishing.md
similarity index 90%
rename from _art/drummer-vanishing.md
rename to _art/2020-10-21-drummer-vanishing.md
index 92c69dd..5669a8c 100644
--- a/_art/drummer-vanishing.md
+++ b/_art/2020-10-21-drummer-vanishing.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "drummer-vanishing"
-date:   2021-03-12
+date:   2020-10-21
 categories: art
 author: Mahdi
 ---
diff --git a/_art/sightings-from-a-dream-1.md b/_art/2020-12-18-sightings-from-a-dream-1.md
similarity index 94%
rename from _art/sightings-from-a-dream-1.md
rename to _art/2020-12-18-sightings-from-a-dream-1.md
index f04cdad..d97d328 100644
--- a/_art/sightings-from-a-dream-1.md
+++ b/_art/2020-12-18-sightings-from-a-dream-1.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "sightings-from-a-dream-1"
-date:   2021-03-12
+date:   2020-12-18
 categories: art
 author: Mahdi
 ---
diff --git a/_art/sightings-from-a-dream-2.md b/_art/2020-12-19-sightings-from-a-dream-2.md
similarity index 91%
rename from _art/sightings-from-a-dream-2.md
rename to _art/2020-12-19-sightings-from-a-dream-2.md
index 290a90a..d0bfb61 100644
--- a/_art/sightings-from-a-dream-2.md
+++ b/_art/2020-12-19-sightings-from-a-dream-2.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "sightings-from-a-dream-2"
-date:   2021-03-12
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 categories: art
 author: Mahdi
 ---
diff --git a/_art/sightings-from-a-dream-3.md b/_art/2020-12-20-sightings-from-a-dream-3.md
similarity index 91%
rename from _art/sightings-from-a-dream-3.md
rename to _art/2020-12-20-sightings-from-a-dream-3.md
index 4ccbc84..3ecbdce 100644
--- a/_art/sightings-from-a-dream-3.md
+++ b/_art/2020-12-20-sightings-from-a-dream-3.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "sightings-from-a-dream-3"
-date:   2021-03-12
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 categories: art
 author: Mahdi
 ---
diff --git a/_art/sightings-from-a-dream-4.md b/_art/2020-12-21-sightings-from-a-dream-4.md
similarity index 91%
rename from _art/sightings-from-a-dream-4.md
rename to _art/2020-12-21-sightings-from-a-dream-4.md
index ba0d42d..e1be591 100644
--- a/_art/sightings-from-a-dream-4.md
+++ b/_art/2020-12-21-sightings-from-a-dream-4.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "sightings-from-a-dream-4"
-date:   2021-03-12
+date:   2020-12-21
 categories: art
 author: Mahdi
 ---
diff --git a/_art/sightings-from-a-dream-5.md b/_art/2020-12-22-sightings-from-a-dream-5.md
similarity index 91%
rename from _art/sightings-from-a-dream-5.md
rename to _art/2020-12-22-sightings-from-a-dream-5.md
index ab60672..64d7449 100644
--- a/_art/sightings-from-a-dream-5.md
+++ b/_art/2020-12-22-sightings-from-a-dream-5.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "sightings-from-a-dream-5"
-date:   2021-03-12
+date:   2020-12-22
 categories: art
 author: Mahdi
 ---
diff --git a/_art/tired-eyes-tired-minds-tired-souls.md b/_art/2020-12-25-tired-eyes-tired-minds-tired-souls.md
similarity index 93%
rename from _art/tired-eyes-tired-minds-tired-souls.md
rename to _art/2020-12-25-tired-eyes-tired-minds-tired-souls.md
index 3fbd420..939465e 100644
--- a/_art/tired-eyes-tired-minds-tired-souls.md
+++ b/_art/2020-12-25-tired-eyes-tired-minds-tired-souls.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "tired-eyes-tired-minds-tired-souls"
-date:   2021-03-12
+date:   2020-12-25
 categories: art
 author: Mahdi
 ---
diff --git a/_art/i-cast-a-spell-on-the-city.md b/_art/2020-12-26-i-cast-a-spell-on-the-city.md
similarity index 92%
rename from _art/i-cast-a-spell-on-the-city.md
rename to _art/2020-12-26-i-cast-a-spell-on-the-city.md
index 30cd5b3..fb2a8f7 100644
--- a/_art/i-cast-a-spell-on-the-city.md
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@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "i-cast-a-spell-on-the-city"
-date:   2021-03-12
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 categories: art
 author: Mahdi
 ---
diff --git a/_art/galileo.md b/_art/2020-12-27-galileo.md
similarity index 93%
rename from _art/galileo.md
rename to _art/2020-12-27-galileo.md
index d1d908a..91abd32 100644
--- a/_art/galileo.md
+++ b/_art/2020-12-27-galileo.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "smell-like-trees"
-date:   2021-02-01
+date:   2020-12-27
 categories: art
 author: Mahdi
 ---
diff --git a/_art/dark-street-light.md b/_art/2020-12-28-dark-street-light.md
similarity index 95%
rename from _art/dark-street-light.md
rename to _art/2020-12-28-dark-street-light.md
index 93b52a8..b8809ac 100644
--- a/_art/dark-street-light.md
+++ b/_art/2020-12-28-dark-street-light.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "dark-street-light"
-date:   2021-03-12
+date:   2020-12-28
 categories: art
 author: Mahdi
 ---
diff --git a/_art/deer-silhouette.md b/_art/2020-12-30-deer-silhouette.md
similarity index 90%
rename from _art/deer-silhouette.md
rename to _art/2020-12-30-deer-silhouette.md
index 7ee58bf..038993d 100644
--- a/_art/deer-silhouette.md
+++ b/_art/2020-12-30-deer-silhouette.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "deer-silhouette"
-date:   2021-03-12
+date:   2020-12-30
 categories: art
 author: Mahdi
 ---
diff --git a/_art/deer-above.md b/_art/2020-12-31-deer-above.md
similarity index 90%
rename from _art/deer-above.md
rename to _art/2020-12-31-deer-above.md
index dde231b..9780162 100644
--- a/_art/deer-above.md
+++ b/_art/2020-12-31-deer-above.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "deer-above"
-date:   2021-03-12
+date:   2020-12-31
 categories: art
 author: Mahdi
 ---
diff --git a/_art/clouds-among-rocks.md b/_art/2021-01-01-clouds-among-rocks.md
similarity index 91%
rename from _art/clouds-among-rocks.md
rename to _art/2021-01-01-clouds-among-rocks.md
index e264e4a..4cf0893 100644
--- a/_art/clouds-among-rocks.md
+++ b/_art/2021-01-01-clouds-among-rocks.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "clouds-among-rocks"
-date:   2021-03-12
+date:   2021-01-01
 categories: art
 author: Mahdi
 ---
diff --git a/_art/yazd-children.md b/_art/2021-01-01-yazd-children.md
similarity index 90%
rename from _art/yazd-children.md
rename to _art/2021-01-01-yazd-children.md
index 74a0147..cc31552 100644
--- a/_art/yazd-children.md
+++ b/_art/2021-01-01-yazd-children.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "yazd-children"
-date:   2021-02-01
+date:   2021-01-01
 categories: art
 author: Mahdi
 ---
diff --git a/_art/organs.md b/_art/2021-01-04-organs.md
similarity index 93%
rename from _art/organs.md
rename to _art/2021-01-04-organs.md
index 3d19709..493dbab 100644
--- a/_art/organs.md
+++ b/_art/2021-01-04-organs.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "organs"
-date:   2021-03-12
+date:   2021-01-04
 categories: art
 author: Mahdi
 ---
diff --git a/_art/smell-like-trees.md b/_art/2021-01-06-smell-like-trees.md
similarity index 95%
rename from _art/smell-like-trees.md
rename to _art/2021-01-06-smell-like-trees.md
index fceb797..48e512e 100644
--- a/_art/smell-like-trees.md
+++ b/_art/2021-01-06-smell-like-trees.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "galileo"
-date:   2021-02-01
+date:   2021-01-06
 categories: art
 author: Mahdi
 ---
diff --git a/_art/birds-in-form.md b/_art/2021-01-08-birds-in-form.md
similarity index 92%
rename from _art/birds-in-form.md
rename to _art/2021-01-08-birds-in-form.md
index d2296a4..0beaa63 100644
--- a/_art/birds-in-form.md
+++ b/_art/2021-01-08-birds-in-form.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "birds-in-form"
-date:   2021-03-12
+date:   2021-01-08
 categories: art
 author: Mahdi
 ---
diff --git a/_art/preparation.md b/_art/2021-01-10-preparation.md
similarity index 92%
rename from _art/preparation.md
rename to _art/2021-01-10-preparation.md
index 41c85ac..1dcc062 100644
--- a/_art/preparation.md
+++ b/_art/2021-01-10-preparation.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "preparation"
-date:   2021-02-01
+date:   2021-01-10
 categories: art
 author: Mahdi
 ---
diff --git a/_art/the-night-has-descended-on-us.md b/_art/2021-01-10-the-night-has-descended-on-us.md
similarity index 92%
rename from _art/the-night-has-descended-on-us.md
rename to _art/2021-01-10-the-night-has-descended-on-us.md
index b99cd06..9b853ff 100644
--- a/_art/the-night-has-descended-on-us.md
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@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "the-night-has-descended-on-us"
-date:   2021-03-12
+date:   2021-01-10
 categories: art
 author: Mahdi
 ---
diff --git a/_art/male-back.md b/_art/2021-01-12-male-back.md
similarity index 92%
rename from _art/male-back.md
rename to _art/2021-01-12-male-back.md
index 983f035..2012c4a 100644
--- a/_art/male-back.md
+++ b/_art/2021-01-12-male-back.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "male-back"
-date:   2021-03-12
+date:   2021-01-12
 categories: art
 author: Mahdi
 ---
diff --git a/_art/on-mourra-seul.md b/_art/2021-01-13-on-mourra-seul.md
similarity index 90%
rename from _art/on-mourra-seul.md
rename to _art/2021-01-13-on-mourra-seul.md
index 077b815..7fb99dd 100644
--- a/_art/on-mourra-seul.md
+++ b/_art/2021-01-13-on-mourra-seul.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "on-mourra-seul"
-date:   2021-02-01
+date:   2021-01-13
 categories: art
 author: Mahdi
 ---
diff --git a/_art/god-will-pardon-me.md b/_art/2021-01-28-god-will-pardon-me.md
similarity index 92%
rename from _art/god-will-pardon-me.md
rename to _art/2021-01-28-god-will-pardon-me.md
index 81878a3..25e4b1f 100644
--- a/_art/god-will-pardon-me.md
+++ b/_art/2021-01-28-god-will-pardon-me.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "god-will-pardon-me"
-date:   2021-03-12
+date:   2021-01-28
 categories: art
 author: Mahdi
 ---
diff --git a/_art/la-vida.md b/_art/2021-02-25-la-vida.md
similarity index 91%
rename from _art/la-vida.md
rename to _art/2021-02-25-la-vida.md
index 2980d42..837fb32 100644
--- a/_art/la-vida.md
+++ b/_art/2021-02-25-la-vida.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "la-vida"
-date:   2021-02-01
+date:   2021-02-25
 categories: art
 author: Mahdi
 ---
diff --git a/_art/un-grand-peut-etre.md b/_art/2021-03-01-un-grand-peut-etre.md
similarity index 91%
rename from _art/un-grand-peut-etre.md
rename to _art/2021-03-01-un-grand-peut-etre.md
index 4a8e655..bb5c2d9 100644
--- a/_art/un-grand-peut-etre.md
+++ b/_art/2021-03-01-un-grand-peut-etre.md
@@ -1,7 +1,7 @@
 ---
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 title: "un-grand-peut-etre"
-date:   2021-03-12
+date:   2021-03-01
 categories: art
 author: Mahdi
 ---
diff --git a/_art/sky.md b/_art/2021-03-06-sky.md
similarity index 93%
rename from _art/sky.md
rename to _art/2021-03-06-sky.md
index c15b067..9ffc71d 100644
--- a/_art/sky.md
+++ b/_art/2021-03-06-sky.md
@@ -1,7 +1,7 @@
 ---
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 title: "sky"
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 ---
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similarity index 92%
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index af4a69b..c863616 100644
--- a/_art/history-so-close-it-comes-alive.md
+++ b/_art/2021-03-07-history-so-close-it-comes-alive.md
@@ -1,7 +1,7 @@
 ---
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-date:   2021-03-12
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 ---
diff --git a/_art/boy.md b/_art/2021-05-12-boy.md
similarity index 87%
rename from _art/boy.md
rename to _art/2021-05-12-boy.md
index 14f4f9e..317b4dc 100644
--- a/_art/boy.md
+++ b/_art/2021-05-12-boy.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "boy"
-date:   2021-03-12
+date:   2021-05-12
 categories: art
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 ---
diff --git a/_art/ireland-abandoned.md b/_art/2021-05-22-ireland-abandoned.md
similarity index 91%
rename from _art/ireland-abandoned.md
rename to _art/2021-05-22-ireland-abandoned.md
index 4370aaa..c9a1081 100644
--- a/_art/ireland-abandoned.md
+++ b/_art/2021-05-22-ireland-abandoned.md
@@ -1,7 +1,7 @@
 ---
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 title: "ireland-abandoned"
-date:   2021-03-12
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similarity index 88%
rename from _art/grand.md
rename to _art/2021-06-19-grand.md
index 89ad8c7..50450ae 100644
--- a/_art/grand.md
+++ b/_art/2021-06-19-grand.md
@@ -1,7 +1,7 @@
 ---
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 title: "grand"
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similarity index 91%
rename from _art/blue-contagious-smile.md
rename to _art/2021-06-21-blue-contagious-smile.md
index 91e6399..181a4f1 100644
--- a/_art/blue-contagious-smile.md
+++ b/_art/2021-06-21-blue-contagious-smile.md
@@ -1,7 +1,7 @@
 ---
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 title: "blue-contagious-smile"
-date:   2021-03-12
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 ---
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similarity index 92%
rename from _art/head-wall.md
rename to _art/2021-06-23-head-wall.md
index c88027f..87519bf 100644
--- a/_art/head-wall.md
+++ b/_art/2021-06-23-head-wall.md
@@ -1,7 +1,7 @@
 ---
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-date:   2021-03-12
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 ---
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similarity index 96%
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rename to _art/2021-06-29-girl-among-grains.md
index 3996d44..14d7b23 100644
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+++ b/_art/2021-06-29-girl-among-grains.md
@@ -1,7 +1,7 @@
 ---
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-date:   2021-02-01
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 ---
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similarity index 92%
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@@ -1,7 +1,7 @@
 ---
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-date:   2021-03-12
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similarity index 87%
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index 638bd1a..33b4d3f 100644
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 title: "sigh"
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index 496a282..23af6df 100644
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@@ -1,7 +1,7 @@
 ---
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diff --git a/_art/concrete-jungle-trees.md b/_art/2021-08-20-concrete-jungle-trees.md
similarity index 91%
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rename to _art/2021-08-20-concrete-jungle-trees.md
index 68a6dcf..34a921d 100644
--- a/_art/concrete-jungle-trees.md
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@@ -1,7 +1,7 @@
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-date:   2021-03-12
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similarity index 90%
rename from _art/punk-gangster.md
rename to _art/2021-08-20-punk-gangster.md
index 369eccc..edd907c 100644
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@@ -1,7 +1,7 @@
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similarity index 92%
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index cb254e6..9d71780 100644
--- a/_art/et-les-extremes-se-touchent.md
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-date:   2021-03-12
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diff --git a/_art/girl-eye-flowers-1.md b/_art/2021-08-21-girl-eye-flowers-1.md
similarity index 90%
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index 82b14b7..038ac73 100644
--- a/_art/girl-eye-flowers-1.md
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@@ -1,7 +1,7 @@
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-date:   2021-03-12
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diff --git a/_art/girl-eye-flowers-2.md b/_art/2021-08-21-girl-eye-flowers-2.md
similarity index 90%
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index f8723b0..232fdeb 100644
--- a/_art/girl-eye-flowers-2.md
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@@ -1,7 +1,7 @@
 ---
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 title: "girl-eye-flowers-2"
-date:   2021-03-12
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diff --git a/_art/girl-eye-flowers-3.md b/_art/2021-08-21-girl-eye-flowers-3.md
similarity index 90%
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index 3a76fdd..81343f2 100644
--- a/_art/girl-eye-flowers-3.md
+++ b/_art/2021-08-21-girl-eye-flowers-3.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "girl-eye-flowers-3"
-date:   2021-03-12
+date:   2021-08-21
 categories: art
 author: Mahdi
 ---
diff --git a/_art/the-right-way-is-the-untrodden.md b/_art/2021-08-29-the-right-way-is-the-untrodden.md
similarity index 93%
rename from _art/the-right-way-is-the-untrodden.md
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index 432ab45..040cfc3 100644
--- a/_art/the-right-way-is-the-untrodden.md
+++ b/_art/2021-08-29-the-right-way-is-the-untrodden.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "the-right-way-is-the-untrodden"
-date:   2021-03-12
+date:   2021-08-29
 categories: art
 author: Mahdi
 ---
diff --git a/_art/hill-of-tara.md b/_art/2021-09-24-hill-of-tara.md
similarity index 90%
rename from _art/hill-of-tara.md
rename to _art/2021-09-24-hill-of-tara.md
index 9300bfb..e72ff3f 100644
--- a/_art/hill-of-tara.md
+++ b/_art/2021-09-24-hill-of-tara.md
@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "hill-of-tara"
-date:   2021-03-12
+date:   2021-09-24
 categories: art
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 ---
diff --git a/_art/time-traveller.md b/_art/2021-11-30-time-traveller.md
similarity index 90%
rename from _art/time-traveller.md
rename to _art/2021-11-30-time-traveller.md
index 9959608..f6d2d48 100644
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@@ -1,7 +1,7 @@
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diff --git a/_art/milan-cathedral.md b/_art/2021-12-23-milan-cathedral.md
similarity index 92%
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rename to _art/2021-12-23-milan-cathedral.md
index cde3038..646d925 100644
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@@ -1,7 +1,7 @@
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 title: "milan-cathedral"
-date:   2021-03-12
+date:   2021-12-23
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diff --git a/_art/mount-tibidabo-cathedral.md b/_art/2021-12-24-mount-tibidabo-cathedral.md
similarity index 95%
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index d65bc29..f9c4d8d 100644
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@@ -1,7 +1,7 @@
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diff --git a/_art/switzerland-white-tree.md b/_art/2021-12-27-switzerland-white-tree.md
similarity index 91%
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rename to _art/2021-12-27-switzerland-white-tree.md
index 1ef8f7d..cbd13f3 100644
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@@ -1,7 +1,7 @@
 ---
 layout: post
 title: "switzerland-white-tree"
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 categories: art
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diff --git a/_art/crucifixion-sagrada-familia.md b/_art/2022-01-13-crucifixion-sagrada-familia.md
similarity index 91%
rename from _art/crucifixion-sagrada-familia.md
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index 5cbde0c..4dd1717 100644
--- a/_art/crucifixion-sagrada-familia.md
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@@ -1,7 +1,7 @@
 ---
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 title: "crucifixion-sagrada-familia"
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 categories: art
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 ---
diff --git a/_art/dead-baluga.md b/_art/2022-06-27-dead-baluga.md
similarity index 100%
rename from _art/dead-baluga.md
rename to _art/2022-06-27-dead-baluga.md
diff --git a/_art/highland-cow-1.md b/_art/2022-06-27-highland-cow-1.md
similarity index 100%
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rename to _art/2022-06-27-highland-cow-1.md
diff --git a/_art/highland-cow-2.md b/_art/2022-06-27-highland-cow-2.md
similarity index 100%
rename from _art/highland-cow-2.md
rename to _art/2022-06-27-highland-cow-2.md
diff --git a/_art/lundy-nature-reserve.md b/_art/2022-06-27-lundy-nature-reserve.md
similarity index 100%
rename from _art/lundy-nature-reserve.md
rename to _art/2022-06-27-lundy-nature-reserve.md
diff --git a/_art/pelican-of-london.md b/_art/2022-06-27-pelican-of-london.md
similarity index 100%
rename from _art/pelican-of-london.md
rename to _art/2022-06-27-pelican-of-london.md
diff --git a/_art/puffin.md b/_art/2022-06-27-puffin.md
similarity index 100%
rename from _art/puffin.md
rename to _art/2022-06-27-puffin.md
diff --git a/_art/seals.md b/_art/2022-06-27-seals.md
similarity index 100%
rename from _art/seals.md
rename to _art/2022-06-27-seals.md
diff --git a/_art/baled-hay.md b/_art/2022-08-05-baled-hay.md
similarity index 89%
rename from _art/baled-hay.md
rename to _art/2022-08-05-baled-hay.md
index e6dd3ed..59828f3 100644
--- a/_art/baled-hay.md
+++ b/_art/2022-08-05-baled-hay.md
@@ -1,7 +1,7 @@
 ---
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 title: "baled-hay"
-date:   2021-03-12
+date:   2021-08-05
 categories: art
 author: Mahdi
 ---
diff --git a/art.html b/art.html
index d5496e8..ff5243e 100644
--- a/art.html
+++ b/art.html
@@ -4,7 +4,7 @@ layout: default
 
 <div class="home art">
   <ul class="post-list">
-    {% for post in site.art %}
+    {% for post in site.art reversed %}
       {% if post.published == false %}
         {% continue %}
       {% endif %}
diff --git a/life.html b/life.html
deleted file mode 100644
index 83cc7ea..0000000
--- a/life.html
+++ /dev/null
@@ -1,4 +0,0 @@
----
-layout: category
-category: life
----
diff --git a/math.html b/math.html
deleted file mode 100644
index 117fd7c..0000000
--- a/math.html
+++ /dev/null
@@ -1,4 +0,0 @@
----
-layout: category
-category: math
----
diff --git a/programming.html b/programming.html
deleted file mode 100644
index ca2fb3e..0000000
--- a/programming.html
+++ /dev/null
@@ -1,4 +0,0 @@
----
-layout: category
-category: programming
----
diff --git a/site/CNAME b/site/CNAME
new file mode 100644
index 0000000..309da1f
--- /dev/null
+++ b/site/CNAME
@@ -0,0 +1 @@
+theread.me
diff --git a/site/README.md b/site/README.md
new file mode 100644
index 0000000..6050a08
--- /dev/null
+++ b/site/README.md
@@ -0,0 +1,3 @@
+mahdi.blog
+==========
+
diff --git a/site/about/index.html b/site/about/index.html
new file mode 100644
index 0000000..6fc5fe0
--- /dev/null
+++ b/site/about/index.html
@@ -0,0 +1,110 @@
+<!DOCTYPE html>
+<html>
+
+  <head>
+  <meta charset="utf-8">
+  <meta http-equiv="X-UA-Compatible" content="IE=edge">
+  <meta name="viewport" content="width=device-width, initial-scale=1">
+
+  <title>About</title>
+  <meta name="description" content="a rabbit hole">
+
+  <link href="https://fonts.googleapis.com/css?family=Secular+One|Nunito|Mononoki" rel="stylesheet"> 
+  <link rel="stylesheet" href="/css/main.css">
+  <link rel="canonical" href="http://localhost:4000/about/">
+  <link rel="alternate" type="application/rss+xml" title="mahdi" href="http://localhost:4000/feed.xml" />
+
+  
+
+  <!--<script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script>-->
+
+  <script>
+    var channel = new BroadcastChannel('egg');
+
+    channel.addEventListener('message', message => {
+      alert('Got a message from the other tab:\n' + message.data);
+    });
+  </script>
+</head>
+
+
+
+  <body>
+
+    <header class="site-header">
+
+  <h1>
+    <a class='site-title' href='/'>
+      mahdi
+    </a>
+  </h1>
+
+  <nav>
+    <p>
+      <a href="/snippets">snippets</a>
+      <a href="/art">pictures</a>
+    </p>
+    <!--<p class='categories'>-->
+      <!---->
+        <!---->
+        <!--<a href="">art</a>-->
+        <!---->
+      <!---->
+        <!---->
+      <!---->
+    <!--</p>-->
+    <p>
+      <a href='mailto:mdibaiee@pm.me'>email</a>
+      <a href='https://git.mahdi.blog/mahdi'>git</a>
+      <a href='https://www.librarything.com/profile/mdibaiee'>librarything</a>
+      <a href="http://localhost:4000/feed.xml">feed</a>
+    </p>
+  </nav>
+
+</header>
+
+
+    <div class="page-content">
+      <div class="wrapper">
+        <h1 class="page-heading"></h1>
+        
+          <div class="post">
+
+  <div class="post-header">
+    <h1 class="post-title"><p>About</p>
+</h1>
+  </div>
+
+  <article class="post-content">
+    <p>Hi, it’s Mahdi. I was born 24th of July, 1998. I write about a variety of topics here, whatever I find worthwhile to share with others.
+I like so many things I’d better just list them instead of boring you by making up a fancy sentence about them, so here, in no particular order:</p>
+
+<ul>
+  <li>Programming</li>
+  <li>Mathematics</li>
+  <li>Nature</li>
+  <li>Artificial Intelligence</li>
+  <li>Fitness</li>
+  <li>Parkour</li>
+  <li>All sorts of extreme sports: Skydiving, Scuba Diving, etc.</li>
+  <li>Primitive Living</li>
+  <li>Leadership</li>
+  <li>Human relationships</li>
+  <li>Reading</li>
+  <li>Music and Art in general</li>
+  <li>Philosophy</li>
+</ul>
+
+<p>I like communicating with people, exploring and discovering about new concepts and new possibilities, and every human being is a new concept to discover. In simpler terms, I would like to get to know you, so feel free to shoot me an email: hi@mahdi.blog</p>
+
+  </article>
+
+</div>
+
+        
+      </div>
+    </div>
+
+  </body>
+
+</html>
diff --git a/site/alternative-objectivity-and-inherent-subjectivity/index.html b/site/alternative-objectivity-and-inherent-subjectivity/index.html
new file mode 100644
index 0000000..4be7922
--- /dev/null
+++ b/site/alternative-objectivity-and-inherent-subjectivity/index.html
@@ -0,0 +1,194 @@
+<!DOCTYPE html>
+<html>
+
+  <head>
+  <meta charset="utf-8">
+  <meta http-equiv="X-UA-Compatible" content="IE=edge">
+  <meta name="viewport" content="width=device-width, initial-scale=1">
+
+  <title>On Inherent Subjectivity of Some Things</title>
+  <meta name="description" content="As a computer scientist and someone who loves mathematics and abstractions, I was obsessed with the idea of rationality, that is, an objective and absolute r...">
+
+  <link href="https://fonts.googleapis.com/css?family=Secular+One|Nunito|Mononoki" rel="stylesheet"> 
+  <link rel="stylesheet" href="/css/main.css">
+  <link rel="canonical" href="http://localhost:4000/alternative-objectivity-and-inherent-subjectivity/">
+  <link rel="alternate" type="application/rss+xml" title="mahdi" href="http://localhost:4000/feed.xml" />
+
+  
+
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+      <div class="wrapper">
+        <h1 class="page-heading"></h1>
+        
+          <div class='post lang-en'>
+
+  <div class="post-header">
+    <h1 class="post-title"><p>On Inherent Subjectivity of Some Things</p>
+</h1>
+    
+    <h2 class="post-subtitle"><p>An Alternative Definition of Objectivity for Rigid Scientists</p>
+</h1>
+    
+    <p class="post-meta">
+      <span>Oct 30, 2021</span>
+      
+      • <span>Reading time: 8  minutes</span>
+    </p>
+  </div>
+
+  <article class="post-content">
+    <p>As a computer scientist and someone who loves <a href="/mathematical-induction-proving-tiling-methods">mathematics</a> and <a href="/typoclassopedia-exercise-solutions">abstractions</a>, I was obsessed with the idea of rationality, that is, an <em>objective</em> and absolute rationality, however I ended up in a philosophy course that showed me the opposite.</p>
+
+<p>I somehow stumbled upon Eliezer Yudkowsky’s <a href="https://www.readthesequences.com/">Rationality: From AI to Zombies</a> about 4 years ago, and it took me two years to go through it all but I was absolutely fascinated by this book. I <em>knew</em> how to be rational now, and I could <em>prove</em> it using mathematics, what else could I ask for!</p>
+
+<p>The book basically looks at the world as a probabilistic system, and everything that happens can be assigned probabilities, and using mathematical theorems such as Bayes Theorem, we can predict outcomes of certain actions and then decide between them. There is a lot of focus on <a href="https://en.wikipedia.org/wiki/List_of_cognitive_biases">cognitive biases</a> as well. I was particularly very interested about these biases, and so I set out to learn more about them, and that’s how I found my current course: <a href="https://cogsci.ucd.ie">Cognitive Science at University College Dublin</a>.</p>
+
+<p>So I enter this course with this mindset: we can objectively analyse the world around us using probability and statistics (mathematics), but we are limited by our cognitive biases, so I want to learn about these cognitive biases: where do they come from, how can they be resisted to allow us to act more rationally and so on. These questions would mainly fall under the umbrella of psychology…</p>
+
+<p>However… I found myself to be more and more interested in the philosophy side of this course than the psychology side, hell I even started to not like the psychology side anymore, but fall in love with the philosophy. This is where I found the opposite of what I had come for: an alternative definition of objectivity, and an inherent subjectivity of some things. This is mainly inspired by Thomas Nagel’s What Is It Like To Be A Bat <a class="citation" href="#nagel1974like">(Nagel, 1974)</a>.</p>
+
+<h2 id="what-is-objectivity-anyway">What is Objectivity Anyway?</h2>
+
+<p>This is probably the main question here. What is objectivity? I don’t think dictionary definitions are particularly authoritative when it comes to philosophy discussions, but I found this dictionary definition interesting to open the topic with:</p>
+
+<blockquote>
+  <p>the quality or character of being objective : lack of favoritism toward one side or another : freedom from bias. <a class="citation" href="#objectivity-merriam-webster">(Merriam-Webster, 2021)</a></p>
+</blockquote>
+
+<p>This definition itself has ambiguous phrases such as “freedom from bias”, what does that mean? When can we say that we are free from bias? Let’s look at how bias is defined in the same dictionary:</p>
+
+<blockquote>
+  <p>an inclination of temperament or outlook <a class="citation" href="#bias-merriam-webster">(Merriam-Webster, 2021)</a></p>
+</blockquote>
+
+<p>But… is it really possible to have no inclination at all in our temperament and outlook? Let’s look at the definition of subjective, that will help us here:</p>
+
+<blockquote>
+  <p>relating to the way a person experiences things in his or her own mind <a class="citation" href="#subjective-merriam-webster">(Merriam-Webster, 2021)</a></p>
+</blockquote>
+
+<p>Is it possible for us to have a view of something without it being part of our experience? It seems not. All that we do, all our views and expressions and our interactions are part of our experience as a person, and it relates to us on an intimate level, which means that everything that we do as individuals is subjective. In that sense, it seems impossible for any individual to be objective, since they will always have some form of inclination about everything.</p>
+
+<p>What does this leave us with then when we ask what is objectivity? A better definition of objectivity in my opinion is one given by Thomas Nagel:</p>
+
+<blockquote>
+  <p>It may be more accurate to think of objectivity as a direction in which the understanding can travel. […] The process of reduction is a move in the direction of greater objectivity, toward a more accurate view of the real nature of things. This is accomplished by reducing our dependence on individual or species-specific points of view toward the object of investigation. We describe it not in terms of the impressions it makes on our senses, but in terms of its more general effects and of properties detectable by means other than the human senses. <a class="citation" href="#nagel1974like">(Nagel, 1974)</a></p>
+</blockquote>
+
+<p>In this sense, there is no black-and-white distinction between subjectivity and objectivity, but rather it is a spectrum, a line on which we can walk from subjectivity towards objectivity.</p>
+
+<p><img src="/img/inherent-subjectivity/subjective-objective.png" alt="Subjective-Objective spectrum: On Subjective side we have Individual perception, in the middle Agreement with others, and on the Objective side Agreement with other apparatus" /></p>
+
+<p>We start with our individual perceptions as the most objective view and description, we then move towards descriptions that allow us to agree with other (human) beings, and finally we move towards descriptions that can be verified and agreed upon by other apparatus, although it is important to understand that even the apparatus that we may use to describe things are not necessarily free from bias, since they are created by biased individuals and groups. By now you may notice that if a measuring device is made to be agreeable between a large group of people, it is already more objective than a device made by a single individual! However, absolute objectivity, which we may call “a view from nowhere” may not be attainable by us, because we will always be viewing things from our own perspectives, even if it is a large, collective perspective that we agree on, it is not a view from nowhere.</p>
+
+<p><img src="/img/inherent-subjectivity/subjective-objective-example.png" alt="Subjective-Objective spectrum: A single person says a ball is 10cm radius, 1/4 objectivity. A group of people say it's 10cm radius, 1/2 objectivity. A group of people with a ruler say it's 10cm radius, 3/4 objectivity" /></p>
+
+<h2 id="inherently-subjective-things">Inherently Subjective Things</h2>
+
+<p>With our definition of objectivity in place, now let’s see: is there something that we cannot move towards objectivity about? Yes. That is our personal experiences.</p>
+
+<p>See, if there is an attempt to give a more objective description of <em>my</em> personal experience, there will need to be either an agreement among a group of beings about this description of my personal experience, or there should be an apparatus that we can agree on that measures my personal experience. However, my personal experience is personal exactly because it is completely dependent and originated from my perspective alone, and no one else’s; and as soon as you try to move towards objectivity by trying to describe this experience in a way that moves away from my person-specific and species-specific standpoint, towards a more agreeable and general description that even non-human beings or apparatus can agree with, you lose the initial personal experience in the process, so you end up with a non-personal description of the experience which misses the point of the actual subjective experience I have.</p>
+
+<p>So, you can come up with <em>some</em> description of my experience, but you can’t actually describe the subjective experience of being me as it really is. The walk towards objectivity requires you to drop the subjectivity of my experience, and hence, some inherently subjective things such as our personal experiences can’t be objectified.</p>
+
+<p>This is how Nagel puts it (I think this may be a bit hard to read without reading the whole paper):</p>
+
+<blockquote>
+  <p>Experience itself, however, does not seem to fit the pattern. The idea of moving from appearance to reality seems to make no sense here. What is the analogue in this case to pursuing a more objective understanding of the same phenomena by abandoning the initial subjective viewpoint toward them in favor of another that is more objective but concerns the same thing? Certainly it appears unlikely that we will get closer to the real nature of human experience by leaving behind the particularity of our human point of view and striving for a description in terms accessible to beings that could not imagine what it was like to be us. If the subjective character of experience is fully comprehensible only from one point of view, then any shift to greater objectivity that is, less attachment to a specific viewpoint does not take us nearer to the real nature of the phenomenon: it takes us farther away from it. <a class="citation" href="#nagel1974like">(Nagel, 1974)</a></p>
+</blockquote>
+
+<h2 id="so-what-or-why-is-this-important">So What? (Or: Why is This Important?)</h2>
+
+<p>This realisation means that objectifying people’s subjective experiences is not possible, we will never be able to decipher someone’s subjective experience of something. This does not mean we should not try to <em>understand</em> people, rather, it means we should always consider that our understanding of someone’s subjective experience will never be objective, it will always be merely our perspective of it. When it comes to people’s personal experiences, we can’t be sure that we are right, the way we are confident we are right after measuring a distance using our agreed-upon metric ruler; when it comes to subjective experiences it’s always only a crude approximation. “In the end one experiences only oneself.” <a class="citation" href="#nietzsche2008thus">(Nietzsche, 2008)</a></p>
+
+<p>This video was sent to me by a friend today, and it is great timing, because it is very relevant:</p>
+
+<iframe class="centered" width="560" height="315" src="https://www.youtube-nocookie.com/embed/oRG2jlQWCsY" title="Good Will Hunting | 'Your Move Chief' (HD) - Matt Damon, Robin Williams | MIRAMAX" frameborder="0" allow="picture-in-picture" allowfullscreen=""></iframe>
+
+<!--https://postcognitivism.wordpress.com/2021/04/06/the-great-escape-can-we-transcend-our-own-conceptual-frameworks/
+https://gatelessgateblog.wordpress.com/
+https://www.sciencedirect.com/science/article/pii/S0388000121000802
+Distinctions and Common Ground in Collective Epistemology-->
+
+<h2 id="references">References</h2>
+
+<ol class="bibliography"><li><span id="nagel1974like">Nagel, T. (1974). What is it like to be a bat. <i>Readings in Philosophy of Psychology</i>, <i>1</i>, 159–168.</span></li>
+<li><span id="objectivity-merriam-webster">Merriam-Webster. (2021). <i>Objectivity. In Merriam-Webster.com dictionary.</i> https://www.merriam-webster.com/dictionary/objectivity</span></li>
+<li><span id="bias-merriam-webster">Merriam-Webster. (2021). <i>Bias. In Merriam-Webster.com dictionary.</i> https://www.merriam-webster.com/dictionary/bias</span></li>
+<li><span id="subjective-merriam-webster">Merriam-Webster. (2021). <i>Subjective. In Merriam-Webster.com dictionary.</i> https://www.merriam-webster.com/dictionary/subjective</span></li>
+<li><span id="nietzsche2008thus">Nietzsche, F. (2008). <i>Thus spoke Zarathustra: A book for everyone and nobody</i>. Oxford University Press.</span></li></ol>
+
+  </article>
+
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+      <a href='mailto:mdibaiee@pm.me'>email</a>
+      <a href='https://git.mahdi.blog/mahdi'>git</a>
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+    </p>
+  </nav>
+
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+
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+    <div class="page-content">
+      <div class="wrapper">
+        <h1 class="page-heading"></h1>
+        
+          <div class="home art">
+  <ul class="post-list">
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2022-06-27-seals/">seals</a>-->
+
+          <!--<p class="post-meta">
+            <span>Jun 27, 2022</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/seals.jpeg" alt="seals" /></p>
+
+<p><span class="image-details">
+Seals meetup.<br />
+Lundy Island
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2022-06-27-puffin/">puffin</a>-->
+
+          <!--<p class="post-meta">
+            <span>Jun 27, 2022</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/puffin.jpeg" alt="puffin" /></p>
+
+<p><span class="image-details">
+Puffin.<br />
+Somewhere in the Irish Sea.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2022-06-27-pelican-of-london/">pelican-of-london</a>-->
+
+          <!--<p class="post-meta">
+            <span>Jun 27, 2022</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/pelican-of-london.jpeg" alt="pelican-of-london" /></p>
+
+<p><span class="image-details">
+Pelican of London.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2022-06-27-lundy-nature-reserve/">lundy-nature-reserve</a>-->
+
+          <!--<p class="post-meta">
+            <span>Jun 27, 2022</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/lundy-nature-reserve.jpeg" alt="lundy-nature-reserve" /></p>
+
+<p><span class="image-details">
+Lundy island nature reserve.<br />
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2022-06-27-highland-cow-2/">highland-cow-2</a>-->
+
+          <!--<p class="post-meta">
+            <span>Jun 27, 2022</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/highland-cow-2.jpg" alt="highland-cow-2" /></p>
+
+<p><span class="image-details">
+Highland cow.<br />
+Lundy Island
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2022-06-27-highland-cow-1/">highland-cow-1</a>-->
+
+          <!--<p class="post-meta">
+            <span>Jun 27, 2022</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/highland-cow-1.jpeg" alt="highland-cow-1" /></p>
+
+<p><span class="image-details">
+Highland cow.<br />
+Lundy Island
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2022-06-27-dead-baluga/">dead-baluga</a>-->
+
+          <!--<p class="post-meta">
+            <span>Jun 27, 2022</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/dead-baluga.jpeg" alt="dead-baluga" /></p>
+
+<p><span class="image-details">
+Dead Baluga.<br />
+Lundy Island
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-un-grand-peut-etre/">un-grand-peut-etre</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/un-grand-peut-etre.jpg" alt="un-grand-peut-etre" /></p>
+
+<p><span class="image-details">
+Un grand peut-être.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-tired-eyes-tired-minds-tired-souls/">tired-eyes-tired-minds-tired-souls</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/tired-eyes-tired-minds-tired-souls.jpg" alt="tired-eyes-tired-minds-tired-souls" /></p>
+
+<p><span class="image-details">
+With tired eyes, tired minds, tired souls, we slept.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-time-traveller/">time-traveller</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/time-traveller.jpg" alt="time-traveller" /></p>
+
+<p><span class="image-details">
+Time traveller.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-the-right-way-is-the-untrodden/">the-right-way-is-the-untrodden</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/the-right-way-is-the-untrodden.jpg" alt="the-right-way-is-the-untrodden" /></p>
+
+<p><span class="image-details">
+The right way is the untrodden. It becomes the wrong when you step on it.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-the-night-has-descended-on-us/">the-night-has-descended-on-us</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/the-night-has-descended-on-us.jpg" alt="the-night-has-descended-on-us" /></p>
+
+<p><span class="image-details">
+The night has descended on us.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-tabatabaei-house/">tabatabaei-house</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/tabatabaei-house.jpg" alt="tabatabaei-house" /></p>
+
+<p><span class="image-details">
+Marvels of hand.<br />
+Kashan, Iran.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-switzerland-white-tree/">switzerland-white-tree</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/switzerland-white-tree.jpg" alt="switzerland-white-tree" /></p>
+
+<p><span class="image-details">
+Encanto blanco.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-sightings-from-a-dream-5/">sightings-from-a-dream-5</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/sightings-from-a-dream-5.jpg" alt="sightings-from-a-dream-5" /></p>
+
+<p><span class="image-details">
+Sightings from a dream.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-sightings-from-a-dream-4/">sightings-from-a-dream-4</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/sightings-from-a-dream-4.jpg" alt="sightings-from-a-dream-4" /></p>
+
+<p><span class="image-details">
+Sightings from a dream.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-sightings-from-a-dream-3/">sightings-from-a-dream-3</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/sightings-from-a-dream-3.jpg" alt="sightings-from-a-dream" /></p>
+
+<p><span class="image-details">
+Sightings from a dream.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-sightings-from-a-dream-2/">sightings-from-a-dream-2</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/sightings-from-a-dream-2.jpg" alt="sightings-from-a-dream-2" /></p>
+
+<p><span class="image-details">
+Sightings from a dream.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-sightings-from-a-dream-1/">sightings-from-a-dream-1</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/sightings-from-a-dream-1.jpg" alt="sightings-from-a-dream-1" /></p>
+
+<p><span class="image-details">
+Sightings from a dream.<br />
+“Charred birds escape from the ruins, and return as cascading blood.” - Agalloch
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-shepherd/">shepherd</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/shepherd.jpg" alt="shepherd" /></p>
+
+<p><span class="image-details">
+Shepherd.<br />
+Semnan, Iran.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-punk-gangster/">punk-gangster</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/punk-gangster.jpg" alt="punk-gangster" /></p>
+
+<p><span class="image-details">
+Punk gangster!
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-organs/">organs</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/organs.jpg" alt="organs" /></p>
+
+<p><span class="image-details">
+At twenty, Bach made a pilgrimage of almost four hundred kilometres, on foot, to hear Buxtehude play the organ. 1705.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-not-silent/">not-silent</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/not-silent.jpg" alt="not-silent" /></p>
+
+<p><span class="image-details">
+This image is not silent.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-mount-tibidabo-cathedral/">mount-tibidabo-cathedral</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/mount-tibidabo-cathedral.jpg" alt="mount-tibidabo-cathedral" /></p>
+
+<p><span class="image-details">
+The Board of Catholic Knights bought the land and began construction of this cathedral atop Mount Tibidabo, as a response to rumours about a plan to build a Protestant church there.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-milan-cathedral/">milan-cathedral</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/milan-cathedral.jpg" alt="milan-cathedral" /></p>
+
+<p><span class="image-details">
+It took 579 years to build the Milan Cathedral. 1386-1965. 
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-male-back/">male-back</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/male-back.jpg" alt="male-back" /></p>
+
+<p><span class="image-details">
+“The stillness covers my ears<br />
+Tenderly, until all sound disappears” - Tamino
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-ireland-abandoned/">ireland-abandoned</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/ireland-abandoned.jpg" alt="ireland-abandoned" /></p>
+
+<p><span class="image-details">
+Is this the real life? Is this just fantasy?
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-iran-yeylaq/">iran-yeylaq</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/iran-yeylaq.jpg" alt="iran-yeylaq" /></p>
+
+<p><span class="image-details">
+Shaft, Iran.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-i-cast-a-spell-on-the-city/">i-cast-a-spell-on-the-city</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/i-cast-a-spell-on-the-city.jpg" alt="i-cast-a-spell-on-the-city" /></p>
+
+<p><span class="image-details">
+I cast a spell on the city, asking it to last.
+</span></p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-holy-money-spitting-machine/">holy-money-spitting-machine</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/holy-money-spitting-machine.jpg" alt="holy-money-spitting-machine" /></p>
+
+<p><span class="image-details">
+Holy money-spitting machine
+</span></p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-history-so-close-it-comes-alive/">history-so-close-it-comes-alive</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/history-so-close-it-comes-alive.jpg" alt="history-so-close-it-comes-alive" /></p>
+
+<p><span class="image-details">
+History so close it comes alive.
+</span></p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-hill-of-tara/">hill-of-tara</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/hill-of-tara.jpg" alt="hill-of-tara" /></p>
+
+<p><span class="image-details">
+Hill of Tara.<br />
+Meath, Ireland.
+</span></p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-head-wall/">head-wall</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/head-wall.jpg" alt="head-wall" /></p>
+
+<p><span class="image-details">
+“I am going to put myself to sleep now for a bit longer than usual. Call it Eternity.” - Jerzy Kosinski
+</span></p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-grey-heron-bushy-park/">grey-heron-bushy-park</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/grey-heron-bushy-park.jpg" alt="grey-heron-bushy-park" /></p>
+
+<p><span class="image-details">
+Grey heron.<br />
+Dublin, Ireland.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-god-will-pardon-me/">god-will-pardon-me</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/god-will-pardon-me.jpg" alt="god-will-pardon-me" /></p>
+
+<p><span class="image-details">
+“Dieu me pardonnera c’est son metier.” - Heinrich Heine
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-girl-eye-flowers-3/">girl-eye-flowers-3</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/girl-eye-flowers-3.jpg" alt="girl-eye-flowers-3" /></p>
+
+<p><span class="image-details">
+A narration.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-girl-eye-flowers-2/">girl-eye-flowers-2</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/girl-eye-flowers-2.jpg" alt="girl-eye-flowers-2" /></p>
+
+<p><span class="image-details">
+A narration.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-girl-eye-flowers-1/">girl-eye-flowers-1</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/girl-eye-flowers-1.jpg" alt="girl-eye-flowers-1" /></p>
+
+<p><span class="image-details">
+A narration.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-flamingos-iran/">flamingos-iran</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/flamingos-iran.jpg" alt="flamingos-iran" /></p>
+
+<p><span class="image-details">
+Breakfast for the flamingos.<br />
+Bandar Abbas, Iran.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-et-les-extremes-se-touchent/">et-les-extremes-se-touchent</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/et-les-extremes-se-touchent.jpg" alt="et-les-extremes-se-touchent" /></p>
+
+<p><span class="image-details">
+Et les extremes se touchent.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-dublin-chimneys/">dublin-chimneys</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/dublin-chimneys.jpg" alt="dublin-chimneys" /></p>
+
+<p><span class="image-details">
+The Chimneys.<br />
+Dublin.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-drummer-vanishing/">drummer-vanishing</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/drummer-vanishing.jpg" alt="drummer-vanishing" /></p>
+
+<p><span class="image-details">
+Vanishing
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-drought-dead-statue/">drought-dead-statue</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/drought-dead-statue.jpg" alt="drought-dead-statue" /></p>
+
+<p><span class="image-details">
+Hold my hands, we take wing tonight.<br />
+We leave nothing behind but memories.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-dog-and-puppy/">dog-and-puppy</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/dog-and-puppy.jpg" alt="dog-and-puppy" /></p>
+
+<p><span class="image-details">
+This mother and daughter were roaming the land freely, it was beautiful to watch the mother scouting the area while the puppy was playing and running around.<br />
+Semnan, Iran
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-deer-silhouette/">deer-silhouette</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/deer-silhouette.jpg" alt="deer-silhouette" /></p>
+
+<p><span class="image-details">
+Killarney, Ireland.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-deer-above/">deer-above</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/deer-above.jpg" alt="deer-above" /></p>
+
+<p><span class="image-details">
+Killarney, Ireland.
+</span></p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-dark-street-light/">dark-street-light</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/dark-street-light.jpg" alt="dark-street-light" /></p>
+
+<p><span class="image-details lang-fa">
+راه فرو بسته گرچه مرغ به آوا<br />
+قالب خاموشی او صدایی گویاست<br />
+می‌گذرد لحظه‌ها به چشمش بیدار<br />
+پیکر او لیک سایه-روشن رویاست - سهراب 
+</span></p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-darak/">darak</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/darak.jpg" alt="darak" /></p>
+
+<p><span class="image-details">
+Where sand dunes meet the sea.<br />
+Darak, Sistan-o-Baluchestan, Iran.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-darak-2/">darak-2</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/darak-2.jpg" alt="darak-2" /></p>
+
+<p><span class="image-details">
+Where sand dunes meet the sea.<br />
+Darak, Sistan-o-Baluchestan, Iran.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-crucifixion-sagrada-familia/">crucifixion-sagrada-familia</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/crucifixion-sagrada-familia.jpg" alt="crucifixion" /></p>
+
+<p><span class="image-details">
+Crucifixion | تصلیب
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-concrete-jungle-trees/">concrete-jungle-trees</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/concrete-jungle-trees.jpg" alt="concrete-jungle-trees" /></p>
+
+<p><span class="image-details">
+Long trees of our concrete jungle.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-clouds-among-rocks/">clouds-among-rocks</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/clouds-among-rocks.jpg" alt="clouds-among-rocks" /></p>
+
+<p><span class="image-details">
+Dance of clouds.<br />
+Killarney, Ireland.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-christmas-day-homeless-man-church/">christmas-day-homeless-man-church</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/christmas-day-homeless-man-church.jpg" alt="christmas-day-homeless-man-church" /></p>
+
+<p><span class="image-details">
+Homeless man praying in front of John’s Lane Church.<br />
+Christmas day. 
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-cemetery/">cemetery</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/cemetery.jpg" alt="cemetery" /></p>
+
+<p><span class="image-details">
+It’s strange how we are reminded of our mortality when something goes completely wrong.<br />
+Mount Venus Cemetery.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-boy/">boy</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/boy.jpg" alt="boy." /></p>
+
+<p><span class="image-details">
+Boy.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-blue-contagious-smile/">blue-contagious-smile</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/blue-contagious-smile.jpg" alt="blue-contagious-smile" /></p>
+
+<p><span class="image-details">
+A blue, contagious smile
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-birds-sunrise-sea-iran/">birds-sunrise-sea-iran</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/birds-sunrise-sea-iran.jpg" alt="birds-sunrise-sea-iran" /></p>
+
+<p><span class="image-details">
+Bandar Abbas, Iran
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-birds-in-form/">birds-in-form</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/birds-in-form.jpg" alt="birds-in-form" /></p>
+
+<p><span class="image-details">
+“Je finis par trouver sacre le desordre de mon esprit.” - Arthur Rimbaud
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-03-12-baled-hay/">baled-hay</a>-->
+
+          <!--<p class="post-meta">
+            <span>Mar 12, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/baled-hay.jpg" alt="baled-hay" /></p>
+
+<p><span class="image-details">
+Somewhere in Ireland
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-02-01-yazd-children/">yazd-children</a>-->
+
+          <!--<p class="post-meta">
+            <span>Feb 1, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/yazd-children.jpg" alt="Children in Yazd" /></p>
+
+<p><span class="image-details">
+Yazd, Iran.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-02-01-windcatcher/">windcatcher</a>-->
+
+          <!--<p class="post-meta">
+            <span>Feb 1, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/windcatcher.jpg" alt="windcatcher" /></p>
+
+<p><span class="image-details">
+Windcatchers (Badgir بادگیر in Persian) are an old Iranian architectural element used to create all-natural ventilation in buildings and water reserves (Ab Anbar and Qanats, see third image). These marvels are so effective at cooling, they can keep water at near-freezing temperature during summer days. They are still present in Iran and in neighbouring countries.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-02-01-smell-like-trees/">galileo</a>-->
+
+          <!--<p class="post-meta">
+            <span>Feb 1, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/galileo.jpg" alt="galileo" /></p>
+
+<p><span class="image-details">
+“With sincere heart and unpretended faith I abjure, curse, and detest the aforesaid errors and heresies and also every other error… contrary to the Holy Church, and I swear that in the future I will never again say or assert… anything that might cause a similar suspicion toward me” - Galileo
+</span></p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-02-01-sky/">sky</a>-->
+
+          <!--<p class="post-meta">
+            <span>Feb 1, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/sky.jpg" alt="sky" /></p>
+
+<p><span class="image-details">
+“At some time in the past, I thought, I must have made a mistake, and now I am living the wrong life.” - Austerlitz, Sabald
+</span></p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-02-01-sigh/">sigh</a>-->
+
+          <!--<p class="post-meta">
+            <span>Feb 1, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/sigh.jpg" alt="sigh" /></p>
+
+<p><span class="image-details">
+Sigh.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-02-01-preparation/">preparation</a>-->
+
+          <!--<p class="post-meta">
+            <span>Feb 1, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/preparation.jpg" alt="preparation" /></p>
+
+<p><span class="image-details">
+“Life is a long preparation for something that never happens.” - Yeats
+</span></p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-02-01-ox-bathing/">ox-bathing</a>-->
+
+          <!--<p class="post-meta">
+            <span>Feb 1, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/ox-bathing.jpg" alt="ox-bathing" /></p>
+
+<p><span class="image-details">
+Iran.
+</span></p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-02-01-on-mourra-seul/">on-mourra-seul</a>-->
+
+          <!--<p class="post-meta">
+            <span>Feb 1, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/on-mourra-seul.jpg" alt="on-mourra-seul" /></p>
+
+<p><span class="image-details">
+On mourra seul.
+</span></p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-02-01-la-vida/">la-vida</a>-->
+
+          <!--<p class="post-meta">
+            <span>Feb 1, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/la-vida.jpg" alt="la-vida" /></p>
+
+<p><span class="image-details">
+“Y la vida no es noble, ni buena, ni sagrada.” - Federico García Lorca
+</span></p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-02-01-jebir/">jebir</a>-->
+
+          <!--<p class="post-meta">
+            <span>Feb 1, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/jebir.jpg" alt="jebir" /></p>
+
+<p><span class="image-details">
+Jebir.<br />
+Hengam Island, Iran.
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-02-01-grand/">grand</a>-->
+
+          <!--<p class="post-meta">
+            <span>Feb 1, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/grand.jpg" alt="grand" /></p>
+
+<p><span class="image-details">
+Cruella?
+</span></p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-02-01-girl-among-grains/">girl-among-grains</a>-->
+
+          <!--<p class="post-meta">
+            <span>Feb 1, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/girl-among-grains.jpg" alt="girl-among-grains" /></p>
+
+<p><span class="image-details">
+“That evening in Marienbad, said Austerlitz, I could not admit to myself how right everything Marie said was, but today I know why I felt obliged to turn away when anyone came too close to me, I know that I thought this turning away made me safe, and that at the same time I saw myself transformed into a frightful and hideous creature, a man beyond the pale.” - Austerlitz, Sabald
+</span></p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <!--<a class="post-link" href="/art/2021-02-01-galileo/">smell-like-trees</a>-->
+
+          <!--<p class="post-meta">
+            <span>Feb 1, 2021</span>
+            
+          </p>-->
+
+        <article class='post-content'>
+          <p><img src="/img/arts/smell-like-trees.jpg" alt="smell-like-trees" /></p>
+
+<p><span class="image-details">
+“Caddy held me, she smelled like trees.” - The Sound and the Fury, William Faulkner
+</span></p>
+
+
+        </article>
+      </li>
+    
+  </ul>
+
+  <p class="rss-subscribe">subscribe <a href="/feed.xml">via rss</a></p>
+
+</div>
+
+        
+      </div>
+    </div>
+
+  </body>
+
+</html>
diff --git a/site/autocomplete-predict-trie/index.html b/site/autocomplete-predict-trie/index.html
new file mode 100644
index 0000000..5a08719
--- /dev/null
+++ b/site/autocomplete-predict-trie/index.html
@@ -0,0 +1,298 @@
+<!DOCTYPE html>
+<html>
+
+  <head>
+  <meta charset="utf-8">
+  <meta http-equiv="X-UA-Compatible" content="IE=edge">
+  <meta name="viewport" content="width=device-width, initial-scale=1">
+
+  <title>Autocomplete using Tries</title>
+  <meta name="description" content="In this article, I’m going over creating an autocompletion/prediction system using a data-structure called Trie, it’s fast and easy to customize.">
+
+  <link href="https://fonts.googleapis.com/css?family=Secular+One|Nunito|Mononoki" rel="stylesheet"> 
+  <link rel="stylesheet" href="/css/main.css">
+  <link rel="canonical" href="http://localhost:4000/autocomplete-predict-trie/">
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+
+  
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+  <!--<script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script>-->
+
+  <script>
+    var channel = new BroadcastChannel('egg');
+
+    channel.addEventListener('message', message => {
+      alert('Got a message from the other tab:\n' + message.data);
+    });
+  </script>
+</head>
+
+
+
+  <body>
+
+    <header class="site-header">
+
+  <h1>
+    <a class='site-title' href='/'>
+      mahdi
+    </a>
+  </h1>
+
+  <nav>
+    <p>
+      <a href="/snippets">snippets</a>
+      <a href="/art">pictures</a>
+    </p>
+    <!--<p class='categories'>-->
+      <!---->
+        <!---->
+        <!--<a href="">art</a>-->
+        <!---->
+      <!---->
+        <!---->
+      <!---->
+    <!--</p>-->
+    <p>
+      <a href='mailto:mdibaiee@pm.me'>email</a>
+      <a href='https://git.mahdi.blog/mahdi'>git</a>
+      <a href='https://www.librarything.com/profile/mdibaiee'>librarything</a>
+      <a href="http://localhost:4000/feed.xml">feed</a>
+    </p>
+  </nav>
+
+</header>
+
+
+    <div class="page-content">
+      <div class="wrapper">
+        <h1 class="page-heading"></h1>
+        
+          <div class='post lang-en'>
+
+  <div class="post-header">
+    <h1 class="post-title"><p>Autocomplete using Tries</p>
+</h1>
+    
+    <p class="post-meta">
+      <span>Jul 24, 2015</span>
+      
+      • <span>Reading time: 8  minutes</span>
+    </p>
+  </div>
+
+  <article class="post-content">
+    <p>In this article, I’m going over creating an autocompletion/prediction system using a data-structure called Trie, it’s fast and easy to customize.</p>
+
+<h1 id="trie">Trie</h1>
+
+<p><a href="https://en.wikipedia.org/wiki/Trie">Trie</a> is a simple data-structure most commonly used as a dictionary, it looks like so:</p>
+
+<p><img src="/img/trie.jpg" alt="Trie" /></p>
+
+<p>As you see, it’s just a <em>tree</em>, a set of nodes connected to other [child] nodes, but the nodes have a special relationship:</p>
+
+<p>Each child node extends it’s parent with one extra character.</p>
+
+<figure class="highlight"><pre><code class="language-javascript" data-lang="javascript"><span class="c1">// Something like this</span>
+<span class="nx">child</span><span class="p">.</span><span class="nx">value</span> <span class="o">=</span> <span class="nx">parent</span><span class="p">.</span><span class="nx">value</span> <span class="o">+</span> <span class="dl">'</span><span class="s1">c</span><span class="dl">'</span><span class="p">;</span></code></pre></figure>
+
+<p>It’s pretty easy to traverse this tree and predict the next possible words.</p>
+
+<h2 id="implementation">Implementation</h2>
+
+<p>We’re going to use ES6 classes to create our <code class="language-plaintext highlighter-rouge">Trie</code> and <code class="language-plaintext highlighter-rouge">Node</code> classes.</p>
+
+<p>Let’s start with our simple Node class:</p>
+
+<figure class="highlight"><pre><code class="language-javascript" data-lang="javascript"><span class="kd">class</span> <span class="nx">Node</span> <span class="p">{</span>
+  <span class="kd">constructor</span><span class="p">(</span><span class="nx">value</span> <span class="o">=</span> <span class="dl">''</span><span class="p">)</span> <span class="p">{</span>
+    <span class="k">this</span><span class="p">.</span><span class="nx">value</span> <span class="o">=</span> <span class="nx">value</span><span class="p">;</span>
+    <span class="k">this</span><span class="p">.</span><span class="nx">children</span> <span class="o">=</span> <span class="p">[];</span>
+  <span class="p">}</span>
+<span class="p">}</span></code></pre></figure>
+
+<p>Unlike <a href="https://en.wikipedia.org/wiki/Binary_tree">binary trees</a> where each node has a left and right child, Trie nodes don’t necessarily have a limit on how many children they can have.</p>
+
+<p>Trie class:</p>
+
+<figure class="highlight"><pre><code class="language-javascript" data-lang="javascript"><span class="kd">class</span> <span class="nx">Trie</span> <span class="p">{</span>
+  <span class="kd">constructor</span><span class="p">()</span> <span class="p">{</span>
+    <span class="k">this</span><span class="p">.</span><span class="nx">root</span> <span class="o">=</span> <span class="k">new</span> <span class="nx">Node</span><span class="p">();</span>
+  <span class="p">}</span>
+
+  <span class="nx">add</span><span class="p">(</span><span class="nx">value</span><span class="p">,</span> <span class="nx">parent</span> <span class="o">=</span> <span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="p">)</span> <span class="p">{</span>
+    <span class="k">for</span> <span class="p">(</span><span class="kd">let</span> <span class="nx">i</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="nx">len</span> <span class="o">=</span> <span class="nx">value</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span> <span class="nx">i</span> <span class="o">&lt;</span> <span class="nx">len</span><span class="p">;</span> <span class="nx">i</span><span class="o">++</span><span class="p">)</span> <span class="p">{</span>
+      <span class="kd">let</span> <span class="nx">node</span> <span class="o">=</span> <span class="nx">parent</span><span class="p">.</span><span class="nx">children</span><span class="p">.</span><span class="nx">find</span><span class="p">(</span><span class="nx">child</span> <span class="o">=&gt;</span> <span class="nx">child</span><span class="p">.</span><span class="nx">value</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span> <span class="o">===</span> <span class="nx">value</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+
+      <span class="k">if</span> <span class="p">(</span><span class="o">!</span><span class="nx">node</span><span class="p">)</span> <span class="p">{</span>
+        <span class="nx">node</span> <span class="o">=</span> <span class="k">new</span> <span class="nx">Node</span><span class="p">(</span><span class="nx">value</span><span class="p">.</span><span class="nx">slice</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nx">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">));</span>
+        <span class="nx">parent</span><span class="p">.</span><span class="nx">children</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+      <span class="p">}</span>
+
+      <span class="nx">parent</span> <span class="o">=</span> <span class="nx">node</span><span class="p">;</span>
+    <span class="p">}</span>
+
+    <span class="k">return</span> <span class="nx">parent</span><span class="p">;</span>
+  <span class="p">}</span>
+
+  <span class="nx">find</span><span class="p">(</span><span class="nx">value</span><span class="p">,</span> <span class="nx">parent</span> <span class="o">=</span> <span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="p">)</span> <span class="p">{</span>
+    <span class="k">for</span> <span class="p">(</span><span class="kd">let</span> <span class="nx">i</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="nx">len</span> <span class="o">=</span> <span class="nx">value</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span> <span class="nx">i</span> <span class="o">&lt;</span> <span class="nx">len</span><span class="p">;</span> <span class="nx">i</span><span class="o">++</span><span class="p">)</span> <span class="p">{</span>
+      <span class="nx">parent</span> <span class="o">=</span> <span class="nx">parent</span><span class="p">.</span><span class="nx">children</span><span class="p">.</span><span class="nx">find</span><span class="p">(</span><span class="nx">child</span> <span class="o">=&gt;</span> <span class="nx">child</span><span class="p">.</span><span class="nx">value</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span> <span class="o">===</span> <span class="nx">value</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
+
+      <span class="k">if</span> <span class="p">(</span><span class="o">!</span><span class="nx">parent</span><span class="p">)</span> <span class="k">return</span> <span class="kc">null</span><span class="p">;</span>
+    <span class="p">}</span>
+    <span class="k">return</span> <span class="nx">parent</span><span class="p">;</span>
+  <span class="p">}</span>
+<span class="p">}</span></code></pre></figure>
+
+<p>Every Trie must have a root node with empty value, that’s how our single-character nodes follow the rule of Tries.</p>
+
+<p>Ok, our first method, <code class="language-plaintext highlighter-rouge">add</code> handles adding a value to the trie, creating necessary parent nodes for our value.
+At each iteration, we compare the <code class="language-plaintext highlighter-rouge">i</code>th character of our value, with <code class="language-plaintext highlighter-rouge">i</code>th character of current node’s children’s value,
+if we find one, we continue to search the next branch, else, we create a node with <code class="language-plaintext highlighter-rouge">value.slice(0, i + 1)</code> and move onto the created node.</p>
+
+<p>It might be a little hard to grasp at first, so I created a visualization of this method to help you understand it easier, take a look:
+<a href="https://mdibaiee.github.io/autocomplete-trie/demo/add.html">Trie Visualization</a></p>
+
+<p>Then we have our find method, which searches for the given value in the trie. The algorithm for searching is the same, comparing by index and moving to the next branch.</p>
+
+<h1 id="example">Example</h1>
+<p>That’s it for our simple Trie class, now let’s create an actual input with autocomplete functionality using our Trie.</p>
+
+<figure class="highlight"><pre><code class="language-html" data-lang="html"><span class="nt">&lt;input&gt;</span>
+
+<span class="nt">&lt;div</span> <span class="na">class=</span><span class="s">'results'</span><span class="nt">&gt;</span>
+
+<span class="nt">&lt;/div&gt;</span></code></pre></figure>
+
+<p>I put some random names and stuff into three categories, results: <a href="https://mdibaiee.github.io/autocomplete-trie/demo/data.json">data.json</a></p>
+
+<p>Now we have to create a Trie of our data:</p>
+
+<figure class="highlight"><pre><code class="language-javascript" data-lang="javascript"><span class="kd">const</span> <span class="nx">trie</span> <span class="o">=</span> <span class="k">new</span> <span class="nx">Trie</span><span class="p">();</span>
+
+<span class="kd">let</span> <span class="nx">data</span> <span class="o">=</span> <span class="p">{...};</span> <span class="c1">// read from data.json</span>
+
+<span class="k">for</span> <span class="p">(</span><span class="kd">let</span> <span class="nx">category</span> <span class="k">in</span> <span class="nx">data</span><span class="p">)</span> <span class="p">{</span>
+  <span class="k">for</span> <span class="p">(</span><span class="kd">let</span> <span class="nx">item</span> <span class="k">of</span> <span class="nx">data</span><span class="p">[</span><span class="nx">category</span><span class="p">])</span> <span class="p">{</span>
+    <span class="kd">let</span> <span class="nx">node</span> <span class="o">=</span> <span class="nx">trie</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">item</span><span class="p">);</span>
+    <span class="nx">node</span><span class="p">.</span><span class="nx">category</span> <span class="o">=</span> <span class="nx">category</span><span class="p">;</span>
+  <span class="p">}</span>
+<span class="p">}</span></code></pre></figure>
+
+<p>As simple as that, our trie is made, it looks like this: <a href="https://mdibaiee.github.io/autocomplete-trie/demo/data.html">Data</a></p>
+
+<p>Now, let’s actually show results:</p>
+
+<figure class="highlight"><pre><code class="language-javascript" data-lang="javascript"><span class="kd">const</span> <span class="nx">input</span> <span class="o">=</span> <span class="nb">document</span><span class="p">.</span><span class="nx">querySelector</span><span class="p">(</span><span class="dl">'</span><span class="s1">input</span><span class="dl">'</span><span class="p">);</span>
+<span class="kd">const</span> <span class="nx">results</span> <span class="o">=</span> <span class="nb">document</span><span class="p">.</span><span class="nx">querySelector</span><span class="p">(</span><span class="dl">'</span><span class="s1">#results</span><span class="dl">'</span><span class="p">);</span>
+
+<span class="nx">input</span><span class="p">.</span><span class="nx">addEventListener</span><span class="p">(</span><span class="dl">'</span><span class="s1">keyup</span><span class="dl">'</span><span class="p">,</span> <span class="p">()</span> <span class="o">=&gt;</span> <span class="p">{</span>
+  <span class="nx">results</span><span class="p">.</span><span class="nx">innerHTML</span> <span class="o">=</span> <span class="dl">''</span><span class="p">;</span>
+
+  <span class="kd">const</span> <span class="nx">nodes</span> <span class="o">=</span> <span class="nx">trie</span><span class="p">.</span><span class="nx">find</span><span class="p">(</span><span class="nx">input</span><span class="p">.</span><span class="nx">value</span><span class="p">);</span>
+
+  <span class="k">if</span> <span class="p">(</span><span class="o">!</span><span class="nx">nodes</span><span class="p">)</span> <span class="k">return</span><span class="p">;</span>
+
+  <span class="k">for</span> <span class="p">(</span><span class="kd">let</span> <span class="nx">node</span> <span class="k">of</span> <span class="nx">nodes</span><span class="p">.</span><span class="nx">children</span><span class="p">)</span> <span class="p">{</span>
+    <span class="kd">const</span> <span class="nx">category</span> <span class="o">=</span> <span class="nx">node</span><span class="p">.</span><span class="nx">category</span> <span class="p">?</span> <span class="s2">`- </span><span class="p">${</span><span class="nx">node</span><span class="p">.</span><span class="nx">category</span><span class="p">}</span><span class="s2">`</span> <span class="p">:</span> <span class="dl">''</span><span class="p">;</span>
+
+    <span class="nx">results</span><span class="p">.</span><span class="nx">innerHTML</span> <span class="o">+=</span> <span class="s2">`&lt;li&gt;</span><span class="p">${</span><span class="nx">node</span><span class="p">.</span><span class="nx">value</span><span class="p">}</span><span class="s2"> </span><span class="p">${</span><span class="nx">category</span><span class="p">}</span><span class="s2">&lt;/li&gt;`</span><span class="p">;</span>
+  <span class="p">}</span>
+<span class="p">});</span></code></pre></figure>
+
+<p><a href="https://mdibaiee.github.io/autocomplete-trie/1.html">Autocomplete 1</a>
+<img src="/img/autocomplete-1.png" alt="Autocomplete 1" />
+This will only show the instant-childs of the word entered, but that’s not what we want, we want to show <em>complete</em> words, how do we do that?</p>
+
+<p>First, we need a way to detect complete words, we can have a flag to recognize complete words, we can modify our <code class="language-plaintext highlighter-rouge">add</code> method to
+automatically flag whole words or we can manually add the flag after adding the node, as we did by setting a category for our words,
+so we already have a flag to recognize whole words, that’s our <code class="language-plaintext highlighter-rouge">category</code> property, now let’s add a new method to our Trie class to find
+whole words.</p>
+
+<figure class="highlight"><pre><code class="language-javascript" data-lang="javascript"><span class="p">...</span>
+  <span class="nx">findWords</span><span class="p">(</span><span class="nx">value</span><span class="p">,</span> <span class="nx">parent</span> <span class="o">=</span> <span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="p">)</span> <span class="p">{</span>
+    <span class="kd">let</span> <span class="nx">top</span> <span class="o">=</span> <span class="k">this</span><span class="p">.</span><span class="nx">find</span><span class="p">(</span><span class="nx">value</span><span class="p">,</span> <span class="nx">parent</span><span class="p">);</span>
+    <span class="k">if</span> <span class="p">(</span><span class="o">!</span><span class="nx">top</span><span class="p">)</span> <span class="k">return</span> <span class="p">[];</span>
+
+    <span class="kd">let</span> <span class="nx">words</span> <span class="o">=</span> <span class="p">[];</span>
+
+    <span class="nx">top</span><span class="p">.</span><span class="nx">children</span><span class="p">.</span><span class="nx">forEach</span><span class="p">(</span><span class="kd">function</span> <span class="nx">getWords</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span> <span class="p">{</span>
+      <span class="k">if</span> <span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">category</span><span class="p">)</span> <span class="nx">words</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
+      <span class="nx">node</span><span class="p">.</span><span class="nx">children</span><span class="p">.</span><span class="nx">forEach</span><span class="p">(</span><span class="nx">getWords</span><span class="p">);</span>
+    <span class="p">});</span>
+
+    <span class="k">return</span> <span class="nx">words</span><span class="p">;</span>
+  <span class="p">}</span>
+<span class="p">...</span></code></pre></figure>
+
+<p>And change our event listener like so:</p>
+
+<figure class="highlight"><pre><code class="language-javascript" data-lang="javascript"><span class="kd">const</span> <span class="nx">input</span> <span class="o">=</span> <span class="nb">document</span><span class="p">.</span><span class="nx">querySelector</span><span class="p">(</span><span class="dl">'</span><span class="s1">input</span><span class="dl">'</span><span class="p">);</span>
+<span class="kd">const</span> <span class="nx">results</span> <span class="o">=</span> <span class="nb">document</span><span class="p">.</span><span class="nx">querySelector</span><span class="p">(</span><span class="dl">'</span><span class="s1">#results</span><span class="dl">'</span><span class="p">);</span>
+
+<span class="nx">input</span><span class="p">.</span><span class="nx">addEventListener</span><span class="p">(</span><span class="dl">'</span><span class="s1">keyup</span><span class="dl">'</span><span class="p">,</span> <span class="p">()</span> <span class="o">=&gt;</span> <span class="p">{</span>
+  <span class="nx">results</span><span class="p">.</span><span class="nx">innerHTML</span> <span class="o">=</span> <span class="dl">''</span><span class="p">;</span>
+
+  <span class="kd">const</span> <span class="nx">nodes</span> <span class="o">=</span> <span class="nx">trie</span><span class="p">.</span><span class="nx">findWords</span><span class="p">(</span><span class="nx">input</span><span class="p">.</span><span class="nx">value</span><span class="p">);</span> <span class="c1">// &lt;&lt; Change</span>
+
+  <span class="k">if</span> <span class="p">(</span><span class="o">!</span><span class="nx">nodes</span><span class="p">.</span><span class="nx">length</span><span class="p">)</span> <span class="k">return</span><span class="p">;</span> <span class="c1">// &lt;&lt; Change</span>
+
+  <span class="k">for</span> <span class="p">(</span><span class="kd">let</span> <span class="nx">node</span> <span class="k">of</span> <span class="nx">nodes</span><span class="p">)</span> <span class="p">{</span> <span class="c1">// &lt;&lt; Change</span>
+    <span class="kd">const</span> <span class="nx">category</span> <span class="o">=</span> <span class="nx">node</span><span class="p">.</span><span class="nx">category</span> <span class="p">?</span> <span class="s2">`- </span><span class="p">${</span><span class="nx">node</span><span class="p">.</span><span class="nx">category</span><span class="p">}</span><span class="s2">`</span> <span class="p">:</span> <span class="dl">''</span><span class="p">;</span>
+
+    <span class="nx">results</span><span class="p">.</span><span class="nx">innerHTML</span> <span class="o">+=</span> <span class="s2">`&lt;li&gt;</span><span class="p">${</span><span class="nx">node</span><span class="p">.</span><span class="nx">value</span><span class="p">}</span><span class="s2"> </span><span class="p">${</span><span class="nx">category</span><span class="p">}</span><span class="s2">&lt;/li&gt;`</span><span class="p">;</span>
+  <span class="p">}</span>
+<span class="p">});</span></code></pre></figure>
+
+<p><a href="https://mdibaiee.github.io/autocomplete-trie/2.html">Autocomplete 2</a>
+<img src="/img/autocomplete-2.png" alt="Autocomplete 2" />
+Ta-daa!</p>
+
+<p>We have our autocomplete working! Let’s add zsh-like-tab-to-next-char functionality.</p>
+
+<figure class="highlight"><pre><code class="language-javascript" data-lang="javascript"><span class="nx">input</span><span class="p">.</span><span class="nx">addEventListener</span><span class="p">(</span><span class="dl">'</span><span class="s1">keydown</span><span class="dl">'</span><span class="p">,</span> <span class="nx">e</span> <span class="o">=&gt;</span> <span class="p">{</span>
+  <span class="c1">// Tab Key</span>
+  <span class="k">if</span> <span class="p">(</span><span class="nx">e</span><span class="p">.</span><span class="nx">keyCode</span> <span class="o">===</span> <span class="mi">9</span><span class="p">)</span> <span class="p">{</span>
+    <span class="nx">e</span><span class="p">.</span><span class="nx">preventDefault</span><span class="p">();</span>
+    <span class="kd">const</span> <span class="nx">current</span> <span class="o">=</span> <span class="nx">trie</span><span class="p">.</span><span class="nx">find</span><span class="p">(</span><span class="nx">input</span><span class="p">.</span><span class="nx">value</span><span class="p">);</span>
+
+    <span class="k">if</span> <span class="p">(</span><span class="o">!</span><span class="nx">current</span><span class="p">.</span><span class="nx">children</span><span class="p">.</span><span class="nx">length</span><span class="p">)</span> <span class="k">return</span><span class="p">;</span>
+
+    <span class="nx">input</span><span class="p">.</span><span class="nx">value</span> <span class="o">=</span> <span class="nx">current</span><span class="p">.</span><span class="nx">children</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="nx">value</span><span class="p">;</span>
+  <span class="p">}</span>
+<span class="p">});</span></code></pre></figure>
+
+<p>That’s it! We have an input with autocomplete and tab-to-next-char. Isn’t it awesome?</p>
+
+<p><a href="https://mdibaiee.github.io/autocomplete-trie/2.html">Final Result</a></p>
+
+<p><em>Pst! I have a repository of algorithm implementations in ES6, you might want to take a look! <a href="https://github.com/mdibaiee/harmony-algorithms">mdibaiee/harmony-algorithms</a></em></p>
+
+  </article>
+
+  <div class="share-page">
+    Share in
+
+    <a href="https://twitter.com/intent/tweet?text=Autocomplete using Tries&url=http://localhost:4000/autocomplete-predict-trie/&via=&related=" rel="nofollow" target="_blank" title="Share on Twitter">Twitter</a>
+    <a href="https://facebook.com/sharer.php?u=http://localhost:4000/autocomplete-predict-trie/" rel="nofollow" target="_blank" title="Share on Facebook">Facebook</a>
+    <a href="https://plus.google.com/share?url=http://localhost:4000/autocomplete-predict-trie/" rel="nofollow" target="_blank" title="Share on Google+">Google+</a>
+</div>
+
+  
+  <div id="commento"></div>
+  <script defer
+    src="//commento.mahdi.blog/js/commento.js">
+  </script>
+
+  <script src="/js/heading-links.js"></script>
+</div>
+
+        
+      </div>
+    </div>
+
+  </body>
+
+</html>
diff --git a/site/broadcastchannel-api/index.html b/site/broadcastchannel-api/index.html
new file mode 100644
index 0000000..5cbc369
--- /dev/null
+++ b/site/broadcastchannel-api/index.html
@@ -0,0 +1,221 @@
+<!DOCTYPE html>
+<html>
+
+  <head>
+  <meta charset="utf-8">
+  <meta http-equiv="X-UA-Compatible" content="IE=edge">
+  <meta name="viewport" content="width=device-width, initial-scale=1">
+
+  <title>BroadcastChannel API</title>
+  <meta name="description" content="BroadcastChannel APIis a new API used to communicate between same-origin tabs opened by the same user.">
+
+  <link href="https://fonts.googleapis.com/css?family=Secular+One|Nunito|Mononoki" rel="stylesheet"> 
+  <link rel="stylesheet" href="/css/main.css">
+  <link rel="canonical" href="http://localhost:4000/broadcastchannel-api/">
+  <link rel="alternate" type="application/rss+xml" title="mahdi" href="http://localhost:4000/feed.xml" />
+
+  
+
+  <!--<script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script>-->
+
+  <script>
+    var channel = new BroadcastChannel('egg');
+
+    channel.addEventListener('message', message => {
+      alert('Got a message from the other tab:\n' + message.data);
+    });
+  </script>
+</head>
+
+
+
+  <body>
+
+    <header class="site-header">
+
+  <h1>
+    <a class='site-title' href='/'>
+      mahdi
+    </a>
+  </h1>
+
+  <nav>
+    <p>
+      <a href="/snippets">snippets</a>
+      <a href="/art">pictures</a>
+    </p>
+    <!--<p class='categories'>-->
+      <!---->
+        <!---->
+        <!--<a href="">art</a>-->
+        <!---->
+      <!---->
+        <!---->
+      <!---->
+    <!--</p>-->
+    <p>
+      <a href='mailto:mdibaiee@pm.me'>email</a>
+      <a href='https://git.mahdi.blog/mahdi'>git</a>
+      <a href='https://www.librarything.com/profile/mdibaiee'>librarything</a>
+      <a href="http://localhost:4000/feed.xml">feed</a>
+    </p>
+  </nav>
+
+</header>
+
+
+    <div class="page-content">
+      <div class="wrapper">
+        <h1 class="page-heading"></h1>
+        
+          <div class='post lang-en'>
+
+  <div class="post-header">
+    <h1 class="post-title"><p>BroadcastChannel API</p>
+</h1>
+    
+    <p class="post-meta">
+      <span>Apr 2, 2015</span>
+      
+      • <span>Reading time: 4  minutes</span>
+    </p>
+  </div>
+
+  <article class="post-content">
+    <p><a href="https://developer.mozilla.org/en-US/docs/Web/API/Broadcast_Channel_API">BroadcastChannel API</a>
+is a new API used to communicate between same-origin tabs opened by the same user.</p>
+
+<h1 id="why">Why</h1>
+<p>Let’s say you open two GitHub tabs, the <a href="https://github.com/rust-lang/rust">rust repository</a> and <a href="https://github.com/stars">your stars</a> page. You decide to star the awesome rust repository, but then you have to
+refresh your stars page to see your new star. That’s sad. There must be a way for GitHub to refresh
+your stars page in case you star something in another tab, right?</p>
+
+<p><img src="/img/broadcast-channels.jpg" alt="Broadcast Channels, SATISFIED" /></p>
+
+<h1 id="show-me-something">Show me something!</h1>
+<p>Okay, open another page of my blog in a new tab. Now open up your console and enter this:</p>
+
+<figure class="highlight"><pre><code class="language-javascript" data-lang="javascript"><span class="nx">channel</span><span class="p">.</span><span class="nx">postMessage</span><span class="p">(</span><span class="dl">'</span><span class="s1">Anybody hears me?</span><span class="dl">'</span><span class="p">);</span></code></pre></figure>
+
+<p>Boom.</p>
+
+<p>I’ve put this code in my <code class="language-plaintext highlighter-rouge">&lt;head&gt;</code>, pretty simple:</p>
+
+<figure class="highlight"><pre><code class="language-javascript" data-lang="javascript"><span class="kd">var</span> <span class="nx">channel</span> <span class="o">=</span> <span class="k">new</span> <span class="nx">BroadcastChannel</span><span class="p">(</span><span class="dl">'</span><span class="s1">egg</span><span class="dl">'</span><span class="p">);</span>
+
+<span class="nx">channel</span><span class="p">.</span><span class="nx">addEventListener</span><span class="p">(</span><span class="dl">'</span><span class="s1">message</span><span class="dl">'</span><span class="p">,</span> <span class="nx">message</span> <span class="o">=&gt;</span> <span class="p">{</span>
+  <span class="nx">alert</span><span class="p">(</span><span class="dl">'</span><span class="s1">Got a message from the other tab:</span><span class="se">\n</span><span class="dl">'</span> <span class="o">+</span> <span class="nx">message</span><span class="p">.</span><span class="nx">data</span><span class="p">);</span>
+
+  <span class="c1">// Egg</span>
+  <span class="nb">document</span><span class="p">.</span><span class="nx">querySelector</span><span class="p">(</span><span class="dl">'</span><span class="s1">header</span><span class="dl">'</span><span class="p">).</span><span class="nx">classList</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="dl">'</span><span class="s1">channel</span><span class="dl">'</span><span class="p">);</span>
+<span class="p">});</span></code></pre></figure>
+
+<h1 id="how">How</h1>
+<p>BroadcastChannels are pretty easy, here I’m going over the small details.</p>
+
+<h2 id="creating-channels">Creating channels</h2>
+<p>BroadcastChannels are constructed with a single argument, their name. Browsing contexts should use
+this name to communicate over a specified channel. There’s no limit to how many channels you can create.</p>
+
+<p>In the first sentence of article I said it’s used to communicate between tabs, but it’s actually “browsing contexts”.
+<a href="http://www.w3.org/TR/html5/browsers.html#browsing-context">Browsing contexts</a> are any environments owning a <code class="language-plaintext highlighter-rouge">Document</code>, e.g. tabs, windows, iframes, etc.</p>
+
+<figure class="highlight"><pre><code class="language-javascript" data-lang="javascript"><span class="kd">var</span> <span class="nx">channel</span> <span class="o">=</span> <span class="k">new</span> <span class="nx">BroadcastChannel</span><span class="p">(</span><span class="dl">'</span><span class="s1">star</span><span class="dl">'</span><span class="p">);</span></code></pre></figure>
+
+<p>Channels have only one property, <code class="language-plaintext highlighter-rouge">name</code>.</p>
+
+<h2 id="methods">Methods</h2>
+<p>Channels have two methods:</p>
+
+<h3 id="postmessagedata-anything">#postMessage(data: Anything)</h3>
+<p>This is the method used to broadcast a message to everyone subscribed to this channel. <code class="language-plaintext highlighter-rouge">data</code> can be any kind of Object.</p>
+
+<h3 id="close">#close()</h3>
+<p>This method is used to leave a channel, in case you don’t want to hear from the channel anymore.</p>
+
+<p>Try leaving <code class="language-plaintext highlighter-rouge">channel</code> from my blog pages, and posting messages with others.</p>
+
+<h2 id="events">Events</h2>
+<p>Channels inherit from <a href="https://developer.mozilla.org/en-US/docs/Web/API/EventTarget"><code class="language-plaintext highlighter-rouge">EventTarget</code></a>, so you can use  <code class="language-plaintext highlighter-rouge">addEventListener</code>, <code class="language-plaintext highlighter-rouge">removeEventListener</code> and <code class="language-plaintext highlighter-rouge">dispatchEvent</code> methods.</p>
+
+<p>Channels have only one event:</p>
+
+<h3 id="message">message</h3>
+<p>The event object passed to this event is a <a href="https://developer.mozilla.org/en-US/docs/Web/API/MessageEvent"><code class="language-plaintext highlighter-rouge">MessageEvent</code></a> with the <code class="language-plaintext highlighter-rouge">data</code> property set to the actual message sent using <code class="language-plaintext highlighter-rouge">postMessage</code>.</p>
+
+<hr />
+
+<h1 id="another-example">Another example</h1>
+<p>Let’s Fix GitHub
+—————-</p>
+
+<p>Okay, let’s try something cool, I promise you will love it. Open a browser with <a href="http://caniuse.com/#feat=broadcastchannel">BroadcastChannel support</a> and Install <a href="http://www.greasespot.net/">GreaseMonkey</a>.</p>
+
+<p>You have to add two scripts, one for repository pages, and one for the stars page.</p>
+
+<p>Click “New User Script”, and fill the inputs like this:</p>
+
+<p><img src="/img/greasemonkey-new-user-script.png" alt="GreaseMonkey New User Script" /></p>
+
+<p><img src="/img/greasemonkey-github-stars.png" alt="GreaseMonkey New Script" /></p>
+
+<p>In the Script Editor, enter this:</p>
+
+<figure class="highlight"><pre><code class="language-javascript" data-lang="javascript"><span class="c1">// join the "Stars" channel</span>
+<span class="kd">var</span> <span class="nx">channel</span> <span class="o">=</span> <span class="k">new</span> <span class="nx">BroadcastChannel</span><span class="p">(</span><span class="dl">'</span><span class="s1">Stars</span><span class="dl">'</span><span class="p">);</span>
+
+<span class="c1">// reload the page when someone from a github.com tab broadcasts a message</span>
+<span class="nx">channel</span><span class="p">.</span><span class="nx">addEventListener</span><span class="p">(</span><span class="dl">'</span><span class="s1">message</span><span class="dl">'</span><span class="p">,</span> <span class="nx">message</span> <span class="o">=&gt;</span> <span class="p">{</span>
+  <span class="nx">location</span><span class="p">.</span><span class="nx">reload</span><span class="p">();</span>
+<span class="p">});</span></code></pre></figure>
+
+<p>Now create another script and fill the form like this:</p>
+
+<p><img src="/img/greasemonkey-github-repositories.png" alt="GreaseMonkey New Script" /></p>
+
+<p>Use this code:</p>
+
+<figure class="highlight"><pre><code class="language-javascript" data-lang="javascript"><span class="c1">// join the "Stars" channel</span>
+<span class="kd">var</span> <span class="nx">channel</span> <span class="o">=</span> <span class="k">new</span> <span class="nx">BroadcastChannel</span><span class="p">(</span><span class="dl">'</span><span class="s1">Stars</span><span class="dl">'</span><span class="p">);</span>
+
+<span class="c1">// once the star/unstar forms are submitted, broadcast a message to</span>
+<span class="c1">// all github.com tabs</span>
+<span class="nx">$</span><span class="p">(</span><span class="dl">'</span><span class="s1">.starring-container form</span><span class="dl">'</span><span class="p">).</span><span class="nx">submit</span><span class="p">(</span><span class="nx">e</span> <span class="o">=&gt;</span> <span class="p">{</span>
+  <span class="nx">channel</span><span class="p">.</span><span class="nx">postMessage</span><span class="p">(</span><span class="dl">'</span><span class="s1">refresh</span><span class="dl">'</span><span class="p">);</span>
+<span class="p">});</span></code></pre></figure>
+
+<p>Save, refresh your pages and Voila! You can now Star/Unstar any repository while your stars page
+is open, and your stars page will refresh immediately.</p>
+
+<hr />
+
+<p>That’s it, I really like this API as it’s best of both worlds, simple and useful.</p>
+
+<p>There are a lot of things which can be done with help of BroadcastChannels, I would love to hear your feedback on this API.</p>
+
+  </article>
+
+  <div class="share-page">
+    Share in
+
+    <a href="https://twitter.com/intent/tweet?text=BroadcastChannel API&url=http://localhost:4000/broadcastchannel-api/&via=&related=" rel="nofollow" target="_blank" title="Share on Twitter">Twitter</a>
+    <a href="https://facebook.com/sharer.php?u=http://localhost:4000/broadcastchannel-api/" rel="nofollow" target="_blank" title="Share on Facebook">Facebook</a>
+    <a href="https://plus.google.com/share?url=http://localhost:4000/broadcastchannel-api/" rel="nofollow" target="_blank" title="Share on Google+">Google+</a>
+</div>
+
+  
+  <div id="commento"></div>
+  <script defer
+    src="//commento.mahdi.blog/js/commento.js">
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+
+  <script src="/js/heading-links.js"></script>
+</div>
+
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+
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+
+</html>
diff --git a/site/css-filters/index.html b/site/css-filters/index.html
new file mode 100644
index 0000000..032192d
--- /dev/null
+++ b/site/css-filters/index.html
@@ -0,0 +1,258 @@
+<!DOCTYPE html>
+<html>
+
+  <head>
+  <meta charset="utf-8">
+  <meta http-equiv="X-UA-Compatible" content="IE=edge">
+  <meta name="viewport" content="width=device-width, initial-scale=1">
+
+  <title>CSS Filters are awesome!</title>
+  <meta name="description" content="I’ve been working on the CSS Filter Editor widget in Firefox Developer Tools for a couple of weeks, thanks to Patrick Brosset for mentoring me and Tim Nguyen...">
+
+  <link href="https://fonts.googleapis.com/css?family=Secular+One|Nunito|Mononoki" rel="stylesheet"> 
+  <link rel="stylesheet" href="/css/main.css">
+  <link rel="canonical" href="http://localhost:4000/css-filters/">
+  <link rel="alternate" type="application/rss+xml" title="mahdi" href="http://localhost:4000/feed.xml" />
+
+  
+
+  <!--<script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script>-->
+
+  <script>
+    var channel = new BroadcastChannel('egg');
+
+    channel.addEventListener('message', message => {
+      alert('Got a message from the other tab:\n' + message.data);
+    });
+  </script>
+</head>
+
+
+
+  <body>
+
+    <header class="site-header">
+
+  <h1>
+    <a class='site-title' href='/'>
+      mahdi
+    </a>
+  </h1>
+
+  <nav>
+    <p>
+      <a href="/snippets">snippets</a>
+      <a href="/art">pictures</a>
+    </p>
+    <!--<p class='categories'>-->
+      <!---->
+        <!---->
+        <!--<a href="">art</a>-->
+        <!---->
+      <!---->
+        <!---->
+      <!---->
+    <!--</p>-->
+    <p>
+      <a href='mailto:mdibaiee@pm.me'>email</a>
+      <a href='https://git.mahdi.blog/mahdi'>git</a>
+      <a href='https://www.librarything.com/profile/mdibaiee'>librarything</a>
+      <a href="http://localhost:4000/feed.xml">feed</a>
+    </p>
+  </nav>
+
+</header>
+
+
+    <div class="page-content">
+      <div class="wrapper">
+        <h1 class="page-heading"></h1>
+        
+          <div class='post lang-en'>
+
+  <div class="post-header">
+    <h1 class="post-title"><p>CSS Filters are awesome!</p>
+</h1>
+    
+    <p class="post-meta">
+      <span>Mar 28, 2015</span>
+      
+      • <span>Reading time: 6  minutes</span>
+    </p>
+  </div>
+
+  <article class="post-content">
+    <p>I’ve been working on the <a href="https://bugzilla.mozilla.org/show_bug.cgi?id=1055181">CSS Filter Editor widget</a> in Firefox Developer Tools for a couple of weeks, thanks to <a href="https://medium.com/@patrickbrosset">Patrick Brosset</a> for mentoring me and <a href="https://github.com/nt1m">Tim Nguyen</a> for his great contributions.</p>
+
+<p>Here is an <a href="http://mdibaiee.github.io/CSS-Filter-Tooltip/">online version</a> to use as a playground. This version is modified to be cross-browser and therefore is a little different from the original widget used in Firefox.</p>
+
+<p>You can also use <a href="http://davidwalsh.name/demo/css-filters.php">David Walsh’s demo</a>, although it doesn’t have as much flexibility.</p>
+
+<p>CSS Filters are supported by most modern browsers (<a href="http://caniuse.com/#feat=css-filters">Can I Use CSS Filters</a>), if your browser doesn’t support this, please change your browser (I recommend <a href="https://www.mozilla.org/en-US/firefox/new/">Firefox</a>).</p>
+
+<p>I don’t like long-bla-bla-articles, so let’s get to it.</p>
+
+<h1 id="introduction">Introduction</h1>
+
+<p>CSS Filters introduce a few useful effects and some image adjusting functions, namely blur, drop-shadow, contrast, brightness, <a href="https://developer.mozilla.org/en-US/docs/Web/CSS/filter">and a few others</a> which can be really useful if used properly.</p>
+
+<p>A simple demo showing blur, contrast and brightness combined (hover over image):</p>
+
+<iframe width="100%" height="300" src="//jsfiddle.net/mdibaiee/zLmyhe7t/embedded/result,css" allowfullscreen="allowfullscreen" frameborder="0"></iframe>
+
+<p>I group filters by the type of value they take, let’s explain them briefly:</p>
+
+<h2 id="length">Length</h2>
+<p>These filters accept a length value (px, em, cm, <a href="http://www.w3.org/Style/Examples/007/units">etc</a>). blur is the only member of this family.</p>
+
+<h2 id="percentage">Percentage</h2>
+<p>These filters accept percentage values, but if you omit the percentage sign, the value is multiplied by 100, e.g. <code class="language-plaintext highlighter-rouge">contrast(2)</code> is another way of writing <code class="language-plaintext highlighter-rouge">contrast(200%)</code>. Negative values have the same effect as zero.</p>
+
+<p>Most filters explain themselves, I’m not going to repeat `Adjusts ${x} level` like a parrot.</p>
+
+<ul>
+  <li>brightness</li>
+  <li>contrast</li>
+  <li>grayscale</li>
+  <li>invert</li>
+  <li>opacity</li>
+  <li>saturate</li>
+  <li>sepia</li>
+</ul>
+
+<h3 id="invert">invert</h3>
+
+<p>I first understood how cool this filter can be after I saw Tim Nguyen using this in theme switching. Yeah you can’t invert everything and “Yay, I have a new theme”, but you can use invert on some elements and it works flawlessly, believe me.</p>
+
+<iframe width="100%" height="100" src="//jsfiddle.net/mdibaiee/373dnby8/embedded/result,css" allowfullscreen="allowfullscreen" frameborder="0"></iframe>
+
+<h3 id="opacity">opacity</h3>
+<p>You might wonder why do we have this function, as we already have an opacity property in CSS, that’s because the opacity property is not hardware accelerated, but the filter property is hardware accelerated in most browsers, which includes this function.</p>
+
+<h2 id="angle">Angle</h2>
+<p>hue-rotate is the only function to accept an angle value (degree / radian).</p>
+
+<p>###hue-rotate
+  If you’re familiar with <a href="https://en.wikipedia.org/wiki/Hue">Hue</a> you probably know that it’s measured by angles. The hue-rotate rotates the hue circle of an image relative to it’s current hue value (360 and 0 have the same results).</p>
+
+<iframe width="100%" height="300" src="//jsfiddle.net/mdibaiee/smk922fh/embedded/result,css" allowfullscreen="allowfullscreen" frameborder="0"></iframe>
+
+<h2 id="special">Special</h2>
+<p>These filter’s don’t fit in any of the groups above, they have special/mixed values.</p>
+
+<h3 id="drop-shadow">drop-shadow</h3>
+<p>The drop-shadow filter accepts a <em>shadow-list</em>, four length values, and one color. box-shadow and text-shadow also accept shadow lists.</p>
+
+<p>You’re probably familiar with shadow lists already: <code class="language-plaintext highlighter-rouge">drop-shadow(x y radius spread color)</code>. Unfortunaly spread doesn’t work in either Chrome or Firefox as of this writing — It is treated as an error.</p>
+
+<p>drop-shadow is pretty cool, as it doensn’t have the limitations of box-shadow and text-shadow. box-shadow applies a shadow to the outer shape, but drop-shadow applies a shadow to elements independant to their shape, they might be triangles, PNG’s with transparent background or just anything.</p>
+
+<p>drop-shadow clones the element’s image, moves it to the offset defined, applies blur and changes it’s color, putting it under the original element. Couldn’t do it better:</p>
+
+<p><img src="/img/dropshadow.gif" alt="drop-shadow explained" /></p>
+
+<p>Here is an example, a PNG image with transparent background and a CSS triangle made using the border hack:</p>
+
+<iframe width="100%" height="150" src="//jsfiddle.net/mdibaiee/z077vbs0/embedded/result,css" allowfullscreen="allowfullscreen" frameborder="0"></iframe>
+
+<h3 id="url">url</h3>
+<p>With the url function we have the power of CSS and SVG Filters in one place. You can reference an SVG element by linking to it with a hash of the filter element’s ID:</p>
+
+<figure class="highlight"><pre><code class="language-css" data-lang="css"><span class="nt">filter</span><span class="o">:</span> <span class="nt">url</span><span class="o">(/</span><span class="nt">example</span><span class="nc">.svg</span><span class="nf">#filter</span><span class="o">)</span></code></pre></figure>
+
+<p>If you want to know more about SVG Filters, I recommend <a href="https://developer.mozilla.org/en-US/docs/Web/SVG/Tutorial/Filter_effects">MDN’s tutorial on SVG Filters</a>.</p>
+
+<h3 id="custom">Custom</h3>
+<p>Now those filters are pretty cool, but what if I told you this is [going to be] done with CSS?</p>
+
+<p><img src="/img/map.jpg" alt="Map Folding with Custom CSS Filters" /></p>
+
+<p><span class="image-caption">Source: http://www.adobe.com/devnet/archive/html5/articles/css-shaders.html</span></p>
+
+<p>Custom Filters allows usage of vertex and fragment shaders which run directly in the GPU. Custom filters’ specs is subject to change, so there’s no implementation yet. For more info on this topic follow the links below:</p>
+
+<ul>
+  <li><a href="http://alteredqualia.com/css-shaders/article/#shaders">Getting started with CSS custom filters</a></li>
+  <li><a href="http://www.adobe.com/devnet/archive/html5/articles/css-shaders.html">Introducing CSS shaders: Cinematic effects for the web</a></li>
+  <li><a href="http://dev.w3.org/fxtf/custom/">CSS shaders specifications</a></li>
+</ul>
+
+<h1 id="gotchas">Gotchas</h1>
+
+<p>You now have a basic understanding of filters, good. Here are a few gotchas you’d better know.</p>
+
+<h2 id="order-matters">Order matters</h2>
+<p>The order in which filters are applied matters. Take this example:</p>
+
+<figure class="highlight"><pre><code class="language-css" data-lang="css"><span class="nt">filter</span><span class="o">:</span> <span class="nt">blur</span><span class="o">(</span><span class="err">10</span><span class="nt">px</span><span class="o">)</span> <span class="nt">contrast</span><span class="o">(</span><span class="err">2</span><span class="o">);</span></code></pre></figure>
+
+<p>Hey, browser, please blur the element, then double the contrast of the blurred element. (blurred parts have their contrast affected)</p>
+
+<figure class="highlight"><pre><code class="language-css" data-lang="css"><span class="nt">filter</span><span class="o">:</span> <span class="nt">contrast</span><span class="o">(</span><span class="err">2</span><span class="o">)</span> <span class="nt">blur</span><span class="o">(</span><span class="err">10</span><span class="nt">px</span><span class="o">);</span></code></pre></figure>
+
+<p>Hey browser, please double the contrast of my element, then blur it out. (high contrast image is blurred normally)</p>
+
+<p>Here is the actual comparison:</p>
+
+<iframe width="100%" height="300" src="//jsfiddle.net/mdibaiee/608yoqrx/embedded/result,css" allowfullscreen="allowfullscreen" frameborder="0"></iframe>
+
+<h2 id="inheritance">Inheritance</h2>
+
+<p>Okay, you now know the order of filters matters, the filter property is not actually <em>inherited</em>, but when you apply a filter on a parent element, of course it’s children are affected too, but what if the children have their own css filters? Ah-ha! CSS properties are applied bottom-up, which means childrens’ filters are applied first.</p>
+
+<iframe width="100%" height="300" src="//jsfiddle.net/mdibaiee/o40d7cs7/embedded/result,css" allowfullscreen="allowfullscreen" frameborder="0"></iframe>
+
+<h2 id="implementation">Implementation</h2>
+
+<p>I said using the url function we have “the power of CSS and SVG filters in one place”, but the CSS filters are actually implemented using SVG filters! You know, the functions are actually referencing to an svg generated in the browser. Here is the list of <a href="http://www.w3.org/TR/filter-effects/#ShorthandEquivalents">CSS Filter equivalents</a>.</p>
+
+<h1 id="go-wild">Go Wild</h1>
+
+<p>You can use CSS Filter on <em>any</em> element, experiment different things; <code class="language-plaintext highlighter-rouge">&lt;video&gt;</code>, <code class="language-plaintext highlighter-rouge">&lt;canvas&gt;</code>, <code class="language-plaintext highlighter-rouge">&lt;iframe&gt;</code>, GIF images, etc.</p>
+
+<p>My try (although I couldn’t get the GIF and CSS animation to be in sync, know a solution? Leave a comment please):</p>
+
+<iframe width="100%" height="300" src="//jsfiddle.net/mdibaiee/hjaL0ka3/embedded/result,css,js" allowfullscreen="allowfullscreen" frameborder="0"></iframe>
+
+<hr />
+
+<p>That’s it, you can subscribe to my <a href="http://localhost:4000/feed.xml">RSS</a> or follow me on <a href="https://twitter.com/">Twitter</a> to get more articles like this.</p>
+
+<style>
+  #mahdi {
+    transition: filter 1s ease;
+    -webkit-transition: filter 1s ease;
+  }
+  #mahdi:hover {
+    filter: blur(3px);
+    -webkit-filter: blur(3px);
+  }
+</style>
+
+
+  </article>
+
+  <div class="share-page">
+    Share in
+
+    <a href="https://twitter.com/intent/tweet?text=CSS Filters are awesome!&url=http://localhost:4000/css-filters/&via=&related=" rel="nofollow" target="_blank" title="Share on Twitter">Twitter</a>
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+
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diff --git a/site/css/main.css b/site/css/main.css
new file mode 100644
index 0000000..c47535b
--- /dev/null
+++ b/site/css/main.css
@@ -0,0 +1,379 @@
+/** Reset some basic elements */
+body, h1, h2, h3, h4, h5, h6, p, blockquote, pre, hr, dl, dd, ol, ul, figure { margin: 0; padding: 0; }
+
+/** Basic styling */
+body { font-family: "Nunito", "Sahel", Open Sans, sans-serif; font-size: 12pt; line-height: 1.5; font-weight: 300; color: #303030; background-color: #FFFCF8; -webkit-text-size-adjust: 100%; }
+
+* { box-sizing: border-box; }
+
+s { display: inline; }
+
+/** Set `margin-bottom` to maintain vertical rhythm */
+h1, h2, h3, h4, h5, h6, p, blockquote, pre, ul, ol, dl, figure { margin-bottom: 15px; }
+
+/** Images */
+img { max-width: 100%; vertical-align: middle; }
+
+/** Figures */
+figure > img { display: block; }
+
+figcaption { font-size: 10.5pt; }
+
+/** Lists */
+ul, ol { margin-left: 30px; }
+
+li > ul, li > ol { margin-bottom: 0; }
+
+/** Headings */
+h1, h2, h3, h4, h5, h6 { font-weight: 300; }
+
+/** Links */
+a { color: #2a7ae2; text-decoration: none; }
+
+a:visited { color: #1756a9; }
+
+a:hover { color: #303030; border-bottom: 1px solid #303030; }
+
+/** Blockquotes */
+blockquote { color: #828282; border-left: 4px solid #e8e8e8; padding-left: 15px; font-size: 18px; letter-spacing: -1px; font-style: italic; }
+
+blockquote > :last-child { margin-bottom: 0; }
+
+/** Code formatting */
+pre, code { font-size: 15px; border: 1px solid #e8e8e8; border-radius: 3px; background-color: white; }
+
+/** Code formatting */
+h1 pre, h1 code, h2 pre, h2 code, h3 pre, h3 code, h4 pre, h4 code { font-size: inherit; }
+
+code { padding: 1px 5px; }
+
+pre { padding: 8px 12px; overflow-x: scroll; }
+
+pre > code { border: 0; padding-right: 0; padding-left: 0; }
+
+/** Wrapper */
+.wrapper { max-width: -webkit-calc(800px - (30px * 2)); max-width: calc(800px - (30px * 2)); margin-right: auto; margin-left: auto; padding-right: 30px; padding-left: 30px; }
+
+@media screen and (max-width: 800px) { .wrapper { max-width: -webkit-calc(800px - (30px)); max-width: calc(800px - (30px)); padding-right: 15px; padding-left: 15px; } }
+
+/** Clearfix */
+.wrapper:after { content: ""; display: table; clear: both; }
+
+/** Icons */
+.icon > svg { display: inline-block; width: 16px; height: 16px; vertical-align: middle; }
+
+.icon > svg path { fill: #828282; }
+
+@font-face { font-family: 'Damion'; src: url(fonts/Damion_gdi.woff); }
+
+@font-face { font-family: 'Ubuntu'; src: url(fonts/Ubuntu_gdi.woff); }
+
+@font-face { font-family: 'Ubuntu Light'; src: url(fonts/Ubuntu-Light_gdi.woff); }
+
+@font-face { font-family: Mononoki; src: url(fonts/mononoki-Regular.woff); }
+
+@font-face { font-family: Sahel; src: url(fonts/Sahel.eot); src: url(fonts/Sahel.eot?#iefix) format("embedded-opentype"), url(fonts/Sahel.woff) format("woff"), url(fonts/Sahel.ttf) format("truetype"); font-weight: normal; }
+
+@font-face { font-family: Sahel; src: url(fonts/Sahel-Bold.eot); src: url(fonts/Sahel-Bold.eot?#iefix) format("embedded-opentype"), url(fonts/Sahel-Bold.woff) format("woff"), url(fonts/Sahel-Bold.ttf) format("truetype"); font-weight: bold; }
+
+@font-face { font-family: Sahel; src: url(fonts/Sahel-Black.eot); src: url(fonts/Sahel-Black.eot?#iefix) format("embedded-opentype"), url(fonts/Sahel-Black.woff) format("woff"), url(fonts/Sahel-Black.ttf) format("truetype"); font-weight: 900; }
+
+body { background: #FFF7EC; height: auto; padding-bottom: 5rem; }
+
+.share-page { padding: 10px 50px; background: rgba(0, 0, 0, 0.1); border-radius: 5px; margin: 50px 0; }
+
+.share-page a { margin-left: 1rem; }
+
+header { width: 100%; text-align: center; padding-top: 30px; }
+
+header img { margin: 30px auto; }
+
+header h1 { font-size: 4rem; font-family: "Secular One", sans-serif; text-transform: lowercase; }
+
+header h1 a, header > a { text-decoration: none; color: #303030 !important; }
+
+header h1 a:hover, header > a:hover { border: none; }
+
+header nav { margin-top: 1rem; margin-bottom: 1rem; }
+
+header nav a { margin: 0 1rem; }
+
+header a:visited { color: #2a7ae2; }
+
+.page-heading { text-align: center; font-style: italic; width: 20%; height: 1px; border: 1px dotted rgba(0, 0, 0, 0.1); margin: 2rem auto 5rem; }
+
+.post-list, .post-header { list-style: none; margin-left: 0; margin-bottom: 5rem; }
+
+.post-list h2, .post-list h1, .post-header h2, .post-header h1 { text-align: center; }
+
+.post-list .post-meta, .post-header .post-meta { font-size: 10.5pt; display: block; text-align: center; margin-bottom: 2rem; }
+
+.post-list .post-meta span, .post-header .post-meta span { margin-left: 1rem; margin-right: 1rem; }
+
+article p img { margin: 2rem auto; display: block; }
+
+article p img.inline { display: inline; margin: 0.1rem; }
+
+strong { font-weight: bold; }
+
+.post article h1 { font-weight: bold; }
+
+.post-list li { margin-top: 100px; }
+
+.post-list li:first-of-type { margin-top: 0; }
+
+.post-list h2 { font-size: 1.5rem; }
+
+.post article h2 { font-size: 1.3rem; }
+
+.post-content { position: relative; }
+
+.post-content [id] { position: relative; }
+
+.post-content [id]:hover .heading-link { opacity: 1; }
+
+.lang-fa { font-family: "Nunito", "Sahel", Open Sans, sans-serif; direction: rtl !important; }
+
+.lang-fa .post-content { text-align: right; font-size: 1.05em; line-height: 1.718em; }
+
+.lang-fa .share-page { direction: ltr; }
+
+.post-content .heading-link { display: block; position: absolute; width: 15px; height: 15px; left: -30px; top: 10px; padding-right: 30px; background: url(/img/link.svg) no-repeat; background-size: contain; opacity: 0; transition: opacity 0.3s ease; }
+
+.post-content .heading-link:hover { border: none; }
+
+article .image-caption { display: block; text-align: center; font-size: 10pt; color: #828282; margin-top: -1.5rem; }
+
+.rss-subscribe { text-align: center; }
+
+hr { border: none; border-top: 1px solid #b5b5b5; margin: 1.5rem 0; }
+
+.channel #mahdi * { fill: #000000 !important; }
+
+.channel > a::before { content: 'BroadcastChannels rock'; color: white; position: absolute; top: 250px; left: calc(50% - 83px); font-size: 15px; text-shadow: 0 0 1px white; }
+
+.centered { margin: 2rem auto; display: block; }
+
+.art .image-details { position: absolute; top: 10px; left: 10px; font-size: 12px; color: white; text-shadow: 1px 1px black; font-family: monospace; text-align: left; transition: opacity 0.2s; }
+
+.art .image-details.lang-fa { left: none; right: 10px; text-align: right; font-family: "Nunito", "Sahel", Open Sans, sans-serif; }
+
+.art .post-content:hover .image-details { opacity: 0; }
+
+/* Tomorrow Light */
+/* For use with Jekyll and Pygments */
+/* ----------------------------------------------------------*/
+pre, code { font-family: 'Mononoki'; font-size: 11pt; overflow-x: auto; }
+
+code { background: #fff; padding: 2px 4px; border-radius: 3px; border: 1px solid #ccc; }
+
+.highlight pre { padding: 8px 10px; }
+
+.highlight pre, .highlight code, .highlight .hll { background-color: #fff; border-radius: 3px; }
+
+.highlight .c { color: #8e908c; }
+
+/* Comment */
+.highlight .err { color: #c82829; }
+
+/* Error */
+.highlight .k { color: #8959a8; }
+
+/* Keyword */
+.highlight .l { color: #f5871f; }
+
+/* Literal */
+.highlight .n { color: #4d4d4c; }
+
+/* Name */
+.highlight .o { color: #3e999f; }
+
+/* Operator */
+.highlight .p { color: #4d4d4c; }
+
+/* Punctuation */
+.highlight .cm { color: #8e908c; }
+
+/* Comment.Multiline */
+.highlight .cp { color: #8e908c; }
+
+/* Comment.Preproc */
+.highlight .c1 { color: #8e908c; }
+
+/* Comment.Single */
+.highlight .cs { color: #8e908c; }
+
+/* Comment.Special */
+.highlight .gd { color: #c82829; }
+
+/* Generic.Deleted */
+.highlight .ge { font-style: italic; }
+
+/* Generic.Emph */
+.highlight .gh { color: #4d4d4c; font-weight: bold; }
+
+/* Generic.Heading */
+.highlight .gi { color: #718c00; }
+
+/* Generic.Inserted */
+.highlight .gp { color: #8e908c; font-weight: bold; }
+
+/* Generic.Prompt */
+.highlight .gs { font-weight: bold; }
+
+/* Generic.Strong */
+.highlight .gu { color: #3e999f; font-weight: bold; }
+
+/* Generic.Subheading */
+.highlight .kc { color: #8959a8; }
+
+/* Keyword.Constant */
+.highlight .kd { color: #8959a8; }
+
+/* Keyword.Declaration */
+.highlight .kn { color: #3e999f; }
+
+/* Keyword.Namespace */
+.highlight .kp { color: #8959a8; }
+
+/* Keyword.Pseudo */
+.highlight .kr { color: #8959a8; }
+
+/* Keyword.Reserved */
+.highlight .kt { color: #eab700; }
+
+/* Keyword.Type */
+.highlight .ld { color: #718c00; }
+
+/* Literal.Date */
+.highlight .m { color: #f5871f; }
+
+/* Literal.Number */
+.highlight .s { color: #718c00; }
+
+/* Literal.String */
+.highlight .na { color: #4271ae; }
+
+/* Name.Attribute */
+.highlight .nb { color: #4d4d4c; }
+
+/* Name.Builtin */
+.highlight .nc { color: #eab700; }
+
+/* Name.Class */
+.highlight .no { color: #c82829; }
+
+/* Name.Constant */
+.highlight .nd { color: #3e999f; }
+
+/* Name.Decorator */
+.highlight .ni { color: #4d4d4c; }
+
+/* Name.Entity */
+.highlight .ne { color: #c82829; }
+
+/* Name.Exception */
+.highlight .nf { color: #4271ae; }
+
+/* Name.Function */
+.highlight .nl { color: #4d4d4c; }
+
+/* Name.Label */
+.highlight .nn { color: #eab700; }
+
+/* Name.Namespace */
+.highlight .nx { color: #4271ae; }
+
+/* Name.Other */
+.highlight .py { color: #4d4d4c; }
+
+/* Name.Property */
+.highlight .nt { color: #3e999f; }
+
+/* Name.Tag */
+.highlight .nv { color: #c82829; }
+
+/* Name.Variable */
+.highlight .ow { color: #3e999f; }
+
+/* Operator.Word */
+.highlight .w { color: #4d4d4c; }
+
+/* Text.Whitespace */
+.highlight .mf { color: #f5871f; }
+
+/* Literal.Number.Float */
+.highlight .mh { color: #f5871f; }
+
+/* Literal.Number.Hex */
+.highlight .mi { color: #f5871f; }
+
+/* Literal.Number.Integer */
+.highlight .mo { color: #f5871f; }
+
+/* Literal.Number.Oct */
+.highlight .sb { color: #718c00; }
+
+/* Literal.String.Backtick */
+.highlight .sc { color: #4d4d4c; }
+
+/* Literal.String.Char */
+.highlight .sd { color: #8e908c; }
+
+/* Literal.String.Doc */
+.highlight .s2 { color: #718c00; }
+
+/* Literal.String.Double */
+.highlight .se { color: #f5871f; }
+
+/* Literal.String.Escape */
+.highlight .sh { color: #718c00; }
+
+/* Literal.String.Heredoc */
+.highlight .si { color: #f5871f; }
+
+/* Literal.String.Interpol */
+.highlight .sx { color: #718c00; }
+
+/* Literal.String.Other */
+.highlight .sr { color: #718c00; }
+
+/* Literal.String.Regex */
+.highlight .s1 { color: #718c00; }
+
+/* Literal.String.Single */
+.highlight .ss { color: #718c00; }
+
+/* Literal.String.Symbol */
+.highlight .bp { color: #4d4d4c; }
+
+/* Name.Builtin.Pseudo */
+.highlight .vc { color: #c82829; }
+
+/* Name.Variable.Class */
+.highlight .vg { color: #c82829; }
+
+/* Name.Variable.Global */
+.highlight .vi { color: #c82829; }
+
+/* Name.Variable.Instance */
+.highlight .il { color: #f5871f; }
+
+/* Literal.Number.Integer.Long */
+.highlight .lineno { user-select: none; -moz-user-select: none; -webkit-user-select: none; }
+
+#toc-container h2 { display: inline-block; }
+
+#toc-container input, #toc-container input + span { margin-left: 1rem; }
+
+#toc-container input { position: absolute; width: 50px; height: 20px; opacity: 0; margin-top: 10px; }
+
+#toc-container input + span::before { content: '[hide]'; }
+
+#toc-container input:checked ~ ul { display: none; }
+
+#toc-container input:checked + span::before { content: '[show]'; }
+
+.bibliography span a.heading-link { left: -40px; top: 5px; }
+
+/*# sourceMappingURL=main.css.map */
\ No newline at end of file
diff --git a/site/css/main.css.map b/site/css/main.css.map
new file mode 100644
index 0000000..303f4b6
--- /dev/null
+++ b/site/css/main.css.map
@@ -0,0 +1,22 @@
+{
+	"version": 3,
+	"file": "main.css",
+	"sources": [
+		"main.scss",
+		"_sass/_base.scss",
+		"_sass/_layout.scss",
+		"_sass/_syntax-highlighting.scss",
+		"_sass/toc.scss",
+		"_sass/bibliography.scss"
+	],
+	"sourcesContent": [
+		"@charset \"utf-8\";\n\n// Our variables\n$base-font-family: 'Nunito', 'Sahel', Open Sans, sans-serif;\n$head-font-family: 'Secular One', sans-serif;\n$base-font-size:   12pt;\n$small-font-size:  $base-font-size * 0.875;\n$base-line-height: 1.5;\n\n$spacing-unit:     30px;\n\n$text-color:       #303030;\n$background-color: #FFFCF8;\n$brand-color:      #2a7ae2;\n\n$grey-color:       #828282;\n$grey-color-light: lighten($grey-color, 40%);\n$grey-color-dark:  darken($grey-color, 25%);\n\n// Width of the content area\n$content-width:    800px;\n\n$on-palm:          600px;\n$on-laptop:        800px;\n\n\n\n// Using media queries with like this:\n// @include media-query($on-palm) {\n//     .wrapper {\n//         padding-right: $spacing-unit / 2;\n//         padding-left: $spacing-unit / 2;\n//     }\n// }\n@mixin media-query($device) {\n    @media screen and (max-width: $device) {\n        @content;\n    }\n}\n\n\n\n// Import partials from `sass_dir` (defaults to `_sass`)\n@import\n        \"base\",\n        \"layout\",\n        \"syntax-highlighting\",\n        \"toc\",\n        \"bibliography\"\n;\n",
+		"/**\n * Reset some basic elements\n */\nbody, h1, h2, h3, h4, h5, h6,\np, blockquote, pre, hr,\ndl, dd, ol, ul, figure {\n    margin: 0;\n    padding: 0;\n}\n\n\n\n/**\n * Basic styling\n */\nbody {\n    font-family: $base-font-family;\n    font-size: $base-font-size;\n    line-height: $base-line-height;\n    font-weight: 300;\n    color: $text-color;\n    background-color: $background-color;\n    -webkit-text-size-adjust: 100%;\n}\n\n* {\n    box-sizing: border-box;\n}\n\ns {\n    display: inline;\n}\n\n\n/**\n * Set `margin-bottom` to maintain vertical rhythm\n */\nh1, h2, h3, h4, h5, h6,\np, blockquote, pre,\nul, ol, dl, figure,\n%vertical-rhythm {\n    margin-bottom: $spacing-unit / 2;\n}\n\n\n\n/**\n * Images\n */\nimg {\n    max-width: 100%;\n    vertical-align: middle;\n}\n\n\n\n/**\n * Figures\n */\nfigure > img {\n    display: block;\n}\n\nfigcaption {\n    font-size: $small-font-size;\n}\n\n\n\n/**\n * Lists\n */\nul, ol {\n    margin-left: $spacing-unit;\n}\n\nli {\n    > ul,\n    > ol {\n         margin-bottom: 0;\n    }\n}\n\n\n\n/**\n * Headings\n */\nh1, h2, h3, h4, h5, h6 {\n    font-weight: 300;\n}\n\n\n\n/**\n * Links\n */\na {\n    color: $brand-color;\n    text-decoration: none;\n\n    &:visited {\n        color: darken($brand-color, 15%);\n    }\n\n    &:hover {\n        color: $text-color;\n        // text-decoration: underline;\n        border-bottom: 1px solid $text-color;\n    }\n}\n\n\n\n/**\n * Blockquotes\n */\nblockquote {\n    color: $grey-color;\n    border-left: 4px solid $grey-color-light;\n    padding-left: $spacing-unit / 2;\n    font-size: 18px;\n    letter-spacing: -1px;\n    font-style: italic;\n\n    > :last-child {\n        margin-bottom: 0;\n    }\n}\n\n\n\n/**\n * Code formatting\n */\npre,\ncode {\n    font-size: 15px;\n    border: 1px solid $grey-color-light;\n    border-radius: 3px;\n    background-color: white;\n}\n\n/**\n * Code formatting\n */\nh1 pre, h1 code,\nh2 pre, h2 code,\nh3 pre, h3 code,\nh4 pre, h4 code {\n    font-size: inherit;\n}\n\ncode {\n    padding: 1px 5px;\n}\n\npre {\n    padding: 8px 12px;\n    overflow-x: scroll;\n\n    > code {\n        border: 0;\n        padding-right: 0;\n        padding-left: 0;\n    }\n}\n\n\n\n/**\n * Wrapper\n */\n.wrapper {\n    max-width: -webkit-calc(#{$content-width} - (#{$spacing-unit} * 2));\n    max-width:         calc(#{$content-width} - (#{$spacing-unit} * 2));\n    margin-right: auto;\n    margin-left: auto;\n    padding-right: $spacing-unit;\n    padding-left: $spacing-unit;\n    @extend %clearfix;\n\n    @include media-query($on-laptop) {\n        max-width: -webkit-calc(#{$content-width} - (#{$spacing-unit}));\n        max-width:         calc(#{$content-width} - (#{$spacing-unit}));\n        padding-right: $spacing-unit / 2;\n        padding-left: $spacing-unit / 2;\n    }\n}\n\n\n\n/**\n * Clearfix\n */\n%clearfix {\n\n    &:after {\n        content: \"\";\n        display: table;\n        clear: both;\n    }\n}\n\n\n\n/**\n * Icons\n */\n.icon {\n\n    > svg {\n        display: inline-block;\n        width: 16px;\n        height: 16px;\n        vertical-align: middle;\n\n        path {\n            fill: $grey-color;\n        }\n    }\n}\n\n@font-face {\n\tfont-family: 'Damion';\n\tsrc: url(fonts/Damion_gdi.woff);\n}\n\n@font-face {\n    font-family: 'Ubuntu';\n    src: url(fonts/Ubuntu_gdi.woff);\n}\n@font-face {\n    font-family: 'Ubuntu Light';\n    src: url(fonts/Ubuntu-Light_gdi.woff);\n}\n//@font-face {\n    //font-family: 'Ubuntu Mono';\n    //src: url(fonts/UbuntuMono-Regular_gdi.woff);\n//}\n@font-face {\n  font-family: Mononoki;\n  src: url(fonts/mononoki-Regular.woff);\n}\n\n@font-face {\n    font-family: Sahel;\n    src: url(fonts/Sahel.eot);\n    src: url(fonts/Sahel.eot?#iefix) format('embedded-opentype'),\n            url(fonts/Sahel.woff) format('woff'),\n            url(fonts/Sahel.ttf) format('truetype');\n    font-weight: normal;\n}\n        \n@font-face {\n    font-family: Sahel;\n    src: url(fonts/Sahel-Bold.eot);\n    src: url(fonts/Sahel-Bold.eot?#iefix) format('embedded-opentype'),\n            url(fonts/Sahel-Bold.woff) format('woff'),\n            url(fonts/Sahel-Bold.ttf) format('truetype');\n    font-weight: bold;\n}\n\n@font-face {\n    font-family: Sahel;\n    src: url(fonts/Sahel-Black.eot);\n    src: url(fonts/Sahel-Black.eot?#iefix) format('embedded-opentype'),\n            url(fonts/Sahel-Black.woff) format('woff'),\n            url(fonts/Sahel-Black.ttf) format('truetype');\n    font-weight: 900;\n}\n",
+		"body {\n  background: #FFF7EC;\n  height: auto;\n  padding-bottom: 5rem;\n}\n\n.share-page {\n  padding: 10px 50px;\n  background: rgba(0, 0, 0, 0.1);\n  border-radius: 5px;\n  margin: 50px 0;\n\n  a {\n    margin-left: 1rem;\n  }\n}\n\nheader {\n  width: 100%;\n  text-align: center;\n  padding-top: $spacing-unit;\n\n  img {\n    // border-radius: 50%;\n    margin: $spacing-unit auto;\n    // border: 1px solid #F5DFC3;\n  }\n  h1 {\n    font-size: 4rem;\n    font-family: $head-font-family;\n    text-transform: lowercase;\n  }\n  h1 a, & > a {\n    text-decoration: none;\n    color: $text-color !important;\n\n    &:hover {\n      border: none;\n    }\n  }\n\n  nav {\n    margin-top: 1rem;\n    margin-bottom: 1rem;\n  }\n  nav a {\n    margin: 0 1rem;\n  }\n\n  a:visited {\n    color: $brand-color;\n  }\n}\n\n.page-heading {\n  text-align: center;\n  font-style: italic;\n  width: 20%;\n  height: 1px;\n  border: 1px dotted rgba(0, 0, 0, 0.1);\n\n  margin: 2rem auto 5rem;\n}\n\n.post-list, .post-header {\n  list-style: none;\n  margin-left: 0;\n  margin-bottom: 5rem;\n\n  h2, h1 {\n    text-align: center;\n  }\n\n  .post-meta {\n    font-size: $small-font-size;\n    display: block;\n    text-align: center;\n    margin-bottom: 2rem;\n\n    span {\n      margin-left: 1rem;\n      margin-right: 1rem;\n    }\n  }\n}\n\narticle p img {\n  margin: 2rem auto;\n  display: block;\n\n  &.inline {\n    display: inline;\n    margin: 0.1rem;\n  }\n}\n\nstrong {\n  font-weight: bold;\n}\n\n.post article h1 {\n  font-weight: bold;\n}\n\n.post-list li {\n  margin-top: 100px;\n}\n\n.post-list li:first-of-type {\n  margin-top: 0;\n}\n\n.post-list h2 {\n  font-size: 1.5rem;\n}\n\n.post article h2 {\n  font-size: 1.3rem;\n}\n\n.post-content {\n  position: relative;\n}\n\n.post-content [id] {\n  position: relative;\n\n  &:hover .heading-link {\n    opacity: 1;\n  }\n}\n\n.lang-fa {\n  font-family: $base-font-family;\n  direction: rtl !important;\n  .post-content {\n    text-align: right;\n    font-size: 1.05em;\n    line-height: 1.718em;\n  }\n  .share-page {\n    direction: ltr;\n  }\n}\n\n.post-content .heading-link {\n  display: block;\n  position: absolute;\n  width: 15px;\n  height: 15px;\n\n  left: -30px;\n  top: 10px;\n\n  padding-right: 30px;\n\n  background: url(/img/link.svg) no-repeat;\n  background-size: contain;\n\n  opacity: 0;\n\n  transition: opacity 0.3s ease;\n\n  &:hover {\n    border: none;\n  }\n}\n\narticle .image-caption {\n  display: block;\n  text-align: center;\n  font-size: 10pt;\n  color: $grey-color;\n  margin-top: -1.5rem;\n}\n\n.rss-subscribe {\n  text-align: center;\n}\n\nhr {\n  border: none;\n  border-top: 1px solid lighten($grey-color, 20%);\n  margin: 1.5rem 0;\n}\n\n.channel {\n  #mahdi * {\n    fill: #000000 !important;\n  }\n\n  & > a::before {\n    content: 'BroadcastChannels rock';\n    color: white;\n    position: absolute;\n    top: 250px;\n    left: calc(50% - 83px);\n    font-size: 15px;\n    text-shadow: 0 0 1px white;\n  }\n}\n\n.centered {\n  margin: 2rem auto;\n  display: block;\n}\n\n.art .image-details {\n  position: absolute;\n  top: 10px;\n  left: 10px;\n  font-size: 12px;\n  color: white;\n  text-shadow: 1px 1px black;\n  font-family: monospace;\n  text-align: left;\n\n  transition: opacity 0.2s;\n}\n\n.art .image-details.lang-fa {\n  left: none;\n  right: 10px;\n  text-align: right;\n  font-family: $base-font-family;\n}\n\n.art .post-content:hover .image-details {\n  opacity: 0;\n}\n",
+		"/* Tomorrow Light */\n \n/* For use with Jekyll and Pygments */\n\n/* ----------------------------------------------------------*/\n\npre, code {\n    font-family: 'Mononoki';\n    font-size: 11pt;\n    overflow-x: auto;\n}\n\ncode {background: #fff; padding: 2px 4px; border-radius: 3px; border: 1px solid #ccc;};\n\n.highlight pre {padding: 8px 10px;}\n\n.highlight pre,\n.highlight code,\n.highlight .hll { background-color: #fff; border-radius: 3px; }\n.highlight .c { color: #8e908c } /* Comment */\n.highlight .err { color: #c82829 } /* Error */\n.highlight .k { color: #8959a8 } /* Keyword */\n.highlight .l { color: #f5871f } /* Literal */\n.highlight .n { color: #4d4d4c } /* Name */\n.highlight .o { color: #3e999f } /* Operator */\n.highlight .p { color: #4d4d4c } /* Punctuation */\n.highlight .cm { color: #8e908c } /* Comment.Multiline */\n.highlight .cp { color: #8e908c } /* Comment.Preproc */\n.highlight .c1 { color: #8e908c } /* Comment.Single */\n.highlight .cs { color: #8e908c } /* Comment.Special */\n.highlight .gd { color: #c82829 } /* Generic.Deleted */\n.highlight .ge { font-style: italic } /* Generic.Emph */\n.highlight .gh { color: #4d4d4c; font-weight: bold } /* Generic.Heading */\n.highlight .gi { color: #718c00 } /* Generic.Inserted */\n.highlight .gp { color: #8e908c; font-weight: bold } /* Generic.Prompt */\n.highlight .gs { font-weight: bold } /* Generic.Strong */\n.highlight .gu { color: #3e999f; font-weight: bold } /* Generic.Subheading */\n.highlight .kc { color: #8959a8 } /* Keyword.Constant */\n.highlight .kd { color: #8959a8 } /* Keyword.Declaration */\n.highlight .kn { color: #3e999f } /* Keyword.Namespace */\n.highlight .kp { color: #8959a8 } /* Keyword.Pseudo */\n.highlight .kr { color: #8959a8 } /* Keyword.Reserved */\n.highlight .kt { color: #eab700 } /* Keyword.Type */\n.highlight .ld { color: #718c00 } /* Literal.Date */\n.highlight .m { color: #f5871f } /* Literal.Number */\n.highlight .s { color: #718c00 } /* Literal.String */\n.highlight .na { color: #4271ae } /* Name.Attribute */\n.highlight .nb { color: #4d4d4c } /* Name.Builtin */\n.highlight .nc { color: #eab700 } /* Name.Class */\n.highlight .no { color: #c82829 } /* Name.Constant */\n.highlight .nd { color: #3e999f } /* Name.Decorator */\n.highlight .ni { color: #4d4d4c } /* Name.Entity */\n.highlight .ne { color: #c82829 } /* Name.Exception */\n.highlight .nf { color: #4271ae } /* Name.Function */\n.highlight .nl { color: #4d4d4c } /* Name.Label */\n.highlight .nn { color: #eab700 } /* Name.Namespace */\n.highlight .nx { color: #4271ae } /* Name.Other */\n.highlight .py { color: #4d4d4c } /* Name.Property */\n.highlight .nt { color: #3e999f } /* Name.Tag */\n.highlight .nv { color: #c82829 } /* Name.Variable */\n.highlight .ow { color: #3e999f } /* Operator.Word */\n.highlight .w { color: #4d4d4c } /* Text.Whitespace */\n.highlight .mf { color: #f5871f } /* Literal.Number.Float */\n.highlight .mh { color: #f5871f } /* Literal.Number.Hex */\n.highlight .mi { color: #f5871f } /* Literal.Number.Integer */\n.highlight .mo { color: #f5871f } /* Literal.Number.Oct */\n.highlight .sb { color: #718c00 } /* Literal.String.Backtick */\n.highlight .sc { color: #4d4d4c } /* Literal.String.Char */\n.highlight .sd { color: #8e908c } /* Literal.String.Doc */\n.highlight .s2 { color: #718c00 } /* Literal.String.Double */\n.highlight .se { color: #f5871f } /* Literal.String.Escape */\n.highlight .sh { color: #718c00 } /* Literal.String.Heredoc */\n.highlight .si { color: #f5871f } /* Literal.String.Interpol */\n.highlight .sx { color: #718c00 } /* Literal.String.Other */\n.highlight .sr { color: #718c00 } /* Literal.String.Regex */\n.highlight .s1 { color: #718c00 } /* Literal.String.Single */\n.highlight .ss { color: #718c00 } /* Literal.String.Symbol */\n.highlight .bp { color: #4d4d4c } /* Name.Builtin.Pseudo */\n.highlight .vc { color: #c82829 } /* Name.Variable.Class */\n.highlight .vg { color: #c82829 } /* Name.Variable.Global */\n.highlight .vi { color: #c82829 } /* Name.Variable.Instance */\n.highlight .il { color: #f5871f } /* Literal.Number.Integer.Long */\n.highlight .lineno {user-select: none; -moz-user-select: none; -webkit-user-select: none;}\n",
+		"#toc-container {\n  h2 {\n    display: inline-block;\n  }\n\n  input, input + span {\n    margin-left: 1rem;\n  }\n\n  input {\n    position: absolute;\n    width: 50px;\n    height: 20px;\n    opacity: 0;\n    margin-top: 10px;\n  }\n\n  input + span::before {\n    content: '[hide]';\n  }\n\n  input:checked ~ ul {\n    display: none;\n  }\n\n  input:checked + span::before {\n    content: '[show]';\n  }\n}\n",
+		".bibliography {\n  span a.heading-link {\n    left: -40px;\n    top: 5px;\n  }\n}\n"
+	],
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diff --git a/site/diy-cardboard-kindle-stand/index.html b/site/diy-cardboard-kindle-stand/index.html
new file mode 100644
index 0000000..b052a7c
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@@ -0,0 +1,130 @@
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+  <title>DIY Cardboard Kindle Stand (for bed)</title>
+  <meta name="description" content="I’ve had a Kindle for more than a year now, but I’ve only recently started to read books on it frequently, I used to read paperworks before that, and I still...">
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+          <div class='post lang-en'>
+
+  <div class="post-header">
+    <h1 class="post-title"><p>DIY Cardboard Kindle Stand (for bed)</p>
+</h1>
+    
+    <p class="post-meta">
+      <span>Sep 24, 2017</span>
+      
+      • <span>Reading time: 1  minute</span>
+    </p>
+  </div>
+
+  <article class="post-content">
+    <p><img src="/img/kindle-stand/1.jpg" alt="a view of the stand + kindle" /></p>
+
+<p>I’ve had a Kindle for more than a year now, but I’ve only recently started to read books on it frequently, I used to read paperworks before that, and I still do sometimes prefer paperbooks if available. Anyways, my Kindle has helped me to fall asleep without struggling with all my thoughts, all I have to do is read until I fall asleep, so in a way, it has also been a remedy for my insomnia.</p>
+
+<p>Now to read the Kindle in bed, you would have to hold it using your hands or buy a stand or make one, motivated by <a href="https://blog.xkcd.com/2009/04/13/the-pursuit-of-laziness/">The Pursuit of Laziness</a> I set to create mine, but I didn’t use a piece of steel, instead I used a single box of cardboard I had in home to create one in minutes. :D</p>
+
+<!--more-->
+
+<p>It’s too easy to need much of an instruction, a few pictures and some explanation will do:</p>
+
+<p><img src="/img/kindle-stand/0.jpg" alt="a view of the stand without kindle" /></p>
+
+<p>So this part shows a simple piece of cardboard cut using scissors on the front, with the sides taped to the bottom (actually if your piece of cardboard is a box, it might already be taped in that way, mine was).</p>
+
+<p><img src="/img/kindle-stand/2.jpg" alt="a view of the stand's back side" /></p>
+
+<p>On the back, there is another piece of cardboard (I took the opening of it which already had a notch line, and the size fit perfectly). I used a stapler to to attach the two sides toghether, and that’s it!</p>
+
+<p>I tried it last night to make sure it’s convenient before posting here, and I tell you, it is totally comfortable and much better than holding with a hand.</p>
+
+  </article>
+
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diff --git a/site/dont-chase-become-the-good-one/index.html b/site/dont-chase-become-the-good-one/index.html
new file mode 100644
index 0000000..85d0fbf
--- /dev/null
+++ b/site/dont-chase-become-the-good-one/index.html
@@ -0,0 +1,160 @@
+<!DOCTYPE html>
+<html>
+
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+  <meta http-equiv="X-UA-Compatible" content="IE=edge">
+  <meta name="viewport" content="width=device-width, initial-scale=1">
+
+  <title>Don't chase: Become the good one</title>
+  <meta name="description" content="When it comes to relationships, most (unsuccessful) people are chasing the good ones.They spend time trying to find their dream partner, the perfect match, b...">
+
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+
+  <div class="post-header">
+    <h1 class="post-title"><p>Don’t chase: Become the good one</p>
+</h1>
+    
+    <p class="post-meta">
+      <span>Feb 4, 2017</span>
+      
+      • <span>Reading time: 3  minutes</span>
+    </p>
+  </div>
+
+  <article class="post-content">
+    <p>When it comes to relationships, most (unsuccessful) people are <em>chasing</em> the good ones.
+They spend time trying to find their dream partner, the perfect match, but hey, do you qualify
+as the dream partner of your dream partner? You fantasize about your dream partner, but have you ever
+thought what kind of partner does he/she dream of?</p>
+
+<p><img src="/img/angel.jpg" alt="I want an angel with..." />
+<span class="image-caption">I want an angel with…</span></p>
+
+<!--more-->
+
+<p>It seems to be pretty acceptable in the society to start <em>looking</em> for a <em>good</em> partner once you
+reach a certain age (depending on the country), and that’s when people start defining for themselves what
+a <em>good</em> partner means. What do they want out of a relationship? Well, most beginners just want sex, that’s one thing,
+but I’m talking about real, intimate relationships. The definition usually goes like this:</p>
+
+<p>I want him/her to have</p>
+<ul>
+  <li>Money</li>
+  <li>Body</li>
+  <li>Sense of Humor</li>
+  <li>Empathy</li>
+  <li>…</li>
+</ul>
+
+<p>Alright fine, that’s a good and necessary step while thinking about a relationship.</p>
+
+<p>Now there are two groups of people after this step, let’s call them Group A and Group B.</p>
+
+<p>Group A’s next step is to start looking for partners, which usually follows by installing Tinder, OkCupid and a bunch of other
+dating apps, spending more time in the bar, etc. Well it makes sense to start looking for a partner at first glance, but people in Group A
+are missing an important point here, they defined what a <em>good partner</em> means in their dictionary of life, but they haven’t
+really looked into their <em>good partner</em>’s dictionary to see what he/she wants out of a relationship, because if you don’t qualify her requirements,
+it’s not a deal.</p>
+
+<p>Now there is a sub-group of Group A, too, and it includes the people who faced with the question “am I what she dreams of?”, they 
+try to cheat and modify their definition of a good partner, adding a line that goes “Loves me however I am”, sorry buddy, but what if I
+tell you she could add the same line to her dictionary? That’s not a deal, you want a good partner as you defined it, you have to be a good partner
+as she defines it.</p>
+
+<p>On the other hand, Group B doesn’t follow the same path as Group A. Group B starts by trying to predict what his dream partner would want
+out of a relationship. Empathy? Loyalty? Knowledge? Body? They take a pen and a paper out and write a list of what they think their dream partner
+would want them to have, what would she want them to be, and they start working on those, and I bet it’s not going to be easy, knowledge doesn’t pop up
+after a good night’s sleep, you have to spend years reading books and learning to get it. A good body doesn’t <em>poof</em> out if you wish it to, you have
+to spend years being committed to exercise and eating well, and that’s not easy. After all, what you define as a good partner ain’t easy either, is it?</p>
+
+<p>Now do you want your dream partner to fall for you the way you fall for her, without having to chase her with a net? Write down a list of 
+qualifications you expect your dream partner to look for, and start working your ass off reaching them, and I tell you, you will have a much easier <em>next step</em> after this. You won’t have to chase girls hoping the 34th one doesn’t reject you because “she likes you however you are”.</p>
+
+<p>If I know one thing about life, it’s the fact that you have to work your ass off in order to reach your dreams, dreams aren’t easy, and a deep, intimate relationship really is a dream.</p>
+
+  </article>
+
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+    <h1 class="post-title"><p>ES7 Array and Generator comprehensions</p>
+</h1>
+    
+    <p class="post-meta">
+      <span>Jun 6, 2015</span>
+      
+      • <span>Reading time: 6  minutes</span>
+    </p>
+  </div>
+
+  <article class="post-content">
+    <p>Array comprehension is a new feature proposed for ES7, with a new syntax
+to create new arrays from existing <a href="http://www.2ality.com/2015/02/es6-iteration.html">iterables</a>,
+comprehensions can replace map and filter.</p>
+
+<p>Generator comprehension brings the same feature to generators, this is a more
+useful feature as it removes the need to write new generators for simple map/filter operations.</p>
+
+<p>Generator comprehensions allow us to easily write single-line generators, which can replace our arrays in some situations, you might ask why we might consider replacing arrays with generators, the most important reason is their <a href="#laziness">laziness</a>. I’ve explained laziness later in the article.</p>
+
+<p>Comprehensions are currently only supported by Firefox, use Firefox 30+ or <a href="https://babeljs.io/repl/">Babel</a> to run the examples. The Node.js version of examples using generator <code class="language-plaintext highlighter-rouge">function* ()</code>s is available at the <a href="https://github.com/mdibaiee/array-vs-generator">repository</a> (doesn’t require transpilation, use latest node).</p>
+
+<h1 id="syntax">Syntax</h1>
+
+<p>The syntax is pretty simple, you can only use <code class="language-plaintext highlighter-rouge">for of</code> and <code class="language-plaintext highlighter-rouge">if</code> inside comprehensions.</p>
+
+<p>Array comprehensions:</p>
+
+<figure class="highlight"><pre><code class="language-javascript" data-lang="javascript"><span class="kd">let</span> <span class="nx">numbers</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">];</span>
+
+<span class="kd">let</span> <span class="nx">even</span> <span class="o">=</span> <span class="p">[</span> <span class="k">for</span> <span class="p">(</span><span class="nx">n</span> <span class="k">of</span> <span class="nx">numbers</span><span class="p">)</span> <span class="k">if</span> <span class="p">(</span><span class="nx">n</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">===</span> <span class="mi">0</span><span class="p">)</span> <span class="nx">n</span> <span class="p">];</span>
+<span class="c1">// equivalent:</span>
+<span class="c1">// let even = numbers.filter(n =&gt; n % 2 === 0);</span>
+
+<span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(...</span><span class="nx">even</span><span class="p">);</span> <span class="c1">// 2 4</span></code></pre></figure>
+
+<p>Generator comprehensions:</p>
+
+<figure class="highlight"><pre><code class="language-javascript" data-lang="javascript"><span class="c1">// yield 0...5</span>
+<span class="kd">let</span> <span class="nx">generator</span> <span class="o">=</span> <span class="kd">function</span><span class="o">*</span> <span class="p">()</span> <span class="p">{</span>
+  <span class="k">for</span> <span class="p">(</span><span class="kd">let</span> <span class="nx">i</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span> <span class="nx">i</span> <span class="o">&lt;</span> <span class="mi">6</span><span class="p">;</span> <span class="nx">i</span><span class="o">++</span><span class="p">)</span> <span class="p">{</span>
+    <span class="k">yield</span> <span class="nx">i</span><span class="p">;</span>
+  <span class="p">}</span>
+<span class="p">}</span>
+
+<span class="kd">let</span> <span class="nx">squared</span> <span class="o">=</span> <span class="p">(</span> <span class="k">for</span> <span class="p">(</span><span class="nx">n</span> <span class="k">of</span> <span class="nx">generator</span><span class="p">())</span> <span class="nx">n</span> <span class="o">*</span> <span class="nx">n</span> <span class="p">);</span>
+<span class="c1">// equivalent:</span>
+<span class="c1">// let squared = Array.from(generator()).map(n =&gt; n * n);</span>
+
+<span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(...</span><span class="nx">squared</span><span class="p">);</span> <span class="c1">// 0 1 4 9 16 25</span></code></pre></figure>
+
+<p>You can also nest comprehensions:</p>
+
+<figure class="highlight"><pre><code class="language-javascript" data-lang="javascript"><span class="c1">// yield 0...5</span>
+<span class="kd">let</span> <span class="nx">generator</span> <span class="o">=</span> <span class="kd">function</span><span class="o">*</span> <span class="p">()</span> <span class="p">{</span>
+  <span class="k">for</span> <span class="p">(</span><span class="kd">let</span> <span class="nx">i</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span> <span class="nx">i</span> <span class="o">&lt;</span> <span class="mi">6</span><span class="p">;</span> <span class="nx">i</span><span class="o">++</span><span class="p">)</span> <span class="p">{</span>
+    <span class="k">yield</span> <span class="nx">i</span><span class="p">;</span>
+  <span class="p">}</span>
+<span class="p">}</span>
+
+<span class="c1">// yield three numbers after number</span>
+<span class="kd">let</span> <span class="nx">after</span> <span class="o">=</span> <span class="kd">function</span><span class="o">*</span> <span class="p">(</span><span class="nx">number</span><span class="p">)</span> <span class="p">{</span>
+  <span class="k">for</span> <span class="p">(</span><span class="kd">let</span> <span class="nx">i</span> <span class="o">=</span> <span class="mi">1</span><span class="p">;</span> <span class="nx">i</span> <span class="o">&lt;</span> <span class="mi">4</span><span class="p">;</span> <span class="nx">i</span><span class="o">++</span><span class="p">)</span> <span class="p">{</span>
+    <span class="k">yield</span> <span class="nx">number</span> <span class="o">+</span> <span class="nx">i</span><span class="p">;</span>
+  <span class="p">}</span>
+<span class="p">}</span>
+
+<span class="c1">// for each number 0...5, yield an array of 3 numbers after it</span>
+<span class="kd">let</span> <span class="nx">nested</span> <span class="o">=</span> <span class="p">(</span> <span class="k">for</span> <span class="p">(</span><span class="nx">n</span> <span class="k">of</span> <span class="nx">generator</span><span class="p">())</span>
+               <span class="p">[</span> <span class="k">for</span> <span class="p">(</span><span class="nx">i</span> <span class="k">of</span> <span class="nx">after</span><span class="p">(</span><span class="nx">n</span><span class="p">))</span> <span class="nx">i</span> <span class="p">]</span>
+             <span class="p">)</span>
+
+<span class="nx">console</span><span class="p">.</span><span class="nx">table</span><span class="p">(</span><span class="nb">Array</span><span class="p">.</span><span class="k">from</span><span class="p">(</span><span class="nx">nested</span><span class="p">));</span>
+<span class="c1">// 1, 2, 3</span>
+<span class="c1">// 2, 3, 4</span>
+<span class="c1">// 3, 4, 5</span>
+<span class="c1">// 4, 5, 6</span>
+<span class="c1">// 5, 6, 7</span>
+<span class="c1">// 6, 7, 8</span></code></pre></figure>
+
+<h1 id="laziness">Laziness</h1>
+<p>This is one of the most important advantages of generators over arrays and things alike.
+The reason why I’m including this here is to give you a good reason to write generators instead of arrays
+ while generator comprehensions make it extremely easy to write them — this is a proof of their usefulness.</p>
+
+<p>In programming, laziness means doing nothing until the results are requested or in simpler terms, avoiding unnecessary work.
+For example, when you create an array and map it, the result will be evaluated no matter you need it now or not, you need the whole thing or a part of it, etc.</p>
+
+<p>Take this example:</p>
+
+<figure class="highlight"><pre><code class="language-javascript" data-lang="javascript"><span class="kd">let</span> <span class="nx">bigArray</span> <span class="o">=</span> <span class="k">new</span> <span class="nb">Array</span><span class="p">(</span><span class="mi">100000</span><span class="p">);</span>
+<span class="k">for</span> <span class="p">(</span><span class="kd">let</span> <span class="nx">i</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span> <span class="nx">i</span> <span class="o">&lt;</span> <span class="mi">100000</span><span class="p">;</span> <span class="nx">i</span><span class="o">++</span><span class="p">)</span> <span class="p">{</span>
+  <span class="nx">bigArray</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span> <span class="o">=</span> <span class="nx">i</span><span class="p">;</span>
+<span class="p">}</span>
+
+<span class="kd">let</span> <span class="nx">first</span> <span class="o">=</span> <span class="nx">bigArray</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="nx">n</span> <span class="o">=&gt;</span> <span class="nx">n</span> <span class="o">*</span> <span class="nx">n</span><span class="p">)[</span><span class="mi">0</span><span class="p">];</span>
+<span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="nx">first</span><span class="p">);</span></code></pre></figure>
+
+<p>You know what happens here, first, map is evaluated, returning thousands of squared numbers, then
+the first element is returned. We must allocate and evaluate the whole squared array to be able to know about it’s first or second element.</p>
+
+<p>Think of optimizing it, is it possible to get the desired result without storing
+temporary arrays in memory? Can we get the first number directly without consuming a big chunk of memory?</p>
+
+<p>Yes, using generators, Look at this:</p>
+
+<figure class="highlight"><pre><code class="language-javascript" data-lang="javascript"><span class="kd">let</span> <span class="nx">bigGenerator</span> <span class="o">=</span> <span class="kd">function</span><span class="o">*</span> <span class="p">()</span> <span class="p">{</span>
+  <span class="k">for</span> <span class="p">(</span><span class="kd">let</span> <span class="nx">i</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span> <span class="nx">i</span> <span class="o">&lt;</span> <span class="mi">100000</span><span class="p">;</span> <span class="nx">i</span><span class="o">++</span><span class="p">)</span> <span class="p">{</span>
+    <span class="k">yield</span> <span class="nx">i</span><span class="p">;</span>
+  <span class="p">}</span>
+<span class="p">}</span>
+
+<span class="kd">let</span> <span class="nx">squared</span> <span class="o">=</span> <span class="p">(</span> <span class="k">for</span> <span class="p">(</span><span class="nx">n</span> <span class="k">of</span> <span class="nx">bigGenerator</span><span class="p">())</span> <span class="nx">n</span> <span class="o">*</span> <span class="nx">n</span> <span class="p">);</span>
+
+<span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="nx">squared</span><span class="p">.</span><span class="nx">next</span><span class="p">());</span></code></pre></figure>
+
+<p>Let’s see what happens in this case.
+Here, we create a generator which will yield numbers 0…100000, nothing is actually allocated or evaluated, we just have a generator which will return a new number every time we call <code class="language-plaintext highlighter-rouge">next()</code>.
+Then we use generator comprehension to create another generator which squares the numbers our <code class="language-plaintext highlighter-rouge">bigGenerator()</code> yields, again, we don’t evaluate or allocate anything, we just create a generator which will call another generator’s <code class="language-plaintext highlighter-rouge">next()</code> method, square the results, and yield it.</p>
+
+<p>Now when we call <code class="language-plaintext highlighter-rouge">squared.next()</code>, the <code class="language-plaintext highlighter-rouge">squared</code> generator calls <code class="language-plaintext highlighter-rouge">bigArray().next()</code>, squares the results and yields it, it doesn’t do any unnecessary work, it’s lazy.</p>
+
+<p><a href="/img/generator-diagram.png">
+  <img src="/img/generator-diagram.png" alt="Generator diagram" />
+</a>
+<span class="image-caption">Calling squared.next() 4 times</span></p>
+
+<p>If you profile heap/memory usage and running time, you will see the difference.</p>
+
+<p>I have prepared a Node.js version of the test case. With the help of <a href="https://nodejs.org/api/process.html#process_process_memoryusage"><code class="language-plaintext highlighter-rouge">process.memoryUsage()</code></a> and <a href="https://developer.mozilla.org/en-US/docs/Web/API/Console/time"><code class="language-plaintext highlighter-rouge">console.time</code></a> we can easily see the difference.
+It’s a lot faster, with less space required, isn’t that awesome?</p>
+
+<p><a href="https://github.com/mdibaiee/array-vs-generator">Repository: mdibaiee/array-vs-generator</a></p>
+
+<p><img src="/img/array-vs-generator.png" alt="Array vs Generator performance" /></p>
+
+<p>If you want to know more about lazy iterators, I recommend raganwald’s <a href="http://raganwald.com/2015/02/17/lazy-iteratables-in-javascript.html">Lazy Iterables in JavaScript</a>.</p>
+
+<p>More:</p>
+
+<p><a href="https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Array_comprehensions">MDN: Array Comprehensions</a></p>
+
+<p><a href="https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Generator_comprehensions">MDN: Generator Comprehensions</a></p>
+
+<p><a href="https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Statements/for...of">MDN: for…of</a></p>
+
+<p><a href="https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Iterators_and_Generators?redirectlocale=en-US&amp;redirectslug=JavaScript%2FGuide%2FIterators_and_Generators">MDN: Iterators and Generators</a></p>
+
+<p><a href="https://hacks.mozilla.org/2015/05/es6-in-depth-generators/?utm_source=javascriptweekly&amp;utm_medium=email">ES6 in Depth: Generators</a></p>
+
+  </article>
+
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diff --git a/site/feed.xml b/site/feed.xml
new file mode 100644
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--- /dev/null
+++ b/site/feed.xml
@@ -0,0 +1,2365 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom">
+  <channel>
+    <title>mahdi</title>
+    <description>a rabbit hole</description>
+    <link>http://localhost:4000/</link>
+    <atom:link href="http://localhost:4000/feed.xml" rel="self" type="application/rss+xml"/>
+    <pubDate>Wed, 06 Jul 2022 17:36:29 +0100</pubDate>
+    <lastBuildDate>Wed, 06 Jul 2022 17:36:29 +0100</lastBuildDate>
+    <generator>Jekyll v4.2.2</generator>
+    
+      
+      <item>
+        <title>What is `Box&lt;str&gt;` and how is it different from `String` in Rust?</title>
+        <description>&lt;p&gt;Today I and a friend went down a rabbit hole about Rust and how it manages the heap when we use &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Box&lt;/code&gt;, or &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;String&lt;/code&gt;, or &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Vec&lt;/code&gt;, and while we were at it, I found out there is such a thing as &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Box&amp;lt;str&amp;gt;&lt;/code&gt;, which might look a bit &lt;em&gt;strange&lt;/em&gt; to an untrained eye, since most of the time the &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;str&lt;/code&gt; primitive type is passed around as &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;&amp;amp;str&lt;/code&gt;.&lt;/p&gt;
+
+&lt;hr /&gt;
+
+&lt;p&gt;TL;DR:&lt;/p&gt;
+
+&lt;p&gt;&lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Box&amp;lt;str&amp;gt;&lt;/code&gt; is a primitive &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;str&lt;/code&gt; allocated on the heap, whereas &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;String&lt;/code&gt; is actually a &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Vec&amp;lt;u8&amp;gt;&lt;/code&gt;, also allocated on the heap, which allows for efficient removals and appends. &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Box&amp;lt;str&amp;gt;&lt;/code&gt; (16 bytes) uses less memory than &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;String&lt;/code&gt; (24 bytes).&lt;/p&gt;
+
+&lt;hr /&gt;
+
+&lt;p&gt;I will be using &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;rust-lldb&lt;/code&gt; throughout this post to understand what is going on in the rust programs we write and run. The source code for this blog post is available on &lt;a href=&quot;https://git.mahdi.blog/mahdi/rust-memory-playground&quot;&gt;mdibaiee/rust-memory-playground&lt;/a&gt;.&lt;/p&gt;
+
+&lt;div class=&quot;language-bash highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;git clone https://git.mahdi.blog/mahdi/rust-memory-playground
+&lt;span class=&quot;nb&quot;&gt;cd &lt;/span&gt;rust-memory-playground
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;h1 id=&quot;the-stack&quot;&gt;The Stack&lt;/h1&gt;
+
+&lt;p&gt;Most of the primitive data types used throughout a program, and the information about the program itself are usually allocated on the stack. Consider this simple program:&lt;/p&gt;
+
+&lt;div class=&quot;language-rust highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;k&quot;&gt;fn&lt;/span&gt; &lt;span class=&quot;nf&quot;&gt;add_ten&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;nb&quot;&gt;u8&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;k&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;nb&quot;&gt;u8&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;{&lt;/span&gt;
+    &lt;span class=&quot;k&quot;&gt;let&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;mi&quot;&gt;10&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;;&lt;/span&gt;
+    &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;+&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;
+&lt;span class=&quot;p&quot;&gt;}&lt;/span&gt;
+
+
+&lt;span class=&quot;k&quot;&gt;fn&lt;/span&gt; &lt;span class=&quot;nf&quot;&gt;main&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;()&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;{&lt;/span&gt;
+    &lt;span class=&quot;nd&quot;&gt;println!&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;s&quot;&gt;&quot;{}&quot;&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;nf&quot;&gt;add_ten&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;9&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;));&lt;/span&gt;
+&lt;span class=&quot;p&quot;&gt;}&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;p&gt;Let’s examine the stack when we are running &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;a + b&lt;/code&gt; by setting a breakpoint on that line:&lt;/p&gt;
+
+&lt;div class=&quot;language-plaintext highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;$ cargo build &amp;amp;&amp;amp; rust-lldb target/debug/stack-program
+
+(lldb) breakpoint set -f main.rs -l 3
+Breakpoint 1: where = stack-program`stack_program::add_ten::h42edbf0bdcb04851 + 24 at main.rs:3:5, address = 0x0000000100001354
+
+(lldb) run
+Process 65188 launched: &apos;/Users/mahdi/workshop/rust-memory-playground/target/debug/stack-program&apos; (arm64)
+Process 65188 stopped
+* thread #1, queue = &apos;com.apple.main-thread&apos;, stop reason = breakpoint 1.1
+    frame #0: 0x0000000100001354 stack-program`stack_program::add_ten::h42edbf0bdcb04851(a=5) at main.rs:3:5
+   1    fn add_ten(a: u8) -&amp;gt; u8 {
+   2        let b = 10;
+-&amp;gt; 3        a + b
+   4    }
+   5
+   6
+   7    fn main() {
+   
+(lldb) frame var -L -f X
+0x000000016fdfed7e: (unsigned char) a = 0x09
+0x000000016fdfed7f: (unsigned char) b = 0x0A
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;p&gt;Our program allocates two variables on the stack directly here. Notice that they are allocated right next to each other, their address only one bit apart. Most primitive types are allocated on the stack, and are copied when being passed around because they are small enough, so that copying them around is more reasonable than allocating them in the heap and passing around a pointer to them. In this case, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;u8&lt;/code&gt; can be allocated in a single byte, it would not make sense for us to allocate a pointer (which can vary in size, but are usually larger than 8 bytes). Every time you call a function, a copy of the values passed to it, along with the values defined in the function itself constitute the stack of that function.&lt;/p&gt;
+
+&lt;p&gt;The stack of a whole program includes more information though, such as the &lt;em&gt;backtrace&lt;/em&gt;, which allows the program to know how to navigate: once I am done with this function, where should I return to? that information is available in the stack as well. Note the first couple of lines here, indicating that we are currently in &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;stack_program::add_then&lt;/code&gt;, and we came here from &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;stack_program::main&lt;/code&gt;, and so once we are finished with &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;add_then&lt;/code&gt;, we will go back to &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;main&lt;/code&gt;:&lt;/p&gt;
+
+&lt;div class=&quot;language-plaintext highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;(lldb) thread backtrace
+* thread #1, queue = &apos;com.apple.main-thread&apos;, stop reason = breakpoint 1.1
+  * frame #0: 0x0000000100001350 stack-program`stack_program::add_ten::hf7dc9cccae290c37(a=&apos;\t&apos;) at main.rs:3:5
+    frame #1: 0x00000001000013a8 stack-program`stack_program::main::he22b9cf577b52c34 at main.rs:8:20
+    frame #2: 0x00000001000015a4 stack-program`core::ops::function::FnOnce::call_once::hd6bac0cd3fcb8c07((null)=(stack-program`stack_program::main::he22b9cf577b52c34 at main.rs:7), (null)=&amp;lt;unavailable&amp;gt;) at function.rs:227:5
+    frame #3: 0x00000001000014c4 stack-program`std::sys_common::backtrace::__rust_begin_short_backtrace::hc4df46810f9a7139(f=(stack-program`stack_program::main::he22b9cf577b52c34 at main.rs:7)) at backtrace.rs:122:18
+    frame #4: 0x0000000100001178 stack-program`std::rt::lang_start::_$u7b$$u7b$closure$u7d$$u7d$::hbec5b809d627978a at rt.rs:145:18
+    frame #5: 0x000000010001440c stack-program`std::rt::lang_start_internal::hc453db0ee48af82e [inlined] core::ops::function::impls::_$LT$impl$u20$core..ops..function..FnOnce$LT$A$GT$$u20$for$u20$$RF$F$GT$::call_once::h485d4c2966ec30a8 at function.rs:259:13 [opt]
+    frame #6: 0x0000000100014400 stack-program`std::rt::lang_start_internal::hc453db0ee48af82e [inlined] std::panicking::try::do_call::h375a887be0bea938 at panicking.rs:492:40 [opt]
+    frame #7: 0x0000000100014400 stack-program`std::rt::lang_start_internal::hc453db0ee48af82e [inlined] std::panicking::try::hecad40482ef3be15 at panicking.rs:456:19 [opt]
+    frame #8: 0x0000000100014400 stack-program`std::rt::lang_start_internal::hc453db0ee48af82e [inlined] std::panic::catch_unwind::haf1f664eb41a88eb at panic.rs:137:14 [opt]
+    frame #9: 0x0000000100014400 stack-program`std::rt::lang_start_internal::hc453db0ee48af82e [inlined] std::rt::lang_start_internal::_$u7b$$u7b$closure$u7d$$u7d$::h976eba434e9ff4cf at rt.rs:128:48 [opt]
+    frame #10: 0x0000000100014400 stack-program`std::rt::lang_start_internal::hc453db0ee48af82e [inlined] std::panicking::try::do_call::h8f2501ab92e340b0 at panicking.rs:492:40 [opt]
+    frame #11: 0x0000000100014400 stack-program`std::rt::lang_start_internal::hc453db0ee48af82e [inlined] std::panicking::try::hbeb9f8df83454d42 at panicking.rs:456:19 [opt]
+    frame #12: 0x0000000100014400 stack-program`std::rt::lang_start_internal::hc453db0ee48af82e [inlined] std::panic::catch_unwind::h0a9390b2202af6e9 at panic.rs:137:14 [opt]
+    frame #13: 0x0000000100014400 stack-program`std::rt::lang_start_internal::hc453db0ee48af82e at rt.rs:128:20 [opt]
+    frame #14: 0x0000000100001140 stack-program`std::rt::lang_start::h69bdd2191bba2dab(main=(stack-program`stack_program::main::he22b9cf577b52c34 at main.rs:7), argc=1, argv=0x000000016fdff168) at rt.rs:144:17
+    frame #15: 0x0000000100001434 stack-program`main + 32
+    frame #16: 0x00000001000750f4 dyld`start + 520
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;h1 id=&quot;box-string-and-vec-pointers-to-heap&quot;&gt;Box, String and Vec: Pointers to Heap&lt;/h1&gt;
+
+&lt;p&gt;There are times when we are working with data types large enough that we would really like to avoid copying them when we are passing them around. Let’s say you have just copied a file that is 1,000,000 bytes (1Mb) in size. In this case it is much more memory and compute efficient to have a pointer to this value (8 bytes) rather than copying all the 1,000,000 bytes.&lt;/p&gt;
+
+&lt;p&gt;This is where types such as &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Box&lt;/code&gt;, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;String&lt;/code&gt; and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Vec&lt;/code&gt; come into play: these types allow you to allocate something on heap, which is a chunk of memory separate from the stack that you can allocate on, and later reference those values using a pointer available on the stack.&lt;/p&gt;
+
+&lt;p&gt;Let’s start with &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Box&lt;/code&gt;, the most generic one, which allows you to allocate some data on the heap, consider this example:&lt;/p&gt;
+
+&lt;div class=&quot;language-rust highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;k&quot;&gt;fn&lt;/span&gt; &lt;span class=&quot;nf&quot;&gt;main&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;()&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;{&lt;/span&gt;
+    &lt;span class=&quot;k&quot;&gt;let&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;nn&quot;&gt;Box&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;::&lt;/span&gt;&lt;span class=&quot;nf&quot;&gt;new&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;5_u8&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;);&lt;/span&gt;
+    &lt;span class=&quot;k&quot;&gt;let&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;mi&quot;&gt;10_u8&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;;&lt;/span&gt;
+    &lt;span class=&quot;nd&quot;&gt;println!&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;s&quot;&gt;&quot;{}, {}&quot;&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;);&lt;/span&gt;
+&lt;span class=&quot;p&quot;&gt;}&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;p&gt;We again use &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;lldb&lt;/code&gt; to check out what is happening:&lt;/p&gt;
+
+&lt;div class=&quot;language-plaintext highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;$ cargo build &amp;amp;&amp;amp; rust-lldb target/debug/stack-and-heap-program
+
+(lldb) breakpoint set -f main.rs -l 4
+Breakpoint 1: where = stack-and-heap-program`stack_and_heap_program::main::ha895783273646dc7 + 100 at main.rs:4:5, address = 0x0000000100005264
+
+(lldb) run
+Process 67451 launched: &apos;/Users/mahdi/workshop/rust-memory-playground/target/debug/stack-and-heap-program&apos; (arm64)
+Process 67451 stopped
+* thread #1, queue = &apos;com.apple.main-thread&apos;, stop reason = breakpoint 1.1
+    frame #0: 0x0000000100005264 stack-and-heap-program`stack_and_heap_program::main::ha895783273646dc7 at main.rs:4:5
+   1    fn main() {
+   2        let a = Box::new(5_u8);
+   3        let b = 10_u8;
+-&amp;gt; 4        println!(&quot;{}, {}&quot;, a, b);
+   5    }
+   
+(lldb) frame var -L -f X
+0x000000016fdfed48: (unsigned char *) a = 0x0000600000008010 &quot;\U00000005&quot;
+0x000000016fdfed57: (unsigned char) b = 0x0A
+
+(lldb) memory read -count 1 -f X 0x0000600000008010
+0x600000008010: 0x05
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;p&gt;Note that here, instead of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;a&lt;/code&gt; having the value &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;5&lt;/code&gt;, has the value &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;0x0000600000008010&lt;/code&gt;, which is a pointer to a location in memory! &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;lldb&lt;/code&gt; is recognises that this is a pointer (note the &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;*&lt;/code&gt; sign beside the variable type) and shows us what the memory location contains, but we can also directly read that memory location, and of course we find &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;5&lt;/code&gt; there. The address of the heap-allocated &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;5&lt;/code&gt; is far from the stack-allocated &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;10&lt;/code&gt;, since stack and heap are separate parts of memory.&lt;/p&gt;
+
+&lt;p&gt;Using &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Box&lt;/code&gt; for an unsigned 8-bit value does not really make sense, the value itself is smaller than the pointer created by &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Box&lt;/code&gt;, however allocating on heap is useful when we have data that we need be able to pass around the program without copying it.&lt;/p&gt;
+
+&lt;p&gt;Turns out, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;String&lt;/code&gt; and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Vec&lt;/code&gt; cover two of the most common cases where we may want to allocate something on heap! Let’s look at what goes on behind allocating a variable of type &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;String&lt;/code&gt;:&lt;/p&gt;
+
+&lt;div class=&quot;language-rust highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;k&quot;&gt;fn&lt;/span&gt; &lt;span class=&quot;nf&quot;&gt;main&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;()&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;{&lt;/span&gt;
+    &lt;span class=&quot;k&quot;&gt;let&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;s&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;nn&quot;&gt;String&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;::&lt;/span&gt;&lt;span class=&quot;nf&quot;&gt;from&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;s&quot;&gt;&quot;hello&quot;&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;);&lt;/span&gt;
+    &lt;span class=&quot;nd&quot;&gt;println!&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;s&quot;&gt;&quot;{}&quot;&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;s&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;);&lt;/span&gt;
+&lt;span class=&quot;p&quot;&gt;}&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;p&gt;And here we go again:&lt;/p&gt;
+&lt;div class=&quot;language-plaintext highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;(lldb) breakpoint set -f main.rs -l 3
+Breakpoint 1: where = string-program`string_program::main::h64ca96ee87b0ceaf + 44 at main.rs:3:5, address = 0x000000010000476c
+
+(lldb) run
+Process 68317 launched: &apos;/Users/mahdi/workshop/rust-memory-playground/target/debug/string-program&apos; (arm64)
+Process 68317 stopped
+* thread #1, queue = &apos;com.apple.main-thread&apos;, stop reason = breakpoint 1.1
+    frame #0: 0x000000010000476c string-program`string_program::main::h64ca96ee87b0ceaf at main.rs:3:5
+   1    fn main() {
+   2        let s = String::from(&quot;hello&quot;);
+-&amp;gt; 3        println!(&quot;{}&quot;, s);
+   4    }
+   
+(lldb) frame var -L -T
+0x000000016fdfed78: (alloc::string::String) s = &quot;hello&quot; {
+0x000000016fdfed78:   (alloc::vec::Vec&amp;lt;unsigned char, alloc::alloc::Global&amp;gt;) vec = size=5 {
+0x0000600000004010:     (unsigned char) [0] = &apos;h&apos;
+0x0000600000004011:     (unsigned char) [1] = &apos;e&apos;
+0x0000600000004012:     (unsigned char) [2] = &apos;l&apos;
+0x0000600000004013:     (unsigned char) [3] = &apos;l&apos;
+0x0000600000004014:     (unsigned char) [4] = &apos;o&apos;
+  }
+}
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;p&gt;This is a formatted output from &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;lldb&lt;/code&gt;, and here you can see that the &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;String&lt;/code&gt; type is basically a &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Vec&amp;lt;unsigned char, alloc::Global&amp;gt;&lt;/code&gt; (note that &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;unsigned char&lt;/code&gt; is represented using &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;u8&lt;/code&gt; in Rust, so in Rust terminology the type is &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Vec&amp;lt;u8&amp;gt;&lt;/code&gt;), let’s now look at the same command but this time raw and unformatted (&lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;-R&lt;/code&gt;):&lt;/p&gt;
+
+&lt;div class=&quot;language-plaintext highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;(lldb) frame var -L -T -R
+0x000000016fdfed78: (alloc::string::String) s = {
+0x000000016fdfed78:   (alloc::vec::Vec&amp;lt;unsigned char, alloc::alloc::Global&amp;gt;) vec = {
+0x000000016fdfed78:     (alloc::raw_vec::RawVec&amp;lt;unsigned char, alloc::alloc::Global&amp;gt;) buf = {
+0x000000016fdfed78:       (core::ptr::unique::Unique&amp;lt;unsigned char&amp;gt;) ptr = {
+0x000000016fdfed78:         (unsigned char *) pointer = 0x0000600000004010
+0x000000016fdfed78:         (core::marker::PhantomData&amp;lt;unsigned char&amp;gt;) _marker = {}
+      }
+0x000000016fdfed80:       (unsigned long) cap = 6
+0x000000016fdfed78:       (alloc::alloc::Global) alloc = {}
+    }
+0x000000016fdfed88:     (unsigned long) len = 6
+  }
+}
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;p&gt;Ah! I see the &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;ptr&lt;/code&gt; field of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;RawVec&lt;/code&gt; with a value of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;0x0000600000004010&lt;/code&gt;, that is the memory address of the beginning of our string (namely the &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;h&lt;/code&gt; of our &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;hello&lt;/code&gt;)! There is also &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;cap&lt;/code&gt; and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;len&lt;/code&gt;, which respectively stand for capacity and length, with the value 6, indicating that our string is of capacity and length 6; the difference between the two being that &lt;a href=&quot;https://doc.rust-lang.org/nightly/std/vec/struct.Vec.html#capacity-and-reallocation&quot;&gt;you can have a &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Vec&lt;/code&gt; with a capacity of 10 while it has zero items&lt;/a&gt;, this would allow you to append 10 items to the &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Vec&lt;/code&gt; without having a new allocation for each append, making the process more efficient, and also a &lt;a href=&quot;https://doc.rust-lang.org/nightly/std/vec/struct.Vec.html#guarantees&quot;&gt;Vec is not automatically shrunk down&lt;/a&gt; in size when items are removed from it to avoid unnecessary deallocations, hence the length might be smaller than the capacity. So in a nutshell, our String is basically something like this (inspired by &lt;a href=&quot;https://doc.rust-lang.org/nightly/std/vec/struct.Vec.html#guarantees&quot;&gt;std::vec::Vec&lt;/a&gt;):&lt;/p&gt;
+
+&lt;div class=&quot;language-plaintext highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;Stack:
+--------------------------------
+| String                       |
+|     \-&amp;gt; Vec                  |
+|          \-&amp;gt; (ptr, cap, len) |
+|                |             |
+-----------------|--------------
+Heap:            v
+-----------------------------
+| (&apos;h&apos;, &apos;e&apos;, &apos;l&apos;, &apos;l&apos;, &apos;o&apos;) |
+-----------------------------
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;p&gt;Okay, so far so good. We have &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;String&lt;/code&gt;, which uses a &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Vec&lt;/code&gt; under the hood, which is represented by a pointer, capacity and length triplet.&lt;/p&gt;
+
+&lt;p&gt;If &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;String&lt;/code&gt; is already heap-allocated, why would anyone want &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Box&amp;lt;str&amp;gt;&lt;/code&gt;!? Let’s look at how &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Box&amp;lt;str&amp;gt;&lt;/code&gt; would be represented in memory:&lt;/p&gt;
+
+&lt;div class=&quot;language-rust highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;k&quot;&gt;fn&lt;/span&gt; &lt;span class=&quot;nf&quot;&gt;main&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;()&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;{&lt;/span&gt;
+    &lt;span class=&quot;k&quot;&gt;let&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;boxed_str&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;nb&quot;&gt;Box&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;&amp;lt;&lt;/span&gt;&lt;span class=&quot;nb&quot;&gt;str&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;&amp;gt;&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;s&quot;&gt;&quot;hello&quot;&lt;/span&gt;&lt;span class=&quot;nf&quot;&gt;.into&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;();&lt;/span&gt;
+
+    &lt;span class=&quot;nd&quot;&gt;println!&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;s&quot;&gt;&quot;boxed_str: {}&quot;&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;boxed_str&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;);&lt;/span&gt;
+&lt;span class=&quot;p&quot;&gt;}&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;p&gt;And &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;lldb&lt;/code&gt; tells us:&lt;/p&gt;
+
+&lt;div class=&quot;language-plaintext highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;0x000000016fdfed80: (alloc::boxed::Box&amp;lt;&amp;gt;) boxed_str = {
+0x000000016fdfed80:   data_ptr = 0x0000600000004010 &quot;hello&quot;
+0x000000016fdfed88:   length = 5
+}
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;p&gt;Okay, so a &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Box&amp;lt;str&amp;gt;&lt;/code&gt; is much simpler than a &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;String&lt;/code&gt;: there is no &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Vec&lt;/code&gt;, and no &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;capacity&lt;/code&gt;, and the underlying data is a primitive &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;str&lt;/code&gt; that does not allow efficient appending or removing. It is a smaller representation as well, due to the missing &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;capacity&lt;/code&gt; field, comparing their memory size on stack using &lt;a href=&quot;https://doc.rust-lang.org/std/mem/fn.size_of_val.html&quot;&gt;std::mem::size_of_val&lt;/a&gt;:&lt;/p&gt;
+
+&lt;div class=&quot;language-rust highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;k&quot;&gt;let&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;boxed_str&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;nb&quot;&gt;Box&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;&amp;lt;&lt;/span&gt;&lt;span class=&quot;nb&quot;&gt;str&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;&amp;gt;&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;s&quot;&gt;&quot;hello&quot;&lt;/span&gt;&lt;span class=&quot;nf&quot;&gt;.into&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;();&lt;/span&gt;
+&lt;span class=&quot;nd&quot;&gt;println!&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;s&quot;&gt;&quot;size of boxed_str on stack: {}&quot;&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;nn&quot;&gt;std&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;::&lt;/span&gt;&lt;span class=&quot;nn&quot;&gt;mem&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;::&lt;/span&gt;&lt;span class=&quot;nf&quot;&gt;size_of_val&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;&amp;amp;&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;boxed_str&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;));&lt;/span&gt;
+
+&lt;span class=&quot;k&quot;&gt;let&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;s&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;nn&quot;&gt;String&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;::&lt;/span&gt;&lt;span class=&quot;nf&quot;&gt;from&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;s&quot;&gt;&quot;hello&quot;&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;);&lt;/span&gt;
+&lt;span class=&quot;nd&quot;&gt;println!&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;s&quot;&gt;&quot;size of string on stack: {}&quot;&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;nn&quot;&gt;std&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;::&lt;/span&gt;&lt;span class=&quot;nn&quot;&gt;mem&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;::&lt;/span&gt;&lt;span class=&quot;nf&quot;&gt;size_of_val&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;&amp;amp;&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;s&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;));&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;p&gt;Results in:&lt;/p&gt;
+
+&lt;div class=&quot;language-plaintext highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;size of boxed_str on stack: 16
+size of string on stack: 24
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;p&gt;Note that their size on heap is the same, because they are both storing the bytes for &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;hello&lt;/code&gt; on the heap (the measurements below show all of the heap allocations of the program, and not only the string. What matters here is that these two programs have exact same heap size in total):&lt;/p&gt;
+
+&lt;div class=&quot;language-plaintext highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;$ cargo run --bin string-dhat
+    Finished dev [unoptimized + debuginfo] target(s) in 0.01s
+     Running `target/debug/string-dhat`
+hello
+dhat: Total:     1,029 bytes in 2 blocks
+dhat: At t-gmax: 1,029 bytes in 2 blocks
+dhat: At t-end:  1,024 bytes in 1 blocks
+dhat: The data has been saved to dhat-heap.json, and is viewable with dhat/dh_view.html
+
+$ cargo run --bin box-str-dhat
+    Finished dev [unoptimized + debuginfo] target(s) in 0.01s
+     Running `target/debug/box-str-dhat`
+boxed_str: hello
+dhat: Total:     1,029 bytes in 2 blocks
+dhat: At t-gmax: 1,029 bytes in 2 blocks
+dhat: At t-end:  1,024 bytes in 1 blocks
+dhat: The data has been saved to dhat-heap.json, and is viewable with dhat/dh_view.html
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;p&gt;There is also &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Box&amp;lt;[T]&amp;gt;&lt;/code&gt; which is the fixed size counterpart to &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Vec&amp;lt;T&amp;gt;&lt;/code&gt;.&lt;/p&gt;
+
+&lt;h1 id=&quot;should-i-use-boxstr-or-string&quot;&gt;Should I use &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Box&amp;lt;str&amp;gt;&lt;/code&gt; or &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;String&lt;/code&gt;?&lt;/h1&gt;
+
+&lt;p&gt;The only use case for &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Box&amp;lt;str&amp;gt;&lt;/code&gt; over &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;String&lt;/code&gt; that I can think of, is optimising for memory usage when the string is fixed and you do not intend to append or remove from it. I looked for examples of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Box&amp;lt;str&amp;gt;&lt;/code&gt; being used, and I found a few examples:&lt;/p&gt;
+
+&lt;ul&gt;
+  &lt;li&gt;Hyper uses it in a part to reduce memory usage, since the string they have is read-only: &lt;a href=&quot;https://github.com/hyperium/hyper/pull/2727&quot;&gt;hyper#2727&lt;/a&gt;&lt;/li&gt;
+  &lt;li&gt;Rust-analyzer uses it to store some strings in their snippets data structre: &lt;a href=&quot;https://github.com/rust-lang/rust-analyzer/blob/5c88d9344c5b32988bfbfc090f50aba5de1db062/crates/ide-completion/src/snippet.rs#L123&quot;&gt;rust-lang/rust-analyzer/crates/ide-completion/src/snippet.rs&lt;/a&gt;&lt;/li&gt;
+  &lt;li&gt;It is also used in some parts in the compiler itself, probably with the same aim of optimising memory usage: &lt;a href=&quot;https://github.com/rust-lang/rust/blob/7846610470392abc3ab1470853bbe7b408fe4254/src/libsyntax/symbol.rs#L82-L85&quot;&gt;rust-lang/rust/src/libsyntax/symbol.rs&lt;/a&gt;&lt;/li&gt;
+&lt;/ul&gt;
+</description>
+        <pubDate>Thu, 16 Jun 2022 01:00:00 +0100</pubDate>
+        <link>http://localhost:4000/rust-box-str-vs-string/</link>
+        <guid isPermaLink="true">http://localhost:4000/rust-box-str-vs-string/</guid>
+        
+        
+        <category>programming</category>
+        
+      </item>
+    
+      
+      <item>
+        <title>On Inherent Subjectivity of Some Things</title>
+        <description>&lt;p&gt;As a computer scientist and someone who loves &lt;a href=&quot;/mathematical-induction-proving-tiling-methods&quot;&gt;mathematics&lt;/a&gt; and &lt;a href=&quot;/typoclassopedia-exercise-solutions&quot;&gt;abstractions&lt;/a&gt;, I was obsessed with the idea of rationality, that is, an &lt;em&gt;objective&lt;/em&gt; and absolute rationality, however I ended up in a philosophy course that showed me the opposite.&lt;/p&gt;
+
+&lt;p&gt;I somehow stumbled upon Eliezer Yudkowsky’s &lt;a href=&quot;https://www.readthesequences.com/&quot;&gt;Rationality: From AI to Zombies&lt;/a&gt; about 4 years ago, and it took me two years to go through it all but I was absolutely fascinated by this book. I &lt;em&gt;knew&lt;/em&gt; how to be rational now, and I could &lt;em&gt;prove&lt;/em&gt; it using mathematics, what else could I ask for!&lt;/p&gt;
+
+&lt;p&gt;The book basically looks at the world as a probabilistic system, and everything that happens can be assigned probabilities, and using mathematical theorems such as Bayes Theorem, we can predict outcomes of certain actions and then decide between them. There is a lot of focus on &lt;a href=&quot;https://en.wikipedia.org/wiki/List_of_cognitive_biases&quot;&gt;cognitive biases&lt;/a&gt; as well. I was particularly very interested about these biases, and so I set out to learn more about them, and that’s how I found my current course: &lt;a href=&quot;https://cogsci.ucd.ie&quot;&gt;Cognitive Science at University College Dublin&lt;/a&gt;.&lt;/p&gt;
+
+&lt;p&gt;So I enter this course with this mindset: we can objectively analyse the world around us using probability and statistics (mathematics), but we are limited by our cognitive biases, so I want to learn about these cognitive biases: where do they come from, how can they be resisted to allow us to act more rationally and so on. These questions would mainly fall under the umbrella of psychology…&lt;/p&gt;
+
+&lt;p&gt;However… I found myself to be more and more interested in the philosophy side of this course than the psychology side, hell I even started to not like the psychology side anymore, but fall in love with the philosophy. This is where I found the opposite of what I had come for: an alternative definition of objectivity, and an inherent subjectivity of some things. This is mainly inspired by Thomas Nagel’s What Is It Like To Be A Bat &lt;a class=&quot;citation&quot; href=&quot;#nagel1974like&quot;&gt;(Nagel, 1974)&lt;/a&gt;.&lt;/p&gt;
+
+&lt;h2 id=&quot;what-is-objectivity-anyway&quot;&gt;What is Objectivity Anyway?&lt;/h2&gt;
+
+&lt;p&gt;This is probably the main question here. What is objectivity? I don’t think dictionary definitions are particularly authoritative when it comes to philosophy discussions, but I found this dictionary definition interesting to open the topic with:&lt;/p&gt;
+
+&lt;blockquote&gt;
+  &lt;p&gt;the quality or character of being objective : lack of favoritism toward one side or another : freedom from bias. &lt;a class=&quot;citation&quot; href=&quot;#objectivity-merriam-webster&quot;&gt;(Merriam-Webster, 2021)&lt;/a&gt;&lt;/p&gt;
+&lt;/blockquote&gt;
+
+&lt;p&gt;This definition itself has ambiguous phrases such as “freedom from bias”, what does that mean? When can we say that we are free from bias? Let’s look at how bias is defined in the same dictionary:&lt;/p&gt;
+
+&lt;blockquote&gt;
+  &lt;p&gt;an inclination of temperament or outlook &lt;a class=&quot;citation&quot; href=&quot;#bias-merriam-webster&quot;&gt;(Merriam-Webster, 2021)&lt;/a&gt;&lt;/p&gt;
+&lt;/blockquote&gt;
+
+&lt;p&gt;But… is it really possible to have no inclination at all in our temperament and outlook? Let’s look at the definition of subjective, that will help us here:&lt;/p&gt;
+
+&lt;blockquote&gt;
+  &lt;p&gt;relating to the way a person experiences things in his or her own mind &lt;a class=&quot;citation&quot; href=&quot;#subjective-merriam-webster&quot;&gt;(Merriam-Webster, 2021)&lt;/a&gt;&lt;/p&gt;
+&lt;/blockquote&gt;
+
+&lt;p&gt;Is it possible for us to have a view of something without it being part of our experience? It seems not. All that we do, all our views and expressions and our interactions are part of our experience as a person, and it relates to us on an intimate level, which means that everything that we do as individuals is subjective. In that sense, it seems impossible for any individual to be objective, since they will always have some form of inclination about everything.&lt;/p&gt;
+
+&lt;p&gt;What does this leave us with then when we ask what is objectivity? A better definition of objectivity in my opinion is one given by Thomas Nagel:&lt;/p&gt;
+
+&lt;blockquote&gt;
+  &lt;p&gt;It may be more accurate to think of objectivity as a direction in which the understanding can travel. […] The process of reduction is a move in the direction of greater objectivity, toward a more accurate view of the real nature of things. This is accomplished by reducing our dependence on individual or species-specific points of view toward the object of investigation. We describe it not in terms of the impressions it makes on our senses, but in terms of its more general effects and of properties detectable by means other than the human senses. &lt;a class=&quot;citation&quot; href=&quot;#nagel1974like&quot;&gt;(Nagel, 1974)&lt;/a&gt;&lt;/p&gt;
+&lt;/blockquote&gt;
+
+&lt;p&gt;In this sense, there is no black-and-white distinction between subjectivity and objectivity, but rather it is a spectrum, a line on which we can walk from subjectivity towards objectivity.&lt;/p&gt;
+
+&lt;p&gt;&lt;img src=&quot;/img/inherent-subjectivity/subjective-objective.png&quot; alt=&quot;Subjective-Objective spectrum: On Subjective side we have Individual perception, in the middle Agreement with others, and on the Objective side Agreement with other apparatus&quot; /&gt;&lt;/p&gt;
+
+&lt;p&gt;We start with our individual perceptions as the most objective view and description, we then move towards descriptions that allow us to agree with other (human) beings, and finally we move towards descriptions that can be verified and agreed upon by other apparatus, although it is important to understand that even the apparatus that we may use to describe things are not necessarily free from bias, since they are created by biased individuals and groups. By now you may notice that if a measuring device is made to be agreeable between a large group of people, it is already more objective than a device made by a single individual! However, absolute objectivity, which we may call “a view from nowhere” may not be attainable by us, because we will always be viewing things from our own perspectives, even if it is a large, collective perspective that we agree on, it is not a view from nowhere.&lt;/p&gt;
+
+&lt;p&gt;&lt;img src=&quot;/img/inherent-subjectivity/subjective-objective-example.png&quot; alt=&quot;Subjective-Objective spectrum: A single person says a ball is 10cm radius, 1/4 objectivity. A group of people say it&apos;s 10cm radius, 1/2 objectivity. A group of people with a ruler say it&apos;s 10cm radius, 3/4 objectivity&quot; /&gt;&lt;/p&gt;
+
+&lt;h2 id=&quot;inherently-subjective-things&quot;&gt;Inherently Subjective Things&lt;/h2&gt;
+
+&lt;p&gt;With our definition of objectivity in place, now let’s see: is there something that we cannot move towards objectivity about? Yes. That is our personal experiences.&lt;/p&gt;
+
+&lt;p&gt;See, if there is an attempt to give a more objective description of &lt;em&gt;my&lt;/em&gt; personal experience, there will need to be either an agreement among a group of beings about this description of my personal experience, or there should be an apparatus that we can agree on that measures my personal experience. However, my personal experience is personal exactly because it is completely dependent and originated from my perspective alone, and no one else’s; and as soon as you try to move towards objectivity by trying to describe this experience in a way that moves away from my person-specific and species-specific standpoint, towards a more agreeable and general description that even non-human beings or apparatus can agree with, you lose the initial personal experience in the process, so you end up with a non-personal description of the experience which misses the point of the actual subjective experience I have.&lt;/p&gt;
+
+&lt;p&gt;So, you can come up with &lt;em&gt;some&lt;/em&gt; description of my experience, but you can’t actually describe the subjective experience of being me as it really is. The walk towards objectivity requires you to drop the subjectivity of my experience, and hence, some inherently subjective things such as our personal experiences can’t be objectified.&lt;/p&gt;
+
+&lt;p&gt;This is how Nagel puts it (I think this may be a bit hard to read without reading the whole paper):&lt;/p&gt;
+
+&lt;blockquote&gt;
+  &lt;p&gt;Experience itself, however, does not seem to fit the pattern. The idea of moving from appearance to reality seems to make no sense here. What is the analogue in this case to pursuing a more objective understanding of the same phenomena by abandoning the initial subjective viewpoint toward them in favor of another that is more objective but concerns the same thing? Certainly it appears unlikely that we will get closer to the real nature of human experience by leaving behind the particularity of our human point of view and striving for a description in terms accessible to beings that could not imagine what it was like to be us. If the subjective character of experience is fully comprehensible only from one point of view, then any shift to greater objectivity that is, less attachment to a specific viewpoint does not take us nearer to the real nature of the phenomenon: it takes us farther away from it. &lt;a class=&quot;citation&quot; href=&quot;#nagel1974like&quot;&gt;(Nagel, 1974)&lt;/a&gt;&lt;/p&gt;
+&lt;/blockquote&gt;
+
+&lt;h2 id=&quot;so-what-or-why-is-this-important&quot;&gt;So What? (Or: Why is This Important?)&lt;/h2&gt;
+
+&lt;p&gt;This realisation means that objectifying people’s subjective experiences is not possible, we will never be able to decipher someone’s subjective experience of something. This does not mean we should not try to &lt;em&gt;understand&lt;/em&gt; people, rather, it means we should always consider that our understanding of someone’s subjective experience will never be objective, it will always be merely our perspective of it. When it comes to people’s personal experiences, we can’t be sure that we are right, the way we are confident we are right after measuring a distance using our agreed-upon metric ruler; when it comes to subjective experiences it’s always only a crude approximation. “In the end one experiences only oneself.” &lt;a class=&quot;citation&quot; href=&quot;#nietzsche2008thus&quot;&gt;(Nietzsche, 2008)&lt;/a&gt;&lt;/p&gt;
+
+&lt;p&gt;This video was sent to me by a friend today, and it is great timing, because it is very relevant:&lt;/p&gt;
+
+&lt;iframe class=&quot;centered&quot; width=&quot;560&quot; height=&quot;315&quot; src=&quot;https://www.youtube-nocookie.com/embed/oRG2jlQWCsY&quot; title=&quot;Good Will Hunting | &apos;Your Move Chief&apos; (HD) - Matt Damon, Robin Williams | MIRAMAX&quot; frameborder=&quot;0&quot; allow=&quot;picture-in-picture&quot; allowfullscreen=&quot;&quot;&gt;&lt;/iframe&gt;
+
+&lt;!--https://postcognitivism.wordpress.com/2021/04/06/the-great-escape-can-we-transcend-our-own-conceptual-frameworks/
+https://gatelessgateblog.wordpress.com/
+https://www.sciencedirect.com/science/article/pii/S0388000121000802
+Distinctions and Common Ground in Collective Epistemology--&gt;
+
+&lt;h2 id=&quot;references&quot;&gt;References&lt;/h2&gt;
+
+&lt;ol class=&quot;bibliography&quot;&gt;&lt;li&gt;&lt;span id=&quot;nagel1974like&quot;&gt;Nagel, T. (1974). What is it like to be a bat. &lt;i&gt;Readings in Philosophy of Psychology&lt;/i&gt;, &lt;i&gt;1&lt;/i&gt;, 159–168.&lt;/span&gt;&lt;/li&gt;
+&lt;li&gt;&lt;span id=&quot;objectivity-merriam-webster&quot;&gt;Merriam-Webster. (2021). &lt;i&gt;Objectivity. In Merriam-Webster.com dictionary.&lt;/i&gt; https://www.merriam-webster.com/dictionary/objectivity&lt;/span&gt;&lt;/li&gt;
+&lt;li&gt;&lt;span id=&quot;bias-merriam-webster&quot;&gt;Merriam-Webster. (2021). &lt;i&gt;Bias. In Merriam-Webster.com dictionary.&lt;/i&gt; https://www.merriam-webster.com/dictionary/bias&lt;/span&gt;&lt;/li&gt;
+&lt;li&gt;&lt;span id=&quot;subjective-merriam-webster&quot;&gt;Merriam-Webster. (2021). &lt;i&gt;Subjective. In Merriam-Webster.com dictionary.&lt;/i&gt; https://www.merriam-webster.com/dictionary/subjective&lt;/span&gt;&lt;/li&gt;
+&lt;li&gt;&lt;span id=&quot;nietzsche2008thus&quot;&gt;Nietzsche, F. (2008). &lt;i&gt;Thus spoke Zarathustra: A book for everyone and nobody&lt;/i&gt;. Oxford University Press.&lt;/span&gt;&lt;/li&gt;&lt;/ol&gt;
+</description>
+        <pubDate>Sat, 30 Oct 2021 13:57:46 +0100</pubDate>
+        <link>http://localhost:4000/alternative-objectivity-and-inherent-subjectivity/</link>
+        <guid isPermaLink="true">http://localhost:4000/alternative-objectivity-and-inherent-subjectivity/</guid>
+        
+        
+        <category>philosophy</category>
+        
+      </item>
+    
+      
+      <item>
+        <title>Iran Sanctions: A Story of Discrimination and Isolation</title>
+        <description>&lt;p&gt;Let me take you through a story on what it feels like to be isolated from the world, not by choice, but rather, by force. This is a story of discrimination, of monopoly, of people shrugging to these issues and of utterances that affect lives of millions.&lt;/p&gt;
+
+&lt;p&gt;Living in Iran, or any sanctioned country for that matter, you learn to read “anyone, anywhere” with an appendix of “except you”. You soon learn “worldwide shipping” excludes you, that’s when you start wondering, are you not living in “the world”? Where is this “world” they talk about?&lt;/p&gt;
+
+&lt;p&gt;Here is an example of a beautiful, hopeful message from Khan Academy:&lt;/p&gt;
+
+&lt;p&gt;&lt;img src=&quot;/img/discrimination/khan-academy.png&quot; alt=&quot;Khan Academy&apos;s Landing Page: We’re a nonprofit with the mission to provide a free, world-class education for anyone, anywhere.&quot; /&gt;&lt;/p&gt;
+
+&lt;p&gt;&lt;span class=&quot;image-caption&quot;&gt;“We’re a nonprofit with the mission to provide a free, world-class education for anyone, anywhere.”&lt;/span&gt;&lt;/p&gt;
+
+&lt;p&gt;No one probably realizes that this is not true, but yes, Khan Academy is not available to Iranians, Cubans, Syrians, people of Crimea, and some others. That’s because &lt;a href=&quot;https://cloud.google.com/customers/khan-academy/&quot;&gt;they run on Google Cloud&lt;/a&gt;, an infrastructure provider that completely blocks all sanctioned countries from accessing any application hosted on it. Who else hosts their service there? Take a look at &lt;a href=&quot;https://cloud.google.com/customers/&quot;&gt;342 notable customers&lt;/a&gt; of Google Cloud, but remember, there are thousands more customers of Google Cloud and similar American infrastructure providers.&lt;/p&gt;
+
+&lt;p&gt;But the story doesn’t end here, of course. Let’s go through the effects of sanctions on everyday lives of people, who have nothing to do with the politics of the country they are living in, and who are being discriminated only because they were born in geographical coordinates that lie in a certain boundary defined by people they don’t even know.&lt;/p&gt;
+
+&lt;h1 id=&quot;the-internet&quot;&gt;The Internet&lt;/h1&gt;
+
+&lt;p&gt;The internet, the tool of the global society for communicating across the planet, &lt;em&gt;the&lt;/em&gt; tool for sharing knowledge with the human population across the world.&lt;/p&gt;
+
+&lt;p&gt;As if the Iranian government’s blockage and censorship of the internet wasn’t enough, we now have to deal with external sanctions blocking our access as well. Here’s a gallery of blocked access messages we see on a daily basis:&lt;/p&gt;
+
+&lt;p&gt;&lt;img src=&quot;/img/discrimination/403-forbidden-iran-sanctions.jpg&quot; alt=&quot;Various websites and their respective webpages seen only by sanctioned countries&quot; /&gt;
+&lt;span class=&quot;image-caption&quot;&gt;Various websites and their respective webpages seen only by sanctioned countries&lt;/span&gt;&lt;/p&gt;
+
+&lt;p&gt;These websites include GitHub, Slack, Kaggle, Docker, GitLab, Amazon AWS, Twitter, Bluemix, Khan Academy and more. Here is a longer, developer-oriented (but definitely not exhaustive) list of hosts blocking our access: &lt;a href=&quot;https://raw.githubusercontent.com/freedomofdevelopers/fod/master/domains&quot;&gt;freedomofdevelopers/domains&lt;/a&gt;.&lt;/p&gt;
+
+&lt;p&gt;The websites that blocked our access mostly did it without prior notice, they just disabled our accounts, took our data from us, and did not let us even backup or export our data afterwards, in other words, lost messages, lost files and credentials.&lt;/p&gt;
+
+&lt;p&gt;This, in part, is caused by the global monopoly of American companies such as Google, Amazon, GitHub and alike in their respective fields. This means if The United States decides to pressure a specific target, the target population is likely to be left without much of an alternative or option, since a great proportion of the land is covered by American companies.&lt;/p&gt;
+
+&lt;p&gt;Iranian users rely heavily on use of VPN services and proxy servers to bypass censorship, but now with most Cloud Providers blocking access of Iranians, we are left with limited, usually more expensive options for setting up these servers.&lt;/p&gt;
+
+&lt;p&gt;This is a clear discrimination based on nationality and a breach of &lt;a href=&quot;https://en.wikipedia.org/wiki/Internet_freedom&quot;&gt;Internet Freedom&lt;/a&gt;. These websites do not block us because we acted in a wrong way, or even, at cases, because we live in Iran, but because we were &lt;em&gt;born&lt;/em&gt; in Iran. Now, you may say this is because of the law and they have no choice. That’s true in some cases, though most of the time the implementation of these laws seem to go further than what the laws actually require. The companies seem to go the &lt;em&gt;easy&lt;/em&gt; way by blocking access as much as they can to avoid holes in their system.&lt;/p&gt;
+
+&lt;h1 id=&quot;drugs-medicine-and-medical-devices&quot;&gt;Drugs, Medicine, and Medical Devices&lt;/h1&gt;
+
+&lt;p&gt;There are various sources and articles on how the U.S. sanctions have affected Iranian patients by limiting exports of drugs, medical devices or by indirectly disrupting the pharmaceutical industry by cutting exports of raw material used by these companies to produce medical drugs. Almost every person living in Iran can consciously feel the shortage of drugs and their growing price, but I will refer to an article on NCBI as a proof.&lt;/p&gt;
+
+&lt;p&gt;Quoting from &lt;a href=&quot;https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4897941/&quot;&gt;NCBI: Addressing the impact of economic sanctions on Iranian drug shortages in the joint comprehensive plan of action: promoting access to medicines and health diplomacy&lt;/a&gt;:&lt;/p&gt;
+
+&lt;blockquote&gt;
+Although the revised and current Iranian sanctions regime does not specifically prohibit the export of humanitarian goods and pharmaceuticals, many of the administrative and regulatory processes have made it difficult to export life-saving medicines to Iran. This includes the need to navigate a complex export control regulatory process, the inability of Iranian banks to do business with the international banking system and U.S. corporations, currency shortages, and the inability to secure terms of shipping, insurance and other services needed to facilitate medicines trade [4]. As a result, millions of Iranians that suffer from life-threatening diseases have experienced “exorbitant prices”, stock outs of medicines, and are often forced to purchase drugs from the black market.
+
+[...]
+
+Severe medication shortages in Iran are diverse and span several therapeutic classes and disease states. This includes drug shortages for other critical areas of healthcare delivery, including organ transplant drugs, and even vaccine shortages.
+&lt;/blockquote&gt;
+
+&lt;p&gt;And on the topic of weakening of the pharmaceutical companies:&lt;/p&gt;
+
+&lt;blockquote&gt;
+Inaccessibility of vital medications and their raw ingredients combined with Iran’s weakening domestic pharmaceutical industry has also resulted in an influx of counterfeit, fraudulent, and substandard medicines into Iran’s health care system. An unregulated black market has developed as a byproduct of drug shortages, introducing medications whose origins and authenticity are often unknown, and has led to expired medications’ distribution and sale, even at potentially very high prices [8]. Hence, the global counterfeit medicines trade, recognized as a serious public health concern, is one that is currently being enabled as a consequence of drug shortages and ongoing Iranian economic sanctions 
+&lt;/blockquote&gt;
+
+&lt;p&gt;Foreign Policy also writes &lt;a href=&quot;https://foreignpolicy.com/2019/08/14/u-s-sanctions-are-killing-cancer-patients-in-iran/&quot;&gt;U.S. Sanctions Are Killing Cancer Patients in Iran&lt;/a&gt;:&lt;/p&gt;
+
+&lt;blockquote&gt;
+  &lt;p&gt;Washington claims that maximum pressure won’t stop the supply of medicine and other humanitarian necessities, but banking sanctions are driving up import prices, blocking supply chains, and creating deadly drug shortages.&lt;/p&gt;
+&lt;/blockquote&gt;
+
+&lt;blockquote&gt;
+  &lt;p&gt;Although U.S. sanctions are engineered in a way that may appear not to target humanitarian access to food and medicine, in practice U.S. sanctions function as a tool of economic war.&lt;/p&gt;
+&lt;/blockquote&gt;
+
+&lt;p&gt;&lt;a href=&quot;https://www.who.int/mediacentre/news/statements/fundamental-human-right/en/&quot;&gt;Health is a fundamental human right&lt;/a&gt;, but the embargo clearly goes against giving people access to life-saving medicine. It brings tears to my eyes to think about people losing a loved one over inability to access a drug or medical device that’s no longer available in Iran.&lt;/p&gt;
+
+&lt;h1 id=&quot;currency-fluctuations-an-unpredictable-life&quot;&gt;Currency Fluctuations: An Unpredictable Life&lt;/h1&gt;
+
+&lt;p&gt;I’m pretty sure most of the people reading this blog post, unless they are Iranians, will not find this section familiar. It’s [fortunately] not a common experience across the planet, but let me tell you about living a life of zero predictability.&lt;/p&gt;
+
+&lt;p&gt;Imagine this: You sell your car today, and you start a hunt for a new car to buy as a replacement. For the sake of the example, you are looking for a second-hand car.
+I will use a dummy currency unit here to simplify the example. You sold  your car for 1000 units, and during the week you are looking for a new car, you start to see the car you just sold and every other car on the market, is gaining price exponentially. After a week, the same car that you sold is priced at 1800 units of currency and it’s growing. It’s like putting a car on neutral in a downward slope and seeing it go up the hill! Now you are left with 1000 units of currency, and you are only able to buy the same car if you put in your extra 800 savings, otherwise you are going to ride a car with significantly less quality or no car at all. More on &lt;a href=&quot;https://www.reuters.com/article/us-iran-economy-imf-idUSKCN1S509Q&quot;&gt;Iran’s inflation&lt;/a&gt; as a result of tighter sanctions.&lt;/p&gt;
+
+&lt;p&gt;I am pretty sure no matter how much I try to help you visualize this, you can not comprehend what it means to live in such a situation. I always use the metaphor of being a circus actor trying to balance on a moving cylinder to describe what it means to survive the fluctuations of our currency, which in turn affects all your expenses, but not your income.&lt;/p&gt;
+
+&lt;p&gt;&lt;img src=&quot;/img/discrimination/act04-1.jpg&quot; alt=&quot;Circus actor balancing on cylinders&quot; /&gt;&lt;/p&gt;
+
+&lt;p&gt;This is also an effect of the sanctions on the economy that we people feel with our every inch and are pressured by. This in turn causes a &lt;a href=&quot;#a-weak-economys-rippling-effect&quot;&gt;rippling effect&lt;/a&gt; on every other part of the society. Quoting &lt;a href=&quot;https://www.thenational.ae/business/economy/explainer-the-collapse-of-the-iranian-rial-1.754707&quot;&gt;Explainer: the collapse of the Iranian rial&lt;/a&gt;&lt;/p&gt;
+
+&lt;blockquote&gt;
+Has the US decision made things worse?
+
+Yes. Mr Trump’s decision to exit the US-Iran nuclear agreement signed in 2015 has dented Iran’s economic outlook and set in motion a cascade of damaging effects. It has deterred global companies from doing business with Iran, leading to a liquidity crunch and a lack of foreign exchange in the country. US measures also put pressure on a banking system already strained by the previous sanctions regime before the adoption of the JCPOA in January 2016.
+
+A re-imposition of sanctions is expected to cause a drop in Iranian oil exports, with severe repercussions. Iran is home to the world’s largest reserves of gas and is the Middle East’s third-largest oil producer. In May, BMI downgraded its GDP growth forecast for Iran to 3.1 per cent in 2018 and 0.8 per cent in 2019, from 4.3 per cent and 4.5 per cent previously.
+
+“Iran is likely to experience depreciatory pressures on the rial and rising inflation as a result of lower foreign currency inflows that will constrain domestic investment and consumption,” BMI said.
+&lt;/blockquote&gt;
+
+&lt;p&gt;Unpredictability is only part of the story, in general a high inflation rate means a degradation of life quality over time, and a lower quality of life includes a lack of access to even the most basic needs. It means having to put your children in less qualified schools, it means avoiding doctor appointments by any means necessary, it means cutting corners in every section of your life, it means a less balanced environment to live in, an environment where people get angry more easily since they are under a constant pressure as a cause of their degrading lives. No matter how hard you try, your life quality only goes downhill, never up.&lt;/p&gt;
+
+&lt;h1 id=&quot;a-weak-economys-rippling-effect&quot;&gt;A Weak Economy’s Rippling Effect&lt;/h1&gt;
+
+&lt;p&gt;You have probably heard of &lt;a href=&quot;https://en.wikipedia.org/wiki/Maslow&apos;s_hierarchy_of_needs&quot;&gt;Maslow’s Hierarchy of Needs&lt;/a&gt;. This is what it looks like:&lt;/p&gt;
+
+&lt;p&gt;&lt;img src=&quot;/img/discrimination/maslow.jpg&quot; alt=&quot;Maslow&apos;s Hierarchy of Needs. A pyramid, from top to bottom: Self-Actualization, Esteem, Love/Belonging, Safety, Physiological&quot; /&gt;&lt;/p&gt;
+
+&lt;p&gt;At the bottom, there are physiological needs, like health, food, water, sleep, shelter and sex. Only once these needs are fulfilled properly, you get motivated to even think about the next level. That means, if your physiological needs are not properly safisfied, you will not even think about safety, love and belonging, self-esteem or self-actualization.&lt;/p&gt;
+
+&lt;p&gt;Now, what all these physiological needs have in common is that they are fulfilled when there is a stable economic backbone in the country you live in. Once the economic backbone is broken, you begin losing access to these physiological needs. Slowly, but surely, you lose your motivation for self-actualization, for self-esteem, for love and belonging and for safety and you hunt for your physiological needs. Once this happens for a whole population in a country, you are left with people with only one goal in their lives: to survive &lt;em&gt;by any means&lt;/em&gt;.&lt;/p&gt;
+
+&lt;p&gt;With no motivation for building strong friendships and relationships, no motivation for security and safety, for feeling of accomplishment and for creative acts, the population transitions towards becoming one unsafe, cold, threatening, untrustable environment with no sense of joy or creativity.&lt;/p&gt;
+
+&lt;p&gt;I’m driving from my friend’s house back to mine, it’s roughly 10pm and streets are a little crowded. I’m going through streets of Azadi District, when I see two children who are probably between 15 and 17, punching each other in the face and kicking each other’s stomach over a large trash container at the side of the street. They are fighting, as if for their lives, with a ferocity you can hardly imagine to find in a child of their age. These children do not look anything like your children, their hands are black from their fingertips to their elbows from collecting trash all day long; their clothes are not new, they do not change their clothes or take showers daily, and their backs are arched for hauling a large bag of trash for a whole day over their shoulder and back. They are fighting to win a trash container. This is what happens when you put pressure on the economy of a country. This is what the media is not telling you about the effects of sanctions. This is what needs to stop about these sanctions. This is what needs action from every person knowledgable to do something to stop it. Abuse, rape and misuse of children and adults alike is a significant, visible effect of sanctions that’s often overlooked.&lt;/p&gt;
+
+&lt;p&gt;It’s sad that I can not find any content regarding this matter in the media by searching. I think more content on these topics is necessary to help people be aware of the unethical and inhumane effects of sanctions on lives of innocent people.&lt;/p&gt;
+
+&lt;p&gt;&lt;img src=&quot;/img/discrimination/trash-collecting.jpg&quot; alt=&quot;A teenager collecting trash in Iran&quot; /&gt;
+&lt;span class=&quot;image-caption&quot;&gt;A teenage collecting trash in the streets of Tehran.&lt;/span&gt;&lt;/p&gt;
+
+&lt;p&gt;The rippling effects of a weakening economy are far worse and far-reaching than what the sanctions are supposed to do. I think it’s too optimistic to think sanctions to weaken an economy will prevent a country from spending money on something they want to spend on. What ends up happening, or at least has happened in case of Iran, is that the money is drained from places where it affects peoples lives, but I doubt anything has changed at the actual target.&lt;/p&gt;
+
+&lt;h1 id=&quot;of-rolling-eyes-and-shrugs&quot;&gt;Of Rolling Eyes and Shrugs&lt;/h1&gt;
+
+&lt;p&gt;Often when similar stories of this kind are shared, I am ready to see comments of people shrugging to the issue with responses like “they have to comply because it’s the law” or “that’s how you respond to a country that wants to build nuclear weapons” or similar. They just roll their eyes and shrug it off like this is how it’s supposed to be.&lt;/p&gt;
+
+&lt;p&gt;Sometimes, that’s true that it’s the law and the companies have to comply (though most of the time the application of the law goes way beyond necessity). What these responses get wrong is that there is no involvement by us, the people, in the decisions and policies of our country. Solely because I live my daily life in a geographical location that resides in the boundaries of a place on Earth known as “Iran” doesn’t mean I agree with the politics of this country, or that I should be isolated from the rest of the world because some people in my country make certain decisions.&lt;/p&gt;
+
+&lt;p&gt;What these replies get wrong is that in democratic countries, laws can change based on what people demand. Instead of shrugging these humanitarian issues off, please hear us out, and help echo our voice. You may not realize, but we, the people of Iran, do not have a say in what what politics our government follows or how it interacts with other countries, but you do have a say in yours. The only thing we can do is to spread the word.&lt;/p&gt;
+
+&lt;p&gt;What we feel when we see these responses is: “They are terrorists so let them be”, but we are not. We are normal people like you, with less privileges, solely because of our living region.&lt;/p&gt;
+
+&lt;p&gt;It seems like the Iranian people are now the common enemy of all sides of a global conflict. The ever-increasing pressure we feel is not from a single source, but rather, from all sides. We have internet censorship from the inside and restricted access from the outside. We have economic pressure from the inside, with a direct influence from the outside, and the same applies to every part of this conflict.&lt;/p&gt;
+
+&lt;h1 id=&quot;final-message&quot;&gt;Final Message&lt;/h1&gt;
+
+&lt;p&gt;&lt;a href=&quot;https://en.wikipedia.org/wiki/Racism&quot;&gt;Racism&lt;/a&gt; is defined as  “prejudice, &lt;a href=&quot;https://en.wikipedia.org/wiki/Discrimination&quot;&gt;discrimination&lt;/a&gt;, or antagonism directed towards other people because they are of a different race or ethnicity”. Sanctions, likewise, are a clear case of prejudice, discrimination and antagonism directed towards people because they are born in a certain country, or reside in a certain part of the planet.&lt;/p&gt;
+
+&lt;p&gt;If a person is jailed, or killed because of the color of their skin, you feel furious and protest against the act to show that racism has no place in your country. Sanctions are a case of jailing a whole country, killing the people inside by cutting their lifelines and causing lifetime distress for innocent people who didn’t do anything wrong. It’s discrimination on the scale of a whole population of millions. Although the people who are being effected by these sanctions are far away from your home, their misery is caused by your country’s policies and actions, and you have the right to stand up against these discriminations.&lt;/p&gt;
+
+&lt;p&gt;Ron Paul, former congressman &lt;a href=&quot;https://twitter.com/RonPaul/status/1162067004733476864&quot;&gt;touches on topic in an interview&lt;/a&gt;:&lt;/p&gt;
+
+&lt;blockquote&gt;
+  &lt;p&gt;I think sanctions are really really bad, because it brings people in to think that “well I’m not quite as violent as other people who would use a drone”, well, hopefully it is a little bit less violent, but it’s every bit as dangerous, it’s still attacking personal liberties and it’s undermining the principle of trying to get along with people with free trade.&lt;/p&gt;
+&lt;/blockquote&gt;
+
+&lt;p&gt;&lt;a href=&quot;https://en.wikipedia.org/wiki/Universal_Declaration_of_Human_Rights&quot;&gt;The Universal Declaration of Human Rights&lt;/a&gt;, Article 2, states:&lt;/p&gt;
+
+&lt;blockquote&gt;
+  &lt;p&gt;Everyone is entitled to all the rights and freedoms set forth in this Declaration, without distinction of any kind, such as race, colour, sex, language, religion, political or other opinion, national or social origin, property, birth or other status.
+Furthermore, no distinction shall be made on the basis of the political, jurisdictional or international status of the country or territory to which a person belongs, whether it be independent, trust, non-self-governing or under any other limitation of sovereignty.&lt;/p&gt;
+&lt;/blockquote&gt;
+
+&lt;p&gt;That doesn’t sound like what’s happening now by enforcement of sanctions. Silence on this massive case of discrimination against people around the world must be broken, it must be recognized that discrimination, in any form, is not to be tolerated by humans.&lt;/p&gt;
+
+&lt;hr /&gt;
+
+&lt;h3 id=&quot;links&quot;&gt;Links&lt;/h3&gt;
+
+&lt;ul&gt;
+  &lt;li&gt;&lt;a href=&quot;https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4897941/&quot;&gt;NCBI: Addressing the impact of economic sanctions on Iranian drug shortages in the joint comprehensive plan of action: promoting access to medicines and health diplomacy&lt;/a&gt;&lt;/li&gt;
+  &lt;li&gt;&lt;a href=&quot;https://medium.com/@hamed/yellow-badges-are-back-this-time-not-by-nazi-germany-not-for-jews-but-by-u-s-tech-companies-48e92d690176&quot;&gt;Hamed Saeedi: Yellow badges are back. This time not by Nazi Germany &amp;amp; not for Jews, but by U.S. tech companies&lt;/a&gt;&lt;/li&gt;
+  &lt;li&gt;&lt;a href=&quot;https://medium.com/@hamed/yellow-badges-are-back-this-time-not-by-nazi-germany-not-for-jews-but-by-u-s-tech-companies-48e92d690176&quot;&gt;Foreign Policy: U.S. Sanctions Are Killing Cancer Patients in Iran&lt;/a&gt;&lt;/li&gt;
+  &lt;li&gt;&lt;a href=&quot;https://twitter.com/RonPaul/status/1162067004733476864&quot;&gt;Ron Paul: “Sanctions Are A Deadly Act Of War”&lt;/a&gt;&lt;/li&gt;
+&lt;/ul&gt;
+</description>
+        <pubDate>Sat, 27 Jul 2019 18:13:46 +0100</pubDate>
+        <link>http://localhost:4000/sanctions-discrimination-isolation-iran</link>
+        <guid isPermaLink="true">http://localhost:4000/sanctions-discrimination-isolation-iran</guid>
+        
+        
+        <category>life,</category>
+        
+        <category>iran</category>
+        
+      </item>
+    
+      
+      <item>
+        <title>Going Self-Hosted: Moving away from Google and others</title>
+        <description>&lt;p&gt;Since 3 years ago, I have always been eager to move away from Google and other privacy-invading companies. I have had my successes and failures in doing so, here I’m going to put out my stack of tools for moving away from Google and going self-hosted.&lt;/p&gt;
+
+&lt;!--more--&gt;
+
+&lt;p&gt;I first tried to move away from Google 3 years ago, and at the time, I did not have enough resources to self-host much. I started by creating my own email server, but I couldn’t afford a cloud storage. I also did not know about the alternatives available to Google Calendar, Google Keep, and other tools I was using at the time, so it was pretty hard keeping up that way.&lt;/p&gt;
+
+&lt;p&gt;After a year and a half, after my phone was stolen, I decided I will stick with Google apps with the coming of my new phone. I kept using Google services for less than a year, but I was frustrated. I had given up my privacy and control over my data for convenience, but that’s not what I wanted. So I decided I’m going to switch away again, and I will self-host the tools necessary.&lt;/p&gt;
+
+&lt;p&gt;A lot has changed since the first time I switched away, I will sketch below the tools that I have replaced and how.&lt;/p&gt;
+
+&lt;h1 id=&quot;microg&quot;&gt;microG&lt;/h1&gt;
+
+&lt;p&gt;If you want to avoid using Google Services on your Android phone, there is &lt;a href=&quot;https://microg.org/&quot;&gt;microG&lt;/a&gt; for that. I flashed my phone with an &lt;a href=&quot;http://aospextended.com/&quot;&gt;AEX&lt;/a&gt; ROM which supports microG, so it was not particularly hard to set-up on my phone, but I’ve heard it can be hard to set it up since it’s doing some trickery to replace Google’s services on your phone.&lt;/p&gt;
+
+&lt;p&gt;This also means you have to flash a custom ROM and root your device in order to do this, so maybe this option is not for everyone, but I think with Google Services active in your phone, you can’t really be sure what’s going on behind the curtains.&lt;/p&gt;
+
+&lt;h1 id=&quot;email&quot;&gt;Email&lt;/h1&gt;
+
+&lt;p&gt;One of the most common means of communication for us in the digital world, we exchange a lot of information through email, including personal and work-related information. As such, I deem email an important piece of privacy-sensitive information.&lt;/p&gt;
+
+&lt;p&gt;My solution for email is a self-hosted Postfix + Dovecot + SpamAssassin on my server. It is not the most straightforward thing to set up, by &lt;a href=&quot;https://www.digitalocean.com/community/tutorials/how-to-configure-a-mail-server-using-postfix-dovecot-mysql-and-spamassassin&quot;&gt;this DigitalOcean tutorial&lt;/a&gt; makes it all the easier.&lt;/p&gt;
+
+&lt;p&gt;I have also heard of &lt;a href=&quot;https://mailinabox.email/&quot;&gt;Mail-in-a-Box&lt;/a&gt; which is supposed to make setting up your own mail server a breeze! I didn’t know about this at the time I set up my server, but it could be a better choice, so perhaps give it a try and let me know.&lt;/p&gt;
+
+&lt;h1 id=&quot;cloud-storage&quot;&gt;Cloud Storage&lt;/h1&gt;
+
+&lt;p&gt;A cloud storage is necessary for syncng your data among your devices and keeping your information safe from physical loss. I chose &lt;a href=&quot;https://nextcloud.com/&quot;&gt;Nextcloud&lt;/a&gt; and I couldn’t be more satisfied. It has clients for every major operating system, and I use it to back up my files, synchronize my calendar and contacts between my Linux and my Android devices.&lt;/p&gt;
+
+&lt;p&gt;The installation and activation is fairly straightforward, and again, I followed a &lt;a href=&quot;https://www.digitalocean.com/community/tutorials/how-to-install-and-configure-nextcloud-on-ubuntu-16-04&quot;&gt;DigitalOcean tutorial&lt;/a&gt; to set up the service and have been using it since.&lt;/p&gt;
+
+&lt;p&gt;I also bought a DigitalOcean Space for $5/month, with a capacity of 250G, which is a fairly good price and worth its value. See &lt;a href=&quot;https://www.digitalocean.com/community/questions/is-it-possible-to-mount-do-spaces-as-external-storage-in-nextcloud-as-i-mount-aws-s3-storage&quot;&gt;this discussion&lt;/a&gt; about attaching a DigitalOcean space to Nextcloud.&lt;/p&gt;
+
+&lt;h1 id=&quot;contacts-and-calendar&quot;&gt;Contacts and Calendar&lt;/h1&gt;
+
+&lt;p&gt;I learned about &lt;a href=&quot;https://f-droid.org/packages/at.bitfire.davdroid/&quot;&gt;DAVx&lt;/a&gt; and &lt;a href=&quot;https://f-droid.org/en/packages/at.bitfire.icsdroid/&quot;&gt;ICSx&lt;/a&gt;, which are tools for syncing your contacts and calendar, with support for Google Calendar as well. This means that I can still have access to my workplace calendar which is on Google, and have my own personal calendars synchronized using Nextcloud.&lt;/p&gt;
+
+&lt;p&gt;These tools integrate with whatever Calendar and Contacts application you are using on your phone, so you are free to choose whatever calendar and contacts application you like.&lt;/p&gt;
+
+&lt;h1 id=&quot;notes&quot;&gt;Notes&lt;/h1&gt;
+
+&lt;p&gt;For note-taking, I use a simple Markdown/todo.txt editor called &lt;a href=&quot;https://f-droid.org/en/packages/net.gsantner.markor/&quot;&gt;Markor&lt;/a&gt; while Nextcloud handles the synchronization so I have access to my notes both on my computer and my phone. I use &lt;a href=&quot;https://github.com/vimwiki/vimwiki&quot;&gt;vimwiki&lt;/a&gt; to organize and edit my notes on my computer. Nextcloud also provides extra applications for editing Markdown files on the web interface, which is great if you like doing everything in your browser.&lt;/p&gt;
+
+&lt;h1 id=&quot;application-store&quot;&gt;Application Store&lt;/h1&gt;
+
+&lt;p&gt;For downloading applications, I default to searching through &lt;a href=&quot;https://f-droid.org/en/&quot;&gt;F-Droid&lt;/a&gt;, and in case I don’t find the tool I’m looking for (which I mostly do!), or I’m looking for a properietary application, such as Slack, I use &lt;a href=&quot;https://f-droid.org/en/packages/com.dragons.aurora/&quot;&gt;Aurora Store&lt;/a&gt; or &lt;a href=&quot;https://f-droid.org/en/packages/com.github.yeriomin.yalpstore/&quot;&gt;Yalp Store&lt;/a&gt;, which lets you search through all Google Play applications and install applications without a fuss.&lt;/p&gt;
+
+&lt;p&gt;Of course, you can install the official Google Play store as well if you would like to, but I personally am cautious about using any of Google’s applications.&lt;/p&gt;
+
+&lt;h1 id=&quot;two-factor-authentication&quot;&gt;Two-factor Authentication&lt;/h1&gt;
+
+&lt;p&gt;I use &lt;a href=&quot;https://github.com/andOTP/andOTP/&quot;&gt;andOTP&lt;/a&gt; instead of Google Authenticator. One feature I love about andOTP is the ability to take an encrypted backup of your OTP keys, so you do not have to re-set all your two-factor authentications across all services if you ever want to switch your phone.&lt;/p&gt;
+
+&lt;h1 id=&quot;password-manager&quot;&gt;Password Manager&lt;/h1&gt;
+
+&lt;p&gt;I switched from LastPass, with its ugly, broken and distorted user experience to &lt;a href=&quot;https://bitwarden.com/&quot;&gt;BitWarden&lt;/a&gt;, and I couldn’t ask for more! The user experience is far superior compared to LastPass, the extension doesn’t kill my browser’s performance and the Android application is great, too!&lt;/p&gt;
+
+&lt;h1 id=&quot;firefox-containers&quot;&gt;Firefox Containers&lt;/h1&gt;
+
+&lt;p&gt;Lastly, it’s natural that we can’t completely avoid using Google’s tools, we can just try to limit Google’s access to our data and avoid being tracked as much as possible. For this purpose, I started using Firefox Containers, and God, this is a killer feature!&lt;/p&gt;
+
+&lt;p&gt;So now, I have a few containers set up:&lt;/p&gt;
+
+&lt;ul&gt;
+  &lt;li&gt;Personal: This one includes my personal accounts on websites other than Google that I want to stay logged-in on.&lt;/li&gt;
+  &lt;li&gt;Work: I’m logged into services that I use for work here, and it includes Google as well, but only for work.&lt;/li&gt;
+  &lt;li&gt;Google: This one, I use for accessing a personal Google Account I keep for YouTube and other services, but I’m not a serious user.&lt;/li&gt;
+  &lt;li&gt;&lt;a href=&quot;https://addons.mozilla.org/en-US/firefox/addon/temporary-containers/&quot;&gt;Temporary Containers&lt;/a&gt;: Any websites that I have not explicitly chosen to be opened in one of the above containers, opens up in a new, temporary container, which means it doesn’t have access to any cookies or information from the other containers. I may sometimes choose to open Google or other services in Temporary Containers as well if I don’t see the necessity to be logged in.&lt;/li&gt;
+&lt;/ul&gt;
+
+&lt;p&gt;This means Google will not be able to track me using my account when I’m logged in to other services since they live in a different container, even though other methods such as &lt;a href=&quot;https://clearcode.cc/blog/device-fingerprinting/&quot;&gt;device fingerprinting&lt;/a&gt; are still possible. With Firefox’s Tracking Protection and &lt;a href=&quot;https://addons.mozilla.org/en-US/firefox/addon/ublock/&quot;&gt;uBlock&lt;/a&gt; always turned on, I am less concerned about tracking.&lt;/p&gt;
+
+&lt;h1 id=&quot;not-the-easiet-thing&quot;&gt;Not the easiet thing&lt;/h1&gt;
+
+&lt;p&gt;I have to admit, it’s not the easiest thing to move your digital life away from the giants, their products are built for maximum convenience, so you can’t expect to have that maximum convenience if you stop using those products, and I think it’s a far-fetched ideal to expect the same level of convenience using free applications and tools, but I personally think it’s worth it.&lt;/p&gt;
+
+</description>
+        <pubDate>Mon, 11 Feb 2019 00:00:00 +0000</pubDate>
+        <link>http://localhost:4000/self-hosted/</link>
+        <guid isPermaLink="true">http://localhost:4000/self-hosted/</guid>
+        
+        
+        <category>life</category>
+        
+      </item>
+    
+      
+      <item>
+        <title>Mathematical Induction for proving tiling methods</title>
+        <description>&lt;p&gt;On my way towards self-taught data science, I’ve stumbled upon the need to be proficient with mathematical proofs, so I picked up the amazing &lt;a href=&quot;https://www.amazon.com/How-Prove-It-Structured-Approach/dp/0521675995&quot;&gt;How To Prove It: A Structured Approach&lt;/a&gt; by Daniel J. Velleman; and I’ve been fascinated by mathematical proofs since then.&lt;/p&gt;
+
+&lt;p&gt;One of the uses for &lt;a href=&quot;https://en.wikipedia.org/wiki/Mathematical_induction&quot;&gt;Mathematical Induction&lt;/a&gt; which I’ve found to be pretty cool is proving methods for tiling shapes.&lt;/p&gt;
+
+&lt;p&gt;Here is an example:&lt;/p&gt;
+
+&lt;p&gt;Suppose $n$ is a positive integer. An equilateral triangle is cut into $4^n$ congruent equilateral triangles, and one corner is removed. Show that the remaining area can be covered by trapezoidal tiles like this: &lt;img src=&quot;/img/tiling/trapezoidal.jpg&quot; class=&quot;inline&quot; width=&quot;30&quot; /&gt;&lt;/p&gt;
+
+&lt;canvas id=&quot;tiling-triangle&quot; width=&quot;200&quot; height=&quot;200&quot; class=&quot;centered&quot;&gt;&lt;/canvas&gt;
+&lt;p&gt;&lt;span class=&quot;image-caption&quot;&gt;An example of n = 2. The dark tile is removed.&lt;/span&gt;&lt;/p&gt;
+
+&lt;p&gt;Just to be clear, by &lt;em&gt;cover&lt;/em&gt; we mean covering without any overlaps, so you can’t have two overlapping trapezoidal tiles.&lt;/p&gt;
+
+&lt;p&gt;As with any mathematical induction solution, we start with the base case, which is $n = 1$, in that case the triangle looks like this:&lt;/p&gt;
+
+&lt;canvas id=&quot;base-case&quot; width=&quot;100&quot; height=&quot;100&quot; class=&quot;centered&quot;&gt;&lt;/canvas&gt;
+
+&lt;p&gt;In this case, it’s obvious that we can cover the leftover area using trapezoidal tiles consisting of three equilateral triangles (the second row), so:&lt;/p&gt;
+
+&lt;hr /&gt;
+
+&lt;p&gt;Base case: $n = 1$ then the triangle has $4^1 = 4$ tiles, and by removing the top-most tile, the second row can be covered using a single trapezoidal tile.&lt;/p&gt;
+
+&lt;hr /&gt;
+
+&lt;p&gt;Now for the induction step, we have to somehow show that after adding 1 to $n$, that is, by multiplying the tiles by $4$, we can still cover the triangle by trapezoidal tiles. To show this, we start by assuming we have a triangle with $4^n$ tiles, which we know can be covered by trapezoidal tiles, then we add the new tiles and show that they, too, can be covered by trapezoidal tiles.&lt;/p&gt;
+
+&lt;hr /&gt;
+
+&lt;p&gt;Induction Step: Suppose we have a triangle split into $4^n$ tiles, and we know by induction hypothesis that it can be covered by trapezoidal tiles.&lt;/p&gt;
+
+&lt;p&gt;Now suppose we have another triangle with $4^{n+1}$ tiles, that means, $4$ times as many triangles as our original triangle. We can then group the new bigger triangle into 4 congruent triangles, one of which we know can be split into trapezoidal tiles by removing one of it’s tiles.&lt;/p&gt;
+
+&lt;p&gt;For the three left triangles, we can find a neighbouring corner and assume the tile on that corner to be removed, and then cover the rest by trapezoidal tiles. Afterwards, since we had three such corners, and they are neighbouring corners, we can cover these three corners with one trapezoidal tile, thus completing the triangle.&lt;/p&gt;
+
+&lt;hr /&gt;
+
+&lt;p&gt;Now that’s a mouthful, in simpler terms, we are following these steps (for $n = 2$):&lt;/p&gt;
+
+&lt;canvas id=&quot;n-2&quot; width=&quot;200&quot; height=&quot;200&quot; class=&quot;centered&quot;&gt;&lt;/canvas&gt;
+
+&lt;p&gt;First, we split the whole triangle into 4 smaller groups:&lt;/p&gt;
+
+&lt;canvas id=&quot;n-2-grouped&quot; width=&quot;200&quot; height=&quot;200&quot; class=&quot;centered&quot;&gt;&lt;/canvas&gt;
+
+&lt;p&gt;Then, we know that one of the triangles can be covered by trapezoidal tiles if we remove one of it’s tiles, that’s the induction hypothesis (the case for $4^n$ which is proved in the base case):&lt;/p&gt;
+
+&lt;canvas id=&quot;n-2-grouped-removed&quot; width=&quot;200&quot; height=&quot;200&quot; class=&quot;centered&quot;&gt;&lt;/canvas&gt;
+
+&lt;p&gt;Leaving the top triangle behind, we now find neighbouring corners among the three left triangles, and we assume the tiles in those corners to be removed (they are not actually removed as we are constrained to remove only one tile):&lt;/p&gt;
+
+&lt;canvas id=&quot;n-2-grouped-neighbours&quot; width=&quot;200&quot; height=&quot;200&quot; class=&quot;centered&quot;&gt;&lt;/canvas&gt;
+
+&lt;p&gt;Now we can cover the rest of these triangles by a single trapezoidal tile, similar to the case of $n = 1$.&lt;/p&gt;
+
+&lt;p&gt;Afterwards, we see that the three neighbouring tiles form a trapezoidal tile, therefore we can now put the last piece there to complete the tiles.&lt;/p&gt;
+
+&lt;canvas id=&quot;final&quot; width=&quot;200&quot; height=&quot;200&quot; class=&quot;centered&quot;&gt;&lt;/canvas&gt;
+
+&lt;p&gt;This procedure can be applied recursively on larger values of $n$ as well, so this concludes a proof of tiling an equilateral triangle divided into $4^n$ equilateral triangles using trapezoidal tiles after removing a single piece.&lt;/p&gt;
+
+&lt;script&gt;
+  (function() {
+    var tilingTriangle = document.getElementById(&apos;tiling-triangle&apos;);
+    var c = tilingTriangle.getContext(&apos;2d&apos;);
+    
+    function TriangleCanvas(id) {
+      this.element = document.getElementById(id);
+      this.context = this.element.getContext(&apos;2d&apos;);
+    }
+
+    function modifyColor(c, p) {
+      var e = document.createElement(&apos;i&apos;);
+      e.style.background = c;
+      var r = getComputedStyle(e).backgroundColor.slice(4, -1).split(&apos;,&apos;).map(parseFloat);
+      return &apos;rgb(&apos; + [r[0] + p, r[1] + p, r[2] + p].join(&apos;,&apos;) + &apos;)&apos;;
+    }
+
+    function dedup(list) {
+      return list.reduce(function(newList, item) {
+        if (!newList.some(function(a) { return deepCompare(a, item) })) {
+          return newList.concat(item);
+        }
+        return newList;
+      }, []);
+    }
+
+    function deepCompare () {
+      var i, l, leftChain, rightChain;
+
+      function compare2Objects (x, y) {
+        var p;
+
+        // remember that NaN === NaN returns false
+        // and isNaN(undefined) returns true
+        if (isNaN(x) &amp;&amp; isNaN(y) &amp;&amp; typeof x === &apos;number&apos; &amp;&amp; typeof y === &apos;number&apos;) {
+            return true;
+        }
+
+        // Compare primitives and functions.     
+        // Check if both arguments link to the same object.
+        // Especially useful on the step where we compare prototypes
+        if (x === y) {
+            return true;
+        }
+
+        // Works in case when functions are created in constructor.
+        // Comparing dates is a common scenario. Another built-ins?
+        // We can even handle functions passed across iframes
+        if ((typeof x === &apos;function&apos; &amp;&amp; typeof y === &apos;function&apos;) ||
+          (x instanceof Date &amp;&amp; y instanceof Date) ||
+          (x instanceof RegExp &amp;&amp; y instanceof RegExp) ||
+          (x instanceof String &amp;&amp; y instanceof String) ||
+          (x instanceof Number &amp;&amp; y instanceof Number)) {
+            return x.toString() === y.toString();
+        }
+
+        // At last checking prototypes as good as we can
+        if (!(x instanceof Object &amp;&amp; y instanceof Object)) {
+            return false;
+        }
+
+        if (x.isPrototypeOf(y) || y.isPrototypeOf(x)) {
+            return false;
+        }
+
+        if (x.constructor !== y.constructor) {
+            return false;
+        }
+
+        if (x.prototype !== y.prototype) {
+            return false;
+        }
+
+        // Check for infinitive linking loops
+        if (leftChain.indexOf(x) &gt; -1 || rightChain.indexOf(y) &gt; -1) {
+            return false;
+        }
+
+        // Quick checking of one object being a subset of another.
+        // todo: cache the structure of arguments[0] for performance
+        for (p in y) {
+            if (y.hasOwnProperty(p) !== x.hasOwnProperty(p)) {
+                return false;
+            }
+            else if (typeof y[p] !== typeof x[p]) {
+                return false;
+            }
+        }
+
+        for (p in x) {
+            if (y.hasOwnProperty(p) !== x.hasOwnProperty(p)) {
+                return false;
+            }
+            else if (typeof y[p] !== typeof x[p]) {
+                return false;
+            }
+
+            switch (typeof (x[p])) {
+                case &apos;object&apos;:
+                case &apos;function&apos;:
+
+                    leftChain.push(x);
+                    rightChain.push(y);
+
+                    if (!compare2Objects (x[p], y[p])) {
+                        return false;
+                    }
+
+                    leftChain.pop();
+                    rightChain.pop();
+                    break;
+
+                default:
+                    if (x[p] !== y[p]) {
+                        return false;
+                    }
+                    break;
+            }
+        }
+
+        return true;
+      }
+
+      if (arguments.length &lt; 1) {
+        return true; //Die silently? Don&apos;t know how to handle such case, please help...
+        // throw &quot;Need two or more arguments to compare&quot;;
+      }
+
+      for (i = 1, l = arguments.length; i &lt; l; i++) {
+
+          leftChain = []; //Todo: this can be cached
+          rightChain = [];
+
+          if (!compare2Objects(arguments[0], arguments[i])) {
+              return false;
+          }
+      }
+
+      return true;
+    }
+
+    TriangleCanvas.prototype.drawTriangle = function(x, y, size, fill, reversed) {
+      var c = this.context;
+      var corners = [{
+        x: x,
+        y: y,
+      }, {
+        x: x - size / 2,
+        y: y + size,
+      }, {
+        x: x + size / 2,
+        y: y + size,
+      }];
+
+      if (reversed) {
+        corners = [{
+          x: x + size / 2,
+          y: y,
+        }, {
+          x: x - size / 2,
+          y: y,
+        }, {
+          x: x,
+          y: y + size
+        }];
+      }
+
+      if (fill) {
+        this.drawShape(corners, modifyColor(fill, 20), fill);
+      } else {
+        this.drawShape(corners);
+      }
+    }
+
+    TriangleCanvas.prototype.drawTrapezoid = function(tiles, size, strokeStyle, fillStyle) {
+      var corners = tiles
+                    .map(function(o) {
+                      return { x: o[0] * size, y: o[1] * size };
+                    });
+
+      console.log(corners);
+
+      this.drawShape(corners, strokeStyle, fillStyle);
+    }
+
+    TriangleCanvas.prototype.drawShape = function(corners, strokeStyle, fillStyle) {
+      var c = this.context;
+      c.beginPath();
+
+      c.moveTo(corners[0].x, corners[0].y);
+      corners.slice(1).concat([corners[0]]).forEach(function(object, index) {
+        c.lineTo(object.x, object.y);
+      }); 
+
+      c.closePath();
+      if (fillStyle) {
+        c.fillStyle = fillStyle;
+        c.fill();
+      }
+      if (strokeStyle) c.strokeStyle = strokeStyle;
+      c.stroke();
+    }
+
+    TriangleCanvas.prototype.drawSplittedTriangle = function(x, y, size, split, blocks, rest) {
+      var c = this.context;
+
+      var rows = Math.sqrt(split);
+      var rowHeight = size / rows;
+      var triangleSize = size / rows;
+
+      for (var i = 0; i &lt; rows * 2; i += 2) {
+        var row = Math.floor(i / 2);
+
+        for (var j = 0; j &lt; i + 1; j++) {
+          var position = {
+            x: x + triangleSize * j / 2 - (row * triangleSize / 2),
+            y: y + row * rowHeight,
+          };
+
+          var block = blocks.reduce(function(c, a) {
+            return (a[0] === row &amp;&amp; a[1] === j) ? (a[2] || &apos;black&apos;) : c;
+          }, null);
+
+          this.drawTriangle(position.x, position.y, triangleSize, block || rest, j % 2 == 1);
+        }
+      }
+    }
+    
+    var c1 = new TriangleCanvas(&apos;tiling-triangle&apos;);
+    c1.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), [[0, 0, &apos;#435062&apos;]], &apos;#92afd7&apos;);
+
+    var c2 = new TriangleCanvas(&apos;base-case&apos;);
+    c2.drawSplittedTriangle(50, 0, 100, 4, [[0, 0, &apos;#435062&apos;]], &apos;#92afd7&apos;);
+
+    var c3 = new TriangleCanvas(&apos;n-2&apos;);
+    c3.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), [[0, 0, &apos;#435062&apos;]], &apos;#92afd7&apos;);
+
+    var c4 = new TriangleCanvas(&apos;n-2-grouped&apos;);
+    var groups = [
+      [0, 0, &apos;#809bce&apos;], [1, 0, &apos;#809bce&apos;], [1, 1, &apos;#809bce&apos;], [1, 2, &apos;#809bce&apos;], 
+      [2, 0, &apos;#95b8d1&apos;], [3, 0, &apos;#95b8d1&apos;], [3, 1, &apos;#95b8d1&apos;], [3, 2, &apos;#95b8d1&apos;], 
+      [2, 1, &apos;#b8e0d2&apos;], [2, 2, &apos;#b8e0d2&apos;], [2, 3, &apos;#b8e0d2&apos;], [3, 3, &apos;#b8e0d2&apos;], 
+      [2, 4, &apos;#d6eadf&apos;], [3, 4, &apos;#d6eadf&apos;], [3, 5, &apos;#d6eadf&apos;], [3, 6, &apos;#d6eadf&apos;], 
+    ];
+    c4.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
+
+    var c5 = new TriangleCanvas(&apos;n-2-grouped-removed&apos;);
+    var groups = [
+      [0, 0, &apos;rgb(90, 90, 90)&apos;], [1, 0, &apos;#809bce&apos;], [1, 1, &apos;#809bce&apos;], [1, 2, &apos;#809bce&apos;], 
+      [2, 0, &apos;#95b8d1&apos;], [3, 0, &apos;#95b8d1&apos;], [3, 1, &apos;#95b8d1&apos;], [3, 2, &apos;#95b8d1&apos;], 
+      [2, 1, &apos;#b8e0d2&apos;], [2, 2, &apos;#b8e0d2&apos;], [2, 3, &apos;#b8e0d2&apos;], [3, 3, &apos;#b8e0d2&apos;], 
+      [2, 4, &apos;#d6eadf&apos;], [3, 4, &apos;#d6eadf&apos;], [3, 5, &apos;#d6eadf&apos;], [3, 6, &apos;#d6eadf&apos;], 
+    ];
+    c5.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
+    c5.context.strokeStyle = &apos;#ff7777&apos;;
+    c5.context.lineWidth = 3;
+    c5.drawTriangle(100, 0, 100);
+
+    var c6 = new TriangleCanvas(&apos;n-2-grouped-neighbours&apos;);
+    var groups = [
+      [0, 0, &apos;#e7ecf6&apos;], [1, 0, &apos;#e7ecf6&apos;], [1, 1, &apos;#e7ecf6&apos;], [1, 2, &apos;#e7ecf6&apos;], 
+      [2, 0, &apos;#95b8d1&apos;], [3, 0, &apos;#95b8d1&apos;], [3, 1, &apos;#95b8d1&apos;], [3, 2, &apos;#6d8699&apos;], 
+      [2, 1, &apos;#b8e0d2&apos;], [2, 2, &apos;#b8e0d2&apos;], [2, 3, &apos;#b8e0d2&apos;], [3, 3, &apos;#657b73&apos;], 
+      [2, 4, &apos;#d6eadf&apos;], [3, 4, &apos;#89958e&apos;], [3, 5, &apos;#d6eadf&apos;], [3, 6, &apos;#d6eadf&apos;], 
+    ];
+    c6.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
+    
+    var trapezoids = [
+      [[1, 2], [3, 2], [2.5, 3], [1.5, 3]],
+      [[1, 2], [1.5, 3], [1, 4], [0, 4]],
+      [[3, 2], [4, 4], [3, 4], [2.5, 3]],
+    ];
+    c6.drawTrapezoid(trapezoids[0], 200 / 4, &apos;#ff7777&apos;);
+    c6.drawTrapezoid(trapezoids[1], 200 / 4, &apos;#ff7777&apos;);
+    c6.drawTrapezoid(trapezoids[2], 200 / 4, &apos;#ff7777&apos;);
+
+    var c7 = new TriangleCanvas(&apos;final&apos;);
+    var groups = [
+      [0, 0, &apos;#435062&apos;], [1, 0, &apos;#92afd7&apos;], [1, 1, &apos;#92afd7&apos;], [1, 2, &apos;#92afd7&apos;], 
+      [2, 0, &apos;#95b8d1&apos;], [3, 0, &apos;#95b8d1&apos;], [3, 1, &apos;#95b8d1&apos;], [3, 2, &apos;#95b8d1&apos;], 
+      [2, 1, &apos;#b8e0d2&apos;], [2, 2, &apos;#b8e0d2&apos;], [2, 3, &apos;#b8e0d2&apos;], [3, 3, &apos;#b8e0d2&apos;], 
+      [2, 4, &apos;#d6eadf&apos;], [3, 4, &apos;#d6eadf&apos;], [3, 5, &apos;#d6eadf&apos;], [3, 6, &apos;#d6eadf&apos;], 
+    ];
+    c7.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
+    
+    var trapezoids = [
+      [[1.5, 1], [2.5, 1], [3, 2], [1, 2]],
+      [[1, 2], [3, 2], [2.5, 3], [1.5, 3]],
+      [[1, 2], [1.5, 3], [1, 4], [0, 4]],
+      [[3, 2], [4, 4], [3, 4], [2.5, 3]],
+      [[1.5, 3], [1, 4], [3, 4], [2.5, 3]],
+    ];
+    trapezoids.forEach(function(el) {
+      c7.drawTrapezoid(el, 200 / 4, &apos;#ff7777&apos;);
+    });
+  }());
+&lt;/script&gt;
+
+</description>
+        <pubDate>Thu, 19 Oct 2017 00:00:00 +0100</pubDate>
+        <link>http://localhost:4000/mathematical-induction-proving-tiling-methods/</link>
+        <guid isPermaLink="true">http://localhost:4000/mathematical-induction-proving-tiling-methods/</guid>
+        
+        
+        <category>math</category>
+        
+      </item>
+    
+      
+      <item>
+        <title>Typoclassopedia: Exercise solutions</title>
+        <description>&lt;p&gt;I wanted to get proficient in Haskell so I decided to follow &lt;a href=&quot;http://www.stephendiehl.com/posts/essential_haskell.html&quot;&gt;An [Essential] Haskell Reading List&lt;/a&gt;. There I stumbled upon &lt;a href=&quot;https://wiki.haskell.org/Typeclassopedia&quot;&gt;Typoclassopedia&lt;/a&gt;, while the material is great, I couldn’t find solutions for the exercises to check against, so I decided I would write my own and hopefully the solutions would get fixed in case I have gone wrong by others. So if you think a solution is wrong, let me know in the comments!&lt;/p&gt;
+
+&lt;p&gt;In each section below, I left some reference material for the exercises and then the solutions.&lt;/p&gt;
+
+&lt;p&gt;Note: The post will be updated as I progress in Typoclassopedia myself&lt;/p&gt;
+
+&lt;h1 id=&quot;functor&quot;&gt;Functor&lt;/h1&gt;
+&lt;h2 id=&quot;instances&quot;&gt;Instances&lt;/h2&gt;
+
+&lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Functor&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;_&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt;     &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;
+  &lt;span class=&quot;c1&quot;&gt;-- or we could just say fmap = map&lt;/span&gt;
+ 
+&lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Functor&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;_&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Nothing&lt;/span&gt;  &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Nothing&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;blockquote&gt;
+  &lt;p&gt;((,) e) represents a container which holds an “annotation” of type e along with the actual value it holds. It might be clearer to write it as (e,), by analogy with an operator section like (1+), but that syntax is not allowed in types (although it is allowed in expressions with the TupleSections extension enabled). However, you can certainly think of it as (e,).&lt;/p&gt;
+&lt;/blockquote&gt;
+
+&lt;blockquote&gt;
+  &lt;p&gt;((-&amp;gt;) e) (which can be thought of as (e -&amp;gt;); see above), the type of functions which take a value of type e as a parameter, is a Functor. As a container, (e -&amp;gt; a) represents a (possibly infinite) set of values of a, indexed by values of e. Alternatively, and more usefully, ((-&amp;gt;) e) can be thought of as a context in which a value of type e is available to be consulted in a read-only fashion. This is also why ((-&amp;gt;) e) is sometimes referred to as the reader monad; more on this later.&lt;/p&gt;
+&lt;/blockquote&gt;
+
+&lt;h3 id=&quot;exercises&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Functor&lt;/code&gt; instances for &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Either e&lt;/code&gt; and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;((-&amp;gt;) e)&lt;/code&gt;.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Functor&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Either&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;e&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;_&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Left&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;e&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Left&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;e&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Right&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Right&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+      
+&lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Functor&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;((&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;e&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Functor&lt;/code&gt; instances for &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;((,) e)&lt;/code&gt; and for &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Pair&lt;/code&gt;, defined as below. Explain their similarities and differences.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Functor&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;((,)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;e&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; 
+      
+      
+&lt;span class=&quot;kr&quot;&gt;data&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Pair&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Pair&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+&lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Functor&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Pair&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Pair&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Pair&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+
+    &lt;p&gt;Their similarity is in the fact that they both represent types of two values.
+Their difference is that &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;((,) e)&lt;/code&gt; (tuples of two) can have values of different types (kind of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(,)&lt;/code&gt; is &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;* -&amp;gt; *&lt;/code&gt;) while both values of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Pair&lt;/code&gt; have the same type &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;a&lt;/code&gt;, so &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Pair&lt;/code&gt; has kind &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;*&lt;/code&gt;.&lt;/p&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement a &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Functor&lt;/code&gt; instance for the type &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;ITree&lt;/code&gt;, defined as&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;kr&quot;&gt;data&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;ITree&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Leaf&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Int&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+             &lt;span class=&quot;o&quot;&gt;|&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Node&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;ITree&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Functor&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;ITree&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Leaf&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Leaf&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Node&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Node&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+
+    &lt;p&gt;To test this instance, I defined a function to apply the tree to an &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Int&lt;/code&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;applyTree&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;ITree&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Int&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;applyTree&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Leaf&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;i&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;i&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;applyTree&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Node&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;_&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;applyTree&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Node&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;i&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;applyTree&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;i&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;++&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;applyTree&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Node&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;i&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+
+    &lt;p&gt;This is not a standard tree traversing algorithm, I just wanted it to be simple for testing.&lt;/p&gt;
+
+    &lt;p&gt;Now test the instance:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;err&quot;&gt;λ&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;let&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Node&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Node&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Leaf&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;+&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;5&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;),&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Leaf&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;+&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;1&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)],&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Leaf&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;*&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)]&lt;/span&gt;
+ &lt;span class=&quot;err&quot;&gt;λ&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;applyTree&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;mi&quot;&gt;1&lt;/span&gt;
+ &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;6&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+ &lt;span class=&quot;err&quot;&gt;λ&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;applyTree&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;mi&quot;&gt;1&lt;/span&gt;
+ &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;6&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+ &lt;span class=&quot;err&quot;&gt;λ&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;applyTree&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;+&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;10&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;mi&quot;&gt;1&lt;/span&gt;
+ &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;16&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;mi&quot;&gt;12&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;mi&quot;&gt;12&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Give an example of a type of kind &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;* -&amp;gt; *&lt;/code&gt; which cannot be made an instance of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Functor&lt;/code&gt; (without using &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;undefined&lt;/code&gt;).&lt;/p&gt;
+
+    &lt;p&gt;I don’t know the answer to this one yet!&lt;/p&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Is this statement true or false?&lt;/p&gt;
+
+    &lt;blockquote&gt;
+      &lt;p&gt;The composition of two &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Functor&lt;/code&gt;s is also a &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Functor&lt;/code&gt;.&lt;/p&gt;
+    &lt;/blockquote&gt;
+
+    &lt;p&gt;If false, give a counterexample; if true, prove it by exhibiting some appropriate Haskell code.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;p&gt;It’s true, and can be proved by the following function:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;ffmap&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Functor&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Functor&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;j&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;j&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;j&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;ffmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+
+    &lt;p&gt;You can test this on arbitrary compositions of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Functor&lt;/code&gt;s:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;main&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;do&lt;/span&gt;
+   &lt;span class=&quot;kr&quot;&gt;let&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;result&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Either&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;String&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Int&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;ffmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;+&lt;/span&gt; &lt;span class=&quot;mi&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Right&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;$&lt;/span&gt; &lt;span class=&quot;mi&quot;&gt;5&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;print&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;result&lt;/span&gt; &lt;span class=&quot;c1&quot;&gt;-- (Just (Right 7))&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h2 id=&quot;functor-laws&quot;&gt;Functor Laws&lt;/h2&gt;
+
+&lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt;
+&lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;h&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;h&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;h3 id=&quot;exercises-1&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;Although it is not possible for a Functor instance to satisfy the first Functor law but not the second (excluding undefined), the reverse is possible. Give an example of a (bogus) Functor instance which satisfies the second law but not the first.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;p&gt;This is easy, consider this instance:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Functor&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;_&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;1&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+
+    &lt;p&gt;Then, you can test the first and second laws:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;err&quot;&gt;λ&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt; &lt;span class=&quot;c1&quot;&gt;-- [1], breaks the first law&lt;/span&gt;
+ &lt;span class=&quot;err&quot;&gt;λ&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;((&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;+&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;1&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;+&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;1&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt; &lt;span class=&quot;c1&quot;&gt;-- [4, 5], second law holds&lt;/span&gt;
+ &lt;span class=&quot;err&quot;&gt;λ&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;+&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;1&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;+&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;$&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;1&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt; &lt;span class=&quot;c1&quot;&gt;-- [4, 5]&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Which laws are violated by the evil Functor instance for list shown above: both laws, or the first law alone? Give specific counterexamples.&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;c1&quot;&gt;-- Evil Functor instance&lt;/span&gt;
+ &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Functor&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;_&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;p&gt;The instance defined breaks the first law (&lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;fmap id [1] -- [1,1]&lt;/code&gt;), but holds for the second law.&lt;/p&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h1 id=&quot;category-theory&quot;&gt;Category Theory&lt;/h1&gt;
+
+&lt;p&gt;The Functor section links to &lt;a href=&quot;https://en.wikibooks.org/wiki/Haskell/Category_theory&quot;&gt;Category Theory&lt;/a&gt;, so here I’m going to cover the exercises of that page, too.&lt;/p&gt;
+
+&lt;h2 id=&quot;introduction-to-categories&quot;&gt;Introduction to categories&lt;/h2&gt;
+
+&lt;h3 id=&quot;category-laws&quot;&gt;Category laws:&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;The compositions of morphisms need to be &lt;strong&gt;associative&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;p&gt;$f \circ (g \circ h) = (f \circ g) \circ h$&lt;/p&gt;
+  &lt;/li&gt;
+  &lt;li&gt;The category needs to be &lt;strong&gt;closed&lt;/strong&gt; under the composition operator. So if $f : B \to C$ and $g: A \to B$, then there must be some $h: A \to C$ in the category such that $h = f \circ g$.&lt;/li&gt;
+  &lt;li&gt;Every object $A$ in a category must have an identity morphism, $id_A : A \to A$ that is an identity of composition with other morphisms. So for every morphism $g: A \to B$:
+ $g \circ id_A = id_B \circ g = g$.&lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h3 id=&quot;exercises-2&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;As was mentioned, any partial order $(P, \leq)$ is a category with objects as the elements of P and a morphism between elements a and b iff $a \leq b$. Which of the above laws guarantees the transitivity of $\leq$?&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;p&gt;The second law, which states that the category needs to be closed under the composition operator guarantess that because we have a morphism $a \leq b$, and another morphism $b \leq c$, there must also be some other morphism such that $a \leq c$.&lt;/p&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;If we add another morphism to the above example, as illustrated below, it fails to be a category. Why? Hint: think about associativity of the composition operation.&lt;/p&gt;
+
+    &lt;p&gt;&lt;img src=&quot;/img/typoclassopedia/not-a-cat.png&quot; alt=&quot;not a category, an additional h: B -&amp;gt; A&quot; /&gt;&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;p&gt;The first law does not hold:&lt;/p&gt;
+
+    &lt;p&gt;$f \circ (g \circ h) = (f \circ g) \circ h$&lt;/p&gt;
+
+    &lt;p&gt;To see that, we can evaluate each side to get an inequality:&lt;/p&gt;
+
+    &lt;p&gt;$g \circ h = id_B$&lt;/p&gt;
+
+    &lt;p&gt;$f \circ g = id_A$&lt;/p&gt;
+
+    &lt;p&gt;$f \circ (g \circ h) = f \circ id_B = f$&lt;/p&gt;
+
+    &lt;p&gt;$(f \circ g) \circ h = id_A \circ h = h$&lt;/p&gt;
+
+    &lt;p&gt;$f \neq h$&lt;/p&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h2 id=&quot;functors&quot;&gt;Functors&lt;/h2&gt;
+
+&lt;h3 id=&quot;functor-laws-1&quot;&gt;Functor laws:&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;Given an identity morphism $id_A$ on an object $A$, $F(id_A)$ must be the identity morphism on $F(A)$, so:
+ $F(id_A) = id_{F(A)}$&lt;/p&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Functors must distribute over morphism composition:
+ $F(f \circ g) = F(f) \circ F(g)$&lt;/p&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h3 id=&quot;exercises-3&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;Check the functor laws for the diagram below.&lt;/p&gt;
+
+    &lt;p&gt;&lt;img src=&quot;/img/typoclassopedia/functor-diagram.png&quot; alt=&quot;functor diagram&quot; /&gt;&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;p&gt;The first law is obvious as it’s directly written, the pale blue dotted arrows from $id_C$ to $F(id_C) = id_{F(C)}$ and $id_A$ and $id_B$ to $F(id_A) = F(id_B) = id_{F(A)} = id_{F(B)}$ show this.&lt;/p&gt;
+
+    &lt;p&gt;The second law also holds, the only compositions in category $C$ are between $f$ and identities, and $g$ and identities, there is no composition between $f$ and $g$.&lt;/p&gt;
+
+    &lt;p&gt;(Note: The second law always hold as long as the first one does, as was seen in Typoclassopedia)&lt;/p&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Check the laws for the Maybe and List functors.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Functor&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;_&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt;     &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;
+    
+ &lt;span class=&quot;c1&quot;&gt;-- check the first law for each part:&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt; &lt;span class=&quot;c1&quot;&gt;-- the first law holds recursively&lt;/span&gt;
+    
+ &lt;span class=&quot;c1&quot;&gt;-- check the second law for each part:&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Functor&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;_&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Nothing&lt;/span&gt;  &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Nothing&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+    
+ &lt;span class=&quot;c1&quot;&gt;-- check the first law for each part:&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Nothing&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Nothing&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+    
+ &lt;span class=&quot;c1&quot;&gt;-- check the second law for each part:&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Nothing&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Nothing&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;((&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;((&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h1 id=&quot;applicative&quot;&gt;Applicative&lt;/h1&gt;
+
+&lt;h2 id=&quot;laws&quot;&gt;Laws&lt;/h2&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;The identity law:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;v&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;v&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Homomorphism:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+
+    &lt;p&gt;Intuitively, applying a non-effectful function to a non-effectful argument in an effectful context is the same as just applying the function to the argument and then injecting the result into the context with pure.&lt;/p&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Interchange:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;u&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;y&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;y&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;u&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+
+    &lt;p&gt;Intuitively, this says that when evaluating the application of an effectful function to a pure argument, the order in which we evaluate the function and its argument doesn’t matter.&lt;/p&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Composition:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;u&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;v&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;w&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;.&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;u&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;v&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;w&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+
+    &lt;p&gt;This one is the trickiest law to gain intuition for. In some sense it is expressing a sort of associativity property of (&lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;&amp;lt;*&amp;gt;&lt;/code&gt;). The reader may wish to simply convince themselves that this law is type-correct.&lt;/p&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h3 id=&quot;exercises-4&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;p&gt;(Tricky) One might imagine a variant of the interchange law that says something about applying a pure function to an effectful argument. Using the above laws, prove that&lt;/p&gt;
+
+&lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;flip&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+&lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;flip&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;
+  &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;flip&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;c1&quot;&gt;-- &amp;lt;*&amp;gt; is left-associative&lt;/span&gt;
+  &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;flip&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;c1&quot;&gt;-- interchange&lt;/span&gt;
+  &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;.&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;flip&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;c1&quot;&gt;-- composition&lt;/span&gt;
+  &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;((&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;flip&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)))&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;c1&quot;&gt;-- homomorphism&lt;/span&gt;
+  &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;((&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;flip&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;flip&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)))&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;c1&quot;&gt;-- identical&lt;/span&gt;
+  &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+&lt;p&gt;Explanation of the last transformation:&lt;/p&gt;
+
+&lt;p&gt;&lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;flip ($)&lt;/code&gt; has type &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;a -&amp;gt; (a -&amp;gt; c) -&amp;gt; c&lt;/code&gt;, intuitively, it first takes an argument of type &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;a&lt;/code&gt;, then a function that accepts that argument, and in the end it calls the function with the first argument. So &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(flip ($) 5)&lt;/code&gt; takes as argument a function which gets called with &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;5&lt;/code&gt; as it’s argument. If we pass &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(+ 2)&lt;/code&gt; to &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(flip ($) 5)&lt;/code&gt;, we get &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(flip ($) 5) (+2)&lt;/code&gt; which is equivalent to the expression &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(+2) $ 5&lt;/code&gt;, evaluating to &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;7&lt;/code&gt;.&lt;/p&gt;
+
+&lt;p&gt;&lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;flip ($) f&lt;/code&gt; is equivalent to &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;\x -&amp;gt; x $ f&lt;/code&gt;, that means, it takes as input a function and calls it with the function &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;f&lt;/code&gt; as argument.&lt;/p&gt;
+
+&lt;p&gt;The composition of these functions works like this: First &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;flip ($)&lt;/code&gt; takes &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;x&lt;/code&gt; as it’s first argument, and returns a function &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(flip ($) x)&lt;/code&gt;, this function is awaiting a function as it’s last argument, which will be called with &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;x&lt;/code&gt; as it’s argument. Now this function &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(flip ($) x)&lt;/code&gt; is passed to &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;flip ($) f&lt;/code&gt;, or to write it’s equivalent &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(\x -&amp;gt; x $ f) (flip ($) x)&lt;/code&gt;, this results in the expression &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(flip ($) x) f&lt;/code&gt;, which is equivalent to &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;f $ x&lt;/code&gt;.&lt;/p&gt;
+
+&lt;p&gt;You can check the type of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(flip ($) f) . (flip ($))&lt;/code&gt; is something like this (depending on your function &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;f&lt;/code&gt;):&lt;/p&gt;
+
+&lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;err&quot;&gt;λ&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;let&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;sqrt&lt;/span&gt;
+&lt;span class=&quot;err&quot;&gt;λ&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;:&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;flip&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;flip&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt;
+&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;flip&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;flip&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Floating&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;p&gt;Also see &lt;a href=&quot;https://stackoverflow.com/questions/46503793/applicative-prove-pure-f-x-pure-flip-x-pure-f/46505868#46505868&quot;&gt;this question on Stack Overflow&lt;/a&gt; which includes alternative proofs.&lt;/p&gt;
+
+&lt;h2 id=&quot;instances-1&quot;&gt;Instances&lt;/h2&gt;
+
+&lt;p&gt;Applicative instance of lists as a collection of values:&lt;/p&gt;
+
+&lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;kr&quot;&gt;newtype&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;{&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;getZipList&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;}&lt;/span&gt;
+ 
+&lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Applicative&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;undefined&lt;/span&gt;   &lt;span class=&quot;c1&quot;&gt;-- exercise&lt;/span&gt;
+ 
+  &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;
+  &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;gs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;zipWith&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;gs&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;p&gt;Applicative instance of lists as a non-deterministic computation context:&lt;/p&gt;
+
+&lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Applicative&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+ 
+  &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;gs&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;|&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;gs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;h3 id=&quot;exercises-5&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement an instance of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Applicative&lt;/code&gt; for &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Maybe&lt;/code&gt;.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Applicative&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;
+      
+   &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;
+   &lt;span class=&quot;kr&quot;&gt;_&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Nothing&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Nothing&lt;/span&gt;
+   &lt;span class=&quot;kt&quot;&gt;Nothing&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;_&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Nothing&lt;/span&gt;
+   &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Determine the correct definition of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;pure&lt;/code&gt; for the &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;ZipList&lt;/code&gt; instance of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Applicative&lt;/code&gt;—there is only one implementation that satisfies the law relating &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;pure&lt;/code&gt; and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(&amp;lt;*&amp;gt;)&lt;/code&gt;.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;kr&quot;&gt;newtype&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;{&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;getZipList&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;}&lt;/span&gt;
+    
+ &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Functor&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;list&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;{&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;getZipList&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;list&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;}&lt;/span&gt;
+    
+ &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Applicative&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt;
+    
+   &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;gs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;ZipList&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;zipWith&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;gs&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+
+    &lt;p&gt;You can check the Applicative laws for this implementation.&lt;/p&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h2 id=&quot;utility-functions&quot;&gt;Utility functions&lt;/h2&gt;
+
+&lt;h3 id=&quot;exercises-6&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement a function
+ &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;sequenceAL :: Applicative f =&amp;gt; [f a] -&amp;gt; f [a]&lt;/code&gt;
+ There is a generalized version of this, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;sequenceA&lt;/code&gt;, which works for any &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Traversable&lt;/code&gt; (see the later section on &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Traversable&lt;/code&gt;), but implementing this version specialized to lists is a good exercise.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;createList&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;replicate&lt;/span&gt; &lt;span class=&quot;mi&quot;&gt;1&lt;/span&gt;
+
+ &lt;span class=&quot;n&quot;&gt;sequenceAL&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Applicative&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;sequenceAL&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldr&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;((&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;++&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;createList&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;$&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+
+    &lt;p&gt;Explanation:&lt;/p&gt;
+
+    &lt;p&gt;First, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;createList&lt;/code&gt; is a simple function for creating a list of a single element, e.g. &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;createList 2 == [2]&lt;/code&gt;.&lt;/p&gt;
+
+    &lt;p&gt;Now let’s take &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;sequenceAL&lt;/code&gt; apart, first, it does a fold over the list &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;[f a]&lt;/code&gt;, and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;b&lt;/code&gt; is initialized to &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;pure []&lt;/code&gt;, which results in &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;f [a]&lt;/code&gt; as required by the function’s output.&lt;/p&gt;
+
+    &lt;p&gt;Inside the function, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;createList &amp;lt;$&amp;gt; x&lt;/code&gt; applies &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;createList&lt;/code&gt; to the value inside &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;f a&lt;/code&gt;, resulting in &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;f [a]&lt;/code&gt;, and then &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(++)&lt;/code&gt; is applied to the value again, so it becomes &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;f ((++) [a])&lt;/code&gt;, now we can apply the function &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(++) [a]&lt;/code&gt; to &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;b&lt;/code&gt; by &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;((++) . createList &amp;lt;$&amp;gt; x) &amp;lt;*&amp;gt; b&lt;/code&gt;, which results in &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;f ([a] ++ b)&lt;/code&gt;.&lt;/p&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h2 id=&quot;alternative-formulation&quot;&gt;Alternative formulation&lt;/h2&gt;
+
+&lt;h3 id=&quot;definition&quot;&gt;Definition&lt;/h3&gt;
+
+&lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;kr&quot;&gt;class&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Functor&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Monoidal&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;unit&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;nb&quot;&gt;()&lt;/span&gt;
+  &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;**&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;h3 id=&quot;laws-1&quot;&gt;Laws:&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;Left identity&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;unit&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;v&lt;/span&gt; &lt;span class=&quot;err&quot;&gt;≅&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;v&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Right identity&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;u&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;unit&lt;/span&gt; &lt;span class=&quot;err&quot;&gt;≅&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;u&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Associativity&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;u&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;v&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;w&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;err&quot;&gt;≅&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;u&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;v&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;w&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Neutrality&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;***&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;h&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;u&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;v&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;u&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;h&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;v&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h3 id=&quot;isomorphism&quot;&gt;Isomorphism&lt;/h3&gt;
+
+&lt;p&gt;In the laws above, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;≅&lt;/code&gt; refers to isomorphism rather than equality. In particular we consider:&lt;/p&gt;
+
+&lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;nb&quot;&gt;()&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;err&quot;&gt;≅&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;err&quot;&gt;≅&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;nb&quot;&gt;()&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;span class=&quot;p&quot;&gt;((&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;y&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;),&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;z&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;err&quot;&gt;≅&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;y&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;z&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;h3 id=&quot;exercises-7&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;pure&lt;/code&gt; and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;&amp;lt;*&amp;gt;&lt;/code&gt; in terms of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;unit&lt;/code&gt; and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;**&lt;/code&gt;, and vice versa.&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;unit&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;nb&quot;&gt;()&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;unit&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;nb&quot;&gt;()&lt;/span&gt;
+    
+ &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;**&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(,)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;
+    
+ &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;unit&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;
+    
+ &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;uncurry&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Are there any &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Applicative&lt;/code&gt; instances for which there are also functions &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;f () -&amp;gt; ()&lt;/code&gt; and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;f (a,b) -&amp;gt; (f a, f b)&lt;/code&gt;, satisfying some “reasonable” laws?&lt;/p&gt;
+
+    &lt;p&gt;The &lt;a href=&quot;https://wiki.haskell.org/Typeclassopedia#Arrow&quot;&gt;&lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Arrow&lt;/code&gt;&lt;/a&gt; type class seems to satisfy these criteria.&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;   &lt;span class=&quot;n&quot;&gt;first&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;unit&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;nb&quot;&gt;()&lt;/span&gt;
+      
+   &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;***&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;(Tricky) Prove that given your implementations from the first exercise, the usual Applicative laws and the Monoidal laws stated above are equivalent.&lt;/p&gt;
+
+    &lt;ol&gt;
+      &lt;li&gt;
+        &lt;p&gt;Identity Law&lt;/p&gt;
+
+        &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;v&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;uncurry&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;((&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;unit&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;v&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;uncurry&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;v&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;v&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;v&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;        &lt;/div&gt;
+      &lt;/li&gt;
+      &lt;li&gt;
+        &lt;p&gt;Homomorphism&lt;/p&gt;
+
+        &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;unit&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;unit&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;unit&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;unit&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;        &lt;/div&gt;
+      &lt;/li&gt;
+      &lt;li&gt;
+        &lt;p&gt;Interchange&lt;/p&gt;
+
+        &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;u&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;y&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;uncurry&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;u&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;unit&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;y&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;uncurry&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;u&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;y&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;u&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;y&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;y&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;u&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;y&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;u&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;        &lt;/div&gt;
+      &lt;/li&gt;
+      &lt;li&gt;
+        &lt;p&gt;Composition&lt;/p&gt;
+
+        &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;u&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;v&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;w&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;uncurry&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;u&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;uncurry&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;v&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;w&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)))&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;uncurry&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;$&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;u&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;**&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;v&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;w&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;u&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;v&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;w&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;u&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;v&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;w&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;.&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;u&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;v&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;w&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;        &lt;/div&gt;
+      &lt;/li&gt;
+    &lt;/ol&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h1 id=&quot;monad&quot;&gt;Monad&lt;/h1&gt;
+
+&lt;h2 id=&quot;definition-1&quot;&gt;Definition&lt;/h2&gt;
+
+&lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;kr&quot;&gt;class&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Applicative&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Monad&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;return&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+  &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;  &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;
+  &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;   &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;n&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;kr&quot;&gt;_&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;n&lt;/span&gt;
+ 
+  &lt;span class=&quot;n&quot;&gt;fail&lt;/span&gt;   &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;String&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;h2 id=&quot;instances-2&quot;&gt;Instances&lt;/h2&gt;
+
+&lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Monad&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;return&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;return&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt;
+ 
+  &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;
+  &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;
+  &lt;span class=&quot;kt&quot;&gt;Nothing&lt;/span&gt;  &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;_&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Nothing&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;h3 id=&quot;exercises-8&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement a &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Monad&lt;/code&gt; instance for the list constructor, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;[]&lt;/code&gt;. Follow the types!&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Monad&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;return&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+      
+   &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;_&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt;
+   &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;:&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement a &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Monad&lt;/code&gt; instance for &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;((-&amp;gt;) e)&lt;/code&gt;.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Monad&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;((&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;e&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;return&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;const&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;
+      
+   &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Functor&lt;/code&gt; and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Monad&lt;/code&gt; instance for &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Free f&lt;/code&gt;, defined as:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;kr&quot;&gt;data&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Free&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Var&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+               &lt;span class=&quot;o&quot;&gt;|&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Node&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Free&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+
+    &lt;p&gt;You may assume that &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;f&lt;/code&gt; has a &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Functor&lt;/code&gt; instance. This is known as the &lt;em&gt;free monad&lt;/em&gt; built from the functor f.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Functor&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Free&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Var&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Var&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Node&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Node&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+      
+ &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Monad&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Free&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;return&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Var&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;
+      
+   &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Var&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Var&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+   &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Node&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Node&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h2 id=&quot;intuition&quot;&gt;Intuition&lt;/h2&gt;
+
+&lt;h3 id=&quot;exercises-9&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(&amp;gt;&amp;gt;=)&lt;/code&gt; in terms of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;fmap&lt;/code&gt; (or &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;liftM&lt;/code&gt;) and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;join&lt;/code&gt;.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;join&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Now implement &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;join&lt;/code&gt; and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;fmap&lt;/code&gt; (&lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;liftM&lt;/code&gt;) in terms of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(&amp;gt;&amp;gt;=)&lt;/code&gt; and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;return&lt;/code&gt;.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;return&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;join&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h2 id=&quot;laws-2&quot;&gt;Laws&lt;/h2&gt;
+
+&lt;p&gt;Standard:&lt;/p&gt;
+
+&lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;n&quot;&gt;return&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;k&lt;/span&gt;  &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt;  &lt;span class=&quot;n&quot;&gt;k&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+&lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;return&lt;/span&gt;    &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt;  &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt;
+&lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;k&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;h&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;  &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt;  &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;k&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;h&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;p&gt;In terms of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;&amp;gt;=&amp;gt;&lt;/code&gt;:&lt;/p&gt;
+
+&lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;n&quot;&gt;return&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;  &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt;  &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;
+&lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;return&lt;/span&gt;  &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt;  &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;
+&lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;h&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;k&lt;/span&gt;  &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt;  &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;h&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;k&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;h3 id=&quot;exercises-10&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;Given the definition &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;g &amp;gt;=&amp;gt; h = \x -&amp;gt; g x &amp;gt;&amp;gt;= h&lt;/code&gt;, prove the equivalence of the above laws and the standard monad laws.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;return&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;return&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;
+      
+ &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;return&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;return&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;
+    
+ &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;h&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;k&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;y&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;y&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;h&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;k&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;y&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;y&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;h&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;k&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;y&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;h&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;y&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;k&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;h&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;k&lt;/span&gt;
+   &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;h&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;k&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h1 id=&quot;monad-transformers&quot;&gt;Monad Transformers&lt;/h1&gt;
+
+&lt;h2 id=&quot;definition-and-laws&quot;&gt;Definition and laws&lt;/h2&gt;
+
+&lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;kr&quot;&gt;class&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;MonadTrans&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;lift&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Monad&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;h3 id=&quot;exercises-11&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;What is the kind of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;t&lt;/code&gt; in the declaration of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;MonadTrans&lt;/code&gt;?&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;p&gt;&lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;t&lt;/code&gt; is of the kind &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(* -&amp;gt; *) -&amp;gt; * -&amp;gt; *&lt;/code&gt;, as we see in &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(t m) a&lt;/code&gt;, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;t&lt;/code&gt; accepts a &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Monad&lt;/code&gt; first, which is of type &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;* -&amp;gt; *&lt;/code&gt;, and then
+ another argument of kind &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;*&lt;/code&gt;.&lt;/p&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h2 id=&quot;composing-monads&quot;&gt;Composing Monads&lt;/h2&gt;
+
+&lt;h3 id=&quot;exercises-12&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;join :: M (N (M (N a))) -&amp;gt; M (N a)&lt;/code&gt; given &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;distrib :: N (M a) -&amp;gt; M (N a)&lt;/code&gt; and assuming &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;M&lt;/code&gt; and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;N&lt;/code&gt; are instances of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Monad&lt;/code&gt;.&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;join&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;M&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;N&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;M&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;N&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)))&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;M&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;N&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;join&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;distrib&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;((&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;distrib&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;join&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;join&lt;/span&gt;
+    
+ &lt;span class=&quot;c1&quot;&gt;-- one by one&lt;/span&gt;
+ &lt;span class=&quot;kr&quot;&gt;let&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;M&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;N&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;M&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;N&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)))&lt;/span&gt;
+     &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;distrib&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt;  &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;N&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;M&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;M&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;N&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)))&lt;/span&gt;
+     &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;join&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;N&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;M&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;N&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt;
+     &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;distrib&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;  &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;M&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;N&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;N&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt;
+ &lt;span class=&quot;kr&quot;&gt;in&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;gt;&amp;gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;join&lt;/span&gt;      &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;M&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;N&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h1 id=&quot;monadfix&quot;&gt;MonadFix&lt;/h1&gt;
+
+&lt;h2 id=&quot;examples-and-intuition&quot;&gt;Examples and intuition&lt;/h2&gt;
+
+&lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;n&quot;&gt;maybeFix&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+&lt;span class=&quot;n&quot;&gt;maybeFix&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;ma&lt;/span&gt;
+  &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;ma&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;fromJust&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;ma&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;h3 id=&quot;exercises-13&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement a MonadFix instance for [].&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;listFix&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;])&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;listFix&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;la&lt;/span&gt;
+   &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;la&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;head&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;la&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h1 id=&quot;foldable&quot;&gt;Foldable&lt;/h1&gt;
+
+&lt;h2 id=&quot;definition-2&quot;&gt;Definition&lt;/h2&gt;
+
+&lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;kr&quot;&gt;class&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Foldable&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;fold&lt;/span&gt;    &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Monoid&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Monoid&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;foldr&lt;/span&gt;   &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;foldr&apos;&lt;/span&gt;  &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;foldl&lt;/span&gt;   &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;foldl&apos;&lt;/span&gt;  &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;foldr1&lt;/span&gt;  &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;foldl1&lt;/span&gt;  &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;toList&lt;/span&gt;  &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;null&lt;/span&gt;    &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Bool&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;length&lt;/span&gt;  &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Int&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;elem&lt;/span&gt;    &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Eq&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Bool&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;maximum&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Ord&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;minimum&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Ord&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;sum&lt;/span&gt;     &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Num&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+  &lt;span class=&quot;n&quot;&gt;product&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Num&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;h2 id=&quot;instances-and-examples&quot;&gt;Instances and examples&lt;/h2&gt;
+
+&lt;h3 id=&quot;exercises-14&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;fold&lt;/code&gt; in terms of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;foldMap&lt;/code&gt;.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;fold&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;What would you need in order to implement &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;foldMap&lt;/code&gt; in terms of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;fold&lt;/code&gt;?&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;p&gt;A &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;map&lt;/code&gt; function should exist for the instance, so we can apply the function &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;(a -&amp;gt; m)&lt;/code&gt; to the container first.&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;fold&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;map&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;foldMap&lt;/code&gt; in terms of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;foldr&lt;/code&gt;.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldr&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;mappend&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;mempty&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;foldr&lt;/code&gt; in terms of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;foldMap&lt;/code&gt; (hint: use the &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Endo&lt;/code&gt; monoid).&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;foldr&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Endo&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;`&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;appEndo&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;`&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;What is the type of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;foldMap . foldMap&lt;/code&gt;? Or &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;foldMap . foldMap . foldMap&lt;/code&gt;, etc.? What do they do?&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;p&gt;Each composition makes &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;foldMap&lt;/code&gt; operate on a deeper level, so:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Monoid&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Monoid&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Monoid&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt;
+    
+ &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;1&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;3&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Sum&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Int&lt;/span&gt; &lt;span class=&quot;c1&quot;&gt;-- 6&lt;/span&gt;
+ &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[[&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;1&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;3&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]]&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Sum&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Int&lt;/span&gt; &lt;span class=&quot;c1&quot;&gt;-- 6&lt;/span&gt;
+ &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[[[&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;1&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;mi&quot;&gt;3&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]]]&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Sum&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Int&lt;/span&gt; &lt;span class=&quot;c1&quot;&gt;-- 6&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+    &lt;h2 id=&quot;derived-folds&quot;&gt;Derived folds&lt;/h2&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h3 id=&quot;exercises-15&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;toList :: Foldable f =&amp;gt; f a -&amp;gt; [a]&lt;/code&gt; in terms of either &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;foldr&lt;/code&gt; or &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;foldMap&lt;/code&gt;.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;toList&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;replicate&lt;/span&gt; &lt;span class=&quot;mi&quot;&gt;1&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Show how one could implement the generic version of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;foldr&lt;/code&gt; in terms of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;toList&lt;/code&gt;, assuming we had only the list-specific &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;foldr :: (a -&amp;gt; b -&amp;gt; b) -&amp;gt; b -&amp;gt; [a] -&amp;gt; b&lt;/code&gt;.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;foldr&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldr&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;toList&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Pick some of the following functions to implement: &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;concat&lt;/code&gt;, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;concatMap&lt;/code&gt;, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;and&lt;/code&gt;, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;or&lt;/code&gt;, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;any&lt;/code&gt;, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;all&lt;/code&gt;, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;sum&lt;/code&gt;, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;product&lt;/code&gt;, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;maximum(By)&lt;/code&gt;, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;minimum(By)&lt;/code&gt;, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;elem&lt;/code&gt;, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;notElem&lt;/code&gt;, and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;find&lt;/code&gt;. Figure out how they generalize to &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Foldable&lt;/code&gt; and come up with elegant implementations using &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;fold&lt;/code&gt; or &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;foldMap&lt;/code&gt; along with appropriate &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Monoid&lt;/code&gt; instances.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;concat&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Foldable&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;concat&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt;
+    
+ &lt;span class=&quot;n&quot;&gt;concatMap&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Foldable&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;])&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;concatMap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;replicate&lt;/span&gt; &lt;span class=&quot;mi&quot;&gt;1&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt;
+    
+ &lt;span class=&quot;n&quot;&gt;and&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Foldable&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Bool&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Bool&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;and&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;getAll&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;All&lt;/span&gt;
+    
+ &lt;span class=&quot;n&quot;&gt;or&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Foldable&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Bool&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Bool&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;or&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;getAny&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Any&lt;/span&gt;
+      
+ &lt;span class=&quot;n&quot;&gt;any&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Foldable&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Bool&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Bool&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;any&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;getAny&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Any&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+    
+ &lt;span class=&quot;n&quot;&gt;all&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Foldable&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Bool&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Bool&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;all&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;getAll&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;All&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+    
+ &lt;span class=&quot;n&quot;&gt;sum&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Num&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Foldable&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;sum&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;getSum&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Sum&lt;/span&gt;
+    
+ &lt;span class=&quot;n&quot;&gt;product&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Num&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Foldable&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;product&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;getProduct&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Product&lt;/span&gt;
+    
+ &lt;span class=&quot;c1&quot;&gt;-- I think there are more elegant implementations for maximumBy, leave a comment&lt;/span&gt;
+ &lt;span class=&quot;c1&quot;&gt;-- if you have a suggestion&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;maximumBy&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Foldable&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Ordering&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;maximumBy&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;head&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;$&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;|&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;cmp&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;])&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt;
+   &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+     &lt;span class=&quot;n&quot;&gt;cmp&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;all&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;/=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;LT&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;map&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;lst&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+     &lt;span class=&quot;n&quot;&gt;lst&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;toList&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt;
+    
+ &lt;span class=&quot;n&quot;&gt;elem&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Eq&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Foldable&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Bool&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;elem&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;any&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;==&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt;
+    
+ &lt;span class=&quot;n&quot;&gt;find&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Foldable&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Bool&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; 
+ &lt;span class=&quot;n&quot;&gt;find&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;listToMaybe&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;$&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;foldMap&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;nf&quot;&gt;\&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;|&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;])&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt; 
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h2 id=&quot;utility-functions-1&quot;&gt;Utility functions&lt;/h2&gt;
+
+&lt;ul&gt;
+  &lt;li&gt;
+    &lt;p&gt;&lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;sequenceA_ :: (Applicative f, Foldable t) =&amp;gt; t (f a) -&amp;gt; f ()&lt;/code&gt; takes a container full of computations and runs them in sequence, discarding the results (that is, they are used only for their effects). Since the results are discarded, the container only needs to be Foldable. (Compare with &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;sequenceA :: (Applicative f, Traversable t) =&amp;gt; t (f a) -&amp;gt; f (t a)&lt;/code&gt;, which requires a stronger Traversable constraint in order to be able to reconstruct a container of results having the same shape as the original container.)&lt;/p&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;&lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;traverse_ :: (Applicative f, Foldable t) =&amp;gt; (a -&amp;gt; f b) -&amp;gt; t a -&amp;gt; f ()&lt;/code&gt; applies the given function to each element in a foldable container and sequences the effects (but discards the results).&lt;/p&gt;
+  &lt;/li&gt;
+&lt;/ul&gt;
+
+&lt;h3 id=&quot;exercises-16&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;traverse_&lt;/code&gt; in terms of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;sequenceA_&lt;/code&gt; and vice versa. One of these will need an extra constraint. What is it?&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;sequenceA_&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Applicative&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Foldable&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;nb&quot;&gt;()&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;sequenceA_&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;traverse_&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt;
+    
+ &lt;span class=&quot;n&quot;&gt;traverse_&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Applicative&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Foldable&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Functor&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;nb&quot;&gt;()&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;traverse_&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;sequenceA_&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+
+    &lt;p&gt;The additional constraint for implementing &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;traverse_&lt;/code&gt; in terms of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;sequenceA_&lt;/code&gt; is the requirement of the &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Foldable&lt;/code&gt; instance &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;t&lt;/code&gt; to be a &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Functor&lt;/code&gt; as well.&lt;/p&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h1 id=&quot;traversable&quot;&gt;Traversable&lt;/h1&gt;
+
+&lt;h2 id=&quot;intuition-1&quot;&gt;Intuition&lt;/h2&gt;
+
+&lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt;&lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Applicative&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;span class=&quot;n&quot;&gt;sequenceA&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Applicative&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/div&gt;
+
+&lt;h3 id=&quot;exercises-17&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;There are at least two natural ways to turn a tree of lists into a list of trees. What are they, and why?&lt;/p&gt;
+
+    &lt;p&gt;Note: I’m not really sure whether my solution is &lt;em&gt;natural&lt;/em&gt;, I think the question is rather ambiguous in the sense that it’s not clear whether the trees in the final list of trees can have lists as their values, i.e. &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Tree [Int] -&amp;gt; [Tree [Int]]&lt;/code&gt; is valid or only &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Tree [Int] -&amp;gt; [Tree Int]&lt;/code&gt; is, but let me know if you think otherwise.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;p&gt;One way is to put each &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Node&lt;/code&gt;, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Leaf&lt;/code&gt; or &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Empty&lt;/code&gt; in a list in-order, this way the structure of the tree can be recovered from the list, here is a quick sketch (&lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;[]&lt;/code&gt; is an arbitrary list):&lt;/p&gt;
+
+    &lt;p&gt;&lt;img src=&quot;/img/typoclassopedia/tree.jpg&quot; alt=&quot;tree to list&quot; /&gt;&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;kr&quot;&gt;let&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;tree&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Node&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Node&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Leaf&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Empty&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Leaf&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+ &lt;span class=&quot;kr&quot;&gt;let&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;list&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Node&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Empty&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Empty&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Node&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Empty&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Empty&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Leaf&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Empty&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Leaf&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Give a natural way to turn a list of trees into a tree of lists.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;p&gt;To recover the original tree from the list of trees, whenever we encounter a &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Node&lt;/code&gt; in the list, we catch the next three values as left, value, and right nodes of the original node.&lt;/p&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;What is the type of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;traverse . traverse&lt;/code&gt;? What does it do?&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Applicative&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;t2&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;t2&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;))&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+
+    &lt;p&gt;It traverses on a deeper level, retaining the structure of the first level.&lt;/p&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;traverse&lt;/code&gt; in terms of &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;sequenceA&lt;/code&gt;, and vice versa.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;n&quot;&gt;sequenceA&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;id&lt;/span&gt;
+    
+ &lt;span class=&quot;n&quot;&gt;traverseA&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;sequenceA&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;h2 id=&quot;instances-and-examples-1&quot;&gt;Instances and examples&lt;/h2&gt;
+
+&lt;h3 id=&quot;exercises-18&quot;&gt;Exercises&lt;/h3&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;fmap&lt;/code&gt; and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;foldMap&lt;/code&gt; using only the &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Traversable&lt;/code&gt; methods. (Note that the &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Traversable&lt;/code&gt; module provides these implementations as &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;fmapDefault&lt;/code&gt; and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;foldMapDefault&lt;/code&gt;.)&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;kr&quot;&gt;newtype&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Id&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Id&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;{&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;getId&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;}&lt;/span&gt;
+    
+ &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Functor&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Id&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;fmap&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Id&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Id&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+    
+ &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Applicative&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Id&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Id&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;
+   &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Id&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Id&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Id&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+    
+ &lt;span class=&quot;n&quot;&gt;fmapDefault&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Traversable&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;fmapDefault&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;getId&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Id&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+    
+ &lt;span class=&quot;n&quot;&gt;foldMapDefault&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Monoid&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Traversable&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;m&lt;/span&gt;
+ &lt;span class=&quot;n&quot;&gt;foldMapDefault&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;getConst&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Const&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;.&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+
+    &lt;p&gt;See the &lt;a href=&quot;https://www.stackage.org/haddock/lts-9.9/base-4.9.1.0/src/Data-Functor-Const.html#Const&quot;&gt;Const&lt;/a&gt; Functor’s definition for intuition.&lt;/p&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Implement &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Traversable&lt;/code&gt; instances for &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;[]&lt;/code&gt;, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Maybe&lt;/code&gt;, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;((,) a)&lt;/code&gt;, and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Either a&lt;/code&gt;.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Traversable&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Applicative&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;]&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;_&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;[]&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;:&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;$&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;*&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Main&lt;/span&gt;&lt;span class=&quot;o&quot;&gt;.&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;xs&lt;/span&gt;
+      
+ &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Traversable&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Applicative&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Maybe&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+      
+   &lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;_&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Nothing&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Nothing&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Just&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;$&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;x&lt;/span&gt;
+      
+ &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Traversable&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;((,)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Applicative&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;c&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;c&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+      
+   &lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;c&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(,)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;$&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+      
+ &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Traversable&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Either&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Applicative&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Either&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Either&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+      
+   &lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;_&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Left&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;pure&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Left&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;c&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Right&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Right&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;$&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Explain why &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Set&lt;/code&gt; is &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Foldable&lt;/code&gt; but not &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Traversable&lt;/code&gt;.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;p&gt;First, in terms of laws, &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Set&lt;/code&gt; is not a &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Functor&lt;/code&gt;, thus it cannot be made into a &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Traversable&lt;/code&gt; instance, since &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Traversable&lt;/code&gt; instances require &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Functor&lt;/code&gt; superclasses.&lt;/p&gt;
+
+    &lt;p&gt;Second, on an intuitive level: In &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Foldable&lt;/code&gt;, the goal is not to keep the shape/structure of the original container, we are trying to reduce the container into some value, and the shape of the final result doesn’t matter, but in &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Traversable&lt;/code&gt;, we ought to keep the structure of the final result, but we can’t guarantee this while using &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Set&lt;/code&gt;s, because we can define some transformation &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;f :: Set a -&amp;gt; Set a&lt;/code&gt; which reduces the length of the &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Set&lt;/code&gt;.&lt;/p&gt;
+
+    &lt;p&gt;See &lt;a href=&quot;https://stackoverflow.com/questions/35857733/foldable-vs-traversable&quot;&gt;Foldable vs. Traversable&lt;/a&gt; and &lt;a href=&quot;https://stackoverflow.com/questions/19177125/sets-functors-and-eq-confusion&quot;&gt;Sets, Functors and Eq confusion&lt;/a&gt;. and &lt;a href=&quot;https://wiki.haskell.org/Foldable_and_Traversable&quot;&gt;Foldable and Traversable&lt;/a&gt; for more details.&lt;/p&gt;
+  &lt;/li&gt;
+  &lt;li&gt;
+    &lt;p&gt;Show that &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Traversable&lt;/code&gt; functors compose: that is, implement an instance for &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Traversable (Compose f g)&lt;/code&gt; given &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;Traversable&lt;/code&gt; instances for &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;f&lt;/code&gt; and &lt;code class=&quot;language-plaintext highlighter-rouge&quot;&gt;g&lt;/code&gt;.&lt;/p&gt;
+
+    &lt;p&gt;&lt;strong&gt;Solution&lt;/strong&gt;:&lt;/p&gt;
+
+    &lt;div class=&quot;language-haskell highlighter-rouge&quot;&gt;&lt;div class=&quot;highlight&quot;&gt;&lt;pre class=&quot;highlight&quot;&gt;&lt;code&gt; &lt;span class=&quot;kr&quot;&gt;instance&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Traversable&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Traversable&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Traversable&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Compose&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;kr&quot;&gt;where&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;::&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Applicative&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&amp;gt;&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Compose&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;h&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;a&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;-&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Compose&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;g&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;h&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;b&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt;
+   &lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;kt&quot;&gt;Compose&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;kt&quot;&gt;Compose&lt;/span&gt; &lt;span class=&quot;o&quot;&gt;&amp;lt;$&amp;gt;&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;p&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;n&quot;&gt;traverse&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;p&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;n&quot;&gt;t&lt;/span&gt;
+&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;    &lt;/div&gt;
+  &lt;/li&gt;
+&lt;/ol&gt;
+
+</description>
+        <pubDate>Wed, 27 Sep 2017 00:00:00 +0100</pubDate>
+        <link>http://localhost:4000/typoclassopedia-exercise-solutions/</link>
+        <guid isPermaLink="true">http://localhost:4000/typoclassopedia-exercise-solutions/</guid>
+        
+        
+        <category>programming</category>
+        
+        <category>math</category>
+        
+      </item>
+    
+      
+      <item>
+        <title>DIY Cardboard Kindle Stand (for bed)</title>
+        <description>&lt;p&gt;&lt;img src=&quot;/img/kindle-stand/1.jpg&quot; alt=&quot;a view of the stand + kindle&quot; /&gt;&lt;/p&gt;
+
+&lt;p&gt;I’ve had a Kindle for more than a year now, but I’ve only recently started to read books on it frequently, I used to read paperworks before that, and I still do sometimes prefer paperbooks if available. Anyways, my Kindle has helped me to fall asleep without struggling with all my thoughts, all I have to do is read until I fall asleep, so in a way, it has also been a remedy for my insomnia.&lt;/p&gt;
+
+&lt;p&gt;Now to read the Kindle in bed, you would have to hold it using your hands or buy a stand or make one, motivated by &lt;a href=&quot;https://blog.xkcd.com/2009/04/13/the-pursuit-of-laziness/&quot;&gt;The Pursuit of Laziness&lt;/a&gt; I set to create mine, but I didn’t use a piece of steel, instead I used a single box of cardboard I had in home to create one in minutes. :D&lt;/p&gt;
+
+&lt;!--more--&gt;
+
+&lt;p&gt;It’s too easy to need much of an instruction, a few pictures and some explanation will do:&lt;/p&gt;
+
+&lt;p&gt;&lt;img src=&quot;/img/kindle-stand/0.jpg&quot; alt=&quot;a view of the stand without kindle&quot; /&gt;&lt;/p&gt;
+
+&lt;p&gt;So this part shows a simple piece of cardboard cut using scissors on the front, with the sides taped to the bottom (actually if your piece of cardboard is a box, it might already be taped in that way, mine was).&lt;/p&gt;
+
+&lt;p&gt;&lt;img src=&quot;/img/kindle-stand/2.jpg&quot; alt=&quot;a view of the stand&apos;s back side&quot; /&gt;&lt;/p&gt;
+
+&lt;p&gt;On the back, there is another piece of cardboard (I took the opening of it which already had a notch line, and the size fit perfectly). I used a stapler to to attach the two sides toghether, and that’s it!&lt;/p&gt;
+
+&lt;p&gt;I tried it last night to make sure it’s convenient before posting here, and I tell you, it is totally comfortable and much better than holding with a hand.&lt;/p&gt;
+</description>
+        <pubDate>Sun, 24 Sep 2017 00:00:00 +0100</pubDate>
+        <link>http://localhost:4000/diy-cardboard-kindle-stand/</link>
+        <guid isPermaLink="true">http://localhost:4000/diy-cardboard-kindle-stand/</guid>
+        
+        
+        <category>life</category>
+        
+        <category>diy</category>
+        
+      </item>
+    
+      
+      <item>
+        <title>Difference between Travis CI tests: PR and Push</title>
+        <description>&lt;p&gt;I just want to leave this here as I often tend to look it up myself and the first time it was not as easy to figure out.&lt;/p&gt;
+
+&lt;p&gt;When using Travis CI along with GitHub (or other git integrations), Travis runs two tests: &lt;code&gt;pr&lt;/code&gt; and &lt;code&gt;push&lt;/code&gt;.&lt;/p&gt;
+
+&lt;p&gt;&lt;img src=&quot;/img/travis-ci-pr-push-github.jpg&quot; alt=&quot;travis-pr-push-github&quot; /&gt;&lt;/p&gt;
+
+&lt;p&gt;Most of the time you see both tests passing and you do not have to even wonder how they are different, but it has
+happened to me that one of the tests fails while the other passes and I started to wonder why.&lt;/p&gt;
+
+&lt;h3 id=&quot;pr&quot;&gt;pr&lt;/h3&gt;
+&lt;p&gt;The &lt;code&gt;pr&lt;/code&gt; test is a test run on the result of a merge between the pull-request branch and the main branch.
+As an example, let’s say your pull-request’s branch is called &lt;code&gt;fix-user-auth&lt;/code&gt; and your main branch is &lt;code&gt;master&lt;/code&gt;, 
+in this case, &lt;code&gt;pr&lt;/code&gt; merges &lt;code&gt;fix-user-auth&lt;/code&gt; into &lt;code&gt;master&lt;/code&gt; and then runs the tests on the result of the merge.&lt;/p&gt;
+
+&lt;h3 id=&quot;push&quot;&gt;push&lt;/h3&gt;
+&lt;p&gt;On the other hand, &lt;code&gt;push&lt;/code&gt; is run on the pull-request branch itself, without merging. So in our example above, Travis would checkout to &lt;code&gt;fix-user-auth&lt;/code&gt; and run the tests.&lt;/p&gt;
+
+&lt;h3 id=&quot;a-case-of-difference&quot;&gt;A case of difference&lt;/h3&gt;
+
+&lt;p&gt;A case in which this difference might be more apparent is when your pull-request is based on a branch other than &lt;code&gt;master&lt;/code&gt;, and some changes that your pull-request depends on are missing from &lt;code&gt;master&lt;/code&gt;, in this case the &lt;code&gt;push&lt;/code&gt; test may pass, but the &lt;code&gt;pr&lt;/code&gt; test will fail.&lt;/p&gt;
+
+</description>
+        <pubDate>Sat, 09 Sep 2017 00:00:00 +0100</pubDate>
+        <link>http://localhost:4000/travis-ci-pr-push/</link>
+        <guid isPermaLink="true">http://localhost:4000/travis-ci-pr-push/</guid>
+        
+        
+        <category>programming</category>
+        
+      </item>
+    
+      
+      <item>
+        <title>Primitive Living Lessons Learned, Episode 0</title>
+        <description>&lt;p&gt;&lt;img src=&quot;/img/primitive-living-0.jpg&quot; alt=&quot;general view of the forest&quot; /&gt;&lt;/p&gt;
+
+&lt;p&gt;So I just went on my first primitive living practice trip in the woods, alone, with only a pocket knife.&lt;/p&gt;
+
+&lt;p&gt;I decided I’m going to share the lessons I’ve learned in each trip as they are certainly going to be useful if you want to practice primitive living, I would find these useful if I could find them anywhere. I spend a lot of time reading and watching primitive living guides and experience reports, but they are never exhaustive, and this series is not meant to be exhaustive either.&lt;/p&gt;
+
+&lt;!--more--&gt;
+
+&lt;p&gt;Here we go:&lt;/p&gt;
+
+&lt;h1 id=&quot;what-i-did-know&quot;&gt;What I did know&lt;/h1&gt;
+
+&lt;p&gt;I spent a lot of time studying about edible wild plants, how to butcher and cook different kinds of animals and insects. I also had practiced fire by friction and read a lot and watched videos about theory of making cordages, making a bow-drill and so on. I also knew and had already built shelters for the night. So you can assume I had a basic, broad understanding of the necessary skills, but experience? Not so much.&lt;/p&gt;
+
+&lt;h1 id=&quot;setup&quot;&gt;Setup&lt;/h1&gt;
+
+&lt;p&gt;I had a pocket knife, a Garmin GPS and a pocket first aid kid, I would expect something to go wrong along the way, so I thought I want to be safe, but not comfortable, that’s why I brought emergency necessities, but not any comfort tools and materials. I also had a canned tuna for my first breakfast, but nothing more.&lt;/p&gt;
+
+&lt;p&gt;Now for what is worth, I’m going in around summer’s end, September 5th, in a forest in northern Iran, Mazandaran Province. The forest starts from foothills, covering a few mounts from both sides, so it’s pretty large but also mountaneous, so I it’s hard to move in the forest.&lt;/p&gt;
+
+&lt;h1 id=&quot;arrival-first-night&quot;&gt;Arrival: First Night&lt;/h1&gt;
+
+&lt;p&gt;So I arrived at the entrace of the forest at night, it was already dark and I couldn’t build a shelter or do much, I just slept on the open ground, it was my first night in the woods alone. I was quite scared at first, lots of cracks and movements in bushes by unknown creatures, but after a few hours I figured out all these creatures are small ones that can’t be harmful to me. A few hours before dawn it got bitter cold, and I woke up, unable to go back to sleep. The first night was not the best, but could be worse.&lt;/p&gt;
+
+&lt;h1 id=&quot;first-day&quot;&gt;First Day&lt;/h1&gt;
+
+&lt;p&gt;I woke early at dawn and started moving into the forest, looking for a place to build my shelter in. I decided I’m going to follow these steps:&lt;/p&gt;
+
+&lt;ol&gt;
+  &lt;li&gt;Build a shelter&lt;/li&gt;
+  &lt;li&gt;Find water source&lt;/li&gt;
+  &lt;li&gt;Build a fire&lt;/li&gt;
+  &lt;li&gt;Find food&lt;/li&gt;
+&lt;/ol&gt;
+
+&lt;p&gt;But as was expected, it didn’t go according to the plan.&lt;/p&gt;
+
+&lt;p&gt;&lt;img src=&quot;/img/primitive-living-0-shelter.jpg&quot; alt=&quot;my shelter, done&quot; /&gt;&lt;/p&gt;
+
+&lt;h2 id=&quot;shelter&quot;&gt;Shelter&lt;/h2&gt;
+
+&lt;p&gt;I found a nice place to stay which had a stream passing by, the stream was running and from what I knew about the area, the water was safe to drink, so water was no longer an issue. I started building my shelter, got the base wooden structure down first, but there was a catch: I couldn’t find any dry debris to put on top or inside. Last time I had built the same shelter it was autumn’s end/early spring, so there were lots of dry, fallen leaves on the ground; But this time it’s in the summer and there very few, scattered dry leaves on the ground, uncollectable.&lt;/p&gt;
+
+&lt;p&gt;I decided I’m going with leaves of a small tree I had found nearby which seemed to be abundant around the area and the branches had lots of close leaves on them, looked like a good choice, but it was green. I didn’t find out what I was doing wrong until I tried to sleep at night. The green leaves attracted lots of flies and insects and all sorts of annoying disturbances, and the smell wasn’t helping either. I had to endure the insects throughout the night, because sleeping outside the shelter was a no-go, the dirt beneath was too cold. I hadn’t put as much leaves on the ground, and the leaves were green (which also means they take more heat away), but still, it was much better than sleeping directly on the ground.&lt;/p&gt;
+
+&lt;p&gt;What I learned was, &lt;strong&gt;do not use green leaves for covering your shelter&lt;/strong&gt;. This rule applies to small shelters in which you are close to the covering, as well as the leaves you use as bedding. I’ve seen people using green leaves for covering big shelters which have a high ceiling, though I don’t have any experience with those myself.&lt;/p&gt;
+
+&lt;p&gt;&lt;img src=&quot;/img/primitive-living-0-friction-fire.jpg&quot; alt=&quot;friction fire tries&quot; /&gt;&lt;/p&gt;
+
+&lt;h2 id=&quot;friction-fire&quot;&gt;Friction Fire&lt;/h2&gt;
+
+&lt;p&gt;The most important part of primitive living is fire, without fire you can’t cook, you can’t stay warm and you can’t defy nocturnal predators. You also can’t repel insects. You can’t make a torch, so there goes an infinite list of fire applications that you will miss.&lt;/p&gt;
+
+&lt;p&gt;I knew the theory of friction fire in and out, how and why it works, but what I had missed was, &lt;strong&gt;you are going to be in &lt;em&gt;real trouble&lt;/em&gt; if you can’t find softwood&lt;/strong&gt;. To my surprise, searching portions of the forest, I couldn’t find any softwood tree. Oaks were everywhere, as well as quite some other species of trees, but all of them were hardwood.&lt;/p&gt;
+
+&lt;p&gt;I tried different combinations of the softer woods I could find, but none of them resulted in an ember, I got smoke with one combination, but that was it. After about 5-6 hours of trying, I got real tired and gave up. By the way, I tried hand-drills, I couldn’t succeed with bow-drills as I couldn’t find suitable cordage, I tried with a promising bark that was pretty strong, but it would break as soon as I put some pressure on it, It’s also possible that I might’ve gone wrong in making the bow itself, so it would cause the breakage.&lt;/p&gt;
+
+&lt;p&gt;So the lesson was &lt;strong&gt;make sure the material you are going to practice with is available in your practice area&lt;/strong&gt;, had I known there were no softwood in that particular forest, I would change my destination and probably succeed somewhere else. Sure, a professional survivalist must be able to start a fire in almost all situations, but this is practice and you have to start with easier steps.&lt;/p&gt;
+
+&lt;p&gt;I ended up shaking for 2 hours before the dawn, not a pleasant experience at all. :D&lt;/p&gt;
+
+&lt;h2 id=&quot;food&quot;&gt;Food&lt;/h2&gt;
+
+&lt;p&gt;The difficulties didn’t end there, without a fire, my only hope for food was specific edible plants which can be eaten raw, or fruits. Unlucky as I was, I couldn’t find a single fruit-bearing tree in the forest (I found quite a few fruit-bearing trees along the roads and paths to the forest, but not inside the forest itself), and I also couldn’t find any of the other edible plants (I was mostly looking for the onion family) that I knew of.&lt;/p&gt;
+
+&lt;p&gt;One of the greatest complications when starting primitive living practice anywhere other than the U.S. is that &lt;strong&gt;almost all guides and materials on the topic are from, and for Northern America&lt;/strong&gt;. &lt;a href=&quot;https://www.amazon.com/Edible-Wild-Plants-Falcon-Field/dp/0762774215&quot;&gt;The Falcon Guide to Edible Wild Plants&lt;/a&gt; that I read is all about northern american plants. I knew it, but it’s also the case that the Northern Hemisphere of the Earth have more common of an ecology, so most of the plants found in Northern America can also be found in places like Iran, but they have their differences. Most of the tips and tricks provided in different resources are for Northern American forests, which do not always work in other places.&lt;/p&gt;
+
+&lt;p&gt;So all in all, I ended up not eating anything for the next 24 hours, until I got out of the forest.&lt;/p&gt;
+
+&lt;h2 id=&quot;psychology&quot;&gt;Psychology&lt;/h2&gt;
+
+&lt;p&gt;Apart from all the physical failures that I faced, which in turn caused frustration, I also had strong feelings of loneliness, boredom, and fear upon me. It was after failing to start a fire that I really felt the psychological burden on me. I had read about similar experiences, but believe me, the experience is hardly transmittable by words. A local rancher passing by the forest telling me about the leopard in the forest didn’t make things any easier.&lt;/p&gt;
+
+&lt;p&gt;The psychological pressure was above all other difficulties, at some point I was bursting into tears, but I couldn’t associate it with any one specific feeling, it was a mix of anger, loneliness and fear.&lt;/p&gt;
+
+&lt;p&gt;Anger and frustration because I couldn’t succeed in what I was trying to do. I also cut my finger at some point while carving the woods, so there was that.&lt;/p&gt;
+
+&lt;p&gt;Loneliness because I was all by myself and I had no company to talk to. You can really actually go insane, as seen in &lt;a href=&quot;https://en.wikipedia.org/wiki/Cast_Away&quot;&gt;Cast Away&lt;/a&gt;, after prolonged sessions of loneliness in situations like that. Mine wasn’t long, it was only two days, but I still experienced the thought-fog, I couldn’t think straight.&lt;/p&gt;
+
+&lt;p&gt;Fear because I felt weak compared to the power of nature, my fear was doubled by the fact that I was alone. I felt like being in a place where everything seems to know what it is doing, but I don’t; I felt lost, not knowing what to do after my basic plans had failed.&lt;/p&gt;
+
+&lt;p&gt;Now I don’t know if there is much you can do about the psychological part of it, I think experience is the remedy, at least I felt how different it was between the nights, the first night, even though I wasn’t even &lt;em&gt;inside&lt;/em&gt; the forest much, I was almost at the border of it, it was much more creepy because it was my first time, but the second night, I was in the forest and now I had a &lt;em&gt;leopard&lt;/em&gt; in my mind pouncing on me, but I felt less fear and was more comfortable.&lt;/p&gt;
+
+&lt;p&gt;But in the end, what helped me was that &lt;em&gt;I knew I was going to face a huge mental challenge along the way&lt;/em&gt;, so I was more prepared. I think it’s utterly important to be prepared for such psychological situations, knowing the reason behind your psychological challenges can help you overcome it to some extend.&lt;/p&gt;
+
+&lt;h1 id=&quot;second-night&quot;&gt;Second Night&lt;/h1&gt;
+
+&lt;p&gt;The second and last night was not all that much interesting, but it was damn sure cold and hard. At first I had to deal with the insects biting me everywhere and my feet scratching while trying to sleep in the shelter that I had wrongly built. After getting over that one and sleeping for what seemed to be ~2 hours, I woke up and felt the air temperature decreasing. I still got to sleep in intervals of 30 minutes until I woke up at around ~4 AM and my whole body was shaking. I couldn’t do much, all I did was gather the leaves underneath a little closer and more dense, and crunch my body into a ball so I felt just a little warmer, but still shaking. It took ages for the last two and a half hours to pass until dawn. At dawn I got up quickly and walked around a little to warm myself up, and then waited until I could barely see my surroundings, then I started walking out of the forest.&lt;/p&gt;
+
+&lt;p&gt;Initially I had decided to stay for longer, but the weather forecast had predicted a heavy rain and storm for the next night, there was no way I could withstand that. :D&lt;/p&gt;
+
+&lt;h1 id=&quot;bottom-line&quot;&gt;Bottom Line&lt;/h1&gt;
+
+&lt;p&gt;It was a hard trip, I lost about 2kg (4lb) weight, but all in all the experience was a good one, I certainly learned a lot and I’m not going to make the same mistakes again. I should definitly practice more and keep working on my skills.&lt;/p&gt;
+
+&lt;p&gt;If you are looking forward to practicing primitive living, please make sure you are safe and start small.&lt;/p&gt;
+
+&lt;blockquote&gt;
+  &lt;p&gt;Success is going from failure to failure without losing your enthusiasm. —Winston Churchill&lt;/p&gt;
+&lt;/blockquote&gt;
+</description>
+        <pubDate>Thu, 07 Sep 2017 00:00:00 +0100</pubDate>
+        <link>http://localhost:4000/primitive-living-lessons-0/</link>
+        <guid isPermaLink="true">http://localhost:4000/primitive-living-lessons-0/</guid>
+        
+        
+        <category>life</category>
+        
+        <category>primitive-living</category>
+        
+        <category>travel</category>
+        
+      </item>
+    
+      
+      <item>
+        <title>Don&apos;t chase: Become the good one</title>
+        <description>&lt;p&gt;When it comes to relationships, most (unsuccessful) people are &lt;em&gt;chasing&lt;/em&gt; the good ones.
+They spend time trying to find their dream partner, the perfect match, but hey, do you qualify
+as the dream partner of your dream partner? You fantasize about your dream partner, but have you ever
+thought what kind of partner does he/she dream of?&lt;/p&gt;
+
+&lt;p&gt;&lt;img src=&quot;/img/angel.jpg&quot; alt=&quot;I want an angel with...&quot; /&gt;
+&lt;span class=&quot;image-caption&quot;&gt;I want an angel with…&lt;/span&gt;&lt;/p&gt;
+
+&lt;!--more--&gt;
+
+&lt;p&gt;It seems to be pretty acceptable in the society to start &lt;em&gt;looking&lt;/em&gt; for a &lt;em&gt;good&lt;/em&gt; partner once you
+reach a certain age (depending on the country), and that’s when people start defining for themselves what
+a &lt;em&gt;good&lt;/em&gt; partner means. What do they want out of a relationship? Well, most beginners just want sex, that’s one thing,
+but I’m talking about real, intimate relationships. The definition usually goes like this:&lt;/p&gt;
+
+&lt;p&gt;I want him/her to have&lt;/p&gt;
+&lt;ul&gt;
+  &lt;li&gt;Money&lt;/li&gt;
+  &lt;li&gt;Body&lt;/li&gt;
+  &lt;li&gt;Sense of Humor&lt;/li&gt;
+  &lt;li&gt;Empathy&lt;/li&gt;
+  &lt;li&gt;…&lt;/li&gt;
+&lt;/ul&gt;
+
+&lt;p&gt;Alright fine, that’s a good and necessary step while thinking about a relationship.&lt;/p&gt;
+
+&lt;p&gt;Now there are two groups of people after this step, let’s call them Group A and Group B.&lt;/p&gt;
+
+&lt;p&gt;Group A’s next step is to start looking for partners, which usually follows by installing Tinder, OkCupid and a bunch of other
+dating apps, spending more time in the bar, etc. Well it makes sense to start looking for a partner at first glance, but people in Group A
+are missing an important point here, they defined what a &lt;em&gt;good partner&lt;/em&gt; means in their dictionary of life, but they haven’t
+really looked into their &lt;em&gt;good partner&lt;/em&gt;’s dictionary to see what he/she wants out of a relationship, because if you don’t qualify her requirements,
+it’s not a deal.&lt;/p&gt;
+
+&lt;p&gt;Now there is a sub-group of Group A, too, and it includes the people who faced with the question “am I what she dreams of?”, they 
+try to cheat and modify their definition of a good partner, adding a line that goes “Loves me however I am”, sorry buddy, but what if I
+tell you she could add the same line to her dictionary? That’s not a deal, you want a good partner as you defined it, you have to be a good partner
+as she defines it.&lt;/p&gt;
+
+&lt;p&gt;On the other hand, Group B doesn’t follow the same path as Group A. Group B starts by trying to predict what his dream partner would want
+out of a relationship. Empathy? Loyalty? Knowledge? Body? They take a pen and a paper out and write a list of what they think their dream partner
+would want them to have, what would she want them to be, and they start working on those, and I bet it’s not going to be easy, knowledge doesn’t pop up
+after a good night’s sleep, you have to spend years reading books and learning to get it. A good body doesn’t &lt;em&gt;poof&lt;/em&gt; out if you wish it to, you have
+to spend years being committed to exercise and eating well, and that’s not easy. After all, what you define as a good partner ain’t easy either, is it?&lt;/p&gt;
+
+&lt;p&gt;Now do you want your dream partner to fall for you the way you fall for her, without having to chase her with a net? Write down a list of 
+qualifications you expect your dream partner to look for, and start working your ass off reaching them, and I tell you, you will have a much easier &lt;em&gt;next step&lt;/em&gt; after this. You won’t have to chase girls hoping the 34th one doesn’t reject you because “she likes you however you are”.&lt;/p&gt;
+
+&lt;p&gt;If I know one thing about life, it’s the fact that you have to work your ass off in order to reach your dreams, dreams aren’t easy, and a deep, intimate relationship really is a dream.&lt;/p&gt;
+</description>
+        <pubDate>Sat, 04 Feb 2017 00:00:00 +0000</pubDate>
+        <link>http://localhost:4000/dont-chase-become-the-good-one/</link>
+        <guid isPermaLink="true">http://localhost:4000/dont-chase-become-the-good-one/</guid>
+        
+        
+        <category>life</category>
+        
+      </item>
+    
+  </channel>
+</rss>
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+
+  <div class="post-header">
+    <h1 class="post-title"><p>Immortals go extinct</p>
+</h1>
+    
+    <p class="post-meta">
+      <span>Nov 15, 2016</span>
+      
+      • <span>Reading time: 3  minutes</span>
+    </p>
+  </div>
+
+  <article class="post-content">
+    <p>We are all going to die, we all know that well.<br /><br />
+Now I want to take you to a world of immortals where humans don’t die,
+they live and live and live and… you know, live. From now on, pretend I’m a human
+on this world of immortals, I’m immortal bitches.</p>
+
+<p><img src="/img/immortals.jpg" alt="immortals chatting" />
+<span class="image-caption">There is no campfire because they don’t need it</span></p>
+
+<!--more-->
+<hr />
+
+<p>In this world, there is no excitement in jumping from a cliff or doing flips over walls
+or pretending to be a bird or even loving each other, in general, there is no
+excitement in any experience, because there is nothing to miss if I don’t do that right now,
+I will always have another chance to do that again, even if that’s going to be a thousand years from now,
+because you know, we’re all good at waiting here.</p>
+
+<p>There is no technology and no fast transportation system here,
+because, hell, who gives a fuck about fast transportation systems.</p>
+
+<p>Who gives a shit about tools to harvest more food, or something you can write with,
+you can know about our meaningless past as much as you want, there are always people to tell you about that.</p>
+
+<p>Who cares if 2 + 2 = 4 or 5, I’m not going to die if the non-existing plane crashes because of an error,
+none of that is needed.</p>
+
+<p>We have an infinite amount of time to explore the globe, but we don’t,
+because there is no fun in doing that, how is that, you might ask. Someone from your world told me
+I should explain it this way:</p>
+
+<blockquote>
+  <p>Simple mathematics we know says, in an infinite timespan, no other timespan is significant, basically,
+any number divided by infinity yields zero. Your neighbour could tell you about how he spent a thousand years
+exploring Earth, eating bugs and trying different methods to kill himself, and you could tell him
+he literally spent 0% of his life doing all that, same as you, who just stood there.</p>
+
+  <p><img src="/img/division-by-infinity.jpg" alt="any fucking number / infinity = 0" /></p>
+</blockquote>
+
+<p>Now I don’t understand much of that, but I had enough time, and nothing else to do, to repeat this to myself
+since he told me that until now.</p>
+
+<p>Here, in this world, we can’t suicide, if that was an option, we know well that we would go extinct
+soon after finding out the fact that we are immortals, we really don’t like this numb life.</p>
+
+<hr />
+
+<p><em>Pooof</em></p>
+
+<p>Alright I’m back. You see, we need death, we really do, without death our lives
+would be meaningless, we would have no purpose. Okay we would probably still <a href="https://www.youtube.com/watch?v=HxTnqKuNygE">contribute to increase of entropy of the universe</a>, but that’s not what we <em>want</em> to be here for, we want a higher purpose in life, and it’s death that gifts us this
+higher purpose.</p>
+
+<p>When I was a kid, I was told that in order to stay alive after death, you have to submit your name on this planet, and 
+in this universe if possible. I know, that might sound ridiculous, but aren’t we all fighting for the same thing, but in our own
+ways? Maybe you just want to be remembered between a specific group of people (and that’s perfectly fine) or you might
+actually want to become a global role model, like Gandhi, Albert Einstein and people alike, it doesn’t matter, what matters is,
+we all want to be remembered for what we’ve done in our way to the end.</p>
+
+<p>Immortals go extinct, but mortals find a mission to accomplish before the
+deadline. Be grateful for this gift of death.</p>
+
+<!--It's not all about being famous, it's about being role model for a lot of people, there are lots of famous people and celebrities-->
+<!--that will be forgotten after a decade or two, but some people are remembered forever, either for doing very good or very bad to others,-->
+<!--I don't think Albert Einstein, Gandhi and Hitler will be forgotten in the near future (near as in thousand years).-->
+<!--They are global role models, we want to be like some of them and avoid being like others (okay, maybe not absolutely global, but you get it).-->
+
+  </article>
+
+  <div class="share-page">
+    Share in
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+    <div class="page-content">
+      <div class="wrapper">
+        <h1 class="page-heading"></h1>
+        
+          <div class="home">
+
+  <ul class="post-list">
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <a class="post-link" href="/rust-box-str-vs-string/"><p>What is <code class="language-plaintext highlighter-rouge">Box&lt;str&gt;</code> and how is it different from <code class="language-plaintext highlighter-rouge">String</code> in Rust?</p>
+</a>
+
+          <p class="post-meta">
+            <span>Jun 16, 2022</span>
+            
+            • <span>Reading time: 13  minutes</span>
+          </p>
+        </h2>
+        <article class='post-content'>
+          <p>Today I and a friend went down a rabbit hole about Rust and how it manages the heap when we use <code class="language-plaintext highlighter-rouge">Box</code>, or <code class="language-plaintext highlighter-rouge">String</code>, or <code class="language-plaintext highlighter-rouge">Vec</code>, and while we were at it, I found out there is such a thing as <code class="language-plaintext highlighter-rouge">Box&lt;str&gt;</code>, which might look a bit <em>strange</em> to an untrained eye, since most of the time the <code class="language-plaintext highlighter-rouge">str</code> primitive type is passed around as <code class="language-plaintext highlighter-rouge">&amp;str</code>.</p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <a class="post-link" href="/alternative-objectivity-and-inherent-subjectivity/"><p>On Inherent Subjectivity of Some Things</p>
+</a>
+
+          <p class="post-meta">
+            <span>Oct 30, 2021</span>
+            
+            • <span>Reading time: 8  minutes</span>
+          </p>
+        </h2>
+        <article class='post-content'>
+          <p>As a computer scientist and someone who loves <a href="/mathematical-induction-proving-tiling-methods">mathematics</a> and <a href="/typoclassopedia-exercise-solutions">abstractions</a>, I was obsessed with the idea of rationality, that is, an <em>objective</em> and absolute rationality, however I ended up in a philosophy course that showed me the opposite.</p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <a class="post-link" href="/sanctions-discrimination-isolation-iran"><p>Iran Sanctions: A Story of Discrimination and Isolation</p>
+</a>
+
+          <p class="post-meta">
+            <span>Jul 27, 2019</span>
+            
+            • <span>Reading time: 17  minutes</span>
+          </p>
+        </h2>
+        <article class='post-content'>
+          <p>Let me take you through a story on what it feels like to be isolated from the world, not by choice, but rather, by force. This is a story of discrimination, of monopoly, of people shrugging to these issues and of utterances that affect lives of millions.</p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <a class="post-link" href="/self-hosted/"><p>Going Self-Hosted: Moving away from Google and others</p>
+</a>
+
+          <p class="post-meta">
+            <span>Feb 11, 2019</span>
+            
+            • <span>Reading time: 6  minutes</span>
+          </p>
+        </h2>
+        <article class='post-content'>
+          <p>Since 3 years ago, I have always been eager to move away from Google and other privacy-invading companies. I have had my successes and failures in doing so, here I’m going to put out my stack of tools for moving away from Google and going self-hosted.</p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <a class="post-link" href="/mathematical-induction-proving-tiling-methods/"><p>Mathematical Induction for proving tiling methods</p>
+</a>
+
+          <p class="post-meta">
+            <span>Oct 19, 2017</span>
+            
+            • <span>Reading time: 9  minutes</span>
+          </p>
+        </h2>
+        <article class='post-content'>
+          <p>On my way towards self-taught data science, I’ve stumbled upon the need to be proficient with mathematical proofs, so I picked up the amazing <a href="https://www.amazon.com/How-Prove-It-Structured-Approach/dp/0521675995">How To Prove It: A Structured Approach</a> by Daniel J. Velleman; and I’ve been fascinated by mathematical proofs since then.</p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <a class="post-link" href="/typoclassopedia-exercise-solutions/"><p>Typoclassopedia: Exercise solutions</p>
+</a>
+
+          <p class="post-meta">
+            <span>Sep 27, 2017</span>
+            
+            • <span>Reading time: 55  minutes</span>
+          </p>
+        </h2>
+        <article class='post-content'>
+          <p>I wanted to get proficient in Haskell so I decided to follow <a href="http://www.stephendiehl.com/posts/essential_haskell.html">An [Essential] Haskell Reading List</a>. There I stumbled upon <a href="https://wiki.haskell.org/Typeclassopedia">Typoclassopedia</a>, while the material is great, I couldn’t find solutions for the exercises to check against, so I decided I would write my own and hopefully the solutions would get fixed in case I have gone wrong by others. So if you think a solution is wrong, let me know in the comments!</p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <a class="post-link" href="/diy-cardboard-kindle-stand/"><p>DIY Cardboard Kindle Stand (for bed)</p>
+</a>
+
+          <p class="post-meta">
+            <span>Sep 24, 2017</span>
+            
+            • <span>Reading time: 1  minute</span>
+          </p>
+        </h2>
+        <article class='post-content'>
+          <p><img src="/img/kindle-stand/1.jpg" alt="a view of the stand + kindle" /></p>
+
+<p>I’ve had a Kindle for more than a year now, but I’ve only recently started to read books on it frequently, I used to read paperworks before that, and I still do sometimes prefer paperbooks if available. Anyways, my Kindle has helped me to fall asleep without struggling with all my thoughts, all I have to do is read until I fall asleep, so in a way, it has also been a remedy for my insomnia.</p>
+
+<p>Now to read the Kindle in bed, you would have to hold it using your hands or buy a stand or make one, motivated by <a href="https://blog.xkcd.com/2009/04/13/the-pursuit-of-laziness/">The Pursuit of Laziness</a> I set to create mine, but I didn’t use a piece of steel, instead I used a single box of cardboard I had in home to create one in minutes. :D</p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <a class="post-link" href="/travis-ci-pr-push/"><p>Difference between Travis CI tests: PR and Push</p>
+</a>
+
+          <p class="post-meta">
+            <span>Sep 9, 2017</span>
+            
+            • <span>Reading time: 1  minute</span>
+          </p>
+        </h2>
+        <article class='post-content'>
+          <p>I just want to leave this here as I often tend to look it up myself and the first time it was not as easy to figure out.</p>
+
+<p>When using Travis CI along with GitHub (or other git integrations), Travis runs two tests: <code>pr</code> and <code>push</code>.</p>
+
+<p><img src="/img/travis-ci-pr-push-github.jpg" alt="travis-pr-push-github" /></p>
+
+<p>Most of the time you see both tests passing and you do not have to even wonder how they are different, but it has
+happened to me that one of the tests fails while the other passes and I started to wonder why.</p>
+
+<h3 id="pr">pr</h3>
+<p>The <code>pr</code> test is a test run on the result of a merge between the pull-request branch and the main branch.
+As an example, let’s say your pull-request’s branch is called <code>fix-user-auth</code> and your main branch is <code>master</code>, 
+in this case, <code>pr</code> merges <code>fix-user-auth</code> into <code>master</code> and then runs the tests on the result of the merge.</p>
+
+<h3 id="push">push</h3>
+<p>On the other hand, <code>push</code> is run on the pull-request branch itself, without merging. So in our example above, Travis would checkout to <code>fix-user-auth</code> and run the tests.</p>
+
+<h3 id="a-case-of-difference">A case of difference</h3>
+
+<p>A case in which this difference might be more apparent is when your pull-request is based on a branch other than <code>master</code>, and some changes that your pull-request depends on are missing from <code>master</code>, in this case the <code>push</code> test may pass, but the <code>pr</code> test will fail.</p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <a class="post-link" href="/primitive-living-lessons-0/"><p>Primitive Living Lessons Learned, Episode 0</p>
+</a>
+
+          <p class="post-meta">
+            <span>Sep 7, 2017</span>
+            
+            • <span>Reading time: 11  minutes</span>
+          </p>
+        </h2>
+        <article class='post-content'>
+          <p><img src="/img/primitive-living-0.jpg" alt="general view of the forest" /></p>
+
+<p>So I just went on my first primitive living practice trip in the woods, alone, with only a pocket knife.</p>
+
+<p>I decided I’m going to share the lessons I’ve learned in each trip as they are certainly going to be useful if you want to practice primitive living, I would find these useful if I could find them anywhere. I spend a lot of time reading and watching primitive living guides and experience reports, but they are never exhaustive, and this series is not meant to be exhaustive either.</p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <a class="post-link" href="/dont-chase-become-the-good-one/"><p>Don’t chase: Become the good one</p>
+</a>
+
+          <p class="post-meta">
+            <span>Feb 4, 2017</span>
+            
+            • <span>Reading time: 3  minutes</span>
+          </p>
+        </h2>
+        <article class='post-content'>
+          <p>When it comes to relationships, most (unsuccessful) people are <em>chasing</em> the good ones.
+They spend time trying to find their dream partner, the perfect match, but hey, do you qualify
+as the dream partner of your dream partner? You fantasize about your dream partner, but have you ever
+thought what kind of partner does he/she dream of?</p>
+
+<p><img src="/img/angel.jpg" alt="I want an angel with..." />
+<span class="image-caption">I want an angel with…</span></p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <a class="post-link" href="/stop-high-frequency-fuck-ups/"><p>Stop High-Frequency Fuck-ups</p>
+</a>
+
+          <p class="post-meta">
+            <span>Dec 26, 2016</span>
+            
+            • <span>Reading time: 5  minutes</span>
+          </p>
+        </h2>
+        <article class='post-content'>
+          <p><strong>High-Frequency Fuck-Ups</strong>:</p>
+
+<blockquote>
+  <p>The cyclic process of “pushing yourself hard for a week, getting something done, and then feeling depressed and fucked up
+ for the next week”</p>
+</blockquote>
+
+<p>Sounds familiar? Read on.</p>
+
+<p><img src="/img/productivity-chart.jpg" alt="High-Frequency Fuck-ups" />
+<span class="image-caption">Visual demonstration of High-Frequency Fuck-ups</span></p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <a class="post-link" href="/immortals-go-extinct/"><p>Immortals go extinct</p>
+</a>
+
+          <p class="post-meta">
+            <span>Nov 15, 2016</span>
+            
+            • <span>Reading time: 3  minutes</span>
+          </p>
+        </h2>
+        <article class='post-content'>
+          <p>We are all going to die, we all know that well.<br /><br />
+Now I want to take you to a world of immortals where humans don’t die,
+they live and live and live and… you know, live. From now on, pretend I’m a human
+on this world of immortals, I’m immortal bitches.</p>
+
+<p><img src="/img/immortals.jpg" alt="immortals chatting" />
+<span class="image-caption">There is no campfire because they don’t need it</span></p>
+
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <a class="post-link" href="/open-source-good-bad-ugly/"><p>Open-source: The Good, The Bad and The Ugly</p>
+</a>
+
+          <p class="post-meta">
+            <span>Oct 13, 2015</span>
+            
+            • <span>Reading time: 5  minutes</span>
+          </p>
+        </h2>
+        <article class='post-content'>
+          <p>I have been doing Open-source for a while, I don’t call myself an “expert” or something like that,
+but I’d like to share my opinion and experience on contributing to, and maintaining open-source code.</p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <a class="post-link" href="/autocomplete-predict-trie/"><p>Autocomplete using Tries</p>
+</a>
+
+          <p class="post-meta">
+            <span>Jul 24, 2015</span>
+            
+            • <span>Reading time: 8  minutes</span>
+          </p>
+        </h2>
+        <article class='post-content'>
+          <p>In this article, I’m going over creating an autocompletion/prediction system using a data-structure called Trie, it’s fast and easy to customize.</p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <a class="post-link" href="/es7-array-generator-comprehensions/"><p>ES7 Array and Generator comprehensions</p>
+</a>
+
+          <p class="post-meta">
+            <span>Jun 6, 2015</span>
+            
+            • <span>Reading time: 6  minutes</span>
+          </p>
+        </h2>
+        <article class='post-content'>
+          <p>Array comprehension is a new feature proposed for ES7, with a new syntax
+to create new arrays from existing <a href="http://www.2ality.com/2015/02/es6-iteration.html">iterables</a>,
+comprehensions can replace map and filter.</p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <a class="post-link" href="/broadcastchannel-api/"><p>BroadcastChannel API</p>
+</a>
+
+          <p class="post-meta">
+            <span>Apr 2, 2015</span>
+            
+            • <span>Reading time: 4  minutes</span>
+          </p>
+        </h2>
+        <article class='post-content'>
+          <p><a href="https://developer.mozilla.org/en-US/docs/Web/API/Broadcast_Channel_API">BroadcastChannel API</a>
+is a new API used to communicate between same-origin tabs opened by the same user.</p>
+
+        </article>
+      </li>
+    
+      
+      <li class='lang-en'>
+        <h2>
+          <a class="post-link" href="/css-filters/"><p>CSS Filters are awesome!</p>
+</a>
+
+          <p class="post-meta">
+            <span>Mar 28, 2015</span>
+            
+            • <span>Reading time: 6  minutes</span>
+          </p>
+        </h2>
+        <article class='post-content'>
+          <p>I’ve been working on the <a href="https://bugzilla.mozilla.org/show_bug.cgi?id=1055181">CSS Filter Editor widget</a> in Firefox Developer Tools for a couple of weeks, thanks to <a href="https://medium.com/@patrickbrosset">Patrick Brosset</a> for mentoring me and <a href="https://github.com/nt1m">Tim Nguyen</a> for his great contributions.</p>
+
+        </article>
+      </li>
+    
+  </ul>
+
+  <p class="rss-subscribe">subscribe <a href="/feed.xml">via rss</a></p>
+
+</div>
+
+        
+      </div>
+    </div>
+
+  </body>
+
+</html>
diff --git a/site/js/auto-render.min.js b/site/js/auto-render.min.js
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diff --git a/site/js/heading-links.js b/site/js/heading-links.js
new file mode 100644
index 0000000..2149fcd
--- /dev/null
+++ b/site/js/heading-links.js
@@ -0,0 +1,12 @@
+(function() {
+  var els = document.querySelectorAll('.post-content [id]');
+  var headings = Array.prototype.slice.call(els);
+
+  headings.forEach(function(head) {
+    var link = document.createElement('a');
+    link.className = 'heading-link';
+    link.href = '#' + head.id;
+
+    head.appendChild(link);
+  });
+}());
diff --git a/site/js/katex.min.js b/site/js/katex.min.js
new file mode 100644
index 0000000..a7aba03
--- /dev/null
+++ b/site/js/katex.min.js
@@ -0,0 +1,6 @@
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+  <meta name="viewport" content="width=device-width, initial-scale=1">
+
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+    <!--</p>-->
+    <p>
+      <a href='mailto:mdibaiee@pm.me'>email</a>
+      <a href='https://git.mahdi.blog/mahdi'>git</a>
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+      <a href="http://localhost:4000/feed.xml">feed</a>
+    </p>
+  </nav>
+
+</header>
+
+
+    <div class="page-content">
+      <div class="wrapper">
+        <h1 class="page-heading"></h1>
+        
+          <div class="category">
+  <ul class="post-list">
+    
+      <li>
+        <h2>
+          <a class="post-link" href="/self-hosted/">Going Self-Hosted: Moving away from Google and others</a>
+          <span class="post-meta">Feb 11, 2019</span>
+        </h2>
+        <article class='post-content'>
+          <p>Since 3 years ago, I have always been eager to move away from Google and other privacy-invading companies. I have had my successes and failures in doing so, here I’m going to put out my stack of tools for moving away from Google and going self-hosted.</p>
+
+
+        </article>
+      </li>
+    
+      <li>
+        <h2>
+          <a class="post-link" href="/diy-cardboard-kindle-stand/">DIY Cardboard Kindle Stand (for bed)</a>
+          <span class="post-meta">Sep 24, 2017</span>
+        </h2>
+        <article class='post-content'>
+          <p><img src="/img/kindle-stand/1.jpg" alt="a view of the stand + kindle" /></p>
+
+<p>I’ve had a Kindle for more than a year now, but I’ve only recently started to read books on it frequently, I used to read paperworks before that, and I still do sometimes prefer paperbooks if available. Anyways, my Kindle has helped me to fall asleep without struggling with all my thoughts, all I have to do is read until I fall asleep, so in a way, it has also been a remedy for my insomnia.</p>
+
+<p>Now to read the Kindle in bed, you would have to hold it using your hands or buy a stand or make one, motivated by <a href="https://blog.xkcd.com/2009/04/13/the-pursuit-of-laziness/">The Pursuit of Laziness</a> I set to create mine, but I didn’t use a piece of steel, instead I used a single box of cardboard I had in home to create one in minutes. :D</p>
+
+
+        </article>
+      </li>
+    
+      <li>
+        <h2>
+          <a class="post-link" href="/primitive-living-lessons-0/">Primitive Living Lessons Learned, Episode 0</a>
+          <span class="post-meta">Sep 7, 2017</span>
+        </h2>
+        <article class='post-content'>
+          <p><img src="/img/primitive-living-0.jpg" alt="general view of the forest" /></p>
+
+<p>So I just went on my first primitive living practice trip in the woods, alone, with only a pocket knife.</p>
+
+<p>I decided I’m going to share the lessons I’ve learned in each trip as they are certainly going to be useful if you want to practice primitive living, I would find these useful if I could find them anywhere. I spend a lot of time reading and watching primitive living guides and experience reports, but they are never exhaustive, and this series is not meant to be exhaustive either.</p>
+
+
+        </article>
+      </li>
+    
+      <li>
+        <h2>
+          <a class="post-link" href="/dont-chase-become-the-good-one/">Don't chase: Become the good one</a>
+          <span class="post-meta">Feb 4, 2017</span>
+        </h2>
+        <article class='post-content'>
+          <p>When it comes to relationships, most (unsuccessful) people are <em>chasing</em> the good ones.
+They spend time trying to find their dream partner, the perfect match, but hey, do you qualify
+as the dream partner of your dream partner? You fantasize about your dream partner, but have you ever
+thought what kind of partner does he/she dream of?</p>
+
+<p><img src="/img/angel.jpg" alt="I want an angel with..." />
+<span class="image-caption">I want an angel with…</span></p>
+
+
+        </article>
+      </li>
+    
+      <li>
+        <h2>
+          <a class="post-link" href="/stop-high-frequency-fuck-ups/">Stop High-Frequency Fuck-ups</a>
+          <span class="post-meta">Dec 26, 2016</span>
+        </h2>
+        <article class='post-content'>
+          <p><strong>High-Frequency Fuck-Ups</strong>:</p>
+
+<blockquote>
+  <p>The cyclic process of “pushing yourself hard for a week, getting something done, and then feeling depressed and fucked up
+ for the next week”</p>
+</blockquote>
+
+<p>Sounds familiar? Read on.</p>
+
+<p><img src="/img/productivity-chart.jpg" alt="High-Frequency Fuck-ups" />
+<span class="image-caption">Visual demonstration of High-Frequency Fuck-ups</span></p>
+
+
+        </article>
+      </li>
+    
+      <li>
+        <h2>
+          <a class="post-link" href="/immortals-go-extinct/">Immortals go extinct</a>
+          <span class="post-meta">Nov 15, 2016</span>
+        </h2>
+        <article class='post-content'>
+          <p>We are all going to die, we all know that well.<br /><br />
+Now I want to take you to a world of immortals where humans don’t die,
+they live and live and live and… you know, live. From now on, pretend I’m a human
+on this world of immortals, I’m immortal bitches.</p>
+
+<p><img src="/img/immortals.jpg" alt="immortals chatting" />
+<span class="image-caption">There is no campfire because they don’t need it</span></p>
+
+
+        </article>
+      </li>
+    
+  </ul>
+
+  <p class="rss-subscribe">subscribe <a href="/feed.xml">via rss</a></p>
+</div>
+
+        
+      </div>
+    </div>
+
+  </body>
+
+</html>
diff --git a/site/math/index.html b/site/math/index.html
new file mode 100644
index 0000000..1e1e7a4
--- /dev/null
+++ b/site/math/index.html
@@ -0,0 +1,107 @@
+<!DOCTYPE html>
+<html>
+
+  <head>
+  <meta charset="utf-8">
+  <meta http-equiv="X-UA-Compatible" content="IE=edge">
+  <meta name="viewport" content="width=device-width, initial-scale=1">
+
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+  <meta name="description" content="a rabbit hole">
+
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+  <link rel="stylesheet" href="/css/main.css">
+  <link rel="canonical" href="http://localhost:4000/math/">
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+
+  
+
+  <!--<script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script>-->
+
+  <script>
+    var channel = new BroadcastChannel('egg');
+
+    channel.addEventListener('message', message => {
+      alert('Got a message from the other tab:\n' + message.data);
+    });
+  </script>
+</head>
+
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+
+  <body>
+
+    <header class="site-header">
+
+  <h1>
+    <a class='site-title' href='/'>
+      mahdi
+    </a>
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+
+  <nav>
+    <p>
+      <a href="/snippets">snippets</a>
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+    <!--</p>-->
+    <p>
+      <a href='mailto:mdibaiee@pm.me'>email</a>
+      <a href='https://git.mahdi.blog/mahdi'>git</a>
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+      <a href="http://localhost:4000/feed.xml">feed</a>
+    </p>
+  </nav>
+
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+
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+    <div class="page-content">
+      <div class="wrapper">
+        <h1 class="page-heading"></h1>
+        
+          <div class="category">
+  <ul class="post-list">
+    
+      <li>
+        <h2>
+          <a class="post-link" href="/mathematical-induction-proving-tiling-methods/">Mathematical Induction for proving tiling methods</a>
+          <span class="post-meta">Oct 19, 2017</span>
+        </h2>
+        <article class='post-content'>
+          <p>On my way towards self-taught data science, I’ve stumbled upon the need to be proficient with mathematical proofs, so I picked up the amazing <a href="https://www.amazon.com/How-Prove-It-Structured-Approach/dp/0521675995">How To Prove It: A Structured Approach</a> by Daniel J. Velleman; and I’ve been fascinated by mathematical proofs since then.</p>
+
+        </article>
+      </li>
+    
+      <li>
+        <h2>
+          <a class="post-link" href="/typoclassopedia-exercise-solutions/">Typoclassopedia: Exercise solutions</a>
+          <span class="post-meta">Sep 27, 2017</span>
+        </h2>
+        <article class='post-content'>
+          <p>I wanted to get proficient in Haskell so I decided to follow <a href="http://www.stephendiehl.com/posts/essential_haskell.html">An [Essential] Haskell Reading List</a>. There I stumbled upon <a href="https://wiki.haskell.org/Typeclassopedia">Typoclassopedia</a>, while the material is great, I couldn’t find solutions for the exercises to check against, so I decided I would write my own and hopefully the solutions would get fixed in case I have gone wrong by others. So if you think a solution is wrong, let me know in the comments!</p>
+
+        </article>
+      </li>
+    
+  </ul>
+
+  <p class="rss-subscribe">subscribe <a href="/feed.xml">via rss</a></p>
+</div>
+
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diff --git a/site/mathematical-induction-proving-tiling-methods/index.html b/site/mathematical-induction-proving-tiling-methods/index.html
new file mode 100644
index 0000000..6e8aad6
--- /dev/null
+++ b/site/mathematical-induction-proving-tiling-methods/index.html
@@ -0,0 +1,487 @@
+<!DOCTYPE html>
+<html>
+
+  <head>
+  <meta charset="utf-8">
+  <meta http-equiv="X-UA-Compatible" content="IE=edge">
+  <meta name="viewport" content="width=device-width, initial-scale=1">
+
+  <title>Mathematical Induction for proving tiling methods</title>
+  <meta name="description" content="On my way towards self-taught data science, I’ve stumbled upon the need to be proficient with mathematical proofs, so I picked up the amazing How To Prove It...">
+
+  <link href="https://fonts.googleapis.com/css?family=Secular+One|Nunito|Mononoki" rel="stylesheet"> 
+  <link rel="stylesheet" href="/css/main.css">
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+    <script src='/js/auto-render.min.js'></script>
+
+    <script>
+      document.addEventListener("DOMContentLoaded", function() {
+        renderMathInElement(document.body, {
+          delimiters: [
+            {left: "$$", right: "$$", display: true},
+            {left: "\\[", right: "\\]", display: true},
+            {left: "\\(", right: "\\)", display: false},
+            {left: "$", right: "$", display: false},
+          ],
+        });
+      });
+    </script>
+  
+
+  <!--<script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script>-->
+
+  <script>
+    var channel = new BroadcastChannel('egg');
+
+    channel.addEventListener('message', message => {
+      alert('Got a message from the other tab:\n' + message.data);
+    });
+  </script>
+</head>
+
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+
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+
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+      <a href='mailto:mdibaiee@pm.me'>email</a>
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+      <a href="http://localhost:4000/feed.xml">feed</a>
+    </p>
+  </nav>
+
+</header>
+
+
+    <div class="page-content">
+      <div class="wrapper">
+        <h1 class="page-heading"></h1>
+        
+          <div class='post lang-en'>
+
+  <div class="post-header">
+    <h1 class="post-title"><p>Mathematical Induction for proving tiling methods</p>
+</h1>
+    
+    <p class="post-meta">
+      <span>Oct 19, 2017</span>
+      
+      • <span>Reading time: 9  minutes</span>
+    </p>
+  </div>
+
+  <article class="post-content">
+    <p>On my way towards self-taught data science, I’ve stumbled upon the need to be proficient with mathematical proofs, so I picked up the amazing <a href="https://www.amazon.com/How-Prove-It-Structured-Approach/dp/0521675995">How To Prove It: A Structured Approach</a> by Daniel J. Velleman; and I’ve been fascinated by mathematical proofs since then.</p>
+
+<p>One of the uses for <a href="https://en.wikipedia.org/wiki/Mathematical_induction">Mathematical Induction</a> which I’ve found to be pretty cool is proving methods for tiling shapes.</p>
+
+<p>Here is an example:</p>
+
+<p>Suppose $n$ is a positive integer. An equilateral triangle is cut into $4^n$ congruent equilateral triangles, and one corner is removed. Show that the remaining area can be covered by trapezoidal tiles like this: <img src="/img/tiling/trapezoidal.jpg" class="inline" width="30" /></p>
+
+<canvas id="tiling-triangle" width="200" height="200" class="centered"></canvas>
+<p><span class="image-caption">An example of n = 2. The dark tile is removed.</span></p>
+
+<p>Just to be clear, by <em>cover</em> we mean covering without any overlaps, so you can’t have two overlapping trapezoidal tiles.</p>
+
+<p>As with any mathematical induction solution, we start with the base case, which is $n = 1$, in that case the triangle looks like this:</p>
+
+<canvas id="base-case" width="100" height="100" class="centered"></canvas>
+
+<p>In this case, it’s obvious that we can cover the leftover area using trapezoidal tiles consisting of three equilateral triangles (the second row), so:</p>
+
+<hr />
+
+<p>Base case: $n = 1$ then the triangle has $4^1 = 4$ tiles, and by removing the top-most tile, the second row can be covered using a single trapezoidal tile.</p>
+
+<hr />
+
+<p>Now for the induction step, we have to somehow show that after adding 1 to $n$, that is, by multiplying the tiles by $4$, we can still cover the triangle by trapezoidal tiles. To show this, we start by assuming we have a triangle with $4^n$ tiles, which we know can be covered by trapezoidal tiles, then we add the new tiles and show that they, too, can be covered by trapezoidal tiles.</p>
+
+<hr />
+
+<p>Induction Step: Suppose we have a triangle split into $4^n$ tiles, and we know by induction hypothesis that it can be covered by trapezoidal tiles.</p>
+
+<p>Now suppose we have another triangle with $4^{n+1}$ tiles, that means, $4$ times as many triangles as our original triangle. We can then group the new bigger triangle into 4 congruent triangles, one of which we know can be split into trapezoidal tiles by removing one of it’s tiles.</p>
+
+<p>For the three left triangles, we can find a neighbouring corner and assume the tile on that corner to be removed, and then cover the rest by trapezoidal tiles. Afterwards, since we had three such corners, and they are neighbouring corners, we can cover these three corners with one trapezoidal tile, thus completing the triangle.</p>
+
+<hr />
+
+<p>Now that’s a mouthful, in simpler terms, we are following these steps (for $n = 2$):</p>
+
+<canvas id="n-2" width="200" height="200" class="centered"></canvas>
+
+<p>First, we split the whole triangle into 4 smaller groups:</p>
+
+<canvas id="n-2-grouped" width="200" height="200" class="centered"></canvas>
+
+<p>Then, we know that one of the triangles can be covered by trapezoidal tiles if we remove one of it’s tiles, that’s the induction hypothesis (the case for $4^n$ which is proved in the base case):</p>
+
+<canvas id="n-2-grouped-removed" width="200" height="200" class="centered"></canvas>
+
+<p>Leaving the top triangle behind, we now find neighbouring corners among the three left triangles, and we assume the tiles in those corners to be removed (they are not actually removed as we are constrained to remove only one tile):</p>
+
+<canvas id="n-2-grouped-neighbours" width="200" height="200" class="centered"></canvas>
+
+<p>Now we can cover the rest of these triangles by a single trapezoidal tile, similar to the case of $n = 1$.</p>
+
+<p>Afterwards, we see that the three neighbouring tiles form a trapezoidal tile, therefore we can now put the last piece there to complete the tiles.</p>
+
+<canvas id="final" width="200" height="200" class="centered"></canvas>
+
+<p>This procedure can be applied recursively on larger values of $n$ as well, so this concludes a proof of tiling an equilateral triangle divided into $4^n$ equilateral triangles using trapezoidal tiles after removing a single piece.</p>
+
+<script>
+  (function() {
+    var tilingTriangle = document.getElementById('tiling-triangle');
+    var c = tilingTriangle.getContext('2d');
+    
+    function TriangleCanvas(id) {
+      this.element = document.getElementById(id);
+      this.context = this.element.getContext('2d');
+    }
+
+    function modifyColor(c, p) {
+      var e = document.createElement('i');
+      e.style.background = c;
+      var r = getComputedStyle(e).backgroundColor.slice(4, -1).split(',').map(parseFloat);
+      return 'rgb(' + [r[0] + p, r[1] + p, r[2] + p].join(',') + ')';
+    }
+
+    function dedup(list) {
+      return list.reduce(function(newList, item) {
+        if (!newList.some(function(a) { return deepCompare(a, item) })) {
+          return newList.concat(item);
+        }
+        return newList;
+      }, []);
+    }
+
+    function deepCompare () {
+      var i, l, leftChain, rightChain;
+
+      function compare2Objects (x, y) {
+        var p;
+
+        // remember that NaN === NaN returns false
+        // and isNaN(undefined) returns true
+        if (isNaN(x) && isNaN(y) && typeof x === 'number' && typeof y === 'number') {
+            return true;
+        }
+
+        // Compare primitives and functions.     
+        // Check if both arguments link to the same object.
+        // Especially useful on the step where we compare prototypes
+        if (x === y) {
+            return true;
+        }
+
+        // Works in case when functions are created in constructor.
+        // Comparing dates is a common scenario. Another built-ins?
+        // We can even handle functions passed across iframes
+        if ((typeof x === 'function' && typeof y === 'function') ||
+          (x instanceof Date && y instanceof Date) ||
+          (x instanceof RegExp && y instanceof RegExp) ||
+          (x instanceof String && y instanceof String) ||
+          (x instanceof Number && y instanceof Number)) {
+            return x.toString() === y.toString();
+        }
+
+        // At last checking prototypes as good as we can
+        if (!(x instanceof Object && y instanceof Object)) {
+            return false;
+        }
+
+        if (x.isPrototypeOf(y) || y.isPrototypeOf(x)) {
+            return false;
+        }
+
+        if (x.constructor !== y.constructor) {
+            return false;
+        }
+
+        if (x.prototype !== y.prototype) {
+            return false;
+        }
+
+        // Check for infinitive linking loops
+        if (leftChain.indexOf(x) > -1 || rightChain.indexOf(y) > -1) {
+            return false;
+        }
+
+        // Quick checking of one object being a subset of another.
+        // todo: cache the structure of arguments[0] for performance
+        for (p in y) {
+            if (y.hasOwnProperty(p) !== x.hasOwnProperty(p)) {
+                return false;
+            }
+            else if (typeof y[p] !== typeof x[p]) {
+                return false;
+            }
+        }
+
+        for (p in x) {
+            if (y.hasOwnProperty(p) !== x.hasOwnProperty(p)) {
+                return false;
+            }
+            else if (typeof y[p] !== typeof x[p]) {
+                return false;
+            }
+
+            switch (typeof (x[p])) {
+                case 'object':
+                case 'function':
+
+                    leftChain.push(x);
+                    rightChain.push(y);
+
+                    if (!compare2Objects (x[p], y[p])) {
+                        return false;
+                    }
+
+                    leftChain.pop();
+                    rightChain.pop();
+                    break;
+
+                default:
+                    if (x[p] !== y[p]) {
+                        return false;
+                    }
+                    break;
+            }
+        }
+
+        return true;
+      }
+
+      if (arguments.length < 1) {
+        return true; //Die silently? Don't know how to handle such case, please help...
+        // throw "Need two or more arguments to compare";
+      }
+
+      for (i = 1, l = arguments.length; i < l; i++) {
+
+          leftChain = []; //Todo: this can be cached
+          rightChain = [];
+
+          if (!compare2Objects(arguments[0], arguments[i])) {
+              return false;
+          }
+      }
+
+      return true;
+    }
+
+    TriangleCanvas.prototype.drawTriangle = function(x, y, size, fill, reversed) {
+      var c = this.context;
+      var corners = [{
+        x: x,
+        y: y,
+      }, {
+        x: x - size / 2,
+        y: y + size,
+      }, {
+        x: x + size / 2,
+        y: y + size,
+      }];
+
+      if (reversed) {
+        corners = [{
+          x: x + size / 2,
+          y: y,
+        }, {
+          x: x - size / 2,
+          y: y,
+        }, {
+          x: x,
+          y: y + size
+        }];
+      }
+
+      if (fill) {
+        this.drawShape(corners, modifyColor(fill, 20), fill);
+      } else {
+        this.drawShape(corners);
+      }
+    }
+
+    TriangleCanvas.prototype.drawTrapezoid = function(tiles, size, strokeStyle, fillStyle) {
+      var corners = tiles
+                    .map(function(o) {
+                      return { x: o[0] * size, y: o[1] * size };
+                    });
+
+      console.log(corners);
+
+      this.drawShape(corners, strokeStyle, fillStyle);
+    }
+
+    TriangleCanvas.prototype.drawShape = function(corners, strokeStyle, fillStyle) {
+      var c = this.context;
+      c.beginPath();
+
+      c.moveTo(corners[0].x, corners[0].y);
+      corners.slice(1).concat([corners[0]]).forEach(function(object, index) {
+        c.lineTo(object.x, object.y);
+      }); 
+
+      c.closePath();
+      if (fillStyle) {
+        c.fillStyle = fillStyle;
+        c.fill();
+      }
+      if (strokeStyle) c.strokeStyle = strokeStyle;
+      c.stroke();
+    }
+
+    TriangleCanvas.prototype.drawSplittedTriangle = function(x, y, size, split, blocks, rest) {
+      var c = this.context;
+
+      var rows = Math.sqrt(split);
+      var rowHeight = size / rows;
+      var triangleSize = size / rows;
+
+      for (var i = 0; i < rows * 2; i += 2) {
+        var row = Math.floor(i / 2);
+
+        for (var j = 0; j < i + 1; j++) {
+          var position = {
+            x: x + triangleSize * j / 2 - (row * triangleSize / 2),
+            y: y + row * rowHeight,
+          };
+
+          var block = blocks.reduce(function(c, a) {
+            return (a[0] === row && a[1] === j) ? (a[2] || 'black') : c;
+          }, null);
+
+          this.drawTriangle(position.x, position.y, triangleSize, block || rest, j % 2 == 1);
+        }
+      }
+    }
+    
+    var c1 = new TriangleCanvas('tiling-triangle');
+    c1.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), [[0, 0, '#435062']], '#92afd7');
+
+    var c2 = new TriangleCanvas('base-case');
+    c2.drawSplittedTriangle(50, 0, 100, 4, [[0, 0, '#435062']], '#92afd7');
+
+    var c3 = new TriangleCanvas('n-2');
+    c3.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), [[0, 0, '#435062']], '#92afd7');
+
+    var c4 = new TriangleCanvas('n-2-grouped');
+    var groups = [
+      [0, 0, '#809bce'], [1, 0, '#809bce'], [1, 1, '#809bce'], [1, 2, '#809bce'], 
+      [2, 0, '#95b8d1'], [3, 0, '#95b8d1'], [3, 1, '#95b8d1'], [3, 2, '#95b8d1'], 
+      [2, 1, '#b8e0d2'], [2, 2, '#b8e0d2'], [2, 3, '#b8e0d2'], [3, 3, '#b8e0d2'], 
+      [2, 4, '#d6eadf'], [3, 4, '#d6eadf'], [3, 5, '#d6eadf'], [3, 6, '#d6eadf'], 
+    ];
+    c4.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
+
+    var c5 = new TriangleCanvas('n-2-grouped-removed');
+    var groups = [
+      [0, 0, 'rgb(90, 90, 90)'], [1, 0, '#809bce'], [1, 1, '#809bce'], [1, 2, '#809bce'], 
+      [2, 0, '#95b8d1'], [3, 0, '#95b8d1'], [3, 1, '#95b8d1'], [3, 2, '#95b8d1'], 
+      [2, 1, '#b8e0d2'], [2, 2, '#b8e0d2'], [2, 3, '#b8e0d2'], [3, 3, '#b8e0d2'], 
+      [2, 4, '#d6eadf'], [3, 4, '#d6eadf'], [3, 5, '#d6eadf'], [3, 6, '#d6eadf'], 
+    ];
+    c5.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
+    c5.context.strokeStyle = '#ff7777';
+    c5.context.lineWidth = 3;
+    c5.drawTriangle(100, 0, 100);
+
+    var c6 = new TriangleCanvas('n-2-grouped-neighbours');
+    var groups = [
+      [0, 0, '#e7ecf6'], [1, 0, '#e7ecf6'], [1, 1, '#e7ecf6'], [1, 2, '#e7ecf6'], 
+      [2, 0, '#95b8d1'], [3, 0, '#95b8d1'], [3, 1, '#95b8d1'], [3, 2, '#6d8699'], 
+      [2, 1, '#b8e0d2'], [2, 2, '#b8e0d2'], [2, 3, '#b8e0d2'], [3, 3, '#657b73'], 
+      [2, 4, '#d6eadf'], [3, 4, '#89958e'], [3, 5, '#d6eadf'], [3, 6, '#d6eadf'], 
+    ];
+    c6.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
+    
+    var trapezoids = [
+      [[1, 2], [3, 2], [2.5, 3], [1.5, 3]],
+      [[1, 2], [1.5, 3], [1, 4], [0, 4]],
+      [[3, 2], [4, 4], [3, 4], [2.5, 3]],
+    ];
+    c6.drawTrapezoid(trapezoids[0], 200 / 4, '#ff7777');
+    c6.drawTrapezoid(trapezoids[1], 200 / 4, '#ff7777');
+    c6.drawTrapezoid(trapezoids[2], 200 / 4, '#ff7777');
+
+    var c7 = new TriangleCanvas('final');
+    var groups = [
+      [0, 0, '#435062'], [1, 0, '#92afd7'], [1, 1, '#92afd7'], [1, 2, '#92afd7'], 
+      [2, 0, '#95b8d1'], [3, 0, '#95b8d1'], [3, 1, '#95b8d1'], [3, 2, '#95b8d1'], 
+      [2, 1, '#b8e0d2'], [2, 2, '#b8e0d2'], [2, 3, '#b8e0d2'], [3, 3, '#b8e0d2'], 
+      [2, 4, '#d6eadf'], [3, 4, '#d6eadf'], [3, 5, '#d6eadf'], [3, 6, '#d6eadf'], 
+    ];
+    c7.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
+    
+    var trapezoids = [
+      [[1.5, 1], [2.5, 1], [3, 2], [1, 2]],
+      [[1, 2], [3, 2], [2.5, 3], [1.5, 3]],
+      [[1, 2], [1.5, 3], [1, 4], [0, 4]],
+      [[3, 2], [4, 4], [3, 4], [2.5, 3]],
+      [[1.5, 3], [1, 4], [3, 4], [2.5, 3]],
+    ];
+    trapezoids.forEach(function(el) {
+      c7.drawTrapezoid(el, 200 / 4, '#ff7777');
+    });
+  }());
+</script>
+
+
+  </article>
+
+  <div class="share-page">
+    Share in
+
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+  <meta name="description" content="I have been doing Open-source for a while, I don’t call myself an “expert” or something like that,but I’d like to share my opinion and experience on contribu...">
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+      <div class="wrapper">
+        <h1 class="page-heading"></h1>
+        
+          <div class='post lang-en'>
+
+  <div class="post-header">
+    <h1 class="post-title"><p>Open-source: The Good, The Bad and The Ugly</p>
+</h1>
+    
+    <p class="post-meta">
+      <span>Oct 13, 2015</span>
+      
+      • <span>Reading time: 5  minutes</span>
+    </p>
+  </div>
+
+  <article class="post-content">
+    <p>I have been doing Open-source for a while, I don’t call myself an “expert” or something like that,
+but I’d like to share my opinion and experience on contributing to, and maintaining open-source code.</p>
+
+<p>So, I’ve been following and contributing to open-source projects for quite a time,
+and I have had different experiences every time. There are always good and bad experiences
+along a road, it’s never a heaven, never a hell. I’ve had contributions as small as fixing a typo in README, and as big
+as adding a new feature to Firefox Developer Tools or refactoring a whole repository!</p>
+
+<p>Here I’m going to share my experiences and what I’ve learned along the way that you should consider
+if you want to take this road.</p>
+
+<h2 id="the-good">The Good</h2>
+<p>I love open-source, it’s awesome how people share their efforts with others, and others give feedback to
+the maintainer to make the software better. It’s an always-growing system, even if a maintainer stops maintaining,
+it’s possible to <em>fork</em> a repository and continue it, although not as easy, but possible.</p>
+
+<p>The best part of doing open-source, in my opinion, is building connections and learning from others.</p>
+
+<p>Whether you are maintaining or contributing to a project, you are going to learn new things, it just happens.</p>
+
+<p>If you are a maintainer of a repository with a countable amount of users, you are going to constantly learn your mistakes from others,
+finding these mistakes by yourself is really hard, because you can’t easily look at a subject <em>the other way</em>,
+but users have this potential to look at your code with their eyes, seeing mistakes you can’t see.</p>
+
+<p>If you are contributing, following or just exploring projects, you are definitely going to learn, the solutions people suggest to a problem,
+the way they communicate, etc.
+Usually, not always, the maintainer has a better knowledge over the subject of project than you, so you are going to learn from him and other contributors
+by reading their code or exploring the issues and how they’ve been solved. I personally learned a lot this way. I would volunteer to fix a bug, then the maintainer and other contributors would show up to give their suggestions and ideas on the issue, which I would then learn from. I also subscribe to interesting issues that I don’t know how to fix to see how they get solved.</p>
+
+<h2 id="the-bad">The Bad</h2>
+<p>First off, the most annoying thing about open-source contributions is that people (I’m looking at you, maintainers) think
+that contributors are jobless bored people who don’t know how to spend their time and have come to waste some time on some random open-source project, NO, seriously.</p>
+
+<p>I have a job, I totally care about my time and I’m not making a Pull-request because I’m bored.</p>
+
+<p>Now, why is that important to know: it has happened to me a couple of times that I ask on an issue:</p>
+
+<p><em>”- Okay, I’m interested, what <strong>exactly</strong> has to be done?”</em></p>
+
+<p><em>”- Great, please do x, y, z”</em></p>
+
+<p><em>… some time later</em></p>
+
+<p>_”- Here is x, y and z, please review and merge”</p>
+
+<p>_”- Oh, thank you very much, but you know, now that I think of it, I don’t want x, y or even z. Closing.”</p>
+
+<p>and I’m like:</p>
+
+<!-- ![Are you kidding me?](/img/are-you-kidding-me.jpg) -->
+<p><img alt="Are you kidding me?" src="/img/are-you-kidding-me.jpg" /></p>
+
+<p><span class="image-caption">Are you kidding me?</span></p>
+
+<p>This is the worst thing that can happen to you, try to avoid it, you don’t want your valuable time wasted.</p>
+
+<p>How to avoid it you ask, there is a sign that I’ve found which leads to this problem most of the time and that’s <strong>lack of clear specification</strong>, just like with clients, if the maintainer doesn’t specify what should be done, you should stop.</p>
+
+<p>It happened to me, just like the past discussion, except he didn’t tell me <em>“Please do x, y, z”</em>, he made himself look
+too busy and said: <em>“The title says it all”</em>, no, it doesn’t say it all. “x, y and z” can be implemented in <code class="language-plaintext highlighter-rouge">2^9</code> ways, and sadly,
+you are not going to accept the <code class="language-plaintext highlighter-rouge">192</code>th way, as you “don’t like it”. Do not get trapped in these time-wasting situations, I wish maintainers understood how valuable people’s times are.</p>
+
+<h2 id="the-ugly">The Ugly</h2>
+<p>The sad part about open-source is, if the maintainer decides not to support the project anymore,
+people will <em>kind of</em> suffer. If the maintainer abandons the project, the project is <em>almost</em> doomed, as forking and continuing is really hard, reading the code from bottom up and understanding it isn’t easy, and as there is no outcome, people usually decide to abandon a project once they lose interest in the topic.</p>
+
+<p>If I personally lose interest in a project I’ve made, I’ll abandon it, I will try to guide new users through but I usually
+don’t offer as much support, I have more important things to do, it’s really sad, but true.</p>
+
+<p>To prevent this from happening, you must be able to make money out of your project, or your project must be really interesting
+and challenging to keep you working on it.</p>
+
+<hr />
+
+<p>That’s it, please note that everything you read here is my opinion, it’s not a rule, not a judgment, it’s my opinion and experience. If you would like to discuss this further, put a comment below or reach me at <a href="https://twitter.com/mdibaiee">twitter</a>.</p>
+
+  </article>
+
+  <div class="share-page">
+    Share in
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diff --git a/site/primitive-living-lessons-0/index.html b/site/primitive-living-lessons-0/index.html
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+  <meta http-equiv="X-UA-Compatible" content="IE=edge">
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+
+  <title>Primitive Living Lessons Learned, Episode 0</title>
+  <meta name="description" content="So I just went on my first primitive living practice trip in the woods, alone, with only a pocket knife.I decided I’m going to share the lessons I’ve learned...">
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+      <div class="wrapper">
+        <h1 class="page-heading"></h1>
+        
+          <div class='post lang-en'>
+
+  <div class="post-header">
+    <h1 class="post-title"><p>Primitive Living Lessons Learned, Episode 0</p>
+</h1>
+    
+    <p class="post-meta">
+      <span>Sep 7, 2017</span>
+      
+      • <span>Reading time: 11  minutes</span>
+    </p>
+  </div>
+
+  <article class="post-content">
+    <p><img src="/img/primitive-living-0.jpg" alt="general view of the forest" /></p>
+
+<p>So I just went on my first primitive living practice trip in the woods, alone, with only a pocket knife.</p>
+
+<p>I decided I’m going to share the lessons I’ve learned in each trip as they are certainly going to be useful if you want to practice primitive living, I would find these useful if I could find them anywhere. I spend a lot of time reading and watching primitive living guides and experience reports, but they are never exhaustive, and this series is not meant to be exhaustive either.</p>
+
+<!--more-->
+
+<p>Here we go:</p>
+
+<h1 id="what-i-did-know">What I did know</h1>
+
+<p>I spent a lot of time studying about edible wild plants, how to butcher and cook different kinds of animals and insects. I also had practiced fire by friction and read a lot and watched videos about theory of making cordages, making a bow-drill and so on. I also knew and had already built shelters for the night. So you can assume I had a basic, broad understanding of the necessary skills, but experience? Not so much.</p>
+
+<h1 id="setup">Setup</h1>
+
+<p>I had a pocket knife, a Garmin GPS and a pocket first aid kid, I would expect something to go wrong along the way, so I thought I want to be safe, but not comfortable, that’s why I brought emergency necessities, but not any comfort tools and materials. I also had a canned tuna for my first breakfast, but nothing more.</p>
+
+<p>Now for what is worth, I’m going in around summer’s end, September 5th, in a forest in northern Iran, Mazandaran Province. The forest starts from foothills, covering a few mounts from both sides, so it’s pretty large but also mountaneous, so I it’s hard to move in the forest.</p>
+
+<h1 id="arrival-first-night">Arrival: First Night</h1>
+
+<p>So I arrived at the entrace of the forest at night, it was already dark and I couldn’t build a shelter or do much, I just slept on the open ground, it was my first night in the woods alone. I was quite scared at first, lots of cracks and movements in bushes by unknown creatures, but after a few hours I figured out all these creatures are small ones that can’t be harmful to me. A few hours before dawn it got bitter cold, and I woke up, unable to go back to sleep. The first night was not the best, but could be worse.</p>
+
+<h1 id="first-day">First Day</h1>
+
+<p>I woke early at dawn and started moving into the forest, looking for a place to build my shelter in. I decided I’m going to follow these steps:</p>
+
+<ol>
+  <li>Build a shelter</li>
+  <li>Find water source</li>
+  <li>Build a fire</li>
+  <li>Find food</li>
+</ol>
+
+<p>But as was expected, it didn’t go according to the plan.</p>
+
+<p><img src="/img/primitive-living-0-shelter.jpg" alt="my shelter, done" /></p>
+
+<h2 id="shelter">Shelter</h2>
+
+<p>I found a nice place to stay which had a stream passing by, the stream was running and from what I knew about the area, the water was safe to drink, so water was no longer an issue. I started building my shelter, got the base wooden structure down first, but there was a catch: I couldn’t find any dry debris to put on top or inside. Last time I had built the same shelter it was autumn’s end/early spring, so there were lots of dry, fallen leaves on the ground; But this time it’s in the summer and there very few, scattered dry leaves on the ground, uncollectable.</p>
+
+<p>I decided I’m going with leaves of a small tree I had found nearby which seemed to be abundant around the area and the branches had lots of close leaves on them, looked like a good choice, but it was green. I didn’t find out what I was doing wrong until I tried to sleep at night. The green leaves attracted lots of flies and insects and all sorts of annoying disturbances, and the smell wasn’t helping either. I had to endure the insects throughout the night, because sleeping outside the shelter was a no-go, the dirt beneath was too cold. I hadn’t put as much leaves on the ground, and the leaves were green (which also means they take more heat away), but still, it was much better than sleeping directly on the ground.</p>
+
+<p>What I learned was, <strong>do not use green leaves for covering your shelter</strong>. This rule applies to small shelters in which you are close to the covering, as well as the leaves you use as bedding. I’ve seen people using green leaves for covering big shelters which have a high ceiling, though I don’t have any experience with those myself.</p>
+
+<p><img src="/img/primitive-living-0-friction-fire.jpg" alt="friction fire tries" /></p>
+
+<h2 id="friction-fire">Friction Fire</h2>
+
+<p>The most important part of primitive living is fire, without fire you can’t cook, you can’t stay warm and you can’t defy nocturnal predators. You also can’t repel insects. You can’t make a torch, so there goes an infinite list of fire applications that you will miss.</p>
+
+<p>I knew the theory of friction fire in and out, how and why it works, but what I had missed was, <strong>you are going to be in <em>real trouble</em> if you can’t find softwood</strong>. To my surprise, searching portions of the forest, I couldn’t find any softwood tree. Oaks were everywhere, as well as quite some other species of trees, but all of them were hardwood.</p>
+
+<p>I tried different combinations of the softer woods I could find, but none of them resulted in an ember, I got smoke with one combination, but that was it. After about 5-6 hours of trying, I got real tired and gave up. By the way, I tried hand-drills, I couldn’t succeed with bow-drills as I couldn’t find suitable cordage, I tried with a promising bark that was pretty strong, but it would break as soon as I put some pressure on it, It’s also possible that I might’ve gone wrong in making the bow itself, so it would cause the breakage.</p>
+
+<p>So the lesson was <strong>make sure the material you are going to practice with is available in your practice area</strong>, had I known there were no softwood in that particular forest, I would change my destination and probably succeed somewhere else. Sure, a professional survivalist must be able to start a fire in almost all situations, but this is practice and you have to start with easier steps.</p>
+
+<p>I ended up shaking for 2 hours before the dawn, not a pleasant experience at all. :D</p>
+
+<h2 id="food">Food</h2>
+
+<p>The difficulties didn’t end there, without a fire, my only hope for food was specific edible plants which can be eaten raw, or fruits. Unlucky as I was, I couldn’t find a single fruit-bearing tree in the forest (I found quite a few fruit-bearing trees along the roads and paths to the forest, but not inside the forest itself), and I also couldn’t find any of the other edible plants (I was mostly looking for the onion family) that I knew of.</p>
+
+<p>One of the greatest complications when starting primitive living practice anywhere other than the U.S. is that <strong>almost all guides and materials on the topic are from, and for Northern America</strong>. <a href="https://www.amazon.com/Edible-Wild-Plants-Falcon-Field/dp/0762774215">The Falcon Guide to Edible Wild Plants</a> that I read is all about northern american plants. I knew it, but it’s also the case that the Northern Hemisphere of the Earth have more common of an ecology, so most of the plants found in Northern America can also be found in places like Iran, but they have their differences. Most of the tips and tricks provided in different resources are for Northern American forests, which do not always work in other places.</p>
+
+<p>So all in all, I ended up not eating anything for the next 24 hours, until I got out of the forest.</p>
+
+<h2 id="psychology">Psychology</h2>
+
+<p>Apart from all the physical failures that I faced, which in turn caused frustration, I also had strong feelings of loneliness, boredom, and fear upon me. It was after failing to start a fire that I really felt the psychological burden on me. I had read about similar experiences, but believe me, the experience is hardly transmittable by words. A local rancher passing by the forest telling me about the leopard in the forest didn’t make things any easier.</p>
+
+<p>The psychological pressure was above all other difficulties, at some point I was bursting into tears, but I couldn’t associate it with any one specific feeling, it was a mix of anger, loneliness and fear.</p>
+
+<p>Anger and frustration because I couldn’t succeed in what I was trying to do. I also cut my finger at some point while carving the woods, so there was that.</p>
+
+<p>Loneliness because I was all by myself and I had no company to talk to. You can really actually go insane, as seen in <a href="https://en.wikipedia.org/wiki/Cast_Away">Cast Away</a>, after prolonged sessions of loneliness in situations like that. Mine wasn’t long, it was only two days, but I still experienced the thought-fog, I couldn’t think straight.</p>
+
+<p>Fear because I felt weak compared to the power of nature, my fear was doubled by the fact that I was alone. I felt like being in a place where everything seems to know what it is doing, but I don’t; I felt lost, not knowing what to do after my basic plans had failed.</p>
+
+<p>Now I don’t know if there is much you can do about the psychological part of it, I think experience is the remedy, at least I felt how different it was between the nights, the first night, even though I wasn’t even <em>inside</em> the forest much, I was almost at the border of it, it was much more creepy because it was my first time, but the second night, I was in the forest and now I had a <em>leopard</em> in my mind pouncing on me, but I felt less fear and was more comfortable.</p>
+
+<p>But in the end, what helped me was that <em>I knew I was going to face a huge mental challenge along the way</em>, so I was more prepared. I think it’s utterly important to be prepared for such psychological situations, knowing the reason behind your psychological challenges can help you overcome it to some extend.</p>
+
+<h1 id="second-night">Second Night</h1>
+
+<p>The second and last night was not all that much interesting, but it was damn sure cold and hard. At first I had to deal with the insects biting me everywhere and my feet scratching while trying to sleep in the shelter that I had wrongly built. After getting over that one and sleeping for what seemed to be ~2 hours, I woke up and felt the air temperature decreasing. I still got to sleep in intervals of 30 minutes until I woke up at around ~4 AM and my whole body was shaking. I couldn’t do much, all I did was gather the leaves underneath a little closer and more dense, and crunch my body into a ball so I felt just a little warmer, but still shaking. It took ages for the last two and a half hours to pass until dawn. At dawn I got up quickly and walked around a little to warm myself up, and then waited until I could barely see my surroundings, then I started walking out of the forest.</p>
+
+<p>Initially I had decided to stay for longer, but the weather forecast had predicted a heavy rain and storm for the next night, there was no way I could withstand that. :D</p>
+
+<h1 id="bottom-line">Bottom Line</h1>
+
+<p>It was a hard trip, I lost about 2kg (4lb) weight, but all in all the experience was a good one, I certainly learned a lot and I’m not going to make the same mistakes again. I should definitly practice more and keep working on my skills.</p>
+
+<p>If you are looking forward to practicing primitive living, please make sure you are safe and start small.</p>
+
+<blockquote>
+  <p>Success is going from failure to failure without losing your enthusiasm. —Winston Churchill</p>
+</blockquote>
+
+  </article>
+
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+      <li>
+        <h2>
+          <a class="post-link" href="/rust-box-str-vs-string/">What is `Box<str>` and how is it different from `String` in Rust?</a>
+          <span class="post-meta">Jun 16, 2022</span>
+        </h2>
+        <article class='post-content'>
+          <p>Today I and a friend went down a rabbit hole about Rust and how it manages the heap when we use <code class="language-plaintext highlighter-rouge">Box</code>, or <code class="language-plaintext highlighter-rouge">String</code>, or <code class="language-plaintext highlighter-rouge">Vec</code>, and while we were at it, I found out there is such a thing as <code class="language-plaintext highlighter-rouge">Box&lt;str&gt;</code>, which might look a bit <em>strange</em> to an untrained eye, since most of the time the <code class="language-plaintext highlighter-rouge">str</code> primitive type is passed around as <code class="language-plaintext highlighter-rouge">&amp;str</code>.</p>
+
+        </article>
+      </li>
+    
+      <li>
+        <h2>
+          <a class="post-link" href="/typoclassopedia-exercise-solutions/">Typoclassopedia: Exercise solutions</a>
+          <span class="post-meta">Sep 27, 2017</span>
+        </h2>
+        <article class='post-content'>
+          <p>I wanted to get proficient in Haskell so I decided to follow <a href="http://www.stephendiehl.com/posts/essential_haskell.html">An [Essential] Haskell Reading List</a>. There I stumbled upon <a href="https://wiki.haskell.org/Typeclassopedia">Typoclassopedia</a>, while the material is great, I couldn’t find solutions for the exercises to check against, so I decided I would write my own and hopefully the solutions would get fixed in case I have gone wrong by others. So if you think a solution is wrong, let me know in the comments!</p>
+
+        </article>
+      </li>
+    
+      <li>
+        <h2>
+          <a class="post-link" href="/travis-ci-pr-push/">Difference between Travis CI tests: PR and Push</a>
+          <span class="post-meta">Sep 9, 2017</span>
+        </h2>
+        <article class='post-content'>
+          <p>I just want to leave this here as I often tend to look it up myself and the first time it was not as easy to figure out.</p>
+
+<p>When using Travis CI along with GitHub (or other git integrations), Travis runs two tests: <code>pr</code> and <code>push</code>.</p>
+
+<p><img src="/img/travis-ci-pr-push-github.jpg" alt="travis-pr-push-github" /></p>
+
+<p>Most of the time you see both tests passing and you do not have to even wonder how they are different, but it has
+happened to me that one of the tests fails while the other passes and I started to wonder why.</p>
+
+<h3 id="pr">pr</h3>
+<p>The <code>pr</code> test is a test run on the result of a merge between the pull-request branch and the main branch.
+As an example, let’s say your pull-request’s branch is called <code>fix-user-auth</code> and your main branch is <code>master</code>, 
+in this case, <code>pr</code> merges <code>fix-user-auth</code> into <code>master</code> and then runs the tests on the result of the merge.</p>
+
+<h3 id="push">push</h3>
+<p>On the other hand, <code>push</code> is run on the pull-request branch itself, without merging. So in our example above, Travis would checkout to <code>fix-user-auth</code> and run the tests.</p>
+
+<h3 id="a-case-of-difference">A case of difference</h3>
+
+<p>A case in which this difference might be more apparent is when your pull-request is based on a branch other than <code>master</code>, and some changes that your pull-request depends on are missing from <code>master</code>, in this case the <code>push</code> test may pass, but the <code>pr</code> test will fail.</p>
+
+
+        </article>
+      </li>
+    
+      <li>
+        <h2>
+          <a class="post-link" href="/open-source-good-bad-ugly/">Open-source: The Good, The Bad and The Ugly</a>
+          <span class="post-meta">Oct 13, 2015</span>
+        </h2>
+        <article class='post-content'>
+          <p>I have been doing Open-source for a while, I don’t call myself an “expert” or something like that,
+but I’d like to share my opinion and experience on contributing to, and maintaining open-source code.</p>
+
+        </article>
+      </li>
+    
+      <li>
+        <h2>
+          <a class="post-link" href="/autocomplete-predict-trie/">Autocomplete using Tries</a>
+          <span class="post-meta">Jul 24, 2015</span>
+        </h2>
+        <article class='post-content'>
+          <p>In this article, I’m going over creating an autocompletion/prediction system using a data-structure called Trie, it’s fast and easy to customize.</p>
+
+        </article>
+      </li>
+    
+      <li>
+        <h2>
+          <a class="post-link" href="/es7-array-generator-comprehensions/">ES7 Array and Generator comprehensions</a>
+          <span class="post-meta">Jun 6, 2015</span>
+        </h2>
+        <article class='post-content'>
+          <p>Array comprehension is a new feature proposed for ES7, with a new syntax
+to create new arrays from existing <a href="http://www.2ality.com/2015/02/es6-iteration.html">iterables</a>,
+comprehensions can replace map and filter.</p>
+
+        </article>
+      </li>
+    
+      <li>
+        <h2>
+          <a class="post-link" href="/broadcastchannel-api/">BroadcastChannel API</a>
+          <span class="post-meta">Apr 2, 2015</span>
+        </h2>
+        <article class='post-content'>
+          <p><a href="https://developer.mozilla.org/en-US/docs/Web/API/Broadcast_Channel_API">BroadcastChannel API</a>
+is a new API used to communicate between same-origin tabs opened by the same user.</p>
+
+        </article>
+      </li>
+    
+      <li>
+        <h2>
+          <a class="post-link" href="/css-filters/">CSS Filters are awesome!</a>
+          <span class="post-meta">Mar 28, 2015</span>
+        </h2>
+        <article class='post-content'>
+          <p>I’ve been working on the <a href="https://bugzilla.mozilla.org/show_bug.cgi?id=1055181">CSS Filter Editor widget</a> in Firefox Developer Tools for a couple of weeks, thanks to <a href="https://medium.com/@patrickbrosset">Patrick Brosset</a> for mentoring me and <a href="https://github.com/nt1m">Tim Nguyen</a> for his great contributions.</p>
+
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+    
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+      <div class="wrapper">
+        <h1 class="page-heading"></h1>
+        
+          <div class='post lang-en'>
+
+  <div class="post-header">
+    <h1 class="post-title"><p>What is <code class="language-plaintext highlighter-rouge">Box&lt;str&gt;</code> and how is it different from <code class="language-plaintext highlighter-rouge">String</code> in Rust?</p>
+</h1>
+    
+    <h2 class="post-subtitle"><p>Using <code class="language-plaintext highlighter-rouge">rust-lldb</code> to understand rust memory internals</p>
+</h1>
+    
+    <p class="post-meta">
+      <span>Jun 16, 2022</span>
+      
+      • <span>Reading time: 13  minutes</span>
+    </p>
+  </div>
+
+  <article class="post-content">
+    <p>Today I and a friend went down a rabbit hole about Rust and how it manages the heap when we use <code class="language-plaintext highlighter-rouge">Box</code>, or <code class="language-plaintext highlighter-rouge">String</code>, or <code class="language-plaintext highlighter-rouge">Vec</code>, and while we were at it, I found out there is such a thing as <code class="language-plaintext highlighter-rouge">Box&lt;str&gt;</code>, which might look a bit <em>strange</em> to an untrained eye, since most of the time the <code class="language-plaintext highlighter-rouge">str</code> primitive type is passed around as <code class="language-plaintext highlighter-rouge">&amp;str</code>.</p>
+
+<hr />
+
+<p>TL;DR:</p>
+
+<p><code class="language-plaintext highlighter-rouge">Box&lt;str&gt;</code> is a primitive <code class="language-plaintext highlighter-rouge">str</code> allocated on the heap, whereas <code class="language-plaintext highlighter-rouge">String</code> is actually a <code class="language-plaintext highlighter-rouge">Vec&lt;u8&gt;</code>, also allocated on the heap, which allows for efficient removals and appends. <code class="language-plaintext highlighter-rouge">Box&lt;str&gt;</code> (16 bytes) uses less memory than <code class="language-plaintext highlighter-rouge">String</code> (24 bytes).</p>
+
+<hr />
+
+<p>I will be using <code class="language-plaintext highlighter-rouge">rust-lldb</code> throughout this post to understand what is going on in the rust programs we write and run. The source code for this blog post is available on <a href="https://git.mahdi.blog/mahdi/rust-memory-playground">mdibaiee/rust-memory-playground</a>.</p>
+
+<div class="language-bash highlighter-rouge"><div class="highlight"><pre class="highlight"><code>git clone https://git.mahdi.blog/mahdi/rust-memory-playground
+<span class="nb">cd </span>rust-memory-playground
+</code></pre></div></div>
+
+<h1 id="the-stack">The Stack</h1>
+
+<p>Most of the primitive data types used throughout a program, and the information about the program itself are usually allocated on the stack. Consider this simple program:</p>
+
+<div class="language-rust highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="k">fn</span> <span class="nf">add_ten</span><span class="p">(</span><span class="n">a</span><span class="p">:</span> <span class="nb">u8</span><span class="p">)</span> <span class="k">-&gt;</span> <span class="nb">u8</span> <span class="p">{</span>
+    <span class="k">let</span> <span class="n">b</span> <span class="o">=</span> <span class="mi">10</span><span class="p">;</span>
+    <span class="n">a</span> <span class="o">+</span> <span class="n">b</span>
+<span class="p">}</span>
+
+
+<span class="k">fn</span> <span class="nf">main</span><span class="p">()</span> <span class="p">{</span>
+    <span class="nd">println!</span><span class="p">(</span><span class="s">"{}"</span><span class="p">,</span> <span class="nf">add_ten</span><span class="p">(</span><span class="mi">9</span><span class="p">));</span>
+<span class="p">}</span>
+</code></pre></div></div>
+
+<p>Let’s examine the stack when we are running <code class="language-plaintext highlighter-rouge">a + b</code> by setting a breakpoint on that line:</p>
+
+<div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>$ cargo build &amp;&amp; rust-lldb target/debug/stack-program
+
+(lldb) breakpoint set -f main.rs -l 3
+Breakpoint 1: where = stack-program`stack_program::add_ten::h42edbf0bdcb04851 + 24 at main.rs:3:5, address = 0x0000000100001354
+
+(lldb) run
+Process 65188 launched: '/Users/mahdi/workshop/rust-memory-playground/target/debug/stack-program' (arm64)
+Process 65188 stopped
+* thread #1, queue = 'com.apple.main-thread', stop reason = breakpoint 1.1
+    frame #0: 0x0000000100001354 stack-program`stack_program::add_ten::h42edbf0bdcb04851(a=5) at main.rs:3:5
+   1    fn add_ten(a: u8) -&gt; u8 {
+   2        let b = 10;
+-&gt; 3        a + b
+   4    }
+   5
+   6
+   7    fn main() {
+   
+(lldb) frame var -L -f X
+0x000000016fdfed7e: (unsigned char) a = 0x09
+0x000000016fdfed7f: (unsigned char) b = 0x0A
+</code></pre></div></div>
+
+<p>Our program allocates two variables on the stack directly here. Notice that they are allocated right next to each other, their address only one bit apart. Most primitive types are allocated on the stack, and are copied when being passed around because they are small enough, so that copying them around is more reasonable than allocating them in the heap and passing around a pointer to them. In this case, <code class="language-plaintext highlighter-rouge">u8</code> can be allocated in a single byte, it would not make sense for us to allocate a pointer (which can vary in size, but are usually larger than 8 bytes). Every time you call a function, a copy of the values passed to it, along with the values defined in the function itself constitute the stack of that function.</p>
+
+<p>The stack of a whole program includes more information though, such as the <em>backtrace</em>, which allows the program to know how to navigate: once I am done with this function, where should I return to? that information is available in the stack as well. Note the first couple of lines here, indicating that we are currently in <code class="language-plaintext highlighter-rouge">stack_program::add_then</code>, and we came here from <code class="language-plaintext highlighter-rouge">stack_program::main</code>, and so once we are finished with <code class="language-plaintext highlighter-rouge">add_then</code>, we will go back to <code class="language-plaintext highlighter-rouge">main</code>:</p>
+
+<div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>(lldb) thread backtrace
+* thread #1, queue = 'com.apple.main-thread', stop reason = breakpoint 1.1
+  * frame #0: 0x0000000100001350 stack-program`stack_program::add_ten::hf7dc9cccae290c37(a='\t') at main.rs:3:5
+    frame #1: 0x00000001000013a8 stack-program`stack_program::main::he22b9cf577b52c34 at main.rs:8:20
+    frame #2: 0x00000001000015a4 stack-program`core::ops::function::FnOnce::call_once::hd6bac0cd3fcb8c07((null)=(stack-program`stack_program::main::he22b9cf577b52c34 at main.rs:7), (null)=&lt;unavailable&gt;) at function.rs:227:5
+    frame #3: 0x00000001000014c4 stack-program`std::sys_common::backtrace::__rust_begin_short_backtrace::hc4df46810f9a7139(f=(stack-program`stack_program::main::he22b9cf577b52c34 at main.rs:7)) at backtrace.rs:122:18
+    frame #4: 0x0000000100001178 stack-program`std::rt::lang_start::_$u7b$$u7b$closure$u7d$$u7d$::hbec5b809d627978a at rt.rs:145:18
+    frame #5: 0x000000010001440c stack-program`std::rt::lang_start_internal::hc453db0ee48af82e [inlined] core::ops::function::impls::_$LT$impl$u20$core..ops..function..FnOnce$LT$A$GT$$u20$for$u20$$RF$F$GT$::call_once::h485d4c2966ec30a8 at function.rs:259:13 [opt]
+    frame #6: 0x0000000100014400 stack-program`std::rt::lang_start_internal::hc453db0ee48af82e [inlined] std::panicking::try::do_call::h375a887be0bea938 at panicking.rs:492:40 [opt]
+    frame #7: 0x0000000100014400 stack-program`std::rt::lang_start_internal::hc453db0ee48af82e [inlined] std::panicking::try::hecad40482ef3be15 at panicking.rs:456:19 [opt]
+    frame #8: 0x0000000100014400 stack-program`std::rt::lang_start_internal::hc453db0ee48af82e [inlined] std::panic::catch_unwind::haf1f664eb41a88eb at panic.rs:137:14 [opt]
+    frame #9: 0x0000000100014400 stack-program`std::rt::lang_start_internal::hc453db0ee48af82e [inlined] std::rt::lang_start_internal::_$u7b$$u7b$closure$u7d$$u7d$::h976eba434e9ff4cf at rt.rs:128:48 [opt]
+    frame #10: 0x0000000100014400 stack-program`std::rt::lang_start_internal::hc453db0ee48af82e [inlined] std::panicking::try::do_call::h8f2501ab92e340b0 at panicking.rs:492:40 [opt]
+    frame #11: 0x0000000100014400 stack-program`std::rt::lang_start_internal::hc453db0ee48af82e [inlined] std::panicking::try::hbeb9f8df83454d42 at panicking.rs:456:19 [opt]
+    frame #12: 0x0000000100014400 stack-program`std::rt::lang_start_internal::hc453db0ee48af82e [inlined] std::panic::catch_unwind::h0a9390b2202af6e9 at panic.rs:137:14 [opt]
+    frame #13: 0x0000000100014400 stack-program`std::rt::lang_start_internal::hc453db0ee48af82e at rt.rs:128:20 [opt]
+    frame #14: 0x0000000100001140 stack-program`std::rt::lang_start::h69bdd2191bba2dab(main=(stack-program`stack_program::main::he22b9cf577b52c34 at main.rs:7), argc=1, argv=0x000000016fdff168) at rt.rs:144:17
+    frame #15: 0x0000000100001434 stack-program`main + 32
+    frame #16: 0x00000001000750f4 dyld`start + 520
+</code></pre></div></div>
+
+<h1 id="box-string-and-vec-pointers-to-heap">Box, String and Vec: Pointers to Heap</h1>
+
+<p>There are times when we are working with data types large enough that we would really like to avoid copying them when we are passing them around. Let’s say you have just copied a file that is 1,000,000 bytes (1Mb) in size. In this case it is much more memory and compute efficient to have a pointer to this value (8 bytes) rather than copying all the 1,000,000 bytes.</p>
+
+<p>This is where types such as <code class="language-plaintext highlighter-rouge">Box</code>, <code class="language-plaintext highlighter-rouge">String</code> and <code class="language-plaintext highlighter-rouge">Vec</code> come into play: these types allow you to allocate something on heap, which is a chunk of memory separate from the stack that you can allocate on, and later reference those values using a pointer available on the stack.</p>
+
+<p>Let’s start with <code class="language-plaintext highlighter-rouge">Box</code>, the most generic one, which allows you to allocate some data on the heap, consider this example:</p>
+
+<div class="language-rust highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="k">fn</span> <span class="nf">main</span><span class="p">()</span> <span class="p">{</span>
+    <span class="k">let</span> <span class="n">a</span> <span class="o">=</span> <span class="nn">Box</span><span class="p">::</span><span class="nf">new</span><span class="p">(</span><span class="mi">5_u8</span><span class="p">);</span>
+    <span class="k">let</span> <span class="n">b</span> <span class="o">=</span> <span class="mi">10_u8</span><span class="p">;</span>
+    <span class="nd">println!</span><span class="p">(</span><span class="s">"{}, {}"</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">);</span>
+<span class="p">}</span>
+</code></pre></div></div>
+
+<p>We again use <code class="language-plaintext highlighter-rouge">lldb</code> to check out what is happening:</p>
+
+<div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>$ cargo build &amp;&amp; rust-lldb target/debug/stack-and-heap-program
+
+(lldb) breakpoint set -f main.rs -l 4
+Breakpoint 1: where = stack-and-heap-program`stack_and_heap_program::main::ha895783273646dc7 + 100 at main.rs:4:5, address = 0x0000000100005264
+
+(lldb) run
+Process 67451 launched: '/Users/mahdi/workshop/rust-memory-playground/target/debug/stack-and-heap-program' (arm64)
+Process 67451 stopped
+* thread #1, queue = 'com.apple.main-thread', stop reason = breakpoint 1.1
+    frame #0: 0x0000000100005264 stack-and-heap-program`stack_and_heap_program::main::ha895783273646dc7 at main.rs:4:5
+   1    fn main() {
+   2        let a = Box::new(5_u8);
+   3        let b = 10_u8;
+-&gt; 4        println!("{}, {}", a, b);
+   5    }
+   
+(lldb) frame var -L -f X
+0x000000016fdfed48: (unsigned char *) a = 0x0000600000008010 "\U00000005"
+0x000000016fdfed57: (unsigned char) b = 0x0A
+
+(lldb) memory read -count 1 -f X 0x0000600000008010
+0x600000008010: 0x05
+</code></pre></div></div>
+
+<p>Note that here, instead of <code class="language-plaintext highlighter-rouge">a</code> having the value <code class="language-plaintext highlighter-rouge">5</code>, has the value <code class="language-plaintext highlighter-rouge">0x0000600000008010</code>, which is a pointer to a location in memory! <code class="language-plaintext highlighter-rouge">lldb</code> is recognises that this is a pointer (note the <code class="language-plaintext highlighter-rouge">*</code> sign beside the variable type) and shows us what the memory location contains, but we can also directly read that memory location, and of course we find <code class="language-plaintext highlighter-rouge">5</code> there. The address of the heap-allocated <code class="language-plaintext highlighter-rouge">5</code> is far from the stack-allocated <code class="language-plaintext highlighter-rouge">10</code>, since stack and heap are separate parts of memory.</p>
+
+<p>Using <code class="language-plaintext highlighter-rouge">Box</code> for an unsigned 8-bit value does not really make sense, the value itself is smaller than the pointer created by <code class="language-plaintext highlighter-rouge">Box</code>, however allocating on heap is useful when we have data that we need be able to pass around the program without copying it.</p>
+
+<p>Turns out, <code class="language-plaintext highlighter-rouge">String</code> and <code class="language-plaintext highlighter-rouge">Vec</code> cover two of the most common cases where we may want to allocate something on heap! Let’s look at what goes on behind allocating a variable of type <code class="language-plaintext highlighter-rouge">String</code>:</p>
+
+<div class="language-rust highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="k">fn</span> <span class="nf">main</span><span class="p">()</span> <span class="p">{</span>
+    <span class="k">let</span> <span class="n">s</span> <span class="o">=</span> <span class="nn">String</span><span class="p">::</span><span class="nf">from</span><span class="p">(</span><span class="s">"hello"</span><span class="p">);</span>
+    <span class="nd">println!</span><span class="p">(</span><span class="s">"{}"</span><span class="p">,</span> <span class="n">s</span><span class="p">);</span>
+<span class="p">}</span>
+</code></pre></div></div>
+
+<p>And here we go again:</p>
+<div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>(lldb) breakpoint set -f main.rs -l 3
+Breakpoint 1: where = string-program`string_program::main::h64ca96ee87b0ceaf + 44 at main.rs:3:5, address = 0x000000010000476c
+
+(lldb) run
+Process 68317 launched: '/Users/mahdi/workshop/rust-memory-playground/target/debug/string-program' (arm64)
+Process 68317 stopped
+* thread #1, queue = 'com.apple.main-thread', stop reason = breakpoint 1.1
+    frame #0: 0x000000010000476c string-program`string_program::main::h64ca96ee87b0ceaf at main.rs:3:5
+   1    fn main() {
+   2        let s = String::from("hello");
+-&gt; 3        println!("{}", s);
+   4    }
+   
+(lldb) frame var -L -T
+0x000000016fdfed78: (alloc::string::String) s = "hello" {
+0x000000016fdfed78:   (alloc::vec::Vec&lt;unsigned char, alloc::alloc::Global&gt;) vec = size=5 {
+0x0000600000004010:     (unsigned char) [0] = 'h'
+0x0000600000004011:     (unsigned char) [1] = 'e'
+0x0000600000004012:     (unsigned char) [2] = 'l'
+0x0000600000004013:     (unsigned char) [3] = 'l'
+0x0000600000004014:     (unsigned char) [4] = 'o'
+  }
+}
+</code></pre></div></div>
+
+<p>This is a formatted output from <code class="language-plaintext highlighter-rouge">lldb</code>, and here you can see that the <code class="language-plaintext highlighter-rouge">String</code> type is basically a <code class="language-plaintext highlighter-rouge">Vec&lt;unsigned char, alloc::Global&gt;</code> (note that <code class="language-plaintext highlighter-rouge">unsigned char</code> is represented using <code class="language-plaintext highlighter-rouge">u8</code> in Rust, so in Rust terminology the type is <code class="language-plaintext highlighter-rouge">Vec&lt;u8&gt;</code>), let’s now look at the same command but this time raw and unformatted (<code class="language-plaintext highlighter-rouge">-R</code>):</p>
+
+<div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>(lldb) frame var -L -T -R
+0x000000016fdfed78: (alloc::string::String) s = {
+0x000000016fdfed78:   (alloc::vec::Vec&lt;unsigned char, alloc::alloc::Global&gt;) vec = {
+0x000000016fdfed78:     (alloc::raw_vec::RawVec&lt;unsigned char, alloc::alloc::Global&gt;) buf = {
+0x000000016fdfed78:       (core::ptr::unique::Unique&lt;unsigned char&gt;) ptr = {
+0x000000016fdfed78:         (unsigned char *) pointer = 0x0000600000004010
+0x000000016fdfed78:         (core::marker::PhantomData&lt;unsigned char&gt;) _marker = {}
+      }
+0x000000016fdfed80:       (unsigned long) cap = 6
+0x000000016fdfed78:       (alloc::alloc::Global) alloc = {}
+    }
+0x000000016fdfed88:     (unsigned long) len = 6
+  }
+}
+</code></pre></div></div>
+
+<p>Ah! I see the <code class="language-plaintext highlighter-rouge">ptr</code> field of <code class="language-plaintext highlighter-rouge">RawVec</code> with a value of <code class="language-plaintext highlighter-rouge">0x0000600000004010</code>, that is the memory address of the beginning of our string (namely the <code class="language-plaintext highlighter-rouge">h</code> of our <code class="language-plaintext highlighter-rouge">hello</code>)! There is also <code class="language-plaintext highlighter-rouge">cap</code> and <code class="language-plaintext highlighter-rouge">len</code>, which respectively stand for capacity and length, with the value 6, indicating that our string is of capacity and length 6; the difference between the two being that <a href="https://doc.rust-lang.org/nightly/std/vec/struct.Vec.html#capacity-and-reallocation">you can have a <code class="language-plaintext highlighter-rouge">Vec</code> with a capacity of 10 while it has zero items</a>, this would allow you to append 10 items to the <code class="language-plaintext highlighter-rouge">Vec</code> without having a new allocation for each append, making the process more efficient, and also a <a href="https://doc.rust-lang.org/nightly/std/vec/struct.Vec.html#guarantees">Vec is not automatically shrunk down</a> in size when items are removed from it to avoid unnecessary deallocations, hence the length might be smaller than the capacity. So in a nutshell, our String is basically something like this (inspired by <a href="https://doc.rust-lang.org/nightly/std/vec/struct.Vec.html#guarantees">std::vec::Vec</a>):</p>
+
+<div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>Stack:
+--------------------------------
+| String                       |
+|     \-&gt; Vec                  |
+|          \-&gt; (ptr, cap, len) |
+|                |             |
+-----------------|--------------
+Heap:            v
+-----------------------------
+| ('h', 'e', 'l', 'l', 'o') |
+-----------------------------
+</code></pre></div></div>
+
+<p>Okay, so far so good. We have <code class="language-plaintext highlighter-rouge">String</code>, which uses a <code class="language-plaintext highlighter-rouge">Vec</code> under the hood, which is represented by a pointer, capacity and length triplet.</p>
+
+<p>If <code class="language-plaintext highlighter-rouge">String</code> is already heap-allocated, why would anyone want <code class="language-plaintext highlighter-rouge">Box&lt;str&gt;</code>!? Let’s look at how <code class="language-plaintext highlighter-rouge">Box&lt;str&gt;</code> would be represented in memory:</p>
+
+<div class="language-rust highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="k">fn</span> <span class="nf">main</span><span class="p">()</span> <span class="p">{</span>
+    <span class="k">let</span> <span class="n">boxed_str</span><span class="p">:</span> <span class="nb">Box</span><span class="o">&lt;</span><span class="nb">str</span><span class="o">&gt;</span> <span class="o">=</span> <span class="s">"hello"</span><span class="nf">.into</span><span class="p">();</span>
+
+    <span class="nd">println!</span><span class="p">(</span><span class="s">"boxed_str: {}"</span><span class="p">,</span> <span class="n">boxed_str</span><span class="p">);</span>
+<span class="p">}</span>
+</code></pre></div></div>
+
+<p>And <code class="language-plaintext highlighter-rouge">lldb</code> tells us:</p>
+
+<div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>0x000000016fdfed80: (alloc::boxed::Box&lt;&gt;) boxed_str = {
+0x000000016fdfed80:   data_ptr = 0x0000600000004010 "hello"
+0x000000016fdfed88:   length = 5
+}
+</code></pre></div></div>
+
+<p>Okay, so a <code class="language-plaintext highlighter-rouge">Box&lt;str&gt;</code> is much simpler than a <code class="language-plaintext highlighter-rouge">String</code>: there is no <code class="language-plaintext highlighter-rouge">Vec</code>, and no <code class="language-plaintext highlighter-rouge">capacity</code>, and the underlying data is a primitive <code class="language-plaintext highlighter-rouge">str</code> that does not allow efficient appending or removing. It is a smaller representation as well, due to the missing <code class="language-plaintext highlighter-rouge">capacity</code> field, comparing their memory size on stack using <a href="https://doc.rust-lang.org/std/mem/fn.size_of_val.html">std::mem::size_of_val</a>:</p>
+
+<div class="language-rust highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="k">let</span> <span class="n">boxed_str</span><span class="p">:</span> <span class="nb">Box</span><span class="o">&lt;</span><span class="nb">str</span><span class="o">&gt;</span> <span class="o">=</span> <span class="s">"hello"</span><span class="nf">.into</span><span class="p">();</span>
+<span class="nd">println!</span><span class="p">(</span><span class="s">"size of boxed_str on stack: {}"</span><span class="p">,</span> <span class="nn">std</span><span class="p">::</span><span class="nn">mem</span><span class="p">::</span><span class="nf">size_of_val</span><span class="p">(</span><span class="o">&amp;</span><span class="n">boxed_str</span><span class="p">));</span>
+
+<span class="k">let</span> <span class="n">s</span> <span class="o">=</span> <span class="nn">String</span><span class="p">::</span><span class="nf">from</span><span class="p">(</span><span class="s">"hello"</span><span class="p">);</span>
+<span class="nd">println!</span><span class="p">(</span><span class="s">"size of string on stack: {}"</span><span class="p">,</span> <span class="nn">std</span><span class="p">::</span><span class="nn">mem</span><span class="p">::</span><span class="nf">size_of_val</span><span class="p">(</span><span class="o">&amp;</span><span class="n">s</span><span class="p">));</span>
+</code></pre></div></div>
+
+<p>Results in:</p>
+
+<div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>size of boxed_str on stack: 16
+size of string on stack: 24
+</code></pre></div></div>
+
+<p>Note that their size on heap is the same, because they are both storing the bytes for <code class="language-plaintext highlighter-rouge">hello</code> on the heap (the measurements below show all of the heap allocations of the program, and not only the string. What matters here is that these two programs have exact same heap size in total):</p>
+
+<div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>$ cargo run --bin string-dhat
+    Finished dev [unoptimized + debuginfo] target(s) in 0.01s
+     Running `target/debug/string-dhat`
+hello
+dhat: Total:     1,029 bytes in 2 blocks
+dhat: At t-gmax: 1,029 bytes in 2 blocks
+dhat: At t-end:  1,024 bytes in 1 blocks
+dhat: The data has been saved to dhat-heap.json, and is viewable with dhat/dh_view.html
+
+$ cargo run --bin box-str-dhat
+    Finished dev [unoptimized + debuginfo] target(s) in 0.01s
+     Running `target/debug/box-str-dhat`
+boxed_str: hello
+dhat: Total:     1,029 bytes in 2 blocks
+dhat: At t-gmax: 1,029 bytes in 2 blocks
+dhat: At t-end:  1,024 bytes in 1 blocks
+dhat: The data has been saved to dhat-heap.json, and is viewable with dhat/dh_view.html
+</code></pre></div></div>
+
+<p>There is also <code class="language-plaintext highlighter-rouge">Box&lt;[T]&gt;</code> which is the fixed size counterpart to <code class="language-plaintext highlighter-rouge">Vec&lt;T&gt;</code>.</p>
+
+<h1 id="should-i-use-boxstr-or-string">Should I use <code class="language-plaintext highlighter-rouge">Box&lt;str&gt;</code> or <code class="language-plaintext highlighter-rouge">String</code>?</h1>
+
+<p>The only use case for <code class="language-plaintext highlighter-rouge">Box&lt;str&gt;</code> over <code class="language-plaintext highlighter-rouge">String</code> that I can think of, is optimising for memory usage when the string is fixed and you do not intend to append or remove from it. I looked for examples of <code class="language-plaintext highlighter-rouge">Box&lt;str&gt;</code> being used, and I found a few examples:</p>
+
+<ul>
+  <li>Hyper uses it in a part to reduce memory usage, since the string they have is read-only: <a href="https://github.com/hyperium/hyper/pull/2727">hyper#2727</a></li>
+  <li>Rust-analyzer uses it to store some strings in their snippets data structre: <a href="https://github.com/rust-lang/rust-analyzer/blob/5c88d9344c5b32988bfbfc090f50aba5de1db062/crates/ide-completion/src/snippet.rs#L123">rust-lang/rust-analyzer/crates/ide-completion/src/snippet.rs</a></li>
+  <li>It is also used in some parts in the compiler itself, probably with the same aim of optimising memory usage: <a href="https://github.com/rust-lang/rust/blob/7846610470392abc3ab1470853bbe7b408fe4254/src/libsyntax/symbol.rs#L82-L85">rust-lang/rust/src/libsyntax/symbol.rs</a></li>
+</ul>
+
+  </article>
+
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diff --git a/site/sanctions-discrimination-isolation-iran.html b/site/sanctions-discrimination-isolation-iran.html
new file mode 100644
index 0000000..e051832
--- /dev/null
+++ b/site/sanctions-discrimination-isolation-iran.html
@@ -0,0 +1,265 @@
+<!DOCTYPE html>
+<html>
+
+  <head>
+  <meta charset="utf-8">
+  <meta http-equiv="X-UA-Compatible" content="IE=edge">
+  <meta name="viewport" content="width=device-width, initial-scale=1">
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+    <h1 class="post-title"><p>Iran Sanctions: A Story of Discrimination and Isolation</p>
+</h1>
+    
+    <p class="post-meta">
+      <span>Jul 27, 2019</span>
+      
+      • <span>Reading time: 17  minutes</span>
+    </p>
+  </div>
+
+  <article class="post-content">
+    <p>Let me take you through a story on what it feels like to be isolated from the world, not by choice, but rather, by force. This is a story of discrimination, of monopoly, of people shrugging to these issues and of utterances that affect lives of millions.</p>
+
+<p>Living in Iran, or any sanctioned country for that matter, you learn to read “anyone, anywhere” with an appendix of “except you”. You soon learn “worldwide shipping” excludes you, that’s when you start wondering, are you not living in “the world”? Where is this “world” they talk about?</p>
+
+<p>Here is an example of a beautiful, hopeful message from Khan Academy:</p>
+
+<p><img src="/img/discrimination/khan-academy.png" alt="Khan Academy's Landing Page: We’re a nonprofit with the mission to provide a free, world-class education for anyone, anywhere." /></p>
+
+<p><span class="image-caption">“We’re a nonprofit with the mission to provide a free, world-class education for anyone, anywhere.”</span></p>
+
+<p>No one probably realizes that this is not true, but yes, Khan Academy is not available to Iranians, Cubans, Syrians, people of Crimea, and some others. That’s because <a href="https://cloud.google.com/customers/khan-academy/">they run on Google Cloud</a>, an infrastructure provider that completely blocks all sanctioned countries from accessing any application hosted on it. Who else hosts their service there? Take a look at <a href="https://cloud.google.com/customers/">342 notable customers</a> of Google Cloud, but remember, there are thousands more customers of Google Cloud and similar American infrastructure providers.</p>
+
+<p>But the story doesn’t end here, of course. Let’s go through the effects of sanctions on everyday lives of people, who have nothing to do with the politics of the country they are living in, and who are being discriminated only because they were born in geographical coordinates that lie in a certain boundary defined by people they don’t even know.</p>
+
+<h1 id="the-internet">The Internet</h1>
+
+<p>The internet, the tool of the global society for communicating across the planet, <em>the</em> tool for sharing knowledge with the human population across the world.</p>
+
+<p>As if the Iranian government’s blockage and censorship of the internet wasn’t enough, we now have to deal with external sanctions blocking our access as well. Here’s a gallery of blocked access messages we see on a daily basis:</p>
+
+<p><img src="/img/discrimination/403-forbidden-iran-sanctions.jpg" alt="Various websites and their respective webpages seen only by sanctioned countries" />
+<span class="image-caption">Various websites and their respective webpages seen only by sanctioned countries</span></p>
+
+<p>These websites include GitHub, Slack, Kaggle, Docker, GitLab, Amazon AWS, Twitter, Bluemix, Khan Academy and more. Here is a longer, developer-oriented (but definitely not exhaustive) list of hosts blocking our access: <a href="https://raw.githubusercontent.com/freedomofdevelopers/fod/master/domains">freedomofdevelopers/domains</a>.</p>
+
+<p>The websites that blocked our access mostly did it without prior notice, they just disabled our accounts, took our data from us, and did not let us even backup or export our data afterwards, in other words, lost messages, lost files and credentials.</p>
+
+<p>This, in part, is caused by the global monopoly of American companies such as Google, Amazon, GitHub and alike in their respective fields. This means if The United States decides to pressure a specific target, the target population is likely to be left without much of an alternative or option, since a great proportion of the land is covered by American companies.</p>
+
+<p>Iranian users rely heavily on use of VPN services and proxy servers to bypass censorship, but now with most Cloud Providers blocking access of Iranians, we are left with limited, usually more expensive options for setting up these servers.</p>
+
+<p>This is a clear discrimination based on nationality and a breach of <a href="https://en.wikipedia.org/wiki/Internet_freedom">Internet Freedom</a>. These websites do not block us because we acted in a wrong way, or even, at cases, because we live in Iran, but because we were <em>born</em> in Iran. Now, you may say this is because of the law and they have no choice. That’s true in some cases, though most of the time the implementation of these laws seem to go further than what the laws actually require. The companies seem to go the <em>easy</em> way by blocking access as much as they can to avoid holes in their system.</p>
+
+<h1 id="drugs-medicine-and-medical-devices">Drugs, Medicine, and Medical Devices</h1>
+
+<p>There are various sources and articles on how the U.S. sanctions have affected Iranian patients by limiting exports of drugs, medical devices or by indirectly disrupting the pharmaceutical industry by cutting exports of raw material used by these companies to produce medical drugs. Almost every person living in Iran can consciously feel the shortage of drugs and their growing price, but I will refer to an article on NCBI as a proof.</p>
+
+<p>Quoting from <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4897941/">NCBI: Addressing the impact of economic sanctions on Iranian drug shortages in the joint comprehensive plan of action: promoting access to medicines and health diplomacy</a>:</p>
+
+<blockquote>
+Although the revised and current Iranian sanctions regime does not specifically prohibit the export of humanitarian goods and pharmaceuticals, many of the administrative and regulatory processes have made it difficult to export life-saving medicines to Iran. This includes the need to navigate a complex export control regulatory process, the inability of Iranian banks to do business with the international banking system and U.S. corporations, currency shortages, and the inability to secure terms of shipping, insurance and other services needed to facilitate medicines trade [4]. As a result, millions of Iranians that suffer from life-threatening diseases have experienced “exorbitant prices”, stock outs of medicines, and are often forced to purchase drugs from the black market.
+
+[...]
+
+Severe medication shortages in Iran are diverse and span several therapeutic classes and disease states. This includes drug shortages for other critical areas of healthcare delivery, including organ transplant drugs, and even vaccine shortages.
+</blockquote>
+
+<p>And on the topic of weakening of the pharmaceutical companies:</p>
+
+<blockquote>
+Inaccessibility of vital medications and their raw ingredients combined with Iran’s weakening domestic pharmaceutical industry has also resulted in an influx of counterfeit, fraudulent, and substandard medicines into Iran’s health care system. An unregulated black market has developed as a byproduct of drug shortages, introducing medications whose origins and authenticity are often unknown, and has led to expired medications’ distribution and sale, even at potentially very high prices [8]. Hence, the global counterfeit medicines trade, recognized as a serious public health concern, is one that is currently being enabled as a consequence of drug shortages and ongoing Iranian economic sanctions 
+</blockquote>
+
+<p>Foreign Policy also writes <a href="https://foreignpolicy.com/2019/08/14/u-s-sanctions-are-killing-cancer-patients-in-iran/">U.S. Sanctions Are Killing Cancer Patients in Iran</a>:</p>
+
+<blockquote>
+  <p>Washington claims that maximum pressure won’t stop the supply of medicine and other humanitarian necessities, but banking sanctions are driving up import prices, blocking supply chains, and creating deadly drug shortages.</p>
+</blockquote>
+
+<blockquote>
+  <p>Although U.S. sanctions are engineered in a way that may appear not to target humanitarian access to food and medicine, in practice U.S. sanctions function as a tool of economic war.</p>
+</blockquote>
+
+<p><a href="https://www.who.int/mediacentre/news/statements/fundamental-human-right/en/">Health is a fundamental human right</a>, but the embargo clearly goes against giving people access to life-saving medicine. It brings tears to my eyes to think about people losing a loved one over inability to access a drug or medical device that’s no longer available in Iran.</p>
+
+<h1 id="currency-fluctuations-an-unpredictable-life">Currency Fluctuations: An Unpredictable Life</h1>
+
+<p>I’m pretty sure most of the people reading this blog post, unless they are Iranians, will not find this section familiar. It’s [fortunately] not a common experience across the planet, but let me tell you about living a life of zero predictability.</p>
+
+<p>Imagine this: You sell your car today, and you start a hunt for a new car to buy as a replacement. For the sake of the example, you are looking for a second-hand car.
+I will use a dummy currency unit here to simplify the example. You sold  your car for 1000 units, and during the week you are looking for a new car, you start to see the car you just sold and every other car on the market, is gaining price exponentially. After a week, the same car that you sold is priced at 1800 units of currency and it’s growing. It’s like putting a car on neutral in a downward slope and seeing it go up the hill! Now you are left with 1000 units of currency, and you are only able to buy the same car if you put in your extra 800 savings, otherwise you are going to ride a car with significantly less quality or no car at all. More on <a href="https://www.reuters.com/article/us-iran-economy-imf-idUSKCN1S509Q">Iran’s inflation</a> as a result of tighter sanctions.</p>
+
+<p>I am pretty sure no matter how much I try to help you visualize this, you can not comprehend what it means to live in such a situation. I always use the metaphor of being a circus actor trying to balance on a moving cylinder to describe what it means to survive the fluctuations of our currency, which in turn affects all your expenses, but not your income.</p>
+
+<p><img src="/img/discrimination/act04-1.jpg" alt="Circus actor balancing on cylinders" /></p>
+
+<p>This is also an effect of the sanctions on the economy that we people feel with our every inch and are pressured by. This in turn causes a <a href="#a-weak-economys-rippling-effect">rippling effect</a> on every other part of the society. Quoting <a href="https://www.thenational.ae/business/economy/explainer-the-collapse-of-the-iranian-rial-1.754707">Explainer: the collapse of the Iranian rial</a></p>
+
+<blockquote>
+Has the US decision made things worse?
+
+Yes. Mr Trump’s decision to exit the US-Iran nuclear agreement signed in 2015 has dented Iran’s economic outlook and set in motion a cascade of damaging effects. It has deterred global companies from doing business with Iran, leading to a liquidity crunch and a lack of foreign exchange in the country. US measures also put pressure on a banking system already strained by the previous sanctions regime before the adoption of the JCPOA in January 2016.
+
+A re-imposition of sanctions is expected to cause a drop in Iranian oil exports, with severe repercussions. Iran is home to the world’s largest reserves of gas and is the Middle East’s third-largest oil producer. In May, BMI downgraded its GDP growth forecast for Iran to 3.1 per cent in 2018 and 0.8 per cent in 2019, from 4.3 per cent and 4.5 per cent previously.
+
+“Iran is likely to experience depreciatory pressures on the rial and rising inflation as a result of lower foreign currency inflows that will constrain domestic investment and consumption,” BMI said.
+</blockquote>
+
+<p>Unpredictability is only part of the story, in general a high inflation rate means a degradation of life quality over time, and a lower quality of life includes a lack of access to even the most basic needs. It means having to put your children in less qualified schools, it means avoiding doctor appointments by any means necessary, it means cutting corners in every section of your life, it means a less balanced environment to live in, an environment where people get angry more easily since they are under a constant pressure as a cause of their degrading lives. No matter how hard you try, your life quality only goes downhill, never up.</p>
+
+<h1 id="a-weak-economys-rippling-effect">A Weak Economy’s Rippling Effect</h1>
+
+<p>You have probably heard of <a href="https://en.wikipedia.org/wiki/Maslow's_hierarchy_of_needs">Maslow’s Hierarchy of Needs</a>. This is what it looks like:</p>
+
+<p><img src="/img/discrimination/maslow.jpg" alt="Maslow's Hierarchy of Needs. A pyramid, from top to bottom: Self-Actualization, Esteem, Love/Belonging, Safety, Physiological" /></p>
+
+<p>At the bottom, there are physiological needs, like health, food, water, sleep, shelter and sex. Only once these needs are fulfilled properly, you get motivated to even think about the next level. That means, if your physiological needs are not properly safisfied, you will not even think about safety, love and belonging, self-esteem or self-actualization.</p>
+
+<p>Now, what all these physiological needs have in common is that they are fulfilled when there is a stable economic backbone in the country you live in. Once the economic backbone is broken, you begin losing access to these physiological needs. Slowly, but surely, you lose your motivation for self-actualization, for self-esteem, for love and belonging and for safety and you hunt for your physiological needs. Once this happens for a whole population in a country, you are left with people with only one goal in their lives: to survive <em>by any means</em>.</p>
+
+<p>With no motivation for building strong friendships and relationships, no motivation for security and safety, for feeling of accomplishment and for creative acts, the population transitions towards becoming one unsafe, cold, threatening, untrustable environment with no sense of joy or creativity.</p>
+
+<p>I’m driving from my friend’s house back to mine, it’s roughly 10pm and streets are a little crowded. I’m going through streets of Azadi District, when I see two children who are probably between 15 and 17, punching each other in the face and kicking each other’s stomach over a large trash container at the side of the street. They are fighting, as if for their lives, with a ferocity you can hardly imagine to find in a child of their age. These children do not look anything like your children, their hands are black from their fingertips to their elbows from collecting trash all day long; their clothes are not new, they do not change their clothes or take showers daily, and their backs are arched for hauling a large bag of trash for a whole day over their shoulder and back. They are fighting to win a trash container. This is what happens when you put pressure on the economy of a country. This is what the media is not telling you about the effects of sanctions. This is what needs to stop about these sanctions. This is what needs action from every person knowledgable to do something to stop it. Abuse, rape and misuse of children and adults alike is a significant, visible effect of sanctions that’s often overlooked.</p>
+
+<p>It’s sad that I can not find any content regarding this matter in the media by searching. I think more content on these topics is necessary to help people be aware of the unethical and inhumane effects of sanctions on lives of innocent people.</p>
+
+<p><img src="/img/discrimination/trash-collecting.jpg" alt="A teenager collecting trash in Iran" />
+<span class="image-caption">A teenage collecting trash in the streets of Tehran.</span></p>
+
+<p>The rippling effects of a weakening economy are far worse and far-reaching than what the sanctions are supposed to do. I think it’s too optimistic to think sanctions to weaken an economy will prevent a country from spending money on something they want to spend on. What ends up happening, or at least has happened in case of Iran, is that the money is drained from places where it affects peoples lives, but I doubt anything has changed at the actual target.</p>
+
+<h1 id="of-rolling-eyes-and-shrugs">Of Rolling Eyes and Shrugs</h1>
+
+<p>Often when similar stories of this kind are shared, I am ready to see comments of people shrugging to the issue with responses like “they have to comply because it’s the law” or “that’s how you respond to a country that wants to build nuclear weapons” or similar. They just roll their eyes and shrug it off like this is how it’s supposed to be.</p>
+
+<p>Sometimes, that’s true that it’s the law and the companies have to comply (though most of the time the application of the law goes way beyond necessity). What these responses get wrong is that there is no involvement by us, the people, in the decisions and policies of our country. Solely because I live my daily life in a geographical location that resides in the boundaries of a place on Earth known as “Iran” doesn’t mean I agree with the politics of this country, or that I should be isolated from the rest of the world because some people in my country make certain decisions.</p>
+
+<p>What these replies get wrong is that in democratic countries, laws can change based on what people demand. Instead of shrugging these humanitarian issues off, please hear us out, and help echo our voice. You may not realize, but we, the people of Iran, do not have a say in what what politics our government follows or how it interacts with other countries, but you do have a say in yours. The only thing we can do is to spread the word.</p>
+
+<p>What we feel when we see these responses is: “They are terrorists so let them be”, but we are not. We are normal people like you, with less privileges, solely because of our living region.</p>
+
+<p>It seems like the Iranian people are now the common enemy of all sides of a global conflict. The ever-increasing pressure we feel is not from a single source, but rather, from all sides. We have internet censorship from the inside and restricted access from the outside. We have economic pressure from the inside, with a direct influence from the outside, and the same applies to every part of this conflict.</p>
+
+<h1 id="final-message">Final Message</h1>
+
+<p><a href="https://en.wikipedia.org/wiki/Racism">Racism</a> is defined as  “prejudice, <a href="https://en.wikipedia.org/wiki/Discrimination">discrimination</a>, or antagonism directed towards other people because they are of a different race or ethnicity”. Sanctions, likewise, are a clear case of prejudice, discrimination and antagonism directed towards people because they are born in a certain country, or reside in a certain part of the planet.</p>
+
+<p>If a person is jailed, or killed because of the color of their skin, you feel furious and protest against the act to show that racism has no place in your country. Sanctions are a case of jailing a whole country, killing the people inside by cutting their lifelines and causing lifetime distress for innocent people who didn’t do anything wrong. It’s discrimination on the scale of a whole population of millions. Although the people who are being effected by these sanctions are far away from your home, their misery is caused by your country’s policies and actions, and you have the right to stand up against these discriminations.</p>
+
+<p>Ron Paul, former congressman <a href="https://twitter.com/RonPaul/status/1162067004733476864">touches on topic in an interview</a>:</p>
+
+<blockquote>
+  <p>I think sanctions are really really bad, because it brings people in to think that “well I’m not quite as violent as other people who would use a drone”, well, hopefully it is a little bit less violent, but it’s every bit as dangerous, it’s still attacking personal liberties and it’s undermining the principle of trying to get along with people with free trade.</p>
+</blockquote>
+
+<p><a href="https://en.wikipedia.org/wiki/Universal_Declaration_of_Human_Rights">The Universal Declaration of Human Rights</a>, Article 2, states:</p>
+
+<blockquote>
+  <p>Everyone is entitled to all the rights and freedoms set forth in this Declaration, without distinction of any kind, such as race, colour, sex, language, religion, political or other opinion, national or social origin, property, birth or other status.
+Furthermore, no distinction shall be made on the basis of the political, jurisdictional or international status of the country or territory to which a person belongs, whether it be independent, trust, non-self-governing or under any other limitation of sovereignty.</p>
+</blockquote>
+
+<p>That doesn’t sound like what’s happening now by enforcement of sanctions. Silence on this massive case of discrimination against people around the world must be broken, it must be recognized that discrimination, in any form, is not to be tolerated by humans.</p>
+
+<hr />
+
+<h3 id="links">Links</h3>
+
+<ul>
+  <li><a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4897941/">NCBI: Addressing the impact of economic sanctions on Iranian drug shortages in the joint comprehensive plan of action: promoting access to medicines and health diplomacy</a></li>
+  <li><a href="https://medium.com/@hamed/yellow-badges-are-back-this-time-not-by-nazi-germany-not-for-jews-but-by-u-s-tech-companies-48e92d690176">Hamed Saeedi: Yellow badges are back. This time not by Nazi Germany &amp; not for Jews, but by U.S. tech companies</a></li>
+  <li><a href="https://medium.com/@hamed/yellow-badges-are-back-this-time-not-by-nazi-germany-not-for-jews-but-by-u-s-tech-companies-48e92d690176">Foreign Policy: U.S. Sanctions Are Killing Cancer Patients in Iran</a></li>
+  <li><a href="https://twitter.com/RonPaul/status/1162067004733476864">Ron Paul: “Sanctions Are A Deadly Act Of War”</a></li>
+</ul>
+
+  </article>
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+  <div class="post-header">
+    <h1 class="post-title"><p>Going Self-Hosted: Moving away from Google and others</p>
+</h1>
+    
+    <p class="post-meta">
+      <span>Feb 11, 2019</span>
+      
+      • <span>Reading time: 6  minutes</span>
+    </p>
+  </div>
+
+  <article class="post-content">
+    <p>Since 3 years ago, I have always been eager to move away from Google and other privacy-invading companies. I have had my successes and failures in doing so, here I’m going to put out my stack of tools for moving away from Google and going self-hosted.</p>
+
+<!--more-->
+
+<p>I first tried to move away from Google 3 years ago, and at the time, I did not have enough resources to self-host much. I started by creating my own email server, but I couldn’t afford a cloud storage. I also did not know about the alternatives available to Google Calendar, Google Keep, and other tools I was using at the time, so it was pretty hard keeping up that way.</p>
+
+<p>After a year and a half, after my phone was stolen, I decided I will stick with Google apps with the coming of my new phone. I kept using Google services for less than a year, but I was frustrated. I had given up my privacy and control over my data for convenience, but that’s not what I wanted. So I decided I’m going to switch away again, and I will self-host the tools necessary.</p>
+
+<p>A lot has changed since the first time I switched away, I will sketch below the tools that I have replaced and how.</p>
+
+<h1 id="microg">microG</h1>
+
+<p>If you want to avoid using Google Services on your Android phone, there is <a href="https://microg.org/">microG</a> for that. I flashed my phone with an <a href="http://aospextended.com/">AEX</a> ROM which supports microG, so it was not particularly hard to set-up on my phone, but I’ve heard it can be hard to set it up since it’s doing some trickery to replace Google’s services on your phone.</p>
+
+<p>This also means you have to flash a custom ROM and root your device in order to do this, so maybe this option is not for everyone, but I think with Google Services active in your phone, you can’t really be sure what’s going on behind the curtains.</p>
+
+<h1 id="email">Email</h1>
+
+<p>One of the most common means of communication for us in the digital world, we exchange a lot of information through email, including personal and work-related information. As such, I deem email an important piece of privacy-sensitive information.</p>
+
+<p>My solution for email is a self-hosted Postfix + Dovecot + SpamAssassin on my server. It is not the most straightforward thing to set up, by <a href="https://www.digitalocean.com/community/tutorials/how-to-configure-a-mail-server-using-postfix-dovecot-mysql-and-spamassassin">this DigitalOcean tutorial</a> makes it all the easier.</p>
+
+<p>I have also heard of <a href="https://mailinabox.email/">Mail-in-a-Box</a> which is supposed to make setting up your own mail server a breeze! I didn’t know about this at the time I set up my server, but it could be a better choice, so perhaps give it a try and let me know.</p>
+
+<h1 id="cloud-storage">Cloud Storage</h1>
+
+<p>A cloud storage is necessary for syncng your data among your devices and keeping your information safe from physical loss. I chose <a href="https://nextcloud.com/">Nextcloud</a> and I couldn’t be more satisfied. It has clients for every major operating system, and I use it to back up my files, synchronize my calendar and contacts between my Linux and my Android devices.</p>
+
+<p>The installation and activation is fairly straightforward, and again, I followed a <a href="https://www.digitalocean.com/community/tutorials/how-to-install-and-configure-nextcloud-on-ubuntu-16-04">DigitalOcean tutorial</a> to set up the service and have been using it since.</p>
+
+<p>I also bought a DigitalOcean Space for $5/month, with a capacity of 250G, which is a fairly good price and worth its value. See <a href="https://www.digitalocean.com/community/questions/is-it-possible-to-mount-do-spaces-as-external-storage-in-nextcloud-as-i-mount-aws-s3-storage">this discussion</a> about attaching a DigitalOcean space to Nextcloud.</p>
+
+<h1 id="contacts-and-calendar">Contacts and Calendar</h1>
+
+<p>I learned about <a href="https://f-droid.org/packages/at.bitfire.davdroid/">DAVx</a> and <a href="https://f-droid.org/en/packages/at.bitfire.icsdroid/">ICSx</a>, which are tools for syncing your contacts and calendar, with support for Google Calendar as well. This means that I can still have access to my workplace calendar which is on Google, and have my own personal calendars synchronized using Nextcloud.</p>
+
+<p>These tools integrate with whatever Calendar and Contacts application you are using on your phone, so you are free to choose whatever calendar and contacts application you like.</p>
+
+<h1 id="notes">Notes</h1>
+
+<p>For note-taking, I use a simple Markdown/todo.txt editor called <a href="https://f-droid.org/en/packages/net.gsantner.markor/">Markor</a> while Nextcloud handles the synchronization so I have access to my notes both on my computer and my phone. I use <a href="https://github.com/vimwiki/vimwiki">vimwiki</a> to organize and edit my notes on my computer. Nextcloud also provides extra applications for editing Markdown files on the web interface, which is great if you like doing everything in your browser.</p>
+
+<h1 id="application-store">Application Store</h1>
+
+<p>For downloading applications, I default to searching through <a href="https://f-droid.org/en/">F-Droid</a>, and in case I don’t find the tool I’m looking for (which I mostly do!), or I’m looking for a properietary application, such as Slack, I use <a href="https://f-droid.org/en/packages/com.dragons.aurora/">Aurora Store</a> or <a href="https://f-droid.org/en/packages/com.github.yeriomin.yalpstore/">Yalp Store</a>, which lets you search through all Google Play applications and install applications without a fuss.</p>
+
+<p>Of course, you can install the official Google Play store as well if you would like to, but I personally am cautious about using any of Google’s applications.</p>
+
+<h1 id="two-factor-authentication">Two-factor Authentication</h1>
+
+<p>I use <a href="https://github.com/andOTP/andOTP/">andOTP</a> instead of Google Authenticator. One feature I love about andOTP is the ability to take an encrypted backup of your OTP keys, so you do not have to re-set all your two-factor authentications across all services if you ever want to switch your phone.</p>
+
+<h1 id="password-manager">Password Manager</h1>
+
+<p>I switched from LastPass, with its ugly, broken and distorted user experience to <a href="https://bitwarden.com/">BitWarden</a>, and I couldn’t ask for more! The user experience is far superior compared to LastPass, the extension doesn’t kill my browser’s performance and the Android application is great, too!</p>
+
+<h1 id="firefox-containers">Firefox Containers</h1>
+
+<p>Lastly, it’s natural that we can’t completely avoid using Google’s tools, we can just try to limit Google’s access to our data and avoid being tracked as much as possible. For this purpose, I started using Firefox Containers, and God, this is a killer feature!</p>
+
+<p>So now, I have a few containers set up:</p>
+
+<ul>
+  <li>Personal: This one includes my personal accounts on websites other than Google that I want to stay logged-in on.</li>
+  <li>Work: I’m logged into services that I use for work here, and it includes Google as well, but only for work.</li>
+  <li>Google: This one, I use for accessing a personal Google Account I keep for YouTube and other services, but I’m not a serious user.</li>
+  <li><a href="https://addons.mozilla.org/en-US/firefox/addon/temporary-containers/">Temporary Containers</a>: Any websites that I have not explicitly chosen to be opened in one of the above containers, opens up in a new, temporary container, which means it doesn’t have access to any cookies or information from the other containers. I may sometimes choose to open Google or other services in Temporary Containers as well if I don’t see the necessity to be logged in.</li>
+</ul>
+
+<p>This means Google will not be able to track me using my account when I’m logged in to other services since they live in a different container, even though other methods such as <a href="https://clearcode.cc/blog/device-fingerprinting/">device fingerprinting</a> are still possible. With Firefox’s Tracking Protection and <a href="https://addons.mozilla.org/en-US/firefox/addon/ublock/">uBlock</a> always turned on, I am less concerned about tracking.</p>
+
+<h1 id="not-the-easiet-thing">Not the easiet thing</h1>
+
+<p>I have to admit, it’s not the easiest thing to move your digital life away from the giants, their products are built for maximum convenience, so you can’t expect to have that maximum convenience if you stop using those products, and I think it’s a far-fetched ideal to expect the same level of convenience using free applications and tools, but I personally think it’s worth it.</p>
+
+
+  </article>
+
+  <div class="share-page">
+    Share in
+
+    <a href="https://twitter.com/intent/tweet?text=Going Self-Hosted: Moving away from Google and others&url=http://localhost:4000/self-hosted/&via=&related=" rel="nofollow" target="_blank" title="Share on Twitter">Twitter</a>
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diff --git a/site/sitemap.xml b/site/sitemap.xml
new file mode 100644
index 0000000..c8649fd
--- /dev/null
+++ b/site/sitemap.xml
@@ -0,0 +1,107 @@
+<?xml version='1.0' encoding='UTF-8'?>
+<urlset xmlns='http://www.sitemaps.org/schemas/sitemap/0.9'>
+    <url>
+        <loc>http://localhost:4000/css-filters/</loc>
+        <lastmod>2022-06-28T15:49:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/broadcastchannel-api/</loc>
+        <lastmod>2022-06-28T15:49:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/es7-array-generator-comprehensions/</loc>
+        <lastmod>2022-06-28T15:49:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/autocomplete-predict-trie/</loc>
+        <lastmod>2022-06-28T15:49:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/open-source-good-bad-ugly/</loc>
+        <lastmod>2022-06-28T15:49:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/immortals-go-extinct/</loc>
+        <lastmod>2022-06-28T15:49:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/stop-high-frequency-fuck-ups/</loc>
+        <lastmod>2022-06-28T15:49:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/dont-chase-become-the-good-one/</loc>
+        <lastmod>2022-06-28T15:49:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/primitive-living-lessons-0/</loc>
+        <lastmod>2022-06-28T15:49:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/travis-ci-pr-push/</loc>
+        <lastmod>2022-06-28T15:49:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/diy-cardboard-kindle-stand/</loc>
+        <lastmod>2022-06-28T15:49:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/typoclassopedia-exercise-solutions/</loc>
+        <lastmod>2022-06-28T15:49:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/mathematical-induction-proving-tiling-methods/</loc>
+        <lastmod>2022-06-28T15:49:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/self-hosted/</loc>
+        <lastmod>2022-06-28T15:49:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/sanctions-discrimination-isolation-iran</loc>
+        <lastmod>2022-06-28T15:49:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/alternative-objectivity-and-inherent-subjectivity/</loc>
+        <lastmod>2022-06-28T15:49:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/rust-box-str-vs-string/</loc>
+        <lastmod>2022-07-01T10:23:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/about/</loc>
+        <lastmod>2022-06-17T13:42:06+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/art/</loc>
+        <lastmod>2022-07-06T17:36:29+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/</loc>
+        <lastmod>2022-07-01T10:23:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/life/</loc>
+        <lastmod>2022-06-03T18:02:06+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/css/main.css</loc>
+        <lastmod>2022-06-03T18:02:06+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/math/</loc>
+        <lastmod>2022-06-03T18:02:06+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/programming/</loc>
+        <lastmod>2022-06-03T18:02:06+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/snippets/</loc>
+        <lastmod>2022-06-28T15:49:30+01:00</lastmod>
+    </url>
+    <url>
+        <loc>http://localhost:4000/travel/</loc>
+        <lastmod>2022-06-03T18:02:06+01:00</lastmod>
+    </url>
+</urlset>
\ No newline at end of file
diff --git a/site/snippets/index.html b/site/snippets/index.html
new file mode 100644
index 0000000..f417b77
--- /dev/null
+++ b/site/snippets/index.html
@@ -0,0 +1,1561 @@
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+
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+  <meta name="description" content="a rabbit hole">
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+  <link rel="alternate" type="application/rss+xml" title="mahdi" href="http://localhost:4000/feed.xml" />
+
+  
+
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+
+  <script>
+    var channel = new BroadcastChannel('egg');
+
+    channel.addEventListener('message', message => {
+      alert('Got a message from the other tab:\n' + message.data);
+    });
+  </script>
+</head>
+
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+
+  <body>
+
+    <header class="site-header">
+
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+    <a class='site-title' href='/'>
+      mahdi
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+
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+
+
+    <div class="page-content">
+      <div class="wrapper">
+        <h1 class="page-heading"></h1>
+        
+          <div class='post lang-en'>
+
+  <div class="post-header">
+    <h1 class="post-title"><p>Snippets</p>
+</h1>
+    
+    <p class="post-meta">
+      <span>Dec 7, 2020</span>
+      
+      • <span>Reading time: 57  minutes</span>
+    </p>
+  </div>
+
+  <article class="post-content">
+    <p>Short snippets of thought. Ramblings. Random shite.</p>
+
+<hr />
+
+<p>Was thinking about what is creativity: connection of seemingly irrelevant concepts. Puns are creative because they make a non-obvious connection. The connection is not nonsensical, but not obvious either.</p>
+
+<hr />
+
+<p>On Neurodiversity: Dyslexia is not a disorder if society doesn’t depend on reading so much. Reading new invention. What about people who have trouble using technology? Is that a disorder? Is it a bug of the reading and writing systems or humans? What if it was on a computer screen? Would we think of it still as a disease or would we fix the program?</p>
+
+<hr />
+
+<p>Pieces from Austerlitz:
+“As I think of how little we can hold in mind, how everything is constantly lapsing into oblivion with every extinguished life, how the world is, as it were, draining itself, in that the history of countless places and objects which themselves have no power of memory is never heard, never described or passed on”</p>
+
+<p>“All I could think was that such a sentence only appears to mean something, but in truth is at best a makeshift expedient, a kind of unhealthy growth issuing from our ignorance, something which we use, in the same was many sea plants and animals use their tentacles, to grope blindly through the darkness enveloping us. The very thing which may usually convey a sense of purposeful intelligence- the exposition of an idea by means of a certain stylistic facility-now seemed to me nothing but an entirely arbitrary or deluded enterprise.”</p>
+
+<p>“I sensed that in truth, I had neither memory nor the power of thought, nor even any existence, that all my life had been a constant process of obliteration, a turning away from myself and the world. If someone had come then to lead me away to a place of execution I would have gone meekly, without a word, without so much as opening my eyes.”</p>
+
+<p>“In this dreadful state of mind I sat for hours, for days on end with my face to the <i>wall</i>, tormenting myself and gradually discovering the horror of finding that even the smallest task or duty, for instance arranging assorted objects in a drawer, can be beyond one’s power.”</p>
+
+<p>“At some time in the past, I thought, I must have made a mistake, and now I am living the wrong life.”</p>
+
+<p>“Marie moved closer to me and asked whether I had remembered that tomorrow was my birthday. When we wake up tomorrow, she said, I shall with you every happiness, and it will be like telling a machine working by some unknown mechanism that I hope it will run well. Can’t you tell me the reason, she asked, said Austerlitz, why ou remain so unapproachable? Why, she said, have you been like a pool of frozen water ever since we came here? Why do I see your lips opening as if you were about to say something, maybe even cry out loud, and then I hear not the slightest sound? Why did you never unpack when we arrived, always preferring to live out of a rucksack, as it were? We stood there a couple of paces apart, like two actors on stage. The colour of Marie’s eyes changed as the light dimmed. And once again I tried to explain to her and to myself what incomprehensible feelings had been weighing on me over the last few days; how I kept thinking, like a madman, that there were mysterious signs and portents all around me here; how it even seemed to me as if the silent facades of the buildings knew something ominous about me, how I had always believed I must be alone, and in spite of my longing for her I now felt it more than ever before.”</p>
+
+<p>“That evening in Marienbad, said Austerlitz, I could not admit to myself how right everything Marie said was, but today I know why I felt obliged to turn away when anyone came too close to me, I know that I thought this turning away made me safe, and that at the same time I saw myself transformed into a frightful and hideous creature, a man beyond the pale.”</p>
+
+<p>“What made me uneasy at the sight of it, however, was not the question of whether the complex form of the capital, now covered with a puce-tinged encrustation, had really impressed itself on my mind when I passed through Pilsen with the children’s transport in the summer of 1939, but the idea, ridiculous in itself, that this cast-iron column, which with its scaly surface seemed almost to approach the nature of a living being, might remember me and was, if I may so put it, said Austerlitz, a witness to what I could no longer recollect for myself.”</p>
+
+<p>“Might it not be, continued Austerlitz, that we also have appointments to keep in the past, in what has gone before and is for the most part extinguished, and must go there in search of places and people who have some connection with us on the far side of time, so to speak?”</p>
+
+<p>“No one can explain exactly what happens within us when the doors behind which our childhood terrors lurk are flung open.”</p>
+
+<hr />
+
+<p>“What if some day or night, a demon were to steal after you into your loneliest loneliness and say to you: “This life as now live it and have lived it, you will have to live once more and innumerable times more; and there will be nothing new in it, but every pain and every joy and every thought and sigh and everything unutterably small or great in your life will have to return to you, all in the same succession and sequence–even this spider and this moonlight between the trees, and even this moment and I myself. The eternal hourglass of existance is turned upside down again and again, and you with it, speck of dust!” Would you not throw yourself down and gnash your teeth and curse the demon who spoke thus? Or have you once experienced a tremendous moment when you would have answered him: “You are a god and never have I heard anything more divine.” If this thought gained possession of you, it would change you as you are, or perhaps crush you.” - Nietzsche</p>
+
+<hr />
+
+<p>Pieces from The Reader’s Block by David Markson:</p>
+
+<p>“If an ox could paint a picture, his god would look like an ox. Said Xenophanes”</p>
+
+<p>“What has happened? It is life that has happened; and I am old.”</p>
+
+<p>“Despite decades of self analysis, Freud was so anxiety-ridden about missing trains that he would arrive at the station as much as an hour early. Freud.”</p>
+
+<p>Sylvia Plath: Horder prescribed her an anti-depressant, a monoamine oxidase inhibitor, a few days before her suicide. Knowing she was at risk alone with two young children, he says he visited her daily and made strenuous efforts to have her admitted to a hospital; when that failed, he arranged for a live-in nurse. Commentators have argued that because anti-depressants may take up to three weeks to take effect, her prescription from Horder would not have taken full effect.
+The nurse was due to arrive at nine on the morning of February 11, 1963, to help Plath with the care of her children. Upon arrival, she could not get into the flat but eventually gained access with the help of a workman, Charles Langridge. They found Plath dead of carbon monoxide poisoning with her head in the oven, having sealed the rooms between her and her sleeping children with tape, towels and cloths. At approximately 4:30 a.m. Plath had placed her head in the oven, with the gas turned on. She was 30 years old. She left bread and butter and milk in the bedroom for her two children who were sleeping.</p>
+
+<p>“John Donne posed for a painting in his own shroud. And kept it beside his bed during a long final illness.”</p>
+
+<p>“Manet was so vituperatively condemned by critics that for a time he was too embarrassed to ask anyone to pose for him.
+Before Cezanne had gained any recognition he once burst into tears when someone sincerely admired his work”</p>
+
+<p>“The Persians deployed so many bowmen at Thermopylae that it was said their arrows would blot out the sun.
+To which a Spartan commander: all the better, then we will be fighting in the shade
+In fact only two Spartans survived Thermopylae. One was killed in a battle elsewhere. The other hanged himself in disgrace.”</p>
+
+<p>“At twenty, Bach made a pilgrimage of more than two hundred miles, on foot, to hear Buxtehude play the organ.”</p>
+
+<p>“Aesop was a slave. Terence was a slave. Epictetus was a slave.”</p>
+
+<p>“I am weary, Ananda, and wish to lie down.”</p>
+
+<p>Galileo’s Abjuration 1633 …I abjure with sincere heart and unfeigned faith, I curse and detest the said errors and heresies, and generally all and every error and sect contrary to the Holy Catholic Church. And I swear that for the future I will neither say nor assert in speaking or writing such things as may bring upon me similar suspicion; and if I know any heretic, or one suspected of heresy, I will denounce him to this Holy Office, or to the Inquisitor and Ordinary of the place in which I may be. I also swear and promise to adopt and observe entirely all the penances which have been or may be by this Holy Office imposed on me. And if I contravene any of these said promises, protests, or oaths, (which God forbid!) I submit myself to all the pains and penalties which by the Sacred Canons and other Decrees general and particular are against such offenders imposed and promulgated. So help me God and the Holy Gospels, which I touch with my own hands.  I Galileo Galilei aforesaid have abjured, sworn, and promised, and hold myself bound as above; and in token of the truth, with my own hand have subscribed the present schedule of my abjuration, and have recited it word by word. In Rome, at the Convent della Minerva, this 22nd day of June, 1633.  I, Galileo Galilei, have abjured as above, with my own ha</p>
+
+<p><a href="https://en.wikipedia.org/wiki/And_yet_it_moves">“Eppur si muove”</a></p>
+
+<p>“Petrarch sometimes wrote letters to long-dead authors. He was also a dedicated hunter of classic manuscripts. Once, after discovering some previously unknown works of Cicero, he wrote Cicero the news.”</p>
+
+<p>“Poe was expelled from West Point for refusing to obey military orders. Later, James McNeill Whistler would fail there academically.”</p>
+
+<p>“im westen nichts neues: nothing new in the west”</p>
+
+<p>“Impoverished and freezing, Gerard de Nerval hanged himself near a cheap Paris doss-house after no one responded to his late-night knock”</p>
+
+<p>“Walter Benjamin committed suicide at the border between France and Spain in 1940. Fleeing the Nazis, he had been turned back by Spanish authorities.”</p>
+
+<p>“The vocabulary in Shakespeare’s plays includes 29,066 different words. There are 29,899 different words in Ulysses.”</p>
+
+<p>Jarndyce and Jarndyce</p>
+
+<p>Occam’s razor</p>
+
+<p>“Life is a long preparation for something that never happens” -Yeats</p>
+
+<p>“Mark Rothko committed suicide by slashing the inside of his arms at the elbows with a double-edged razor blade. First folding Kleenex over one edge of the blade to keep from cutting his fingers”</p>
+
+<p>“Jacques Louis David’s <em>Death of Socrates</em> shows Plato seated at the scene in despair. In the <em>Phaedo</em>, Plato says he was sick and not there.”</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Maya_Lin?wprov=sfti1">Maya Lin</a></p>
+
+<p>“Horace dictated that a writer should set aside a finished poem for nine years. And only then decide if it is worth publishing.”</p>
+
+<p>“Unquestionably it would have been Mary Magdalen who did the dishes at the Last Supper. Concluded Marguerite Yourcenar.”</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Bohemianism">Bohemianism</a></p>
+
+<p><a href="https://en.wikipedia.org/wiki/Jean-Baptiste_Lully?wprov=sfti1">Lully</a> died from gangrene, having struck his foot with his long conducting staff during a performance of his Te Deum to celebrate Louis XIV’s recovery from surgery. He refused to have his leg amputated so he could still dance.</p>
+
+<p>“The tyranny of the ignoramuses is insurmountable and assured for all time. Said Einstein.”</p>
+
+<p>“Mithridates. Who as Housman says took poison in small doses, to build an immunity. And was run through by a sword.”</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Heinrich_von_Kleist?wprov=sfti1">Heinrich von Kleist</a>: On November 21, 1811, the two traveled from Berlin to Wannsee. Prior to their departure, they both penned farewell letters, which along with an account of the final night they spent at the inn Gasthof Stimming, are now part of world literature. Upon their arrival in the vicinity of the Wannsee in Potsdam, Kleist first shot Henriette and then turned the gun on himself. They were buried together in a common grave at Kleine Wannsee (Bismarckstrasse), which has become a tourist attraction.</p>
+
+<p>“Bertrand Russell, <em>re</em> having contemplated suicide at sixteen: I did not, however, commit suicide, because I wished to know more about mathematics.”</p>
+
+<p>“During his interlude with George Sand, Alfred de Musset more than once woke up not long after exhausting sex to find her gone from bed. Intently at work on a novel.”</p>
+
+<p>“Et Verbum caro factum est: And the Word was made flesh”</p>
+
+<p>“Our life is but a warfare and a stranger’s sojourn -Marcus Aurelius”</p>
+
+<p>”‘<a href="http://www.artandpopularculture.com/Come_Back_to_the_Raft_Ag%27in%2C_Huck_Honey%21">Come Back to the Raft Ag’in, Huck Honey!</a>’ argued a recurrent theme in American literature was an unspoken or implied homoerotic relationship between men, famously using Huckleberry Finn and Jim as examples. Pairs of men flee for wilderness rather than remain in the civilizing and domesticated world of women.”</p>
+
+<p>“Michelangelo finished <em>The Last Judgement</em> in 1541. Fourteen years later Pope Paul IV ordered Daniele da Volterra to drape forty of the naked figures. Which Salvator Rosa would subsequently suggest made the whole wall look like a public bath.”</p>
+
+<p>“Sweet the nails, sweet the wood 
+<br />
+Which bore so sweet a burden”</p>
+
+<p>“Then we will have Homer and <em>Don Quixote</em>, and then we will have saunter and chat, and one more laugh before we die. Said William Cowper, who was mad through most of his life.”</p>
+
+<p>“One does not finish a poem, one only abandons it.”</p>
+
+<p><a href="https://www.youtube.com/watch?v=U_yxtaeFuEQ&amp;feature=youtu.be">Jacqueline du Pré</a></p>
+
+<p>Verweile doch, du bist so schön: Stay a while, you are so beautiful</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Longinus">Longinus</a> is the name given to the <em>unnamed</em> Roman soldier who pierced the side of Jesus with a lance and who in medieval and some modern Christian traditions is described as a convert to Christianity.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Jerusalem_Delivered?wprov=sfti1">Tasso</a> suffered from mental illness and died a few days before he was due to be crowned on the Capitoline Hill as the king of poets by the Pope.</p>
+
+<p>All of Plato came down from antiquity in less maimed form than any other writings, an undeniable sign of the esteem in which it was held.
+Nonetheless when Aquinas and other medieval thinkers referred to <em>the</em> philosopher, with no additional identification, it was universally understood that Aristotle was meant.</p>
+
+<p>il maestro di color che sanno: the master of those who know</p>
+
+<p>Within a few days of his death, Akhmatova wrote:
+<br />
+Terror fingers all things in the dark,
+<br />
+Leads moonlight to the axe.
+<br />
+There’s an ominous knock behind the wall:
+<br />
+A ghost, a thief or a rat…
+<br /></p>
+
+<p>As Nietzsche saw it, the last Christian died on the Cross. (Mahdi: Christianity was not a thing until after Christ’s death though)</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Tecumseh">Tecumseh</a></p>
+
+<p>Mary Shelley was nineteen when she finished Frankenstein</p>
+
+<p>Je finis par trouver sacre le desordre de mon esprit: I end up finding sacred the disorder of my mind</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Simeon_Stylites">Simeon Stylites</a>, who spent thirty-six years on top of a sixty-foot pillar in the Syrian desert. For most of that time his body a mass of maggot-infested sores.
+The maggots no more than eating what God had intended for them, he said.</p>
+
+<p>In 65 AD, Gaius Calpurnius Piso, a Roman statesman, organized a conspiracy against Nero with the help of Subrius Flavus and Sulpicius Asper, a tribune and a centurion of the Praetorian Guard. According to Tacitus, many conspirators wished to “rescue the state” from the emperor and restore the Republic. The freedman Milichus discovered the conspiracy and reported it to Nero’s secretary, Epaphroditos. As a result, the conspiracy failed and its members were executed including Lucan, the poet. Nero’s previous advisor Seneca was accused by Natalis; he denied the charges but was still ordered to commit suicide as by this point he had fallen out of favor with Nero. Also Petronius. Lucan was 25 and recited his own verses as he bled to death.</p>
+
+<p>Three years later Nero would be a suicide on his own part.</p>
+
+<p>Lorenzo Ghiberti worked for 21 years on the eastern gates of the <a href="https://en.wikipedia.org/wiki/Florence_Baptistery">Florence Baptistery</a>. Michelangelo dubbed them the <a href="https://www.khanacademy.org/humanities/renaissance-reformation/early-renaissance1/sculpture-architecture-florence/v/ghiberti-gates-paradise">Gates of Paradise</a>.</p>
+
+<p><a href="https://www.youtube.com/watch?v=QvshzV591Gg&amp;feature=youtu.be">Salomé’s Dance</a></p>
+
+<p>“I tell you before God, and as an honest man, your son is the greatest composer known to me by person and repute, he has taste and what is more the greatest skill in composition”. Joseph Haydn told Mozart’s father.</p>
+
+<p>Children depart, miscellaneous relationships wither. Friends move to distant places. Friends die.</p>
+
+<p>Non amo te</p>
+
+<p>Sempre libera</p>
+
+<p>The question of truth versus legend in Alexander’s having razed Persepolis at the bidding of Thais. The fair certainty that excessive wine played a part.</p>
+
+<p>In Las Meninas, <a href="https://en.wikipedia.org/wiki/Maria_B%C3%A1rbola?wprov=sfti1">Maria Bárbola</a> is depicted in an unusual way for a person in her position at the time. While people with dwarfism normally did not enjoy much respect in the 17th century and were often depicted in an insulting fashion, Maria Bárbola is depicted in a dignified position, standing upright beside the princess, with a thoughtful and controlled expression, meeting the eyes of the viewer.</p>
+
+<p>Cento: patchwork composition of quotations</p>
+
+<p>In Canto IV of the <em>Inferno</em>, which is to say with 96 percent of his chief work yet unwritten, Dante has the temerity to rank himself sixth in the company of Homer, Virgil, Horace, Ovid and Lucan. Underestimating.</p>
+
+<p>Sir John Denham once saved George Wither from being hanged by pleading that so long as Wither was alive, he, Denham, could never be the worst poet in England.</p>
+
+<p>Except for Aquinas and the Bible, Descartes almost never read a word. He called the classics a waste of time.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Animula_vagula_blandula">Animula vagula blandula</a></p>
+
+<p>Bentham defined as the “fundamental axiom” of his philosophy the principle that “it is the greatest happiness of the greatest number that is the measure of right and wrong.”</p>
+
+<p>“Caddy held me. She smelled like trees”</p>
+
+<p>Freud had thirty-three operations for cancer on his mouth and throat. Joyce had twenty-five operations on his eyes.</p>
+
+<p>On mourra seul: we will die alone.</p>
+
+<p>Philosopher: lover of knowledge</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Djuna_Barnes">Djuna Barnes</a> had no formal education whatsoever.</p>
+
+<p>Caxton me fieri fecit: Caxton caused me to be made.</p>
+
+<p>Ah, what a dusty answer gets the soul <br />
+When hot for certainties in this our life</p>
+
+<p>“Art will remain the most astonishing activity of mankind born out of struggle between wisdom and madness, between dream and reality in our mind.” -Magdalena Abakanowicz</p>
+
+<p>God is dead, everything is permitted.</p>
+
+<p>Preoccupied, Beethoven was known to lather his face and then forget to shave. He also possessed an unstrung piano, adequate in his deafness.</p>
+
+<p>From Rabelais’s will: I have nothing. I owe much. The rest I leave to the poor.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Nadezhda_von_Meck">Nadezhda von Meck</a>: She is best known today for her artistic relationship with Pyotr Ilyich Tchaikovsky, supporting him financially for thirteen years, so that he could devote himself full-time to composition, while stipulating that they were never to meet. Tchaikovsky dedicated his Symphony No. 4 in F minor to her. She also gave financial support to several other musicians, including Nikolai Rubinstein and Claude Debussy.</p>
+
+<p>I do not believe in God, though I believe in Picasso, said Diego Rivera.</p>
+
+<p>Thy necessity is greater than mine. Said Philip Sidney, in passing a drink to a dying soldier while dying himself.</p>
+
+<p>No needle marks on your Annunciation’s arm now.</p>
+
+<p>We do not come to thoughts. They come to us.</p>
+
+<p>I am! yet what I am who cares, or knows? <br />
+My friends forsake me like a memory lost. <br />
+I am the self-consumer of my woes.</p>
+
+<p>Wallace Steven’s wife Elsie was the model for the face on the United States dime and half-dollar.<br />
+Wallace Steven’s wife Elsie and Wallace Stevens had separate bedrooms.</p>
+
+<p>When I could have used a wife, I could not support one; when I could support one, I no longer needed any. Said Kant.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Percy_Williams_Bridgman?wprov=sfti1">Percy Williams Bridgman</a>, who received the 1946 Nobel Prize in Physics committed suicide.</p>
+
+<p>By the early Middle Ages, every third church in Europe claimed to possess splinters from the True Cross. Or the nails. Or thorns from the Crown of Thorns. Several heads of John the Baptist existed, at least as many corpses of Mary Magdalen. Not to add Christ’s foreskin.</p>
+
+<p>Nietzsche lost his reason because he thought too much. I do not think and therefore cannot go mad. Said Nijinsky, mad.</p>
+
+<p>When Dickens, at twelve, worked from 8 A.M. until 8 P.M., six days a week, at the blacking factory, he also walked an hour each way to and from his family’s Camden Town slum. And spent Sunday visiting his father in debtor’s prison.</p>
+
+<p>A small inheritance a few months later allowed his family to leave prison. Dickens was finally allowed to attend school over his mother’s objections — she did not want to lose his income. School was short-lived though: At fifteen, Dickens had to return to work. Dickens never got over the time he spent at Warren’s and his fierce sense of betrayal and rage at his mother’s callousness stayed with him for life. Recalling that time, he said: “I never afterwards forgot, I never shall forget, I never can forget, that my mother was warm for my being sent back [to Warren’s Blacking].”</p>
+
+<p>Sir Thomas Browne wished that men could reproduce without intercourse. Like trees, he suggested. Fathering twelve children nevertheless.</p>
+
+<p>‘Between life and death there is a library,’ she said. ‘And within that library, the shelves go on for ever. Every book provides a chance to try another life you could have lived. To see how things would be if you had made other choices . . . Would you have done anything different, if you had the chance to undo your regrets?’ -Matt Haig</p>
+
+<p>October 7, 1849. At forty, in Baltimore. Filthy, starving, drunk and/or with delirium tremens, crying out at unseen creatures.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Ruth_Ann_Steinhagen">Ruth Ann Steinhagen</a>: She told her doctors, after the incident, “I used to go to all the ball games to watch him. We used to wait for them to come out of the clubhouse after the game, and all the time I was watching I was building in my mind that idea of killing him.”[5] In 1948, Steinhagen’s family sent her to a psychiatrist, but her obsession didn’t diminish, even after Waitkus was traded to Philadelphia.[3] After the shooting, police found extensive clippings in her suitcase and even pictures papering the ceiling of her bedroom.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Tanaquil_Le_Clercq">Tanaquil Le Clercq</a>. Performing major roles for Balanchine at seventeen. And in a wheelchair from polio not ten years later.</p>
+
+<p>An enormous dungheap, Voltaire dismissed the sum of Shakespeare as.</p>
+
+<p>Le monde est fait pour aboutir à un beau livre: The world was made in order to result in a beautiful book. Stéphane Mallarmé</p>
+
+<p>Oscar Wilde: “One would have to have a heart of stone to read the death of little Nell without dissolving into tears…of laughter”.</p>
+
+<p>When Hemingway committed suicide, it was by leaning to press his forehead against the barrels of a shotgun braced at the floor. Thirty-odd years earlier his father had used a revolver.</p>
+
+<p>In the decade before his death, Ad Reinhardt painted nothing but black canvases.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Edwin_Arlington_Robinson">Edwin Arlington Robinson</a> who was nominated for Nobel Prizei in Literature four times, was working ten hours a day on the construction of a New York subway in his mid-thirties. Checking materials for twenty cents an hour.</p>
+
+<p>Virgil worked on the <em>Aeneid</em> for eleven years. And said near his death that it was not finished and should be burned.</p>
+
+<p>Levi-Strauss: The invention of melody is the supreme mystery of man.</p>
+
+<p>Men never do evil so completely and so cheerfully as when they do it from religious conviction. Said Pascal.</p>
+
+<p>Jeanne Hebuterne, with child, jumped from a window on the morning after Modigliani’s death.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Enantiosis?wprov=sfti1">Enantiosis</a>:<br />
+By honour and dishonour, by evil report and good report: as deceivers, and yet true; <br />
+As unknown, and yet well known; as dying, and, behold, we live; as chastened, and not killed; <br />
+As sorrowful, yet alway rejoicing; as poor, yet making many rich; as having nothing, and yet possessing all things. <br /></p>
+
+<p>It cost Baudelaire five years of letters and poems to coax Madame Sabatier into bed. Once. Whatever calamity occured, the affair was terminated on the same night.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Dies_irae?wprov=sfti1">Dies irae</a>, latin poem about judgement day.</p>
+
+<p>Kafka laughed repeatedly when he was reading his own work.</p>
+
+<p>Ignis fatuus: will’o the wisp</p>
+
+<p><a href="https://en.wikipedia.org/wiki/K%C3%A4the_Kollwitz">Käthe Kollwitz</a> dark etchings / drawings / illustrations.</p>
+
+<p>Elizabeth Shaw Melville: Herman has taken to writing poetry. You need not tell anyone, for you know how such things get around.</p>
+
+<p>This Way for the Gas, Ladies and Gentlemen. Two years after the book’s appearance Borowski committed suicide. Via gas.</p>
+
+<p>“It was a dark and stormy night; the rain fell in torrents—except at occasional intervals, when it was checked by a violent gust of wind which swept up the streets (for it is in London that our scene lies), rattling along the housetops, and fiercely agitating the scanty flame of the lamps that struggled against the darkness.” (<a href="https://marginalrevolution.com/marginalrevolution/2011/12/the-opening-sentences-of-paul-clifford.html">Opening lines of Paul Clifford</a>)</p>
+
+<p>Kant knew no music. And said that reading novels diluted the mind.</p>
+
+<p>Though I never saw him, or had any personal communication with him, now that he is suddenly dead I realise that he was nearer, dearer and more important to me than anyone else. Said Tolstoy of Dostoievsky. (Mahdi: I used this method to measure how much I love someone. By imagiging how I would feel if they died.)</p>
+
+<p>O yes! I am poison’d; mother, make my bed soon,<br />
+For I’m sick at the heart, and I fain wald lie down.</p>
+
+<p><a href="https://www.wikiart.org/en/kay-sage">Key Sage artworks</a></p>
+
+<p><a href="https://en.wikipedia.org/wiki/Isabel_Nicholas">Isabel Nicholas painter</a></p>
+
+<p>Trying to articulate for himself precisely why or even when it was that he commenced to fall out of touch. Not to call. Not to go. Not to do. Or was he not even that fully aware of the process until he found it to be a fait accompli?</p>
+
+<p>“I am going to put myself to sleep now for a bit longer than usual. Call it Eternity.”- jerzy Kosinski</p>
+
+<p>An audience of fully three thousand gave Akhmatova a standing ovation after a reading in Moscow in 1944. About which Stalin, hearing of it: Who <em>organised</em> this response?</p>
+
+<p>She has no wit, but enough sound human sense to be able to fulfill her duties as a wife and mother. Said Mozart of Constanze.</p>
+
+<p>Kant almost certainly died a virgin.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Lou_Andreas-Salom%C3%A9">Lou Andreas-Salomé</a></p>
+
+<p>Patrick Kavanagh was married for the first time at sixty-three. And died the same year.</p>
+
+<p>It is my general impression that the editors of <em>Partisan Review</em> are capable, educated, intelligent, but have nothing to say. Said Leon Trotsky.</p>
+
+<p>Never to have been born is best.</p>
+
+<p>Jonathan Swift left his money to found a hospital for insane. And died mad.</p>
+
+<p>I couldn’t read it. The human mind isn’t that complex. Said Einstein, returning a Kafka to Thomas Mann.</p>
+
+<p>Pascal was a hypochondriac.</p>
+
+<p>This long disease, my life.
+That long malaise, my life.</p>
+
+<p>Eliot’s first wife Vivien was in a mental institution for the nine years before her death in 1947.</p>
+
+<p>Joyce’s daughter Lucia was in a mental institution for the forty-six years before her death in 1982.</p>
+
+<p>Heinrich Heine: Dieu me pardonnera c’est son metier. (God will pardon me, that’s his job.)</p>
+
+<p>Dein aschenes haar (your ashen hair)</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Ludwig_Boltzmann">Ludwig Boltzmann</a>, who provided the current definition of entropy $S=k_B \ln\Omega$, committed suicide.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/N%C3%A2z%C4%B1m_Hikmet">Nazim Hikmet</a>: Only the Americans didn’t give me a visa.</p>
+
+<p>Praxiteles’ mistress/model Phyrne was once on the verge of being convicted of impiety. It appears factual that the orator Hyperides, defending her, signaled for her to bare her bosom. And won acquittal.</p>
+
+<p>In his <a href="https://en.wikipedia.org/wiki/The_Beheading_of_St_John_the_Baptist_(Caravaggio)"><em>Beheading of John the Baptist</em></a>, Caravaggio spells out his name in some of the Baptist’s spilled blood at the lower edge of the canvas. Otherwise he signed no paintings.</p>
+
+<p>Gaudeamus Igitur (So Let Us Rejoice)</p>
+
+<p>Living in slums, literally pawning clothes to buy food, at times Karl Marx could not afford paper to write on. Between 1850 and 1855 three of his children died. For one he had to beg a loan for a coffin.</p>
+
+<p>The casual face of Judith on <a href="https://en.wikipedia.org/wiki/Judith_Beheading_Holofernes_(Caravaggio)"><em>Judith Beheading Holofernes</em></a></p>
+
+<p><img src="/img/snippets/Judith_Beheading_Holofernes_-_Caravaggio.jpg" alt="Judith BEheading Holofernes" /></p>
+
+<p>Moritz Schlick was shot and killed on the steps of the university library in Vienna by a student whose thesis he had failed.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Jules_Bastien-Lepage">Jules Bastien Lepage</a></p>
+
+<p><img src="/img/snippets/Going_to_School_1882_by_Jules_Bastien-Lepage.jpg" alt="Going_to_School_1882_by_Jules_Bastien-Lepage" /></p>
+
+<p>If indeed three or four years, will Protagonist have at least begun to become accustomed to the solitude? Accustomed, or wearily acquiescent, does Reader mean?</p>
+
+<p>When Queen Christina of Sweden hired Descartes as a personal philosophy tutor in 1649, she dispatched a warship under a full admiral to convey him to Stockholm. But then demanded daily instruction at 5 A.M. in the Scandinavian winter. Descartes caught pneumonia and died.</p>
+
+<p>gnōmōn, literally: “one that knows or examines”</p>
+
+<p>Go tell the Spartans, stranger passing by,<br />
+that here, obedient to their laws, we lie.<br />
+<a href="http://battle-of-thermopylae.eu/main_monuments.html">Steven Pressfield, in Gates of Fire</a></p>
+
+<p><a href="https://en.wikipedia.org/wiki/James_George_Frazer">James George Grazer</a>: The Golden Bough, mythology, etc.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Arthur_Koestler?wprov=sfti1">Arthur Koestler</a> committed suicide with his wife Cynthia. The notes:</p>
+
+<blockquote>
+  <p>To whom it may concern.</p>
+</blockquote>
+
+<blockquote>
+  <p>The purpose of this note is to make it unmistakably clear that I intend to commit suicide by taking an overdose of drugs without the knowledge or aid of any other person. The drugs have been legally obtained and hoarded over a considerable period.</p>
+</blockquote>
+
+<blockquote>
+  <p>Trying to commit suicide is a gamble the outcome of which will be known to the gambler only if the attempt fails, but not if it succeeds. Should this attempt fail and I survive it in a physically or mentally impaired state, in which I can no longer control what is done to me, or communicate my wishes, I hereby request that I be allowed to die in my own home and not be resuscitated or kept alive by artificial means. I further request that my wife, or a physician, or any friend present, should invoke habeas corpus against any attempt to remove me forcibly from my house to hospital.</p>
+</blockquote>
+
+<blockquote>
+  <p>My reasons for deciding to put an end to my life are simple and compelling: Parkinson’s disease and the slow-killing variety of leukaemia (CCI). I kept the latter a secret even from intimate friends to save them distress. After a more or less steady physical decline over the last years, the process has now reached an acute state with added complications which make it advisable to seek self-deliverance now, before I become incapable of making the necessary arrangements.</p>
+</blockquote>
+
+<blockquote>
+  <p>I wish my friends to know that I am leaving their company in a peaceful frame of mind, with some timid hopes for a de-personalised after-life beyond due confines of space, time and matter and beyond the limits of our comprehension. This “oceanic feeling” has often sustained me at difficult moments, and does so now, while I am writing this.</p>
+</blockquote>
+
+<blockquote>
+  <p>What makes it nevertheless hard to take this final step is the reflection of the pain it is bound to inflict on my surviving friends, above all my wife Cynthia. It is to her that I owe the relative peace and happiness that I enjoyed in the last period of my life – and never before.</p>
+</blockquote>
+
+<blockquote>
+  <p>Since the above was written in June 1982, my wife decided that after thirty-four years of working together she could not face life after my death.</p>
+</blockquote>
+
+<p>Cynthias notes:</p>
+
+<blockquote>
+  <p>I fear both death and the act of dying that lies ahead of us. I should have liked to finish my account of working for Arthur – a story which began when our paths happened to cross in 1949. However, I cannot live without Arthur, despite certain inner resources.</p>
+</blockquote>
+
+<blockquote>
+  <p>Double suicide has never appealed to me, but now Arthur’s incurable diseases have reached a stage where there is nothing else to do.</p>
+</blockquote>
+
+<p>Nirvana means without wind, or blown out. In the sense that desire no longer exists.</p>
+
+<p>Abstract Expressionism was invented by New York drunks.</p>
+
+<p>Ombra mai fur: Never was a shade</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Incitatus">Incitatus</a>: swift (horse name)</p>
+
+<p>Pages read and read, who has passed here before me</p>
+
+<p>Prud’hon’s wife died and Mayer had expected that she would marry him. Prone to depression throughout her life, this prompted a crisis in Mayer’s life, “when Prud’hon refused to acknowledge her assistance and marry her after the many years she had served as his assistant and his housekeeper”, she then seized “the artist’s razor, drew it across her throat.”</p>
+
+<p>There is no there there.</p>
+
+<p>There is no now now.</p>
+
+<p>“Là ci darem la mano” (Italian for “There we will give each other our hands”</p>
+
+<p><a href="https://en.wikipedia.org/wiki/George_Eastman">George Eastman</a> who founded Kodak, committed suicide, writing a note: “To my friends: my work is done. Why wait?”</p>
+
+<p>Now I know you. No field, no home, no wife, no woman-no friends, no love.</p>
+
+<p>Jacques Louis David was repeatedly drawn to sketch prisoners being led to the guillotine.</p>
+
+<p>Dear me, I am about to become a god.</p>
+
+<p>Doch das Sein- was ist das Sein?: but be that - what is that to be?</p>
+
+<p>Even in the solemn moments of the mass, when prayer should be the purest… when I should groan for what I have done, I sigh for what I have lost.</p>
+
+<p>Harry Crosby shot himself in the head. After first shooting the young married woman with whom he was having an affair.</p>
+
+<p>Eliot, as an editor, rejected <em>Animal Farm</em>.</p>
+
+<p>dormoir nonchalamment a l’ombre de ses seins: sleeping casually in the shade of her breasts</p>
+
+<p>There is no mention of Achilles’ heel in Homer. In fact there is no mention of it by anyone until Statius, in Latin, nine hundred years later.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/William_Blake">William Blake</a>’s <em>Europe Supported by Africa and America</em></p>
+
+<p><img src="/img/snippets/440px-William_Blake-Europe_Supported_By_Africa_and_America_1796.png" alt="Europe Supported by Africa and America" /></p>
+
+<p>El Greco had to sue the Toledo Cathedral to be paid for his <em>Disrobing of Christ</em>. Which the Cathedral had commissioned.</p>
+
+<p>Ōdī et amō: I hate and I love</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Alan_Turing?wprov=sfti1">Alan Turing</a> committed suicide.</p>
+
+<p>This sentence is a lie.</p>
+
+<p>Louis Althusser spent four years in a psychiatric hospital after strangling his wife.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Hapax_legomenon">Hapax legomenon</a> is a word or an expression that occurs only once within a context: either in the written record of an entire language, in the works of an author, or in a single text.</p>
+
+<p>John Kennedy Toole committed suicide by running a hose from his exhaust pipe into his car.</p>
+
+<p>Like Socrates, Aristotle was charged with impiety late in life. But went into exile rather than stand trial. Refusing to allow Athens to sin twice against philosophy, being how he put it.</p>
+
+<p>Assia Wevill, for whom Ted Hughes left Sylvia Plath, committed suicide the same way Plath did. With the difference that she gassed the child she had had by Hughes a well.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Xanthippe">Xanthippe</a></p>
+
+<p>In Book XVI of the <em>Iliad</em>, Apollo wrenches off Petroclus’s armor, leading to the latter’s death.
+Little more than two hundred lines later, Hector is shown stripping the same armor from Petroclus’s corpse.</p>
+
+<p>It is only the man whose intellect is clouded by his sexual impulses who could give the name of the afir sex to that under-sized, narrow-shouldered, nbroad-hipped and short-legged race. Said Schopenhauer.</p>
+
+<p>There is no such thing as a good painting about nothing. Said Mark Rothko.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Tulsidas">Tulsidas</a> was born into a family of beggars, and abandoned. And said that as a boy he sometimes lived on scraps thrown to dogs.</p>
+
+<p>Ite, missa est: go, the dismissal is made</p>
+
+<p>You care for nothing but shooting, dogs, and rat-catching, and you will be a disgrace to yourself and all your family. Said Charles Darwin’s father.</p>
+
+<p>Du mußt dein Leben ändern: you must change your life</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Virginia_Hill?wprov=sfti1">Virginia Hill</a> was an American organized crime figure.</p>
+
+<p>Lord, don’t help us. But don’t muck it up for us either.</p>
+
+<p>O lente, lente currite, noctis equi!<br />
+O Slowly, Slowly, Run Horses of the Night)<br />
+-Marlowe’s Dr Faustus Act V Sc 2</p>
+
+<p>Melville and Whitman were born within two months of each othera nd died within six. And were in close proximity in or near New York through much of their lives. Never meeting.</p>
+
+<p>The Sleep of Reason Produces Monsters (Spanish: El sueño de la razón produce monstruos)
+<img src="/img/snippets/monsters.png" alt="The Sleep of Reason Produces Monsters" /></p>
+
+<p><a href="https://en.wikipedia.org/wiki/Ilse_Koch">Ilse Koch</a>, also known as The Witch of Buchenwald.</p>
+
+<p>Dear Sir,<br />
+I [am in a Madhouse and] quite forget your Name <br />
+or who you are You must excuse me [for] I have nothing<br />
+to commu(n)icate [or tell of] and why I am shut up<br />
+[I dont know] I have nothing [to say so] I conclude.<br /></p>
+
+<p>[Yours respectfully,]<br />
+John Clare (To James Hipkins, 1860)</p>
+
+<p>Though Dante claims to have seen Beatrice no more than twice himself. While immortalizing her even more extraordinarily.</p>
+
+<p>Conrad Aiken’s father shot his wife and then himself. Leaving it to Aiken, at eleven, to climb a flight of stairs after hearing the shots and walk in on the bodies.</p>
+
+<p>“Der Tod und das Mädchen”, “Death and the Maiden”</p>
+
+<p>Long live the weeds and the wilderness yet.</p>
+
+<p>It is impossible for man’s happiness to be in this world. Said Aquinas.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/L'Origine_du_monde">L’Origine du monde (The Origin of the World)</a>
+<img src="/img/snippets/Origin-of-the-World.jpg" alt="The Origin of the World" /></p>
+
+<p><a href="https://en.wikipedia.org/wiki/Paideia">Paideia</a></p>
+
+<p>Pietro Torrigiano took a hammer to a Madonna he had sculpted in Seville when he was not paid what he anticipated. And was jailed by the Inquisition for sacrilege.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/By_Grand_Central_Station_I_Sat_Down_and_Wept">By Grand Canal Station I Sat Down and Wept</a></p>
+
+<p>In a lawsuit that prevented him from teaching in New York in 1940, Bertrand Russell’s writings were described as lecherous, libidinous, lustful, venerous, erotomaniac, aphrodisiac, irreverent, narrow-minded, untruthful, and bereft of moral fiber. Unquote.</p>
+
+<p><a href="https://en.wikipedia.org/wiki/Vachel_Lindsay">Vachel_Lindsay</a> founder of singing poetry committed suicide.</p>
+
+<p>Why do you always wear black?<br />
+I am in mourning for my life. -Anton Chekhov</p>
+
+<p>ipse dixit: he said</p>
+
+<p>The first edition of Thus Spoke Zarathustra sold forty copies. Nietzsche had had to pay for publication.</p>
+
+<p>I had been only a mediocre caretaker of most of the things left in my hands, even of my talent, Scott Fitzgerald said.</p>
+
+<p>That nearby, Protagonist awakening mornings to the wash of the surf?&lt;/br&gt;
+Mitigating, will it, the mornings recollection of the emptiness of the day before?<br />
+Its anticipation of the emptiness of the day to come?</p>
+
+<p>was willst du, fremder Mensch: what do you want, stranger</p>
+
+<p>Les Nuits d’Été: the summer nights</p>
+
+<p>I am old, and can no longer work, and am without means of livelihood, and my wife is ill.
+Said Paolo Uccello on a tax declaration in Florence in 1469.</p>
+
+<p>un grand peut-être: a grand maybe</p>
+
+<p>Cavafy, acknowledged as the great Greek poet of his time. Who lived his entire writing life in Egypt.</p>
+
+<p>o che dolce cosa é questa prospettiva: or what a sweet thing this prospect is</p>
+
+<p>potestas clavium: the power of the keys</p>
+
+<p>Y la vida no es noble, ni buena, ni sagrada: And life is not noble, nor good, nor sacred</p>
+
+<p>A Christ of our neighbourhood, Ortega called Don Quixote.</p>
+
+<p>Did Jesus ever laugh?</p>
+
+<p>But I was desolate and sick of an old passion</p>
+
+<p>Shakespeare’s mother and father were illiterate. And only one of his two daughters, Susanna, could sign her name. The other, Judith, made a mark.</p>
+
+<p>Did it ever, once, enter even Protagonist’s bleakest conjecturings that he would finish out his life alone?</p>
+
+<p>No survivor could ever recall having ever seen a single bird flying near any of the Nazi death camps.</p>
+
+<p>Toward what final grievous contemplation amid the disarray?</p>
+
+<p>In the end one experiences only one’s self.
+Said Nietzsche.</p>
+
+<p>Nonlinear. Discontinuous. Collage-like. An assemblage.</p>
+
+<p>Wastebasket.</p>
+
+<hr />
+
+<p>“Thinking can hurt your chances, and I want to last”. From the Handmaid’s Tale</p>
+
+<hr />
+
+<p>More and more he went running to the public house. But it was no longer to be among men, it was to get drunk. One might imagine him sitting there thinking those slow thoughts without words. One might predict that the day would come when we would realise very suddenly, very clearly, all that he had been thinking about, and, when this urgent, terrible thought had been translated into its own terms of action, he would be quietly hanged by the neck until he was as dead as he had been before he was alive.</p>
+
+<ul>
+  <li>The Blind Man, James Stephens</li>
+</ul>
+
+<hr />
+
+<p>The familiar saying that the exception proves the rule contains a good deal of wisdom, though from the standpoint of formal logic it became an absurdity as soon as “prove” no longer meant “put on trial.” The old saw began to be profound psychology from the time it ceased to have standing in logic. What it might well suggest to us today is that, if a rule has absolutely no exceptions, it is not recognized as a rule or as anything else; it is then part of the background of experience of which we tend to remain unconscious. Never having experienced anything in contrast to it, we cannot isolate it and formulate it as a rule until we so enlarge our experience and expand our base of reference that we encounter an interruption of its regularity. The situation is somewhat analogous to that of not missing the water till the well runs dry, or not realizing that we need air till we are choking.</p>
+
+<hr />
+
+<p><a href="https://en.wikipedia.org/wiki/The_Human_Condition_(Magritte)">The Human Condition (Magritte)</a></p>
+
+<p><img src="/img/snippets/René_Magritte_The_Human_Condition.jpg" alt="The Human Condition" /></p>
+
+<p>Magritte had this to say of his 1933 work:</p>
+
+<blockquote>
+  <p>In front of a window seen from inside a room, I placed a painting representing exactly that portion of the landscape covered by the painting. Thus, the tree in the picture hid the tree behind it, outside the room. For the spectator, it was both inside the room within the painting and outside in the real landscape.</p>
+</blockquote>
+
+<hr />
+
+<p>This is why you don’t read reliable science from newspapers and magazines, let alone DO science based on them!</p>
+
+<p><a href="/files/Pullum - The great Eskimo vocabulary hoax 1989.pdf">Pullum - The great Eskimo vocabulary hoax 1989.pdf</a></p>
+
+<hr />
+
+<p><a href="https://en.wikipedia.org/wiki/The_Rape_of_Proserpina?wprov=sfti1">The Rape of Proserpina</a></p>
+
+<p><img src="/img/snippets/440px-The_Rape_of_Proserpina_(Rome).jpg" alt="The Rape of Proserpina" /></p>
+
+<hr />
+
+<p>“Think about it. We have all had the experience of uttering or writing a sentence, then stopping and realising that it wasn’t exactly what we meant to say. To have that feeling, there has to be a ‘what we meant to say’ that is different from what we said” - Pinker, The Language Instinct</p>
+
+<hr />
+
+<p>Regarding emotions and hype of a relationship / love:</p>
+
+<p>The pour water on the fire, now the fire that was easy to create is now muddled with water.</p>
+
+<p>Paraffin puts a fire out if poured too fast, but otherwise burns with the fire if done slowly</p>
+
+<hr />
+
+<p>I hold the knife. I just used it to scrap off some tape from my art prints so I could put them on the wall again, with new tape.
+I think of the possibilities. Imagine cutting myself and sitting silently, and calmly, considering that I will be bereft or anything at all in due time. I consider what happens tomorrow (although there will be no notion of tomorrow anymore, soon). What will the people who knew me think? Feel? Anyone feeling guilty? Responsible? Cause and effect?
+Knives look different now. So do bridges, high buildings. The custom house is my favourite, to make it absolutely clear to this place and its people. They will brushing it off as insanity or whatnot anyway. Or will they change? Very unlikely.
+Electric shock. Wall plug.
+Pills? Gun? Rope? I think I prefer the jump. Always loved parkour and skydiving and extreme sports. One last jump where I won’t have to be conscious of a need to open the parachute. One last, free jump. Take in the scenery. Liffey? Asphalt. Bam.</p>
+
+<hr />
+
+<p>In the pale grass, under the vivid colors of the sky, the two gravediggers were lying on their backs, staring silently up at the heavens. The widow looked at them as she paused on the stile. Her thoughts of these men had been indifferent, subconscious up to this instant. They were handsome young men. Perhaps if there had been only one of them the widow would ahve been more attentive. The dark handsomeness did not seem the same thing when repeated. Their beauty, if one could call it beauty, had been collective, the beauty of flowers, of dark, velvety pansies, the distinctive marks of one faithfully duplicated on the other. The good looks of one had, to the mind of the widow, somehow nullified the good looks of the other. There was too much borrowing of Peter to pay Paul in their well-favored features. The first gravedigger spoiled the illusion of individuality in the second gravedigger. The widow had not thought so, but she would have agreed if anybody whispered to her that a good-looking man who wanted to win favor with a woman should never have so complete a twin brother. It would be possible for a woman to part tenderly with a man, and, if she met his iamge and likeness around the corner, knock him down. There is nothing more powerful, but nothing more delicate in life than the valves of individuality.</p>
+
+<p>-The Weaver’s Grave, Seamas O’Kelly</p>
+
+<hr />
+
+<p>I Know the Truth</p>
+
+<p>I know the truth—give up all other truths!<br />
+No need for people anywhere on earth to struggle.<br />
+Look—it is evening, look, it is nearly night:<br />
+what do you speak of, poets, lovers, generals?<br />
+<br />
+The wind is level now, the earth is wet with dew,<br />
+the storm of stars in the sky will turn to quiet.<br />
+And soon all of us will sleep under the earth, we<br />
+who never let each other sleep above it.<br />
+“I know the truth” Tsvetaeva (1915). 
Trans. by Elaine Feinstein</p>
+
+<hr />
+
+<p><a href="https://en.wikipedia.org/wiki/Trees_(poem)">“Trees” (1913)</a></p>
+
+<p>I think that I shall never see
+<br />
+A poem lovely as a tree.</p>
+
+<p>A tree whose hungry mouth is prest
+<br />
+Against the earth’s sweet flowing breast;</p>
+
+<p>A tree that looks at God all day,
+<br />
+And lifts her leafy arms to pray;</p>
+
+<p>A tree that may in Summer wear
+<br />
+A nest of robins in her hair;</p>
+
+<p>Upon whose bosom snow has lain;
+<br />
+Who intimately lives with rain.</p>
+
+<p>Poems are made by fools like me,
+<br />
+But only God can make a tree.</p>
+
+<hr />
+
+<p><a href="https://en.wikipedia.org/wiki/In_Flanders_Fields?wprov=sfti1">In Flanders Fields (1915)</a></p>
+
+<p>In Flanders fields the poppies blow
+<br />
+Between the crosses, row on row,
+<br />
+  That mark our place; and in the sky
+<br />
+  The larks, still bravely singing, fly
+<br />
+Scarce heard amid the guns below.
+<br /></p>
+
+<p>We are the Dead. Short days ago
+<br />
+We lived, felt dawn, saw sunset glow,
+<br />
+  Loved and were loved, and now we lie
+<br />
+      In Flanders fields.
+<br /></p>
+
+<p>Take up our quarrel with the foe:
+<br />
+To you from failing hands we throw
+<br />
+  The torch; be yours to hold it high.
+<br />
+  If ye break faith with us who die
+<br />
+We shall not sleep, though poppies grow
+<br />
+      In Flanders fields.</p>
+
+<hr />
+
+<p>Pieces from Sohrab Sepehri’s poems:</p>
+
+<div class="lang-fa">
+
+شب‌ در من فرود آمد.
+<br />
+
+شبیه هیچ شده ای
+<br />
+خودت را به سردی خاک بسپار
+<br />
+
+این دشت آفتابی را شب کن
+<br />
+تا من، راه گمشده را پیدا کنم، و در جاپای خودم خاموش شوم
+<br />
+
+خاک آیینه کنید از اشک گرم چشمتان سیراب
+<br />
+
+دست های شب مه آلود است
+<br />
+
+ریشه‌های روشنایی می‌شکافد صخره شب را
+<br />
+
+ساقه‌های نور می‌رویند در تالاب تاریکی
+<br />
+
+<br />
+..
+<br />
+
+روزگاری است در این گوشه پژمرده هوا
+<br />
+هر نشاطی مرده است.
+<br />
+
+<br />
+..
+<br />
+
+با درون سوخته دارم سخن.
+<br />
+کی به پایان می‌رسد افسانه‌ام؟
+<br />
+
+<br />
+..
+<br />
+
+گرچه می‌سوزم از این آتش به جان،
+<br />
+لیک بر این سوختن دل بسته‌ام.
+<br />
+<br />
+
+تیرگی پا می‌کشد از بام‌ها:
+<br />
+صبح می‌خندد به راه شهر من.
+<br />
+دود می خیزد هنوز از خلوتم.
+<br />
+با درون سوخته دارم سخن.
+<br />
+
+<br />
+..
+<br />
+
+راه فرو بسته گرچه مرغ به آوا،
+<br />
+قالب خاموشی او صدایی گویاست.
+<br />
+می‌گذرد لحظه‌ها به چشمش بیدار،
+<br />
+پیکر او لیک سایه-روشن رویاست.
+
+<br />
+..
+<br />
+
+تیرگی می‌آید.
+<br />
+دشت می‌گیرد آرام.
+<br />
+قصه رنگی روز
+<br />
+می‌رود رو به تمام.
+<br />
+<br />
+
+شاخه‌ها پژمرده است.
+<br />
+سنگ‌ها افسرده است.
+<br />
+رود می‌نالد.
+<br />
+جغد می‌خواند.
+<br />
+غم بیامیخته با رنگ غروب.
+<br />
+می‌تراود ز لبم قصه سرد:
+<br />
+دلم افسرده در این تنگ غروب.
+<br />
+
+<br />
+..
+<br />
+
+غمی غمناک
+<br />
+
+شب سردی است، و من افسرده.
+<br />
+راه دوری است، و پایی خسته.
+<br />
+تیرگی هست و چراغی مرده.
+<br />
+
+می‌کنم، تنها، از جاده عبور:
+<br />
+دور ماندند ز من آدم‌ها.
+<br />
+سایه‌ای از سر دیوار گذشت،
+<br />
+غمی افزود مرا بر غم‌ها.
+<br />
+
+فکر تاریکی و این ویرانی
+<br />
+بی‌خبر آمد تا با دل من
+<br />
+قصه‌ها ساز کند پنهانی.
+<br />
+
+نیست رنگی که بگوید با من
+<br />
+اندکی صبر، سحر نزدیک است
+<br />
+هر دم این بانگ بر آرم از دل:
+<br />
+وای، این شب چقدر تاریک است.
+<br />
+
+خنده‌ای کو که به دل انگیزم؟
+<br />
+قطره‌ای کو که به دریا ریزم؟
+<br />
+صخره‌ای کو که بدان آویزم؟
+<br />
+
+مثل این است که شب نمناک است.
+<br />
+دیگران را هم غم هست به دل،
+<br />
+غم من، لیک، غمی غمناک است.
+<br />
+
+<br />
+..
+<br />
+
+خشت می‌افتد از این دیوار.
+<br />
+رنج بیهوده نگهبانش برد.
+<br />
+دست باید نرود سوی کلنگ،
+<br />
+سیل اگر آمد آسانش برد.
+<br />
+
+باد نمناک زمان می‌گذرد،
+<br />
+رنگ می‌ریزد از پیکر ما.
+<br />
+خانه را نقش فساد است به سقف،
+<br />
+سر نگون خواهد شد بر سر ما.
+<br />
+
+<br />
+..
+<br />
+
+دره خاموش
+
+سکوت، بند گسسته است.
+<br />
+کنار دره، درخت شکوه پیکر بیدی.
+<br />
+در آسمان شفق رنگ
+<br />
+عبور ابر سپیدی.
+<br />
+
+نسیم در رگ هر برگ می‌دود خاموش.
+<br />
+نشسته در پس هر صخره وحشتی به کمین.
+<br />
+کشیده از پس یک سنگ سوسماری سر.
+<br />
+ز خوف دره خاموش
+<br />
+نهفته جنبش پیکر.
+<br />
+به راه می‌نگرد سرد، خشک، تلخ، غمین.
+<br />
+
+چو مار روی تن کوهی می‌خزد راهی،
+<br />
+به راه، رهگذری.
+<br />
+خیال دره و تنهایی
+<br />
+دوانده در رگ او ترس.
+<br />
+کشیده چشم به هر گوشه نقش چشمه وهم:
+<br />
+ز هر شکاف تن کوه
+<br />
+خزیده بیرون ماری.
+<br />
+
+به خشم از پس هر سنگ
+<br />
+کشیده خنجر خاری.
+<br />
+
+غروب پر زده از کوه.
+<br />
+به چشم گم شده تصویر راه و راهگذر.
+<br />
+غمی بزرگ، پر از وهم
+<br />
+به صخره سار نشسته است.
+<br />
+درون دره تاریک
+<br />
+سکوت بند گسسته است.
+<br />
+
+<br />
+دنگ...
+
+دنگ...، دنگ...
+<br />
+ساعت گیچ زمان در شب عمر
+<br />
+می‌زند پی در پی زنگ.
+<br />
+زهر این فکر که این دم گذر است
+<br />
+می‌شود نقش به دیوار رگ هستی من.
+<br />
+لحظه‌ام پر شده از اذت
+<br />
+پا به زنگار غمی آلوده است.
+<br />
+لیک چون باید این دم گذرد،
+<br />
+پس اگر می‌گریم
+<br />
+گریه آم بی‌ثمر است.
+<br />
+و اگر می‌خندم
+<br />
+خنده‌ام بیهوده است.
+<br />
+
+دنگ...، دنگ...
+<br />
+لحظه‌ها می‌گذرد.
+<br />
+آنچه بگذشت، نمی‌آید باز.
+<br />
+قصه‌ای هست که هرگز دیگر
+<br />
+نتواند شد آغاز.
+<br />
+مثل این است که یک پرسش بی‌پاسخ
+<br />
+بر لب سرد زمان ماسیده است.
+<br />
+تند برمی‌خیزم
+<br />
+تا به دیوار همین لحظه که در آن همه چیز
+<br />
+رنگ اذت دارد، آویزم.
+<br />
+
+آنچه می‌ماند از این جهد به جای:
+<br />
+خنده لحظه پنهان شده از چشمانم.
+<br />
+و آنچه بر پیکر او می‌ماند:
+<br />
+نقش انگشتانم.
+<br />
+
+دنگ...
+<br />
+فرصتی از کف رفت.
+<br />
+قصه‌ای گشت تمام.
+<br />
+لحظه باید پی لحظه گذرد
+<br />
+تا که جان گیرد در فکر دوام،
+<br />
+این دوامی که درون رگ من ریخته زهر،
+<br />
+وا رهانیده از اندیشه من رشته حال
+<br />
+وز رهی دور و دراز
+<br />
+داده پیوندم با فکر زوال.
+<br />
+
+پرده‌ای می‌گذرد،
+<br />
+پرده‌ای می‌آید:
+<br />
+می‌رود نقش پی نقش دگر،
+<br />
+رنگ می‌لغزد بر رنگ.
+<br />
+ساعت گیج زمان در شب عمر
+<br />
+می‌زند پر در پی زنگ:
+<br />
+دنگ...، دنگ...،
+<br />
+دنگ...
+<br />
+
+<br />
+..
+<br />
+
+دریا و مرد
+<br />
+
+تنها، و روی ساحل،
+<br />
+مردی به راه می‌گذرد.
+<br />
+نزدیک پای او
+<br />
+دریا، همه صدا.
+<br />
+شب، گیج در تلاطم امواج.
+<br />
+باد هراس پیکر
+<br />
+رو می‌کند به ساحل و در چشم‌های مرد
+<br />
+نقش خطر را پر رنگ می‌کند.
+<br />
+انگار
+<br />
+هی می‌زند که: مرد! کجا می‌روی، کجا؟
+<br />
+و مرد می‌رود به ره خویش.
+<br />
+و باد سرگردان
+<br />
+هی می‌زند دوباره: کجا می‌روی؟
+<br />
+و مرد می‌رود.
+<br />
+و باد همچنان...
+<br />
+
+امواج، بی امان،
+<br />
+از راه می‌رسند
+<br />
+لبریز از غرور تهاجم.
+<br />
+موجی پر از نهیب
+<br />
+ره می‌کشد به ساحل و می‌لبعد،
+<br />
+یک ساله را که برده شب از پیکرش شکیب.
+<br />
+
+دریا، همه صدا.
+<br />
+شب، گیج در طلاتم امواج،
+<br />
+باد هراس پیکر
+<br />
+رو می‌کند به ساحل و ...
+<br />
+
+<br />
+..
+<br />
+
+روز خاموش است، آرام است.
+<br />
+از چه دیگر میکنی پروا؟
+<br />
+
+<br />
+..
+<br />
+
+<br />
+(مرغ ساز افسردگی می‌کند)
+
+<br />
+..
+<br />
+
+از پی نابودی‌ام، دیری است
+<br />
+زهر می‌ریزد به رگ‌های خود این جادوی بی‌آزرم
+<br />
+تا کند آلوده با آن شیر
+<br />
+پس برای آن که رد فکر او را گم کند فکرم،
+<br />
+می‌کند رفتار با من نرم.
+<br />
+لیک چه غافل!
+<br />
+نقشه‌های او چه بی حاصل!
+<br />
+نبض من هر لحظه می‌خندد به پندارش.
+<br />
+او نمی‌داند که روییده است
+<br />
+هستی پر بار من در منجلاب زهر
+<br />
+و نمی‌داند که من در زهر می‌شویم
+<br />
+پیکر هر گریه، هر خنده،
+<br />
+در نم زهر است کرم فکر من زنده،
+<br />
+در زمین زهر می‌روید گیاه تلخ شعر من.
+<br />
+
+
+<br />
+..
+<br />
+
+هنگامی که او از پنجره بیرون می‌پرید
+<br />
+چشمانش خوابی را گم کرده بود
+<br />
+
+<br />
+..
+<br />
+
+لحظه گمشده
+
+<br />
+مرداب اتاقم کدر شده بود
+<br />
+و من زمزه خون را در رگ‌هایم می‌شنیدم.
+<br />
+زندگی‌ام در تاریکی ژرفی می‌گذشت.
+<br />
+این تاریکی، طرح وجودم را روشن می‌کرد
+<br />
+
+<br />
+در باز شد
+<br />
+و او با فانوسش به درون وزید.
+<br />
+زیبایی رها شده‌ای بود
+<br />
+و من دیده براهش بودم:
+<br />
+رویای بی شکل زندگی‌ام بود.
+<br />
+عطری در چشمم زمزه کرد.
+<br />
+رگ‌هایم از تپش افتاد
+<br />
+همه رشته‌هایی که مرا به من نشان می‌داد
+<br />
+در شعله فانوسش سوخت:
+<br />
+زمان در من نمی‌گذشت.
+<br />
+شور برهنه‌ای بودم.
+<br />
+
+اون فانوسش را به فضا آویخت.
+<br />
+مرا در روشن‌ها می‌جست.
+<br />
+تار و پود اتاقم را پیمود
+<br />
+و به من ره نیافت.
+<br />
+نسیمی شعله فانوس را نوشید.
+<br />
+
+<br />
+..
+<br />
+
+نیلوفر
+<br />
+
+از مرز خوابم می‌گذشتم، سایه تاریک یک نیلوفر
+<br />
+روی همه این ویرانه فرو افتاده بود.
+<br />
+کدامین باد بی‌پروا
+<br />
+دانه این نیلوفر را به سرزمین خواب من آورد؟
+<br />
+
+در پس درهای شیشه‌ای رویاها،
+<br />
+در مرداب بی ته آیینه‌ها،
+<br />
+هر جا که من گوشه‌ای از خودم را مرده بودم
+<br />
+یک نیلوفر روییده بود.
+<br />
+گویی او لحظه لحظه در تهی من می‌ریخت
+<br />
+و من در صدای شکفتن او
+<br />
+لحظه لحظه خودم را می‌مردم.
+<br />
+
+بام ایوان فرو می‌ریزد
+<br />
+و ساقه نیلوفر برگرد همه ستون‌ها می‌پیچد.
+<br />
+کدامین باد بی‌پروا
+<br />
+دانه این نیلوفر را به سرزمین خواب من آورد؟
+<br />
+
+نیلوفر رویید،
+<br />
+ساقه‌اش از ته خواب شفافم سر کشید.
+<br />
+من به رویا بودم،
+<br />
+سیلاب بیداری رسید.
+<br />
+
+جشمانم را در ویرانه خوابم گشودم:
+<br />
+نیلوفر به همه زندگی‌ام پیچیده بود.
+<br />
+در رگ‌هایش، من بودم که می‌دویدم.
+<br />
+هستی‌اش در من ریشه داشت،
+<br />
+همه من بود.
+<br />
+کدامین باد بی‌پروا
+<br />
+دانه این نیلوفر را به سرزمین خواب من آورد؟
+<br />
+
+</div>
+
+<hr />
+
+<p>Bill Murray: “I think if you can take care of yourself, and then maybe try to take care of someone else, that’s sort of how you’re supposed to live.”</p>
+
+<hr />
+
+<p><a href="https://en.wikipedia.org/wiki/Fatalism">Fatalism</a></p>
+
+<hr />
+
+<p>Once upon a time there was a king, then a few dress makers offered to make him a dress that only noble and decent people could see. King really liked the idea and ordered them to make a coat for him. They start sewing their seemingly magical material, meanwhile no one actually sees anything, they look as if they are sewing on the air. They are finished with the coat at last and they carefully put it on the king. The king doesn’t see the dress himself, but because he doesn’t want to be found out to be not noble or decent, he starts praising the coat and pays them. Everyone in the palace also praised the dress in the fear of being found as not noble. Even people on street praise the coat of the king. I feel like someone once said Love and made a big deal out of his fantasy of being with someone and everyone else, in fear of being called weirdos just followed along and now we live in a world obsessed with love even though they can’t hold it together most of times</p>
+
+<hr />
+
+<p>In 1845, the Illustrated London News reported that a Newfoundland dog had been acting less lively over a period of days before being seen “to throw himself in the water and endeavor to sink by preserving perfect stillness of the legs and feet”. Every time he was rescued he attempted to do this again before he finally held his head underwater until death. <a href="https://web.archive.org/web/20150326032017/http://news.discovery.com/animals/zoo-animals/animal-suicide-behavior.htm">source</a></p>
+
+<hr />
+
+<p><a href="https://simple.wikipedia.org/wiki/Category:People_who_committed_suicide">Category: People who committed suicide</a></p>
+
+<hr />
+
+<p>Merda taurorum animas conturbit : Bullshit baffles brains</p>
+
+<hr />
+
+<p>https://en.wikipedia.org/wiki/Krakatoa?wprov=sfti1 - Indonesia islands destroyed by volcanoes / wizard islands (cauldron like)</p>
+
+<hr />
+
+<p><a href="https://www.scotsconnection.com/t-forathat.aspx">A Man’s A Man For A’ That</a></p>
+
+<p>Is there for honest Poverty
+<br />
+That hings his head, an’ a’ that;
+<br />
+The coward slave-we pass him by,
+<br />
+We dare be poor for a’ that!
+<br />
+For a’ that, an’ a’ that.
+<br />
+Our toils obscure an’ a’ that,
+<br />
+The rank is but the guinea’s stamp,
+<br />
+The Man’s the gowd for a’ that.
+<br /></p>
+
+<p>What though on hamely fare we dine,
+<br />
+Wear hoddin grey, an’ a that;
+<br />
+Gie fools their silks, and knaves their wine;
+<br />
+A Man’s a Man for a’ that:
+<br />
+For a’ that, and a’ that,
+<br />
+Their tinsel show, an’ a’ that;
+<br />
+The honest man, tho’ e’er sae poor,
+<br />
+Is king o’ men for a’ that.
+<br /></p>
+
+<p>Ye see yon birkie, ca’d a lord,
+<br />
+Wha struts, an’ stares, an’ a’ that;
+<br />
+Tho’ hundreds worship at his word,
+<br />
+He’s but a coof for a’ that:
+<br />
+For a’ that, an’ a’ that,
+<br />
+His ribband, star, an’ a’ that:
+<br />
+The man o’ independent mind
+<br />
+He looks an’ laughs at a’ that.
+<br /></p>
+
+<p>A prince can mak a belted knight,
+<br />
+A marquis, duke, an’ a’ that;
+<br />
+But an honest man’s abon his might,
+<br />
+Gude faith, he maunna fa’ that!
+<br />
+For a’ that, an’ a’ that,
+<br />
+Their dignities an’ a’ that;
+<br />
+The pith o’ sense, an’ pride o’ worth,
+<br />
+Are higher rank than a’ that.
+<br /></p>
+
+<p>Then let us pray that come it may,
+<br />
+(As come it will for a’ that,)
+<br />
+That Sense and Worth, o’er a’ the earth,
+<br />
+Shall bear the gree, an’ a’ that.
+<br />
+For a’ that, an’ a’ that,
+<br />
+It’s comin’ yet for a’ that,
+<br />
+That Man to Man, the world o’er,
+<br />
+Shall brothers be for a’ that.
+<br /></p>
+
+<hr />
+
+<p>Longfellow poems
+Voices of the Night</p>
+
+<p><img src="/img/snippets/longfellow/prelude-1.jpg" alt="Voices of the Night Prelude Page 1" />
+<img src="/img/snippets/longfellow/prelude-2.jpg" alt="Voices of the Night Prelude Page 2" />
+<img src="/img/snippets/longfellow/prelude-3.jpg" alt="Voices of the Night Prelude Page 3" /></p>
+
+<p>A Psalm of Life</p>
+
+<p><img src="/img/snippets/longfellow/a-psalm-of-life.jpg" alt="A Psalm of Life" /></p>
+
+<p>Footsteps of Angels</p>
+
+<p><img src="/img/snippets/longfellow/footsteps-of-angels.jpg" alt="Footsteps of Angels" /></p>
+
+<p>Flowers</p>
+
+<p><img src="/img/snippets/longfellow/flowers.jpg" alt="Flowers" /></p>
+
+
+  </article>
+
+  <div class="share-page">
+    Share in
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+    <a href="https://twitter.com/intent/tweet?text=Snippets&url=http://localhost:4000/snippets/&via=&related=" rel="nofollow" target="_blank" title="Share on Twitter">Twitter</a>
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+          <div class='post lang-en'>
+
+  <div class="post-header">
+    <h1 class="post-title"><p>Stop High-Frequency Fuck-ups</p>
+</h1>
+    
+    <p class="post-meta">
+      <span>Dec 26, 2016</span>
+      
+      • <span>Reading time: 5  minutes</span>
+    </p>
+  </div>
+
+  <article class="post-content">
+    <p><strong>High-Frequency Fuck-Ups</strong>:</p>
+
+<blockquote>
+  <p>The cyclic process of “pushing yourself hard for a week, getting something done, and then feeling depressed and fucked up
+ for the next week”</p>
+</blockquote>
+
+<p>Sounds familiar? Read on.</p>
+
+<p><img src="/img/productivity-chart.jpg" alt="High-Frequency Fuck-ups" />
+<span class="image-caption">Visual demonstration of High-Frequency Fuck-ups</span></p>
+
+<!--more-->
+
+<p>Basically, you push yourself so fucking hard that you become a superstar in a week, and then all of a sudden
+you are under a rain of hopelessness. All depression triggers start clicking and you are
+lost. At best, you spend a week of depression and start rising to productivity again, but that’s it,
+it’s a cycle you never exit and it gets worse and worse with every iteration, your depressions become longer
+and longer unless you understand you don’t need to climb a slope of 89° to become a superstar,
+you can do it on a 45°, or even 20°, or even 1°, only it takes patience, but works out much better!</p>
+
+<p>I used to be on High-Frequency Fuck-ups for almost a year, after entering college and getting a job at the same time,
+I was under a lot of pressure, I wanted to be best in my work, and in my college, and in everything! Okay, that’s not
+bad on it’s own, but I was on the wrong road, I thought that’s the way it has to work, you push yourself for some time,
+get 5% of the road down, and then you get depressed, but you just have to go through it. But I was wrong, badly wrong.</p>
+
+<p>I only got more and more frustrated with my life, I started hating my job, hating my college and everything in between.
+My depressions used to be a few days at max after each iteration of superstar-ism at first, but it got worse until I reached depressions
+of two weeks. I couldn’t attend to my exercise anymore, I wouldn’t read the books I wanted to, even my social life was
+breaking apart, I was dead, I only knew how to work some stuff out in short spans of time, but I couldn’t control the
+side effect it brought, the depression.</p>
+
+<p>To be honest, those superstar peaks felt really good as I would actually accomplish things I couldn’t do before, in a just week!
+That’s why I kept this habit for a year, but at some point I realised this is not going to work long-term, with the rate of
+depressions getting longer and longer, I was risking <em>my life</em>, who knows what would’ve happened once I got to a whole month,
+or even two months of depression, and I couldn’t be saved, I was in a state of denial, I thought 
+“These people don’t understand! That’s the path you have to take to be great!”, so I wouldn’t listen to anyone telling me to slow the fuck down.</p>
+
+<p>At the time, I had two roommates, and they knew about my state, it was so visible, I would work like robots for a week, bumped up
+and excited, and then I would go down for the next week, feeling groggy and sad the whole time.</p>
+
+<p>One night I and one of my roommates, Saeed, started talking, not directly about this topic, but we got there and he told me
+I should slow down and move at a more controllable pace. He was not the only one telling me that, I was told this a lot,
+either directly or indirectly, but I always denied it. This time, I thought about it, a lot, because I was tired of my High-Frequency Fuck-ups,
+yet I was not sure if he was right or I was, so I continued my High-Frequency Fuck-ups for another two or three months
+before deciding I should at least <em>try</em> slowing down.</p>
+
+<p>I slowly slowed down, the depressions went away, I would accomplish the things I wanted, only slightly longer, but damn, it was great!
+I could continue getting stuff done without feeling fucked up and crying whole days and nights in my bed, I could do the things I loved
+without any fucking side effects!</p>
+
+<p>At first, I had the doubt “Am I becoming one of <em>those</em> people? People who don’t get things done and don’t grow?”, but after some time,
+I realised I am actually getting things done much better! It was easy to see for me and the people around me that I was much happier,
+I was in control of my life and I was enjoying it. The only difference was patience, instead of rushing to get the next big thing done
+in a short amount of time, I took patience in checking my list off, and suddenly everything was much more fun.</p>
+
+<p>Now I study, play an instrument, exercise everyday, go running, read books, watch movies, write, eat and sleep well all at the same time,
+and I don’t feel a bit depressed. Sadness is something, depression is another, I do get sad, but not depressed. I feel alive and active.</p>
+
+<p>I’ve become much better socially, my interactions with my friends are much more alive now. I could see it in my friends’ eyes when I used to
+be a robot, they were like “What the fuck is going on with you man?”, yes, exactly that phrase, but now I’m no longer a slave of High-Frequency Fuck-ups,
+I have so much fun with my friends.</p>
+
+<p>The takeaway is, stop High-Frequency Fuck-ups, slow down, take things one bite at a time and you will eventually accomplish what you are aiming for,
+if only with a little more patience, you won’t have depression blocking your way and fogging your brain every other week.</p>
+
+  </article>
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+        <h2>
+          <a class="post-link" href="/primitive-living-lessons-0/">Primitive Living Lessons Learned, Episode 0</a>
+          <span class="post-meta">Sep 7, 2017</span>
+        </h2>
+        <article class='post-content'>
+          <p><img src="/img/primitive-living-0.jpg" alt="general view of the forest" /></p>
+
+<p>So I just went on my first primitive living practice trip in the woods, alone, with only a pocket knife.</p>
+
+<p>I decided I’m going to share the lessons I’ve learned in each trip as they are certainly going to be useful if you want to practice primitive living, I would find these useful if I could find them anywhere. I spend a lot of time reading and watching primitive living guides and experience reports, but they are never exhaustive, and this series is not meant to be exhaustive either.</p>
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+  <title>Difference between Travis CI tests: PR and Push</title>
+  <meta name="description" content="I just want to leave this here as I often tend to look it up myself and the first time it was not as easy to figure out.When using Travis CI along with GitHu...">
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+        <h1 class="page-heading"></h1>
+        
+          <div class='post lang-en'>
+
+  <div class="post-header">
+    <h1 class="post-title"><p>Difference between Travis CI tests: PR and Push</p>
+</h1>
+    
+    <p class="post-meta">
+      <span>Sep 9, 2017</span>
+      
+      • <span>Reading time: 1  minute</span>
+    </p>
+  </div>
+
+  <article class="post-content">
+    <p>I just want to leave this here as I often tend to look it up myself and the first time it was not as easy to figure out.</p>
+
+<p>When using Travis CI along with GitHub (or other git integrations), Travis runs two tests: <code>pr</code> and <code>push</code>.</p>
+
+<p><img src="/img/travis-ci-pr-push-github.jpg" alt="travis-pr-push-github" /></p>
+
+<p>Most of the time you see both tests passing and you do not have to even wonder how they are different, but it has
+happened to me that one of the tests fails while the other passes and I started to wonder why.</p>
+
+<h3 id="pr">pr</h3>
+<p>The <code>pr</code> test is a test run on the result of a merge between the pull-request branch and the main branch.
+As an example, let’s say your pull-request’s branch is called <code>fix-user-auth</code> and your main branch is <code>master</code>, 
+in this case, <code>pr</code> merges <code>fix-user-auth</code> into <code>master</code> and then runs the tests on the result of the merge.</p>
+
+<h3 id="push">push</h3>
+<p>On the other hand, <code>push</code> is run on the pull-request branch itself, without merging. So in our example above, Travis would checkout to <code>fix-user-auth</code> and run the tests.</p>
+
+<h3 id="a-case-of-difference">A case of difference</h3>
+
+<p>A case in which this difference might be more apparent is when your pull-request is based on a branch other than <code>master</code>, and some changes that your pull-request depends on are missing from <code>master</code>, in this case the <code>push</code> test may pass, but the <code>pr</code> test will fail.</p>
+
+
+  </article>
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+  <meta name="description" content="I wanted to get proficient in Haskell so I decided to follow An [Essential] Haskell Reading List. There I stumbled upon Typoclassopedia, while the material i...">
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+    <h1 class="post-title" id="tocAnchor-1-1"></h1><p>Typoclassopedia: Exercise solutions</p>
+
+    
+    <p class="post-meta">
+      <span>Sep 27, 2017</span>
+      
+      • <span>Reading time: 55  minutes</span>
+    </p>
+  </div><div id="toc-container"><table class="toc" id="toc"><tbody><tr><td><h2>Table of Contents</h2><input type="checkbox" id="toctogglelink" href="#" checked="checked" /><span></span><ul><li class="toc_level-1 toc_section-1"><a href="#tocAnchor-1-1"><span class="tocnumber">1</span> <span class="toctext"></span></a></li><li class="toc_level-1 toc_section-2"><a href="#tocAnchor-1-2"><span class="tocnumber">2</span> <span class="toctext">Functor</span></a><ul><li class="toc_level-2 toc_section-3"><a href="#tocAnchor-1-2-1"><span class="tocnumber">2.1</span> <span class="toctext">Instances</span></a></li><li class="toc_level-2 toc_section-4"><a href="#tocAnchor-1-2-2"><span class="tocnumber">2.2</span> <span class="toctext">Functor Laws</span></a></li></ul></li><li class="toc_level-1 toc_section-5"><a href="#tocAnchor-1-5"><span class="tocnumber">3</span> <span class="toctext">Category Theory</span></a><ul><li class="toc_level-2 toc_section-6"><a href="#tocAnchor-1-5-1"><span class="tocnumber">3.1</span> <span class="toctext">Introduction to categories</span></a></li><li class="toc_level-2 toc_section-7"><a href="#tocAnchor-1-5-2"><span class="tocnumber">3.2</span> <span class="toctext">Functors</span></a></li></ul></li><li class="toc_level-1 toc_section-8"><a href="#tocAnchor-1-8"><span class="tocnumber">4</span> <span class="toctext">Applicative</span></a><ul><li class="toc_level-2 toc_section-9"><a href="#tocAnchor-1-8-1"><span class="tocnumber">4.1</span> <span class="toctext">Laws</span></a></li><li class="toc_level-2 toc_section-10"><a href="#tocAnchor-1-8-2"><span class="tocnumber">4.2</span> <span class="toctext">Instances</span></a></li><li class="toc_level-2 toc_section-11"><a href="#tocAnchor-1-8-3"><span class="tocnumber">4.3</span> <span class="toctext">Utility functions</span></a></li><li class="toc_level-2 toc_section-12"><a href="#tocAnchor-1-8-4"><span class="tocnumber">4.4</span> <span class="toctext">Alternative formulation</span></a></li></ul></li><li class="toc_level-1 toc_section-13"><a href="#tocAnchor-1-13"><span class="tocnumber">5</span> <span class="toctext">Monad</span></a><ul><li class="toc_level-2 toc_section-14"><a href="#tocAnchor-1-13-1"><span class="tocnumber">5.1</span> <span class="toctext">Definition</span></a></li><li class="toc_level-2 toc_section-15"><a href="#tocAnchor-1-13-2"><span class="tocnumber">5.2</span> <span class="toctext">Instances</span></a></li><li class="toc_level-2 toc_section-16"><a href="#tocAnchor-1-13-3"><span class="tocnumber">5.3</span> <span class="toctext">Intuition</span></a></li><li class="toc_level-2 toc_section-17"><a href="#tocAnchor-1-13-4"><span class="tocnumber">5.4</span> <span class="toctext">Laws</span></a></li></ul></li><li class="toc_level-1 toc_section-18"><a href="#tocAnchor-1-18"><span class="tocnumber">6</span> <span class="toctext">Monad Transformers</span></a><ul><li class="toc_level-2 toc_section-19"><a href="#tocAnchor-1-18-1"><span class="tocnumber">6.1</span> <span class="toctext">Definition and laws</span></a></li><li class="toc_level-2 toc_section-20"><a href="#tocAnchor-1-18-2"><span class="tocnumber">6.2</span> <span class="toctext">Composing Monads</span></a></li></ul></li><li class="toc_level-1 toc_section-21"><a href="#tocAnchor-1-21"><span class="tocnumber">7</span> <span class="toctext">MonadFix</span></a><ul><li class="toc_level-2 toc_section-22"><a href="#tocAnchor-1-21-1"><span class="tocnumber">7.1</span> <span class="toctext">Examples and intuition</span></a></li></ul></li><li class="toc_level-1 toc_section-23"><a href="#tocAnchor-1-23"><span class="tocnumber">8</span> <span class="toctext">Foldable</span></a><ul><li class="toc_level-2 toc_section-24"><a href="#tocAnchor-1-23-1"><span class="tocnumber">8.1</span> <span class="toctext">Definition</span></a></li><li class="toc_level-2 toc_section-25"><a href="#tocAnchor-1-23-2"><span class="tocnumber">8.2</span> <span class="toctext">Instances and examples</span></a></li><li class="toc_level-2 toc_section-26"><a href="#tocAnchor-1-23-3"><span class="tocnumber">8.3</span> <span class="toctext">Utility functions</span></a></li></ul></li><li class="toc_level-1 toc_section-27"><a href="#tocAnchor-1-27"><span class="tocnumber">9</span> <span class="toctext">Traversable</span></a><ul><li class="toc_level-2 toc_section-28"><a href="#tocAnchor-1-27-1"><span class="tocnumber">9.1</span> <span class="toctext">Intuition</span></a></li><li class="toc_level-2 toc_section-29"><a href="#tocAnchor-1-27-2"><span class="tocnumber">9.2</span> <span class="toctext">Instances and examples</span></a></li></ul></li></ul></td></tr></tbody></table></div>
+
+  <article class="post-content">
+    <p>I wanted to get proficient in Haskell so I decided to follow <a href="http://www.stephendiehl.com/posts/essential_haskell.html">An [Essential] Haskell Reading List</a>. There I stumbled upon <a href="https://wiki.haskell.org/Typeclassopedia">Typoclassopedia</a>, while the material is great, I couldn’t find solutions for the exercises to check against, so I decided I would write my own and hopefully the solutions would get fixed in case I have gone wrong by others. So if you think a solution is wrong, let me know in the comments!</p>
+
+<p>In each section below, I left some reference material for the exercises and then the solutions.</p>
+
+<p>Note: The post will be updated as I progress in Typoclassopedia myself</p>
+
+<h1 id="tocAnchor-1-2">Functor</h1>
+<h2 id="tocAnchor-1-2-1">Instances</h2>
+
+<div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kr">instance</span> <span class="kt">Functor</span> <span class="kt">[]</span> <span class="kr">where</span>
+  <span class="n">fmap</span> <span class="o">::</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">b</span><span class="p">]</span>
+  <span class="n">fmap</span> <span class="kr">_</span> <span class="kt">[]</span>     <span class="o">=</span> <span class="kt">[]</span>
+  <span class="n">fmap</span> <span class="n">g</span> <span class="p">(</span><span class="n">x</span><span class="o">:</span><span class="n">xs</span><span class="p">)</span> <span class="o">=</span> <span class="n">g</span> <span class="n">x</span> <span class="o">:</span> <span class="n">fmap</span> <span class="n">g</span> <span class="n">xs</span>
+  <span class="c1">-- or we could just say fmap = map</span>
+ 
+<span class="kr">instance</span> <span class="kt">Functor</span> <span class="kt">Maybe</span> <span class="kr">where</span>
+  <span class="n">fmap</span> <span class="o">::</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Maybe</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Maybe</span> <span class="n">b</span>
+  <span class="n">fmap</span> <span class="kr">_</span> <span class="kt">Nothing</span>  <span class="o">=</span> <span class="kt">Nothing</span>
+  <span class="n">fmap</span> <span class="n">g</span> <span class="p">(</span><span class="kt">Just</span> <span class="n">a</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Just</span> <span class="p">(</span><span class="n">g</span> <span class="n">a</span><span class="p">)</span>
+</code></pre></div></div>
+
+<blockquote>
+  <p>((,) e) represents a container which holds an “annotation” of type e along with the actual value it holds. It might be clearer to write it as (e,), by analogy with an operator section like (1+), but that syntax is not allowed in types (although it is allowed in expressions with the TupleSections extension enabled). However, you can certainly think of it as (e,).</p>
+</blockquote>
+
+<blockquote>
+  <p>((-&gt;) e) (which can be thought of as (e -&gt;); see above), the type of functions which take a value of type e as a parameter, is a Functor. As a container, (e -&gt; a) represents a (possibly infinite) set of values of a, indexed by values of e. Alternatively, and more usefully, ((-&gt;) e) can be thought of as a context in which a value of type e is available to be consulted in a read-only fashion. This is also why ((-&gt;) e) is sometimes referred to as the reader monad; more on this later.</p>
+</blockquote>
+
+<h3 id="exercises">Exercises</h3>
+
+<ol>
+  <li>
+    <p>Implement <code class="language-plaintext highlighter-rouge">Functor</code> instances for <code class="language-plaintext highlighter-rouge">Either e</code> and <code class="language-plaintext highlighter-rouge">((-&gt;) e)</code>.</p>
+
+    <p><strong>Solution</strong>:</p>
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kr">instance</span> <span class="kt">Functor</span> <span class="p">(</span><span class="kt">Either</span> <span class="n">e</span><span class="p">)</span> <span class="kr">where</span>
+  <span class="n">fmap</span> <span class="kr">_</span> <span class="p">(</span><span class="kt">Left</span> <span class="n">e</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Left</span> <span class="n">e</span>
+  <span class="n">fmap</span> <span class="n">g</span> <span class="p">(</span><span class="kt">Right</span> <span class="n">a</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Right</span> <span class="p">(</span><span class="n">g</span> <span class="n">a</span><span class="p">)</span>
+      
+<span class="kr">instance</span> <span class="kt">Functor</span> <span class="p">((</span><span class="o">-&gt;</span><span class="p">)</span> <span class="n">e</span><span class="p">)</span> <span class="kr">where</span>
+  <span class="n">fmap</span> <span class="n">g</span> <span class="n">f</span> <span class="o">=</span> <span class="n">g</span> <span class="o">.</span> <span class="n">f</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>Implement <code class="language-plaintext highlighter-rouge">Functor</code> instances for <code class="language-plaintext highlighter-rouge">((,) e)</code> and for <code class="language-plaintext highlighter-rouge">Pair</code>, defined as below. Explain their similarities and differences.</p>
+
+    <p><strong>Solution</strong>:</p>
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kr">instance</span> <span class="kt">Functor</span> <span class="p">((,)</span> <span class="n">e</span><span class="p">)</span> <span class="kr">where</span>
+  <span class="n">fmap</span> <span class="n">g</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="o">=</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">g</span> <span class="n">b</span><span class="p">)</span> 
+      
+      
+<span class="kr">data</span> <span class="kt">Pair</span> <span class="n">a</span> <span class="o">=</span> <span class="kt">Pair</span> <span class="n">a</span> <span class="n">a</span>
+<span class="kr">instance</span> <span class="kt">Functor</span> <span class="kt">Pair</span> <span class="kr">where</span>
+  <span class="n">fmap</span> <span class="n">g</span> <span class="p">(</span><span class="kt">Pair</span> <span class="n">a</span> <span class="n">b</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Pair</span> <span class="p">(</span><span class="n">g</span> <span class="n">a</span><span class="p">)</span> <span class="p">(</span><span class="n">g</span> <span class="n">b</span><span class="p">)</span>
+</code></pre></div>    </div>
+
+    <p>Their similarity is in the fact that they both represent types of two values.
+Their difference is that <code class="language-plaintext highlighter-rouge">((,) e)</code> (tuples of two) can have values of different types (kind of <code class="language-plaintext highlighter-rouge">(,)</code> is <code class="language-plaintext highlighter-rouge">* -&gt; *</code>) while both values of <code class="language-plaintext highlighter-rouge">Pair</code> have the same type <code class="language-plaintext highlighter-rouge">a</code>, so <code class="language-plaintext highlighter-rouge">Pair</code> has kind <code class="language-plaintext highlighter-rouge">*</code>.</p>
+  </li>
+  <li>
+    <p>Implement a <code class="language-plaintext highlighter-rouge">Functor</code> instance for the type <code class="language-plaintext highlighter-rouge">ITree</code>, defined as</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="kr">data</span> <span class="kt">ITree</span> <span class="n">a</span> <span class="o">=</span> <span class="kt">Leaf</span> <span class="p">(</span><span class="kt">Int</span> <span class="o">-&gt;</span> <span class="n">a</span><span class="p">)</span>
+             <span class="o">|</span> <span class="kt">Node</span> <span class="p">[</span><span class="kt">ITree</span> <span class="n">a</span><span class="p">]</span>
+</code></pre></div>    </div>
+
+    <p><strong>Solution</strong>:</p>
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="kr">instance</span> <span class="kt">Functor</span> <span class="kt">ITree</span> <span class="kr">where</span>
+   <span class="n">fmap</span> <span class="n">g</span> <span class="p">(</span><span class="kt">Leaf</span> <span class="n">f</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Leaf</span> <span class="p">(</span><span class="n">g</span> <span class="o">.</span> <span class="n">f</span><span class="p">)</span>
+   <span class="n">fmap</span> <span class="n">g</span> <span class="p">(</span><span class="kt">Node</span> <span class="n">xs</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Node</span> <span class="p">(</span><span class="n">fmap</span> <span class="p">(</span><span class="n">fmap</span> <span class="n">g</span><span class="p">)</span> <span class="n">xs</span><span class="p">)</span>
+</code></pre></div>    </div>
+
+    <p>To test this instance, I defined a function to apply the tree to an <code class="language-plaintext highlighter-rouge">Int</code>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">applyTree</span> <span class="o">::</span> <span class="kt">ITree</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Int</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">a</span><span class="p">]</span>
+ <span class="n">applyTree</span> <span class="p">(</span><span class="kt">Leaf</span> <span class="n">g</span><span class="p">)</span> <span class="n">i</span> <span class="o">=</span> <span class="p">[</span><span class="n">g</span> <span class="n">i</span><span class="p">]</span>
+ <span class="n">applyTree</span> <span class="p">(</span><span class="kt">Node</span> <span class="kt">[]</span><span class="p">)</span> <span class="kr">_</span> <span class="o">=</span> <span class="kt">[]</span>
+ <span class="n">applyTree</span> <span class="p">(</span><span class="kt">Node</span> <span class="p">(</span><span class="n">x</span><span class="o">:</span><span class="n">xs</span><span class="p">))</span> <span class="n">i</span> <span class="o">=</span> <span class="n">applyTree</span> <span class="n">x</span> <span class="n">i</span> <span class="o">++</span> <span class="n">applyTree</span> <span class="p">(</span><span class="kt">Node</span> <span class="n">xs</span><span class="p">)</span> <span class="n">i</span>
+</code></pre></div>    </div>
+
+    <p>This is not a standard tree traversing algorithm, I just wanted it to be simple for testing.</p>
+
+    <p>Now test the instance:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="err">λ</span><span class="o">:</span> <span class="kr">let</span> <span class="n">t</span> <span class="o">=</span> <span class="kt">Node</span> <span class="p">[</span><span class="kt">Node</span> <span class="p">[</span><span class="kt">Leaf</span> <span class="p">(</span><span class="o">+</span><span class="mi">5</span><span class="p">),</span> <span class="kt">Leaf</span> <span class="p">(</span><span class="o">+</span><span class="mi">1</span><span class="p">)],</span> <span class="kt">Leaf</span> <span class="p">(</span><span class="o">*</span><span class="mi">2</span><span class="p">)]</span>
+ <span class="err">λ</span><span class="o">:</span> <span class="n">applyTree</span> <span class="n">t</span> <span class="mi">1</span>
+ <span class="p">[</span><span class="mi">6</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span>
+ <span class="err">λ</span><span class="o">:</span> <span class="n">applyTree</span> <span class="p">(</span><span class="n">fmap</span> <span class="n">id</span> <span class="n">t</span><span class="p">)</span> <span class="mi">1</span>
+ <span class="p">[</span><span class="mi">6</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span>
+ <span class="err">λ</span><span class="o">:</span> <span class="n">applyTree</span> <span class="p">(</span><span class="n">fmap</span> <span class="p">(</span><span class="o">+</span><span class="mi">10</span><span class="p">)</span> <span class="n">t</span><span class="p">)</span> <span class="mi">1</span>
+ <span class="p">[</span><span class="mi">16</span><span class="p">,</span> <span class="mi">12</span><span class="p">,</span> <span class="mi">12</span><span class="p">]</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>Give an example of a type of kind <code class="language-plaintext highlighter-rouge">* -&gt; *</code> which cannot be made an instance of <code class="language-plaintext highlighter-rouge">Functor</code> (without using <code class="language-plaintext highlighter-rouge">undefined</code>).</p>
+
+    <p>I don’t know the answer to this one yet!</p>
+  </li>
+  <li>
+    <p>Is this statement true or false?</p>
+
+    <blockquote>
+      <p>The composition of two <code class="language-plaintext highlighter-rouge">Functor</code>s is also a <code class="language-plaintext highlighter-rouge">Functor</code>.</p>
+    </blockquote>
+
+    <p>If false, give a counterexample; if true, prove it by exhibiting some appropriate Haskell code.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <p>It’s true, and can be proved by the following function:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">ffmap</span> <span class="o">::</span> <span class="p">(</span><span class="kt">Functor</span> <span class="n">f</span><span class="p">,</span> <span class="kt">Functor</span> <span class="n">j</span><span class="p">)</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="p">(</span><span class="n">j</span> <span class="n">a</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="p">(</span><span class="n">j</span> <span class="n">b</span><span class="p">)</span>
+ <span class="n">ffmap</span> <span class="n">g</span> <span class="o">=</span> <span class="n">fmap</span> <span class="p">(</span><span class="n">fmap</span> <span class="n">g</span><span class="p">)</span>
+</code></pre></div>    </div>
+
+    <p>You can test this on arbitrary compositions of <code class="language-plaintext highlighter-rouge">Functor</code>s:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">main</span> <span class="o">=</span> <span class="kr">do</span>
+   <span class="kr">let</span> <span class="n">result</span> <span class="o">::</span> <span class="kt">Maybe</span> <span class="p">(</span><span class="kt">Either</span> <span class="kt">String</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">=</span> <span class="n">ffmap</span> <span class="p">(</span><span class="o">+</span> <span class="mi">2</span><span class="p">)</span> <span class="p">(</span><span class="kt">Just</span> <span class="o">.</span> <span class="kt">Right</span> <span class="o">$</span> <span class="mi">5</span><span class="p">)</span>
+   <span class="n">print</span> <span class="n">result</span> <span class="c1">-- (Just (Right 7))</span>
+</code></pre></div>    </div>
+  </li>
+</ol>
+
+<h2 id="tocAnchor-1-2-2">Functor Laws</h2>
+
+<div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">fmap</span> <span class="n">id</span> <span class="o">=</span> <span class="n">id</span>
+<span class="n">fmap</span> <span class="p">(</span><span class="n">g</span> <span class="o">.</span> <span class="n">h</span><span class="p">)</span> <span class="o">=</span> <span class="p">(</span><span class="n">fmap</span> <span class="n">g</span><span class="p">)</span> <span class="o">.</span> <span class="p">(</span><span class="n">fmap</span> <span class="n">h</span><span class="p">)</span>
+</code></pre></div></div>
+
+<h3 id="exercises-1">Exercises</h3>
+
+<ol>
+  <li>
+    <p>Although it is not possible for a Functor instance to satisfy the first Functor law but not the second (excluding undefined), the reverse is possible. Give an example of a (bogus) Functor instance which satisfies the second law but not the first.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <p>This is easy, consider this instance:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="kr">instance</span> <span class="kt">Functor</span> <span class="kt">[]</span> <span class="kr">where</span>
+   <span class="n">fmap</span> <span class="kr">_</span> <span class="kt">[]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+   <span class="n">fmap</span> <span class="n">g</span> <span class="p">(</span><span class="n">x</span><span class="o">:</span><span class="n">xs</span><span class="p">)</span> <span class="o">=</span> <span class="n">g</span> <span class="n">x</span><span class="o">:</span> <span class="n">fmap</span> <span class="n">g</span> <span class="n">xs</span>
+</code></pre></div>    </div>
+
+    <p>Then, you can test the first and second laws:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="err">λ</span><span class="o">:</span> <span class="n">fmap</span> <span class="n">id</span> <span class="kt">[]</span> <span class="c1">-- [1], breaks the first law</span>
+ <span class="err">λ</span><span class="o">:</span> <span class="n">fmap</span> <span class="p">((</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span> <span class="o">.</span> <span class="p">(</span><span class="o">+</span><span class="mi">2</span><span class="p">))</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span> <span class="c1">-- [4, 5], second law holds</span>
+ <span class="err">λ</span><span class="o">:</span> <span class="n">fmap</span> <span class="p">(</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span> <span class="o">.</span> <span class="n">fmap</span> <span class="p">(</span><span class="o">+</span><span class="mi">2</span><span class="p">)</span> <span class="o">$</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span> <span class="c1">-- [4, 5]</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>Which laws are violated by the evil Functor instance for list shown above: both laws, or the first law alone? Give specific counterexamples.</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="c1">-- Evil Functor instance</span>
+ <span class="kr">instance</span> <span class="kt">Functor</span> <span class="kt">[]</span> <span class="kr">where</span>
+   <span class="n">fmap</span> <span class="o">::</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">b</span><span class="p">]</span>
+   <span class="n">fmap</span> <span class="kr">_</span> <span class="kt">[]</span> <span class="o">=</span> <span class="kt">[]</span>
+   <span class="n">fmap</span> <span class="n">g</span> <span class="p">(</span><span class="n">x</span><span class="o">:</span><span class="n">xs</span><span class="p">)</span> <span class="o">=</span> <span class="n">g</span> <span class="n">x</span> <span class="o">:</span> <span class="n">g</span> <span class="n">x</span> <span class="o">:</span> <span class="n">fmap</span> <span class="n">g</span> <span class="n">xs</span>
+</code></pre></div>    </div>
+
+    <p><strong>Solution</strong>:</p>
+
+    <p>The instance defined breaks the first law (<code class="language-plaintext highlighter-rouge">fmap id [1] -- [1,1]</code>), but holds for the second law.</p>
+  </li>
+</ol>
+
+<h1 id="tocAnchor-1-5">Category Theory</h1>
+
+<p>The Functor section links to <a href="https://en.wikibooks.org/wiki/Haskell/Category_theory">Category Theory</a>, so here I’m going to cover the exercises of that page, too.</p>
+
+<h2 id="tocAnchor-1-5-1">Introduction to categories</h2>
+
+<h3 id="category-laws">Category laws:</h3>
+
+<ol>
+  <li>
+    <p>The compositions of morphisms need to be <strong>associative</strong>:</p>
+
+    <p>$f \circ (g \circ h) = (f \circ g) \circ h$</p>
+  </li>
+  <li>The category needs to be <strong>closed</strong> under the composition operator. So if $f : B \to C$ and $g: A \to B$, then there must be some $h: A \to C$ in the category such that $h = f \circ g$.</li>
+  <li>Every object $A$ in a category must have an identity morphism, $id_A : A \to A$ that is an identity of composition with other morphisms. So for every morphism $g: A \to B$:
+ $g \circ id_A = id_B \circ g = g$.</li>
+</ol>
+
+<h3 id="exercises-2">Exercises</h3>
+
+<ol>
+  <li>
+    <p>As was mentioned, any partial order $(P, \leq)$ is a category with objects as the elements of P and a morphism between elements a and b iff $a \leq b$. Which of the above laws guarantees the transitivity of $\leq$?</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <p>The second law, which states that the category needs to be closed under the composition operator guarantess that because we have a morphism $a \leq b$, and another morphism $b \leq c$, there must also be some other morphism such that $a \leq c$.</p>
+  </li>
+  <li>
+    <p>If we add another morphism to the above example, as illustrated below, it fails to be a category. Why? Hint: think about associativity of the composition operation.</p>
+
+    <p><img src="/img/typoclassopedia/not-a-cat.png" alt="not a category, an additional h: B -&gt; A" /></p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <p>The first law does not hold:</p>
+
+    <p>$f \circ (g \circ h) = (f \circ g) \circ h$</p>
+
+    <p>To see that, we can evaluate each side to get an inequality:</p>
+
+    <p>$g \circ h = id_B$</p>
+
+    <p>$f \circ g = id_A$</p>
+
+    <p>$f \circ (g \circ h) = f \circ id_B = f$</p>
+
+    <p>$(f \circ g) \circ h = id_A \circ h = h$</p>
+
+    <p>$f \neq h$</p>
+  </li>
+</ol>
+
+<h2 id="tocAnchor-1-5-2">Functors</h2>
+
+<h3 id="functor-laws-1">Functor laws:</h3>
+
+<ol>
+  <li>
+    <p>Given an identity morphism $id_A$ on an object $A$, $F(id_A)$ must be the identity morphism on $F(A)$, so:
+ $F(id_A) = id_{F(A)}$</p>
+  </li>
+  <li>
+    <p>Functors must distribute over morphism composition:
+ $F(f \circ g) = F(f) \circ F(g)$</p>
+  </li>
+</ol>
+
+<h3 id="exercises-3">Exercises</h3>
+
+<ol>
+  <li>
+    <p>Check the functor laws for the diagram below.</p>
+
+    <p><img src="/img/typoclassopedia/functor-diagram.png" alt="functor diagram" /></p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <p>The first law is obvious as it’s directly written, the pale blue dotted arrows from $id_C$ to $F(id_C) = id_{F(C)}$ and $id_A$ and $id_B$ to $F(id_A) = F(id_B) = id_{F(A)} = id_{F(B)}$ show this.</p>
+
+    <p>The second law also holds, the only compositions in category $C$ are between $f$ and identities, and $g$ and identities, there is no composition between $f$ and $g$.</p>
+
+    <p>(Note: The second law always hold as long as the first one does, as was seen in Typoclassopedia)</p>
+  </li>
+  <li>
+    <p>Check the laws for the Maybe and List functors.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="kr">instance</span> <span class="kt">Functor</span> <span class="kt">[]</span> <span class="kr">where</span>
+   <span class="n">fmap</span> <span class="o">::</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">b</span><span class="p">]</span>
+   <span class="n">fmap</span> <span class="kr">_</span> <span class="kt">[]</span>     <span class="o">=</span> <span class="kt">[]</span>
+   <span class="n">fmap</span> <span class="n">g</span> <span class="p">(</span><span class="n">x</span><span class="o">:</span><span class="n">xs</span><span class="p">)</span> <span class="o">=</span> <span class="n">g</span> <span class="n">x</span> <span class="o">:</span> <span class="n">fmap</span> <span class="n">g</span> <span class="n">xs</span>
+    
+ <span class="c1">-- check the first law for each part:</span>
+ <span class="n">fmap</span> <span class="n">id</span> <span class="kt">[]</span> <span class="o">=</span> <span class="kt">[]</span>
+ <span class="n">fmap</span> <span class="n">id</span> <span class="p">(</span><span class="n">x</span><span class="o">:</span><span class="n">xs</span><span class="p">)</span> <span class="o">=</span> <span class="n">id</span> <span class="n">x</span> <span class="o">:</span> <span class="n">fmap</span> <span class="n">id</span> <span class="n">xs</span> <span class="o">=</span> <span class="n">x</span> <span class="o">:</span> <span class="n">fmap</span> <span class="n">id</span> <span class="n">xs</span> <span class="c1">-- the first law holds recursively</span>
+    
+ <span class="c1">-- check the second law for each part:</span>
+ <span class="n">fmap</span> <span class="p">(</span><span class="n">f</span> <span class="o">.</span> <span class="n">g</span><span class="p">)</span> <span class="kt">[]</span> <span class="o">=</span> <span class="kt">[]</span>
+ <span class="n">fmap</span> <span class="p">(</span><span class="n">f</span> <span class="o">.</span> <span class="n">g</span><span class="p">)</span> <span class="p">(</span><span class="n">x</span><span class="o">:</span><span class="n">xs</span><span class="p">)</span> <span class="o">=</span> <span class="p">(</span><span class="n">f</span> <span class="o">.</span> <span class="n">g</span><span class="p">)</span> <span class="n">x</span> <span class="o">:</span> <span class="n">fmap</span> <span class="p">(</span><span class="n">f</span> <span class="o">.</span> <span class="n">g</span><span class="p">)</span> <span class="n">xs</span> <span class="o">=</span> <span class="n">f</span> <span class="p">(</span><span class="n">g</span> <span class="n">x</span><span class="p">)</span> <span class="o">:</span> <span class="n">fmap</span> <span class="p">(</span><span class="n">f</span> <span class="o">.</span> <span class="n">g</span><span class="p">)</span> <span class="n">xs</span>
+ <span class="n">fmap</span> <span class="n">f</span> <span class="p">(</span><span class="n">fmap</span> <span class="n">g</span> <span class="p">(</span><span class="n">x</span><span class="o">:</span><span class="n">xs</span><span class="p">))</span> <span class="o">=</span> <span class="n">fmap</span> <span class="n">f</span> <span class="p">(</span><span class="n">g</span> <span class="n">x</span> <span class="o">:</span> <span class="n">fmap</span> <span class="n">g</span> <span class="n">xs</span><span class="p">)</span> <span class="o">=</span> <span class="n">f</span> <span class="p">(</span><span class="n">g</span> <span class="n">x</span><span class="p">)</span> <span class="o">:</span> <span class="n">fmap</span> <span class="p">(</span><span class="n">f</span> <span class="o">.</span> <span class="n">g</span><span class="p">)</span> <span class="n">xs</span>
+</code></pre></div>    </div>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="kr">instance</span> <span class="kt">Functor</span> <span class="kt">Maybe</span> <span class="kr">where</span>
+   <span class="n">fmap</span> <span class="o">::</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Maybe</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Maybe</span> <span class="n">b</span>
+   <span class="n">fmap</span> <span class="kr">_</span> <span class="kt">Nothing</span>  <span class="o">=</span> <span class="kt">Nothing</span>
+   <span class="n">fmap</span> <span class="n">g</span> <span class="p">(</span><span class="kt">Just</span> <span class="n">a</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Just</span> <span class="p">(</span><span class="n">g</span> <span class="n">a</span><span class="p">)</span>
+    
+ <span class="c1">-- check the first law for each part:</span>
+ <span class="n">fmap</span> <span class="n">id</span> <span class="kt">Nothing</span> <span class="o">=</span> <span class="kt">Nothing</span>
+ <span class="n">fmap</span> <span class="n">id</span> <span class="p">(</span><span class="kt">Just</span> <span class="n">a</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Just</span> <span class="p">(</span><span class="n">id</span> <span class="n">a</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Just</span> <span class="n">a</span>
+    
+ <span class="c1">-- check the second law for each part:</span>
+ <span class="n">fmap</span> <span class="p">(</span><span class="n">f</span> <span class="o">.</span> <span class="n">g</span><span class="p">)</span> <span class="kt">Nothing</span> <span class="o">=</span> <span class="kt">Nothing</span>
+ <span class="n">fmap</span> <span class="p">(</span><span class="n">f</span> <span class="o">.</span> <span class="n">g</span><span class="p">)</span> <span class="p">(</span><span class="kt">Just</span> <span class="n">x</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Just</span> <span class="p">((</span><span class="n">f</span> <span class="o">.</span> <span class="n">g</span><span class="p">)</span> <span class="n">x</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Just</span> <span class="p">(</span><span class="n">f</span> <span class="p">(</span><span class="n">g</span> <span class="n">x</span><span class="p">))</span>
+ <span class="n">fmap</span> <span class="n">f</span> <span class="p">(</span><span class="n">fmap</span> <span class="n">g</span> <span class="p">(</span><span class="kt">Just</span> <span class="n">x</span><span class="p">))</span> <span class="o">=</span> <span class="kt">Just</span> <span class="p">(</span><span class="n">f</span> <span class="p">(</span><span class="n">g</span> <span class="n">x</span><span class="p">))</span> <span class="o">=</span> <span class="kt">Just</span> <span class="p">((</span><span class="n">f</span> <span class="o">.</span> <span class="n">g</span><span class="p">)</span> <span class="n">x</span><span class="p">)</span>
+</code></pre></div>    </div>
+  </li>
+</ol>
+
+<h1 id="tocAnchor-1-8">Applicative</h1>
+
+<h2 id="tocAnchor-1-8-1">Laws</h2>
+
+<ol>
+  <li>
+    <p>The identity law:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">pure</span> <span class="n">id</span> <span class="o">&lt;*&gt;</span> <span class="n">v</span> <span class="o">=</span> <span class="n">v</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>Homomorphism:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">pure</span> <span class="n">f</span> <span class="o">&lt;*&gt;</span> <span class="n">pure</span> <span class="n">x</span> <span class="o">=</span> <span class="n">pure</span> <span class="p">(</span><span class="n">f</span> <span class="n">x</span><span class="p">)</span>
+</code></pre></div>    </div>
+
+    <p>Intuitively, applying a non-effectful function to a non-effectful argument in an effectful context is the same as just applying the function to the argument and then injecting the result into the context with pure.</p>
+  </li>
+  <li>
+    <p>Interchange:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">u</span> <span class="o">&lt;*&gt;</span> <span class="n">pure</span> <span class="n">y</span> <span class="o">=</span> <span class="n">pure</span> <span class="p">(</span><span class="o">$</span> <span class="n">y</span><span class="p">)</span> <span class="o">&lt;*&gt;</span> <span class="n">u</span>
+</code></pre></div>    </div>
+
+    <p>Intuitively, this says that when evaluating the application of an effectful function to a pure argument, the order in which we evaluate the function and its argument doesn’t matter.</p>
+  </li>
+  <li>
+    <p>Composition:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">u</span> <span class="o">&lt;*&gt;</span> <span class="p">(</span><span class="n">v</span> <span class="o">&lt;*&gt;</span> <span class="n">w</span><span class="p">)</span> <span class="o">=</span> <span class="n">pure</span> <span class="p">(</span><span class="o">.</span><span class="p">)</span> <span class="o">&lt;*&gt;</span> <span class="n">u</span> <span class="o">&lt;*&gt;</span> <span class="n">v</span> <span class="o">&lt;*&gt;</span> <span class="n">w</span>
+</code></pre></div>    </div>
+
+    <p>This one is the trickiest law to gain intuition for. In some sense it is expressing a sort of associativity property of (<code class="language-plaintext highlighter-rouge">&lt;*&gt;</code>). The reader may wish to simply convince themselves that this law is type-correct.</p>
+  </li>
+</ol>
+
+<h3 id="exercises-4">Exercises</h3>
+
+<p>(Tricky) One might imagine a variant of the interchange law that says something about applying a pure function to an effectful argument. Using the above laws, prove that</p>
+
+<div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">pure</span> <span class="n">f</span> <span class="o">&lt;*&gt;</span> <span class="n">x</span> <span class="o">=</span> <span class="n">pure</span> <span class="p">(</span><span class="n">flip</span> <span class="p">(</span><span class="o">$</span><span class="p">))</span> <span class="o">&lt;*&gt;</span> <span class="n">x</span> <span class="o">&lt;*&gt;</span> <span class="n">pure</span> <span class="n">f</span>
+</code></pre></div></div>
+
+<p><strong>Solution</strong>:</p>
+
+<div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">pure</span> <span class="p">(</span><span class="n">flip</span> <span class="p">(</span><span class="o">$</span><span class="p">))</span> <span class="o">&lt;*&gt;</span> <span class="n">x</span> <span class="o">&lt;*&gt;</span> <span class="n">pure</span> <span class="n">f</span>
+  <span class="o">=</span> <span class="p">(</span><span class="n">pure</span> <span class="p">(</span><span class="n">flip</span> <span class="p">(</span><span class="o">$</span><span class="p">))</span> <span class="o">&lt;*&gt;</span> <span class="n">x</span><span class="p">)</span> <span class="o">&lt;*&gt;</span> <span class="n">pure</span> <span class="n">f</span> <span class="c1">-- &lt;*&gt; is left-associative</span>
+  <span class="o">=</span> <span class="n">pure</span> <span class="p">(</span><span class="o">$</span> <span class="n">f</span><span class="p">)</span> <span class="o">&lt;*&gt;</span> <span class="p">(</span><span class="n">pure</span> <span class="p">(</span><span class="n">flip</span> <span class="p">(</span><span class="o">$</span><span class="p">))</span> <span class="o">&lt;*&gt;</span> <span class="n">x</span><span class="p">)</span> <span class="c1">-- interchange</span>
+  <span class="o">=</span> <span class="n">pure</span> <span class="p">(</span><span class="o">.</span><span class="p">)</span> <span class="o">&lt;*&gt;</span> <span class="n">pure</span> <span class="p">(</span><span class="o">$</span> <span class="n">f</span><span class="p">)</span> <span class="o">&lt;*&gt;</span> <span class="n">pure</span> <span class="p">(</span><span class="n">flip</span> <span class="p">(</span><span class="o">$</span><span class="p">))</span> <span class="o">&lt;*&gt;</span> <span class="n">x</span> <span class="c1">-- composition</span>
+  <span class="o">=</span> <span class="n">pure</span> <span class="p">((</span><span class="o">$</span> <span class="n">f</span><span class="p">)</span> <span class="o">.</span> <span class="p">(</span><span class="n">flip</span> <span class="p">(</span><span class="o">$</span><span class="p">)))</span> <span class="o">&lt;*&gt;</span> <span class="n">x</span> <span class="c1">-- homomorphism</span>
+  <span class="o">=</span> <span class="n">pure</span> <span class="p">((</span><span class="n">flip</span> <span class="p">(</span><span class="o">$</span><span class="p">)</span> <span class="n">f</span><span class="p">)</span> <span class="o">.</span> <span class="p">(</span><span class="n">flip</span> <span class="p">(</span><span class="o">$</span><span class="p">)))</span> <span class="o">&lt;*&gt;</span> <span class="n">x</span> <span class="c1">-- identical</span>
+  <span class="o">=</span> <span class="n">pure</span> <span class="n">f</span> <span class="o">&lt;*&gt;</span> <span class="n">x</span>
+</code></pre></div></div>
+<p>Explanation of the last transformation:</p>
+
+<p><code class="language-plaintext highlighter-rouge">flip ($)</code> has type <code class="language-plaintext highlighter-rouge">a -&gt; (a -&gt; c) -&gt; c</code>, intuitively, it first takes an argument of type <code class="language-plaintext highlighter-rouge">a</code>, then a function that accepts that argument, and in the end it calls the function with the first argument. So <code class="language-plaintext highlighter-rouge">(flip ($) 5)</code> takes as argument a function which gets called with <code class="language-plaintext highlighter-rouge">5</code> as it’s argument. If we pass <code class="language-plaintext highlighter-rouge">(+ 2)</code> to <code class="language-plaintext highlighter-rouge">(flip ($) 5)</code>, we get <code class="language-plaintext highlighter-rouge">(flip ($) 5) (+2)</code> which is equivalent to the expression <code class="language-plaintext highlighter-rouge">(+2) $ 5</code>, evaluating to <code class="language-plaintext highlighter-rouge">7</code>.</p>
+
+<p><code class="language-plaintext highlighter-rouge">flip ($) f</code> is equivalent to <code class="language-plaintext highlighter-rouge">\x -&gt; x $ f</code>, that means, it takes as input a function and calls it with the function <code class="language-plaintext highlighter-rouge">f</code> as argument.</p>
+
+<p>The composition of these functions works like this: First <code class="language-plaintext highlighter-rouge">flip ($)</code> takes <code class="language-plaintext highlighter-rouge">x</code> as it’s first argument, and returns a function <code class="language-plaintext highlighter-rouge">(flip ($) x)</code>, this function is awaiting a function as it’s last argument, which will be called with <code class="language-plaintext highlighter-rouge">x</code> as it’s argument. Now this function <code class="language-plaintext highlighter-rouge">(flip ($) x)</code> is passed to <code class="language-plaintext highlighter-rouge">flip ($) f</code>, or to write it’s equivalent <code class="language-plaintext highlighter-rouge">(\x -&gt; x $ f) (flip ($) x)</code>, this results in the expression <code class="language-plaintext highlighter-rouge">(flip ($) x) f</code>, which is equivalent to <code class="language-plaintext highlighter-rouge">f $ x</code>.</p>
+
+<p>You can check the type of <code class="language-plaintext highlighter-rouge">(flip ($) f) . (flip ($))</code> is something like this (depending on your function <code class="language-plaintext highlighter-rouge">f</code>):</p>
+
+<div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="err">λ</span><span class="o">:</span> <span class="kr">let</span> <span class="n">f</span> <span class="o">=</span> <span class="n">sqrt</span>
+<span class="err">λ</span><span class="o">:</span> <span class="o">:</span><span class="n">t</span> <span class="p">(</span><span class="n">flip</span> <span class="p">(</span><span class="o">$</span><span class="p">)</span> <span class="n">f</span><span class="p">)</span> <span class="o">.</span> <span class="p">(</span><span class="n">flip</span> <span class="p">(</span><span class="o">$</span><span class="p">))</span>
+<span class="p">(</span><span class="n">flip</span> <span class="p">(</span><span class="o">$</span><span class="p">)</span> <span class="n">f</span><span class="p">)</span> <span class="o">.</span> <span class="p">(</span><span class="n">flip</span> <span class="p">(</span><span class="o">$</span><span class="p">))</span> <span class="o">::</span> <span class="kt">Floating</span> <span class="n">c</span> <span class="o">=&gt;</span> <span class="n">c</span> <span class="o">-&gt;</span> <span class="n">c</span>
+</code></pre></div></div>
+
+<p>Also see <a href="https://stackoverflow.com/questions/46503793/applicative-prove-pure-f-x-pure-flip-x-pure-f/46505868#46505868">this question on Stack Overflow</a> which includes alternative proofs.</p>
+
+<h2 id="tocAnchor-1-8-2">Instances</h2>
+
+<p>Applicative instance of lists as a collection of values:</p>
+
+<div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kr">newtype</span> <span class="kt">ZipList</span> <span class="n">a</span> <span class="o">=</span> <span class="kt">ZipList</span> <span class="p">{</span> <span class="n">getZipList</span> <span class="o">::</span> <span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="p">}</span>
+ 
+<span class="kr">instance</span> <span class="kt">Applicative</span> <span class="kt">ZipList</span> <span class="kr">where</span>
+  <span class="n">pure</span> <span class="o">::</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">ZipList</span> <span class="n">a</span>
+  <span class="n">pure</span> <span class="o">=</span> <span class="n">undefined</span>   <span class="c1">-- exercise</span>
+ 
+  <span class="p">(</span><span class="o">&lt;*&gt;</span><span class="p">)</span> <span class="o">::</span> <span class="kt">ZipList</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">ZipList</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">ZipList</span> <span class="n">b</span>
+  <span class="p">(</span><span class="kt">ZipList</span> <span class="n">gs</span><span class="p">)</span> <span class="o">&lt;*&gt;</span> <span class="p">(</span><span class="kt">ZipList</span> <span class="n">xs</span><span class="p">)</span> <span class="o">=</span> <span class="kt">ZipList</span> <span class="p">(</span><span class="n">zipWith</span> <span class="p">(</span><span class="o">$</span><span class="p">)</span> <span class="n">gs</span> <span class="n">xs</span><span class="p">)</span>
+</code></pre></div></div>
+
+<p>Applicative instance of lists as a non-deterministic computation context:</p>
+
+<div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kr">instance</span> <span class="kt">Applicative</span> <span class="kt">[]</span> <span class="kr">where</span>
+  <span class="n">pure</span> <span class="o">::</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">a</span><span class="p">]</span>
+  <span class="n">pure</span> <span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="n">x</span><span class="p">]</span>
+ 
+  <span class="p">(</span><span class="o">&lt;*&gt;</span><span class="p">)</span> <span class="o">::</span> <span class="p">[</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span><span class="p">]</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">b</span><span class="p">]</span>
+  <span class="n">gs</span> <span class="o">&lt;*&gt;</span> <span class="n">xs</span> <span class="o">=</span> <span class="p">[</span> <span class="n">g</span> <span class="n">x</span> <span class="o">|</span> <span class="n">g</span> <span class="o">&lt;-</span> <span class="n">gs</span><span class="p">,</span> <span class="n">x</span> <span class="o">&lt;-</span> <span class="n">xs</span> <span class="p">]</span>
+</code></pre></div></div>
+
+<h3 id="exercises-5">Exercises</h3>
+
+<ol>
+  <li>
+    <p>Implement an instance of <code class="language-plaintext highlighter-rouge">Applicative</code> for <code class="language-plaintext highlighter-rouge">Maybe</code>.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="kr">instance</span> <span class="kt">Applicative</span> <span class="p">(</span><span class="kt">Maybe</span> <span class="n">a</span><span class="p">)</span> <span class="kr">where</span>
+   <span class="n">pure</span> <span class="o">::</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Maybe</span> <span class="n">a</span>
+   <span class="n">pure</span> <span class="n">x</span> <span class="o">=</span> <span class="kt">Just</span> <span class="n">x</span>
+      
+   <span class="p">(</span><span class="o">&lt;*&gt;</span><span class="p">)</span> <span class="o">::</span> <span class="kt">Maybe</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Maybe</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Maybe</span> <span class="n">b</span>
+   <span class="kr">_</span> <span class="o">&lt;*&gt;</span> <span class="kt">Nothing</span> <span class="o">=</span> <span class="kt">Nothing</span>
+   <span class="kt">Nothing</span> <span class="o">&lt;*&gt;</span> <span class="kr">_</span> <span class="o">=</span> <span class="kt">Nothing</span>
+   <span class="p">(</span><span class="kt">Just</span> <span class="n">f</span><span class="p">)</span> <span class="o">&lt;*&gt;</span> <span class="p">(</span><span class="kt">Just</span> <span class="n">x</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Just</span> <span class="p">(</span><span class="n">f</span> <span class="n">x</span><span class="p">)</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>Determine the correct definition of <code class="language-plaintext highlighter-rouge">pure</code> for the <code class="language-plaintext highlighter-rouge">ZipList</code> instance of <code class="language-plaintext highlighter-rouge">Applicative</code>—there is only one implementation that satisfies the law relating <code class="language-plaintext highlighter-rouge">pure</code> and <code class="language-plaintext highlighter-rouge">(&lt;*&gt;)</code>.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="kr">newtype</span> <span class="kt">ZipList</span> <span class="n">a</span> <span class="o">=</span> <span class="kt">ZipList</span> <span class="p">{</span> <span class="n">getZipList</span> <span class="o">::</span> <span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="p">}</span>
+    
+ <span class="kr">instance</span> <span class="kt">Functor</span> <span class="kt">ZipList</span> <span class="kr">where</span>
+   <span class="n">fmap</span> <span class="n">f</span> <span class="p">(</span><span class="kt">ZipList</span> <span class="n">list</span><span class="p">)</span> <span class="o">=</span> <span class="kt">ZipList</span> <span class="p">{</span> <span class="n">getZipList</span> <span class="o">=</span> <span class="n">fmap</span> <span class="n">f</span> <span class="n">list</span> <span class="p">}</span>
+    
+ <span class="kr">instance</span> <span class="kt">Applicative</span> <span class="kt">ZipList</span> <span class="kr">where</span>
+   <span class="n">pure</span> <span class="o">=</span> <span class="kt">ZipList</span> <span class="o">.</span> <span class="n">pure</span>
+    
+   <span class="p">(</span><span class="kt">ZipList</span> <span class="n">gs</span><span class="p">)</span> <span class="o">&lt;*&gt;</span> <span class="p">(</span><span class="kt">ZipList</span> <span class="n">xs</span><span class="p">)</span> <span class="o">=</span> <span class="kt">ZipList</span> <span class="p">(</span><span class="n">zipWith</span> <span class="p">(</span><span class="o">$</span><span class="p">)</span> <span class="n">gs</span> <span class="n">xs</span><span class="p">)</span>
+</code></pre></div>    </div>
+
+    <p>You can check the Applicative laws for this implementation.</p>
+  </li>
+</ol>
+
+<h2 id="tocAnchor-1-8-3">Utility functions</h2>
+
+<h3 id="exercises-6">Exercises</h3>
+
+<ol>
+  <li>
+    <p>Implement a function
+ <code class="language-plaintext highlighter-rouge">sequenceAL :: Applicative f =&gt; [f a] -&gt; f [a]</code>
+ There is a generalized version of this, <code class="language-plaintext highlighter-rouge">sequenceA</code>, which works for any <code class="language-plaintext highlighter-rouge">Traversable</code> (see the later section on <code class="language-plaintext highlighter-rouge">Traversable</code>), but implementing this version specialized to lists is a good exercise.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">createList</span> <span class="o">=</span> <span class="n">replicate</span> <span class="mi">1</span>
+
+ <span class="n">sequenceAL</span> <span class="o">::</span> <span class="kt">Applicative</span> <span class="n">f</span> <span class="o">=&gt;</span> <span class="p">[</span><span class="n">f</span> <span class="n">a</span><span class="p">]</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="p">[</span><span class="n">a</span><span class="p">]</span>
+ <span class="n">sequenceAL</span> <span class="o">=</span> <span class="n">foldr</span> <span class="p">(</span><span class="nf">\</span><span class="n">x</span> <span class="n">b</span> <span class="o">-&gt;</span> <span class="p">((</span><span class="o">++</span><span class="p">)</span> <span class="o">.</span> <span class="n">createList</span> <span class="o">&lt;$&gt;</span> <span class="n">x</span><span class="p">)</span> <span class="o">&lt;*&gt;</span> <span class="n">b</span><span class="p">)</span> <span class="p">(</span><span class="n">pure</span> <span class="kt">[]</span><span class="p">)</span>
+</code></pre></div>    </div>
+
+    <p>Explanation:</p>
+
+    <p>First, <code class="language-plaintext highlighter-rouge">createList</code> is a simple function for creating a list of a single element, e.g. <code class="language-plaintext highlighter-rouge">createList 2 == [2]</code>.</p>
+
+    <p>Now let’s take <code class="language-plaintext highlighter-rouge">sequenceAL</code> apart, first, it does a fold over the list <code class="language-plaintext highlighter-rouge">[f a]</code>, and <code class="language-plaintext highlighter-rouge">b</code> is initialized to <code class="language-plaintext highlighter-rouge">pure []</code>, which results in <code class="language-plaintext highlighter-rouge">f [a]</code> as required by the function’s output.</p>
+
+    <p>Inside the function, <code class="language-plaintext highlighter-rouge">createList &lt;$&gt; x</code> applies <code class="language-plaintext highlighter-rouge">createList</code> to the value inside <code class="language-plaintext highlighter-rouge">f a</code>, resulting in <code class="language-plaintext highlighter-rouge">f [a]</code>, and then <code class="language-plaintext highlighter-rouge">(++)</code> is applied to the value again, so it becomes <code class="language-plaintext highlighter-rouge">f ((++) [a])</code>, now we can apply the function <code class="language-plaintext highlighter-rouge">(++) [a]</code> to <code class="language-plaintext highlighter-rouge">b</code> by <code class="language-plaintext highlighter-rouge">((++) . createList &lt;$&gt; x) &lt;*&gt; b</code>, which results in <code class="language-plaintext highlighter-rouge">f ([a] ++ b)</code>.</p>
+  </li>
+</ol>
+
+<h2 id="tocAnchor-1-8-4">Alternative formulation</h2>
+
+<h3 id="definition">Definition</h3>
+
+<div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kr">class</span> <span class="kt">Functor</span> <span class="n">f</span> <span class="o">=&gt;</span> <span class="kt">Monoidal</span> <span class="n">f</span> <span class="kr">where</span>
+  <span class="n">unit</span> <span class="o">::</span> <span class="n">f</span> <span class="nb">()</span>
+  <span class="p">(</span><span class="o">**</span><span class="p">)</span> <span class="o">::</span> <span class="n">f</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="n">b</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="n">b</span><span class="p">)</span>
+</code></pre></div></div>
+
+<h3 id="laws-1">Laws:</h3>
+
+<ol>
+  <li>
+    <p>Left identity</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">unit</span> <span class="o">**</span> <span class="n">v</span> <span class="err">≅</span> <span class="n">v</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>Right identity</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">u</span> <span class="o">**</span> <span class="n">unit</span> <span class="err">≅</span> <span class="n">u</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>Associativity</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">u</span> <span class="o">**</span> <span class="p">(</span><span class="n">v</span> <span class="o">**</span> <span class="n">w</span><span class="p">)</span> <span class="err">≅</span> <span class="p">(</span><span class="n">u</span> <span class="o">**</span> <span class="n">v</span><span class="p">)</span> <span class="o">**</span> <span class="n">w</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>Neutrality</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">fmap</span> <span class="p">(</span><span class="n">g</span> <span class="o">***</span> <span class="n">h</span><span class="p">)</span> <span class="p">(</span><span class="n">u</span> <span class="o">**</span> <span class="n">v</span><span class="p">)</span> <span class="o">=</span> <span class="n">fmap</span> <span class="n">g</span> <span class="n">u</span> <span class="o">**</span> <span class="n">fmap</span> <span class="n">h</span> <span class="n">v</span>
+</code></pre></div>    </div>
+  </li>
+</ol>
+
+<h3 id="isomorphism">Isomorphism</h3>
+
+<p>In the laws above, <code class="language-plaintext highlighter-rouge">≅</code> refers to isomorphism rather than equality. In particular we consider:</p>
+
+<div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="nb">()</span><span class="p">)</span> <span class="err">≅</span> <span class="n">x</span> <span class="err">≅</span> <span class="p">(</span><span class="nb">()</span><span class="p">,</span><span class="n">x</span><span class="p">)</span>
+<span class="p">((</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">),</span><span class="n">z</span><span class="p">)</span> <span class="err">≅</span> <span class="p">(</span><span class="n">x</span><span class="p">,(</span><span class="n">y</span><span class="p">,</span><span class="n">z</span><span class="p">))</span>
+</code></pre></div></div>
+
+<h3 id="exercises-7">Exercises</h3>
+
+<ol>
+  <li>
+    <p>Implement <code class="language-plaintext highlighter-rouge">pure</code> and <code class="language-plaintext highlighter-rouge">&lt;*&gt;</code> in terms of <code class="language-plaintext highlighter-rouge">unit</code> and <code class="language-plaintext highlighter-rouge">**</code>, and vice versa.</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">unit</span> <span class="o">::</span> <span class="n">f</span> <span class="nb">()</span>
+ <span class="n">unit</span> <span class="o">=</span> <span class="n">pure</span> <span class="nb">()</span>
+    
+ <span class="p">(</span><span class="o">**</span><span class="p">)</span> <span class="o">::</span> <span class="n">f</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="n">b</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
+ <span class="n">a</span> <span class="o">**</span> <span class="n">b</span> <span class="o">=</span> <span class="n">fmap</span> <span class="p">(,)</span> <span class="n">a</span> <span class="o">&lt;*&gt;</span> <span class="n">b</span>
+    
+ <span class="n">pure</span> <span class="o">::</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="n">a</span>
+ <span class="n">pure</span> <span class="n">x</span> <span class="o">=</span> <span class="n">unit</span> <span class="o">**</span> <span class="n">x</span>
+    
+ <span class="p">(</span><span class="o">&lt;*&gt;</span><span class="p">)</span> <span class="o">::</span> <span class="n">f</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="n">b</span>
+ <span class="n">f</span> <span class="o">&lt;*&gt;</span> <span class="n">a</span> <span class="o">=</span> <span class="n">fmap</span> <span class="p">(</span><span class="n">uncurry</span> <span class="p">(</span><span class="o">$</span><span class="p">))</span> <span class="p">(</span><span class="n">f</span> <span class="o">**</span> <span class="n">a</span><span class="p">)</span> <span class="o">=</span> <span class="n">fmap</span> <span class="p">(</span><span class="nf">\</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="n">a</span><span class="p">)</span> <span class="p">(</span><span class="n">f</span> <span class="o">**</span> <span class="n">a</span><span class="p">)</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>Are there any <code class="language-plaintext highlighter-rouge">Applicative</code> instances for which there are also functions <code class="language-plaintext highlighter-rouge">f () -&gt; ()</code> and <code class="language-plaintext highlighter-rouge">f (a,b) -&gt; (f a, f b)</code>, satisfying some “reasonable” laws?</p>
+
+    <p>The <a href="https://wiki.haskell.org/Typeclassopedia#Arrow"><code class="language-plaintext highlighter-rouge">Arrow</code></a> type class seems to satisfy these criteria.</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code>   <span class="n">first</span> <span class="n">unit</span> <span class="o">=</span> <span class="nb">()</span>
+      
+   <span class="p">(</span><span class="n">id</span> <span class="o">***</span> <span class="n">f</span><span class="p">)</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="o">=</span> <span class="p">(</span><span class="n">f</span> <span class="n">a</span><span class="p">,</span> <span class="n">f</span> <span class="n">b</span><span class="p">)</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>(Tricky) Prove that given your implementations from the first exercise, the usual Applicative laws and the Monoidal laws stated above are equivalent.</p>
+
+    <ol>
+      <li>
+        <p>Identity Law</p>
+
+        <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">pure</span> <span class="n">id</span> <span class="o">&lt;*&gt;</span> <span class="n">v</span>
+   <span class="o">=</span> <span class="n">fmap</span> <span class="p">(</span><span class="n">uncurry</span> <span class="p">(</span><span class="o">$</span><span class="p">))</span> <span class="p">((</span><span class="n">unit</span> <span class="o">**</span> <span class="n">id</span><span class="p">)</span> <span class="o">**</span> <span class="n">v</span><span class="p">)</span>
+   <span class="o">=</span> <span class="n">fmap</span> <span class="p">(</span><span class="n">uncurry</span> <span class="p">(</span><span class="o">$</span><span class="p">))</span> <span class="p">(</span><span class="n">id</span> <span class="o">**</span> <span class="n">v</span><span class="p">)</span>
+   <span class="o">=</span> <span class="n">fmap</span> <span class="n">id</span> <span class="n">v</span>
+   <span class="o">=</span> <span class="n">v</span>
+</code></pre></div>        </div>
+      </li>
+      <li>
+        <p>Homomorphism</p>
+
+        <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">pure</span> <span class="n">f</span> <span class="o">&lt;*&gt;</span> <span class="n">pure</span> <span class="n">x</span>
+   <span class="o">=</span> <span class="p">(</span><span class="n">unit</span> <span class="o">**</span> <span class="n">f</span><span class="p">)</span> <span class="o">&lt;*&gt;</span> <span class="p">(</span><span class="n">unit</span> <span class="o">**</span> <span class="n">x</span><span class="p">)</span>
+   <span class="o">=</span> <span class="n">fmap</span> <span class="p">(</span><span class="nf">\</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="n">a</span><span class="p">)</span> <span class="p">(</span><span class="n">unit</span> <span class="o">**</span> <span class="n">f</span><span class="p">)</span> <span class="p">(</span><span class="n">unit</span> <span class="o">**</span> <span class="n">x</span><span class="p">)</span>
+   <span class="o">=</span> <span class="n">fmap</span> <span class="p">(</span><span class="nf">\</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="n">a</span><span class="p">)</span> <span class="p">(</span><span class="n">f</span> <span class="o">**</span> <span class="n">x</span><span class="p">)</span>
+   <span class="o">=</span> <span class="n">fmap</span> <span class="n">f</span> <span class="n">x</span>
+   <span class="o">=</span> <span class="n">pure</span> <span class="p">(</span><span class="n">f</span> <span class="n">x</span><span class="p">)</span>
+</code></pre></div>        </div>
+      </li>
+      <li>
+        <p>Interchange</p>
+
+        <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">u</span> <span class="o">&lt;*&gt;</span> <span class="n">pure</span> <span class="n">y</span>
+   <span class="o">=</span> <span class="n">fmap</span> <span class="p">(</span><span class="n">uncurry</span> <span class="p">(</span><span class="o">$</span><span class="p">))</span> <span class="p">(</span><span class="n">u</span> <span class="o">**</span> <span class="p">(</span><span class="n">unit</span> <span class="o">**</span> <span class="n">y</span><span class="p">))</span>
+   <span class="o">=</span> <span class="n">fmap</span> <span class="p">(</span><span class="n">uncurry</span> <span class="p">(</span><span class="o">$</span><span class="p">))</span> <span class="p">(</span><span class="n">u</span> <span class="o">**</span> <span class="n">y</span><span class="p">)</span>
+   <span class="o">=</span> <span class="n">fmap</span> <span class="p">(</span><span class="n">u</span> <span class="o">$</span><span class="p">)</span> <span class="n">y</span>
+   <span class="o">=</span> <span class="n">fmap</span> <span class="p">(</span><span class="o">$</span> <span class="n">y</span><span class="p">)</span> <span class="n">u</span>
+   <span class="o">=</span> <span class="n">pure</span> <span class="p">(</span><span class="o">$</span> <span class="n">y</span><span class="p">)</span> <span class="o">&lt;*&gt;</span> <span class="n">u</span>
+</code></pre></div>        </div>
+      </li>
+      <li>
+        <p>Composition</p>
+
+        <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">u</span> <span class="o">&lt;*&gt;</span> <span class="p">(</span><span class="n">v</span> <span class="o">&lt;*&gt;</span> <span class="n">w</span><span class="p">)</span>
+   <span class="o">=</span> <span class="n">fmap</span> <span class="p">(</span><span class="n">uncurry</span> <span class="p">(</span><span class="o">$</span><span class="p">))</span> <span class="p">(</span><span class="n">u</span> <span class="o">**</span> <span class="p">(</span><span class="n">fmap</span> <span class="p">(</span><span class="n">uncurry</span> <span class="p">(</span><span class="o">$</span><span class="p">))</span> <span class="p">(</span><span class="n">v</span> <span class="o">**</span> <span class="n">w</span><span class="p">)))</span>
+   <span class="o">=</span> <span class="n">fmap</span> <span class="p">(</span><span class="n">uncurry</span> <span class="p">(</span><span class="o">$</span><span class="p">))</span> <span class="p">(</span><span class="n">u</span> <span class="o">**</span> <span class="p">(</span><span class="n">fmap</span> <span class="n">v</span> <span class="n">w</span><span class="p">))</span>
+   <span class="o">=</span> <span class="n">fmap</span> <span class="n">u</span> <span class="p">(</span><span class="n">fmap</span> <span class="n">v</span> <span class="n">w</span><span class="p">)</span>
+   <span class="o">=</span> <span class="n">fmap</span> <span class="p">(</span><span class="n">u</span> <span class="o">.</span> <span class="n">v</span><span class="p">)</span> <span class="n">w</span>
+   <span class="o">=</span> <span class="n">pure</span> <span class="p">(</span><span class="o">.</span><span class="p">)</span> <span class="o">&lt;*&gt;</span> <span class="n">u</span> <span class="o">&lt;*&gt;</span> <span class="n">v</span> <span class="o">&lt;*&gt;</span> <span class="n">w</span> <span class="o">=</span>
+</code></pre></div>        </div>
+      </li>
+    </ol>
+  </li>
+</ol>
+
+<h1 id="tocAnchor-1-13">Monad</h1>
+
+<h2 id="tocAnchor-1-13-1">Definition</h2>
+
+<div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kr">class</span> <span class="kt">Applicative</span> <span class="n">m</span> <span class="o">=&gt;</span> <span class="kt">Monad</span> <span class="n">m</span> <span class="kr">where</span>
+  <span class="n">return</span> <span class="o">::</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">m</span> <span class="n">a</span>
+  <span class="p">(</span><span class="o">&gt;&gt;=</span><span class="p">)</span>  <span class="o">::</span> <span class="n">m</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">m</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">m</span> <span class="n">b</span>
+  <span class="p">(</span><span class="o">&gt;&gt;</span><span class="p">)</span>   <span class="o">::</span> <span class="n">m</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">m</span> <span class="n">b</span> <span class="o">-&gt;</span> <span class="n">m</span> <span class="n">b</span>
+  <span class="n">m</span> <span class="o">&gt;&gt;</span> <span class="n">n</span> <span class="o">=</span> <span class="n">m</span> <span class="o">&gt;&gt;=</span> <span class="nf">\</span><span class="kr">_</span> <span class="o">-&gt;</span> <span class="n">n</span>
+ 
+  <span class="n">fail</span>   <span class="o">::</span> <span class="kt">String</span> <span class="o">-&gt;</span> <span class="n">m</span> <span class="n">a</span>
+</code></pre></div></div>
+
+<h2 id="tocAnchor-1-13-2">Instances</h2>
+
+<div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kr">instance</span> <span class="kt">Monad</span> <span class="kt">Maybe</span> <span class="kr">where</span>
+  <span class="n">return</span> <span class="o">::</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Maybe</span> <span class="n">a</span>
+  <span class="n">return</span> <span class="o">=</span> <span class="kt">Just</span>
+ 
+  <span class="p">(</span><span class="o">&gt;&gt;=</span><span class="p">)</span> <span class="o">::</span> <span class="kt">Maybe</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Maybe</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Maybe</span> <span class="n">b</span>
+  <span class="p">(</span><span class="kt">Just</span> <span class="n">x</span><span class="p">)</span> <span class="o">&gt;&gt;=</span> <span class="n">g</span> <span class="o">=</span> <span class="n">g</span> <span class="n">x</span>
+  <span class="kt">Nothing</span>  <span class="o">&gt;&gt;=</span> <span class="kr">_</span> <span class="o">=</span> <span class="kt">Nothing</span>
+</code></pre></div></div>
+
+<h3 id="exercises-8">Exercises</h3>
+
+<ol>
+  <li>
+    <p>Implement a <code class="language-plaintext highlighter-rouge">Monad</code> instance for the list constructor, <code class="language-plaintext highlighter-rouge">[]</code>. Follow the types!</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="kr">instance</span> <span class="kt">Monad</span> <span class="kt">[]</span> <span class="kr">where</span>
+   <span class="n">return</span> <span class="n">a</span> <span class="o">=</span> <span class="p">[</span><span class="n">a</span><span class="p">]</span>
+      
+   <span class="kt">[]</span> <span class="o">&gt;&gt;</span> <span class="kr">_</span> <span class="o">=</span> <span class="kt">[]</span>
+   <span class="p">(</span><span class="n">x</span><span class="o">:</span><span class="n">xs</span><span class="p">)</span> <span class="o">&gt;&gt;=</span> <span class="n">f</span> <span class="o">=</span> <span class="n">f</span> <span class="n">x</span> <span class="o">:</span> <span class="n">xs</span> <span class="o">&gt;&gt;=</span> <span class="n">f</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>Implement a <code class="language-plaintext highlighter-rouge">Monad</code> instance for <code class="language-plaintext highlighter-rouge">((-&gt;) e)</code>.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="kr">instance</span> <span class="kt">Monad</span> <span class="p">((</span><span class="o">-&gt;</span><span class="p">)</span> <span class="n">e</span><span class="p">)</span> <span class="kr">where</span>
+   <span class="n">return</span> <span class="n">x</span> <span class="o">=</span> <span class="n">const</span> <span class="n">x</span>
+      
+   <span class="n">g</span> <span class="o">&gt;&gt;=</span> <span class="n">f</span> <span class="o">=</span> <span class="n">f</span> <span class="o">.</span> <span class="n">g</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>Implement <code class="language-plaintext highlighter-rouge">Functor</code> and <code class="language-plaintext highlighter-rouge">Monad</code> instance for <code class="language-plaintext highlighter-rouge">Free f</code>, defined as:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="kr">data</span> <span class="kt">Free</span> <span class="n">f</span> <span class="n">a</span> <span class="o">=</span> <span class="kt">Var</span> <span class="n">a</span>
+               <span class="o">|</span> <span class="kt">Node</span> <span class="p">(</span><span class="n">f</span> <span class="p">(</span><span class="kt">Free</span> <span class="n">f</span> <span class="n">a</span><span class="p">))</span>
+</code></pre></div>    </div>
+
+    <p>You may assume that <code class="language-plaintext highlighter-rouge">f</code> has a <code class="language-plaintext highlighter-rouge">Functor</code> instance. This is known as the <em>free monad</em> built from the functor f.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="kr">instance</span> <span class="kt">Functor</span> <span class="p">(</span><span class="kt">Free</span> <span class="n">f</span><span class="p">)</span> <span class="kr">where</span>
+   <span class="n">fmap</span> <span class="n">f</span> <span class="p">(</span><span class="kt">Var</span> <span class="n">a</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Var</span> <span class="p">(</span><span class="n">f</span> <span class="n">a</span><span class="p">)</span>
+   <span class="n">fmap</span> <span class="n">f</span> <span class="p">(</span><span class="kt">Node</span> <span class="n">x</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Node</span> <span class="p">(</span><span class="n">f</span> <span class="n">x</span><span class="p">)</span>
+      
+ <span class="kr">instance</span> <span class="kt">Monad</span> <span class="p">(</span><span class="kt">Free</span> <span class="n">f</span><span class="p">)</span> <span class="kr">where</span>
+   <span class="n">return</span> <span class="n">x</span> <span class="o">=</span> <span class="kt">Var</span> <span class="n">x</span>
+      
+   <span class="p">(</span><span class="kt">Var</span> <span class="n">x</span><span class="p">)</span> <span class="o">&gt;&gt;=</span> <span class="n">f</span> <span class="o">=</span> <span class="kt">Var</span> <span class="p">(</span><span class="n">f</span> <span class="n">x</span><span class="p">)</span>
+   <span class="p">(</span><span class="kt">Node</span> <span class="n">x</span><span class="p">)</span> <span class="o">&gt;&gt;=</span> <span class="n">f</span> <span class="o">=</span> <span class="kt">Node</span> <span class="p">(</span><span class="n">fmap</span> <span class="n">f</span> <span class="n">x</span><span class="p">)</span>
+</code></pre></div>    </div>
+  </li>
+</ol>
+
+<h2 id="tocAnchor-1-13-3">Intuition</h2>
+
+<h3 id="exercises-9">Exercises</h3>
+
+<ol>
+  <li>
+    <p>Implement <code class="language-plaintext highlighter-rouge">(&gt;&gt;=)</code> in terms of <code class="language-plaintext highlighter-rouge">fmap</code> (or <code class="language-plaintext highlighter-rouge">liftM</code>) and <code class="language-plaintext highlighter-rouge">join</code>.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">a</span> <span class="o">&gt;&gt;=</span> <span class="n">f</span> <span class="o">=</span> <span class="n">join</span> <span class="p">(</span><span class="n">fmap</span> <span class="n">f</span> <span class="n">a</span><span class="p">)</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>Now implement <code class="language-plaintext highlighter-rouge">join</code> and <code class="language-plaintext highlighter-rouge">fmap</code> (<code class="language-plaintext highlighter-rouge">liftM</code>) in terms of <code class="language-plaintext highlighter-rouge">(&gt;&gt;=)</code> and <code class="language-plaintext highlighter-rouge">return</code>.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">fmap</span> <span class="n">f</span> <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">&gt;&gt;=</span> <span class="p">(</span><span class="n">return</span> <span class="o">.</span> <span class="n">f</span><span class="p">)</span>
+ <span class="n">join</span> <span class="n">m</span> <span class="o">=</span> <span class="n">m</span> <span class="o">&gt;&gt;=</span> <span class="n">id</span>
+</code></pre></div>    </div>
+  </li>
+</ol>
+
+<h2 id="tocAnchor-1-13-4">Laws</h2>
+
+<p>Standard:</p>
+
+<div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">return</span> <span class="n">a</span> <span class="o">&gt;&gt;=</span> <span class="n">k</span>  <span class="o">=</span>  <span class="n">k</span> <span class="n">a</span>
+<span class="n">m</span> <span class="o">&gt;&gt;=</span> <span class="n">return</span>    <span class="o">=</span>  <span class="n">m</span>
+<span class="n">m</span> <span class="o">&gt;&gt;=</span> <span class="p">(</span><span class="nf">\</span><span class="n">x</span> <span class="o">-&gt;</span> <span class="n">k</span> <span class="n">x</span> <span class="o">&gt;&gt;=</span> <span class="n">h</span><span class="p">)</span>  <span class="o">=</span>  <span class="p">(</span><span class="n">m</span> <span class="o">&gt;&gt;=</span> <span class="n">k</span><span class="p">)</span> <span class="o">&gt;&gt;=</span> <span class="n">h</span>
+</code></pre></div></div>
+
+<p>In terms of <code class="language-plaintext highlighter-rouge">&gt;=&gt;</code>:</p>
+
+<div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">return</span> <span class="o">&gt;=&gt;</span> <span class="n">g</span>  <span class="o">=</span>  <span class="n">g</span>
+<span class="n">g</span> <span class="o">&gt;=&gt;</span> <span class="n">return</span>  <span class="o">=</span>  <span class="n">g</span>
+<span class="p">(</span><span class="n">g</span> <span class="o">&gt;=&gt;</span> <span class="n">h</span><span class="p">)</span> <span class="o">&gt;=&gt;</span> <span class="n">k</span>  <span class="o">=</span>  <span class="n">g</span> <span class="o">&gt;=&gt;</span> <span class="p">(</span><span class="n">h</span> <span class="o">&gt;=&gt;</span> <span class="n">k</span><span class="p">)</span>
+</code></pre></div></div>
+
+<h3 id="exercises-10">Exercises</h3>
+
+<ol>
+  <li>
+    <p>Given the definition <code class="language-plaintext highlighter-rouge">g &gt;=&gt; h = \x -&gt; g x &gt;&gt;= h</code>, prove the equivalence of the above laws and the standard monad laws.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">return</span> <span class="o">&gt;=&gt;</span> <span class="n">g</span>
+   <span class="o">=</span> <span class="nf">\</span><span class="n">x</span> <span class="o">-&gt;</span> <span class="n">return</span> <span class="n">x</span> <span class="o">&gt;&gt;=</span> <span class="n">g</span>
+   <span class="o">=</span> <span class="nf">\</span><span class="n">x</span> <span class="o">-&gt;</span> <span class="n">g</span> <span class="n">x</span>
+   <span class="o">=</span> <span class="n">g</span>
+      
+ <span class="n">g</span> <span class="o">&gt;=&gt;</span> <span class="n">return</span>
+   <span class="o">=</span> <span class="nf">\</span><span class="n">x</span> <span class="o">-&gt;</span> <span class="n">g</span> <span class="n">x</span> <span class="o">&gt;&gt;=</span> <span class="n">return</span>
+   <span class="o">=</span> <span class="nf">\</span><span class="n">x</span> <span class="o">-&gt;</span> <span class="n">g</span> <span class="n">x</span>
+   <span class="o">=</span> <span class="n">g</span>
+    
+ <span class="n">g</span> <span class="o">&gt;=&gt;</span> <span class="p">(</span><span class="n">h</span> <span class="o">&gt;=&gt;</span> <span class="n">k</span><span class="p">)</span>
+   <span class="o">=</span> <span class="nf">\</span><span class="n">y</span> <span class="o">-&gt;</span> <span class="n">g</span> <span class="n">y</span> <span class="o">&gt;&gt;=</span> <span class="p">(</span><span class="nf">\</span><span class="n">x</span> <span class="o">-&gt;</span> <span class="n">h</span> <span class="n">x</span> <span class="o">&gt;&gt;=</span> <span class="n">k</span><span class="p">)</span>
+   <span class="o">=</span> <span class="nf">\</span><span class="n">y</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="n">g</span> <span class="n">y</span> <span class="o">&gt;&gt;=</span> <span class="n">h</span><span class="p">)</span> <span class="o">&gt;&gt;=</span> <span class="n">k</span>
+   <span class="o">=</span> <span class="nf">\</span><span class="n">y</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="nf">\</span><span class="n">x</span> <span class="o">-&gt;</span> <span class="n">g</span> <span class="n">x</span> <span class="o">&gt;&gt;=</span> <span class="n">h</span><span class="p">)</span> <span class="n">y</span> <span class="o">&gt;&gt;=</span> <span class="n">k</span>
+   <span class="o">=</span> <span class="p">(</span><span class="nf">\</span><span class="n">x</span> <span class="o">-&gt;</span> <span class="n">g</span> <span class="n">x</span> <span class="o">&gt;&gt;=</span> <span class="n">h</span><span class="p">)</span> <span class="o">&gt;=&gt;</span> <span class="n">k</span>
+   <span class="o">=</span> <span class="p">(</span><span class="n">g</span> <span class="o">&gt;=&gt;</span> <span class="n">h</span><span class="p">)</span> <span class="o">&gt;=&gt;</span> <span class="n">k</span>
+</code></pre></div>    </div>
+  </li>
+</ol>
+
+<h1 id="tocAnchor-1-18">Monad Transformers</h1>
+
+<h2 id="tocAnchor-1-18-1">Definition and laws</h2>
+
+<div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kr">class</span> <span class="kt">MonadTrans</span> <span class="n">t</span> <span class="kr">where</span>
+  <span class="n">lift</span> <span class="o">::</span> <span class="kt">Monad</span> <span class="n">m</span> <span class="o">=&gt;</span> <span class="n">m</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">m</span> <span class="n">a</span>
+</code></pre></div></div>
+
+<h3 id="exercises-11">Exercises</h3>
+
+<ol>
+  <li>
+    <p>What is the kind of <code class="language-plaintext highlighter-rouge">t</code> in the declaration of <code class="language-plaintext highlighter-rouge">MonadTrans</code>?</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <p><code class="language-plaintext highlighter-rouge">t</code> is of the kind <code class="language-plaintext highlighter-rouge">(* -&gt; *) -&gt; * -&gt; *</code>, as we see in <code class="language-plaintext highlighter-rouge">(t m) a</code>, <code class="language-plaintext highlighter-rouge">t</code> accepts a <code class="language-plaintext highlighter-rouge">Monad</code> first, which is of type <code class="language-plaintext highlighter-rouge">* -&gt; *</code>, and then
+ another argument of kind <code class="language-plaintext highlighter-rouge">*</code>.</p>
+  </li>
+</ol>
+
+<h2 id="tocAnchor-1-18-2">Composing Monads</h2>
+
+<h3 id="exercises-12">Exercises</h3>
+
+<ol>
+  <li>
+    <p>Implement <code class="language-plaintext highlighter-rouge">join :: M (N (M (N a))) -&gt; M (N a)</code> given <code class="language-plaintext highlighter-rouge">distrib :: N (M a) -&gt; M (N a)</code> and assuming <code class="language-plaintext highlighter-rouge">M</code> and <code class="language-plaintext highlighter-rouge">N</code> are instances of <code class="language-plaintext highlighter-rouge">Monad</code>.</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">join</span> <span class="o">::</span> <span class="kt">M</span> <span class="p">(</span><span class="kt">N</span> <span class="p">(</span><span class="kt">M</span> <span class="p">(</span><span class="kt">N</span> <span class="n">a</span><span class="p">)))</span> <span class="o">-&gt;</span> <span class="kt">M</span> <span class="p">(</span><span class="kt">N</span> <span class="n">a</span><span class="p">)</span>
+ <span class="n">join</span> <span class="n">m</span> <span class="o">=</span> <span class="n">distrib</span> <span class="p">((</span><span class="n">distrib</span> <span class="n">m</span><span class="p">)</span> <span class="o">&gt;&gt;=</span> <span class="n">join</span><span class="p">)</span> <span class="o">&gt;&gt;=</span> <span class="n">join</span>
+    
+ <span class="c1">-- one by one</span>
+ <span class="kr">let</span> <span class="n">m</span> <span class="o">::</span> <span class="kt">M</span> <span class="p">(</span><span class="kt">N</span> <span class="p">(</span><span class="kt">M</span> <span class="p">(</span><span class="kt">N</span> <span class="n">a</span><span class="p">)))</span>
+     <span class="n">a</span> <span class="o">=</span> <span class="n">distrib</span> <span class="n">m</span>  <span class="o">::</span> <span class="kt">N</span> <span class="p">(</span><span class="kt">M</span> <span class="p">(</span><span class="kt">M</span> <span class="p">(</span><span class="kt">N</span> <span class="n">a</span><span class="p">)))</span>
+     <span class="n">b</span> <span class="o">=</span> <span class="n">a</span> <span class="o">&gt;&gt;=</span> <span class="n">join</span> <span class="o">::</span> <span class="kt">N</span> <span class="p">(</span><span class="kt">M</span> <span class="p">(</span><span class="kt">N</span> <span class="n">a</span><span class="p">))</span>
+     <span class="n">c</span> <span class="o">=</span> <span class="n">distrib</span> <span class="n">b</span>  <span class="o">::</span> <span class="kt">M</span> <span class="p">(</span><span class="kt">N</span> <span class="p">(</span><span class="kt">N</span> <span class="n">a</span><span class="p">))</span>
+ <span class="kr">in</span> <span class="n">c</span> <span class="o">&gt;&gt;=</span> <span class="n">join</span>      <span class="o">::</span> <span class="kt">M</span> <span class="p">(</span><span class="kt">N</span> <span class="n">a</span><span class="p">)</span>
+</code></pre></div>    </div>
+  </li>
+</ol>
+
+<h1 id="tocAnchor-1-21">MonadFix</h1>
+
+<h2 id="tocAnchor-1-21-1">Examples and intuition</h2>
+
+<div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">maybeFix</span> <span class="o">::</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Maybe</span> <span class="n">a</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Maybe</span> <span class="n">a</span>
+<span class="n">maybeFix</span> <span class="n">f</span> <span class="o">=</span> <span class="n">ma</span>
+  <span class="kr">where</span> <span class="n">ma</span> <span class="o">=</span> <span class="n">f</span> <span class="p">(</span><span class="n">fromJust</span> <span class="n">ma</span><span class="p">)</span>
+</code></pre></div></div>
+
+<h3 id="exercises-13">Exercises</h3>
+
+<ol>
+  <li>
+    <p>Implement a MonadFix instance for [].</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">listFix</span> <span class="o">::</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">a</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">a</span><span class="p">]</span>
+ <span class="n">listFix</span> <span class="n">f</span> <span class="o">=</span> <span class="n">la</span>
+   <span class="kr">where</span> <span class="n">la</span> <span class="o">=</span> <span class="n">f</span> <span class="p">(</span><span class="n">head</span> <span class="n">la</span><span class="p">)</span>
+</code></pre></div>    </div>
+  </li>
+</ol>
+
+<h1 id="tocAnchor-1-23">Foldable</h1>
+
+<h2 id="tocAnchor-1-23-1">Definition</h2>
+
+<div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kr">class</span> <span class="kt">Foldable</span> <span class="n">t</span> <span class="kr">where</span>
+  <span class="n">fold</span>    <span class="o">::</span> <span class="kt">Monoid</span> <span class="n">m</span> <span class="o">=&gt;</span> <span class="n">t</span> <span class="n">m</span> <span class="o">-&gt;</span> <span class="n">m</span>
+  <span class="n">foldMap</span> <span class="o">::</span> <span class="kt">Monoid</span> <span class="n">m</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">m</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">m</span>
+  <span class="n">foldr</span>   <span class="o">::</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span> <span class="o">-&gt;</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">b</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span>
+  <span class="n">foldr'</span>  <span class="o">::</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span> <span class="o">-&gt;</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">b</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span>
+  <span class="n">foldl</span>   <span class="o">::</span> <span class="p">(</span><span class="n">b</span> <span class="o">-&gt;</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">b</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span>
+  <span class="n">foldl'</span>  <span class="o">::</span> <span class="p">(</span><span class="n">b</span> <span class="o">-&gt;</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">b</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span>
+  <span class="n">foldr1</span>  <span class="o">::</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">a</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">a</span>
+  <span class="n">foldl1</span>  <span class="o">::</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">a</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">a</span>
+  <span class="n">toList</span>  <span class="o">::</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">a</span><span class="p">]</span>
+  <span class="n">null</span>    <span class="o">::</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Bool</span>
+  <span class="n">length</span>  <span class="o">::</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Int</span>
+  <span class="n">elem</span>    <span class="o">::</span> <span class="kt">Eq</span> <span class="n">a</span> <span class="o">=&gt;</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Bool</span>
+  <span class="n">maximum</span> <span class="o">::</span> <span class="kt">Ord</span> <span class="n">a</span> <span class="o">=&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">a</span>
+  <span class="n">minimum</span> <span class="o">::</span> <span class="kt">Ord</span> <span class="n">a</span> <span class="o">=&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">a</span>
+  <span class="n">sum</span>     <span class="o">::</span> <span class="kt">Num</span> <span class="n">a</span> <span class="o">=&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">a</span>
+  <span class="n">product</span> <span class="o">::</span> <span class="kt">Num</span> <span class="n">a</span> <span class="o">=&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">a</span>
+</code></pre></div></div>
+
+<h2 id="tocAnchor-1-23-2">Instances and examples</h2>
+
+<h3 id="exercises-14">Exercises</h3>
+
+<ol>
+  <li>
+    <p>Implement <code class="language-plaintext highlighter-rouge">fold</code> in terms of <code class="language-plaintext highlighter-rouge">foldMap</code>.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">fold</span> <span class="o">=</span> <span class="n">foldMap</span> <span class="n">id</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>What would you need in order to implement <code class="language-plaintext highlighter-rouge">foldMap</code> in terms of <code class="language-plaintext highlighter-rouge">fold</code>?</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <p>A <code class="language-plaintext highlighter-rouge">map</code> function should exist for the instance, so we can apply the function <code class="language-plaintext highlighter-rouge">(a -&gt; m)</code> to the container first.</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">foldMap</span> <span class="n">f</span> <span class="o">=</span> <span class="n">fold</span> <span class="o">.</span> <span class="n">map</span> <span class="n">f</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>Implement <code class="language-plaintext highlighter-rouge">foldMap</code> in terms of <code class="language-plaintext highlighter-rouge">foldr</code>.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">foldMap</span> <span class="n">f</span> <span class="o">=</span> <span class="n">foldr</span> <span class="p">(</span><span class="nf">\</span><span class="n">a</span> <span class="n">b</span> <span class="o">-&gt;</span> <span class="n">mappend</span> <span class="p">(</span><span class="n">f</span> <span class="n">a</span><span class="p">)</span> <span class="n">b</span><span class="p">)</span> <span class="n">mempty</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>Implement <code class="language-plaintext highlighter-rouge">foldr</code> in terms of <code class="language-plaintext highlighter-rouge">foldMap</code> (hint: use the <code class="language-plaintext highlighter-rouge">Endo</code> monoid).</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">foldr</span> <span class="n">f</span> <span class="n">b</span> <span class="n">c</span> <span class="o">=</span> <span class="n">foldMap</span> <span class="p">(</span><span class="kt">Endo</span> <span class="o">.</span> <span class="n">f</span><span class="p">)</span> <span class="n">c</span> <span class="p">`</span><span class="n">appEndo</span><span class="p">`</span> <span class="n">b</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>What is the type of <code class="language-plaintext highlighter-rouge">foldMap . foldMap</code>? Or <code class="language-plaintext highlighter-rouge">foldMap . foldMap . foldMap</code>, etc.? What do they do?</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <p>Each composition makes <code class="language-plaintext highlighter-rouge">foldMap</code> operate on a deeper level, so:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">foldMap</span> <span class="o">::</span> <span class="kt">Monoid</span> <span class="n">m</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">m</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">m</span>
+ <span class="n">foldMap</span> <span class="o">.</span> <span class="n">foldMap</span> <span class="o">::</span> <span class="kt">Monoid</span> <span class="n">m</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">m</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="p">(</span><span class="n">t</span> <span class="n">a</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">m</span>
+ <span class="n">foldMap</span> <span class="o">.</span> <span class="n">foldMap</span> <span class="o">.</span> <span class="n">foldMap</span> <span class="o">::</span> <span class="kt">Monoid</span> <span class="n">m</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">m</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="p">(</span><span class="n">t</span> <span class="p">(</span><span class="n">t</span> <span class="n">a</span><span class="p">))</span> <span class="o">-&gt;</span> <span class="n">m</span>
+    
+ <span class="n">foldMap</span> <span class="n">id</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">]</span> <span class="o">::</span> <span class="kt">Sum</span> <span class="kt">Int</span> <span class="c1">-- 6</span>
+ <span class="p">(</span><span class="n">foldMap</span> <span class="o">.</span> <span class="n">foldMap</span><span class="p">)</span> <span class="n">id</span> <span class="p">[[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">]]</span> <span class="o">::</span> <span class="kt">Sum</span> <span class="kt">Int</span> <span class="c1">-- 6</span>
+ <span class="p">(</span><span class="n">foldMap</span> <span class="o">.</span> <span class="n">foldMap</span> <span class="o">.</span> <span class="n">foldMap</span><span class="p">)</span> <span class="n">id</span> <span class="p">[[[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">]]]</span> <span class="o">::</span> <span class="kt">Sum</span> <span class="kt">Int</span> <span class="c1">-- 6</span>
+</code></pre></div>    </div>
+    <h2 id="derived-folds">Derived folds</h2>
+  </li>
+</ol>
+
+<h3 id="exercises-15">Exercises</h3>
+
+<ol>
+  <li>
+    <p>Implement <code class="language-plaintext highlighter-rouge">toList :: Foldable f =&gt; f a -&gt; [a]</code> in terms of either <code class="language-plaintext highlighter-rouge">foldr</code> or <code class="language-plaintext highlighter-rouge">foldMap</code>.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">toList</span> <span class="o">=</span> <span class="n">foldMap</span> <span class="p">(</span><span class="n">replicate</span> <span class="mi">1</span><span class="p">)</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>Show how one could implement the generic version of <code class="language-plaintext highlighter-rouge">foldr</code> in terms of <code class="language-plaintext highlighter-rouge">toList</code>, assuming we had only the list-specific <code class="language-plaintext highlighter-rouge">foldr :: (a -&gt; b -&gt; b) -&gt; b -&gt; [a] -&gt; b</code>.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">foldr</span> <span class="n">f</span> <span class="n">b</span> <span class="n">c</span> <span class="o">=</span> <span class="n">foldr</span> <span class="n">f</span> <span class="n">b</span> <span class="p">(</span><span class="n">toList</span> <span class="n">c</span><span class="p">)</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>Pick some of the following functions to implement: <code class="language-plaintext highlighter-rouge">concat</code>, <code class="language-plaintext highlighter-rouge">concatMap</code>, <code class="language-plaintext highlighter-rouge">and</code>, <code class="language-plaintext highlighter-rouge">or</code>, <code class="language-plaintext highlighter-rouge">any</code>, <code class="language-plaintext highlighter-rouge">all</code>, <code class="language-plaintext highlighter-rouge">sum</code>, <code class="language-plaintext highlighter-rouge">product</code>, <code class="language-plaintext highlighter-rouge">maximum(By)</code>, <code class="language-plaintext highlighter-rouge">minimum(By)</code>, <code class="language-plaintext highlighter-rouge">elem</code>, <code class="language-plaintext highlighter-rouge">notElem</code>, and <code class="language-plaintext highlighter-rouge">find</code>. Figure out how they generalize to <code class="language-plaintext highlighter-rouge">Foldable</code> and come up with elegant implementations using <code class="language-plaintext highlighter-rouge">fold</code> or <code class="language-plaintext highlighter-rouge">foldMap</code> along with appropriate <code class="language-plaintext highlighter-rouge">Monoid</code> instances.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">concat</span> <span class="o">::</span> <span class="kt">Foldable</span> <span class="n">t</span> <span class="o">=&gt;</span> <span class="n">t</span> <span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">a</span><span class="p">]</span>
+ <span class="n">concat</span> <span class="o">=</span> <span class="n">foldMap</span> <span class="n">id</span>
+    
+ <span class="n">concatMap</span> <span class="o">::</span> <span class="kt">Foldable</span> <span class="n">t</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">b</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">b</span><span class="p">]</span>
+ <span class="n">concatMap</span> <span class="n">f</span> <span class="o">=</span> <span class="n">foldMap</span> <span class="p">(</span><span class="n">foldMap</span> <span class="p">(</span><span class="n">replicate</span> <span class="mi">1</span> <span class="o">.</span> <span class="n">f</span><span class="p">))</span>
+    
+ <span class="n">and</span> <span class="o">::</span> <span class="kt">Foldable</span> <span class="n">t</span> <span class="o">=&gt;</span> <span class="n">t</span> <span class="kt">Bool</span> <span class="o">-&gt;</span> <span class="kt">Bool</span>
+ <span class="n">and</span> <span class="o">=</span> <span class="n">getAll</span> <span class="o">.</span> <span class="n">foldMap</span> <span class="kt">All</span>
+    
+ <span class="n">or</span> <span class="o">::</span> <span class="kt">Foldable</span> <span class="n">t</span> <span class="o">=&gt;</span> <span class="n">t</span> <span class="kt">Bool</span> <span class="o">-&gt;</span> <span class="kt">Bool</span>
+ <span class="n">or</span> <span class="o">=</span> <span class="n">getAny</span> <span class="o">.</span> <span class="n">foldMap</span> <span class="kt">Any</span>
+      
+ <span class="n">any</span> <span class="o">::</span> <span class="kt">Foldable</span> <span class="n">t</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Bool</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Bool</span>
+ <span class="n">any</span> <span class="n">f</span> <span class="o">=</span> <span class="n">getAny</span> <span class="o">.</span> <span class="n">foldMap</span> <span class="p">(</span><span class="kt">Any</span> <span class="o">.</span> <span class="n">f</span><span class="p">)</span>
+    
+ <span class="n">all</span> <span class="o">::</span> <span class="kt">Foldable</span> <span class="n">t</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Bool</span><span class="p">)</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Bool</span>
+ <span class="n">all</span> <span class="n">f</span> <span class="o">=</span> <span class="n">getAll</span> <span class="o">.</span> <span class="n">foldMap</span> <span class="p">(</span><span class="kt">All</span> <span class="o">.</span> <span class="n">f</span><span class="p">)</span>
+    
+ <span class="n">sum</span> <span class="o">::</span> <span class="p">(</span><span class="kt">Num</span> <span class="n">a</span><span class="p">,</span> <span class="kt">Foldable</span> <span class="n">t</span><span class="p">)</span> <span class="o">=&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">a</span>
+ <span class="n">sum</span> <span class="o">=</span> <span class="n">getSum</span> <span class="o">.</span> <span class="n">foldMap</span> <span class="kt">Sum</span>
+    
+ <span class="n">product</span> <span class="o">::</span> <span class="p">(</span><span class="kt">Num</span> <span class="n">a</span><span class="p">,</span> <span class="kt">Foldable</span> <span class="n">t</span><span class="p">)</span> <span class="o">=&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">a</span>
+ <span class="n">product</span> <span class="o">=</span> <span class="n">getProduct</span> <span class="o">.</span> <span class="n">foldMap</span> <span class="kt">Product</span>
+    
+ <span class="c1">-- I think there are more elegant implementations for maximumBy, leave a comment</span>
+ <span class="c1">-- if you have a suggestion</span>
+ <span class="n">maximumBy</span> <span class="o">::</span> <span class="kt">Foldable</span> <span class="n">t</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Ordering</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">a</span>
+ <span class="n">maximumBy</span> <span class="n">f</span> <span class="n">c</span> <span class="o">=</span> <span class="n">head</span> <span class="o">$</span> <span class="n">foldMap</span> <span class="p">(</span><span class="nf">\</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">a</span> <span class="o">|</span> <span class="n">cmp</span> <span class="n">a</span><span class="p">])</span> <span class="n">c</span>
+   <span class="kr">where</span>
+     <span class="n">cmp</span> <span class="n">a</span> <span class="o">=</span> <span class="n">all</span> <span class="p">(</span><span class="o">/=</span> <span class="kt">LT</span><span class="p">)</span> <span class="p">(</span><span class="n">map</span> <span class="p">(</span><span class="n">f</span> <span class="n">a</span><span class="p">)</span> <span class="n">lst</span><span class="p">)</span>
+     <span class="n">lst</span> <span class="o">=</span> <span class="n">toList</span> <span class="n">c</span>
+    
+ <span class="n">elem</span> <span class="o">::</span> <span class="p">(</span><span class="kt">Eq</span> <span class="n">a</span><span class="p">,</span> <span class="kt">Foldable</span> <span class="n">t</span><span class="p">)</span> <span class="o">=&gt;</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Bool</span>
+ <span class="n">elem</span> <span class="n">x</span> <span class="n">c</span> <span class="o">=</span> <span class="n">any</span> <span class="p">(</span><span class="o">==</span><span class="n">x</span><span class="p">)</span> <span class="n">c</span>
+    
+ <span class="n">find</span> <span class="o">::</span> <span class="kt">Foldable</span> <span class="n">t</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Bool</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="kt">Maybe</span> <span class="n">a</span> 
+ <span class="n">find</span> <span class="n">f</span> <span class="n">c</span> <span class="o">=</span> <span class="n">listToMaybe</span> <span class="o">$</span> <span class="n">foldMap</span> <span class="p">(</span><span class="nf">\</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">a</span> <span class="o">|</span> <span class="n">f</span> <span class="n">a</span><span class="p">])</span> <span class="n">c</span> 
+</code></pre></div>    </div>
+  </li>
+</ol>
+
+<h2 id="tocAnchor-1-23-3">Utility functions</h2>
+
+<ul>
+  <li>
+    <p><code class="language-plaintext highlighter-rouge">sequenceA_ :: (Applicative f, Foldable t) =&gt; t (f a) -&gt; f ()</code> takes a container full of computations and runs them in sequence, discarding the results (that is, they are used only for their effects). Since the results are discarded, the container only needs to be Foldable. (Compare with <code class="language-plaintext highlighter-rouge">sequenceA :: (Applicative f, Traversable t) =&gt; t (f a) -&gt; f (t a)</code>, which requires a stronger Traversable constraint in order to be able to reconstruct a container of results having the same shape as the original container.)</p>
+  </li>
+  <li>
+    <p><code class="language-plaintext highlighter-rouge">traverse_ :: (Applicative f, Foldable t) =&gt; (a -&gt; f b) -&gt; t a -&gt; f ()</code> applies the given function to each element in a foldable container and sequences the effects (but discards the results).</p>
+  </li>
+</ul>
+
+<h3 id="exercises-16">Exercises</h3>
+
+<ol>
+  <li>
+    <p>Implement <code class="language-plaintext highlighter-rouge">traverse_</code> in terms of <code class="language-plaintext highlighter-rouge">sequenceA_</code> and vice versa. One of these will need an extra constraint. What is it?</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">sequenceA_</span> <span class="o">::</span> <span class="p">(</span><span class="kt">Applicative</span> <span class="n">f</span><span class="p">,</span> <span class="kt">Foldable</span> <span class="n">t</span><span class="p">)</span> <span class="o">=&gt;</span> <span class="n">t</span> <span class="p">(</span><span class="n">f</span> <span class="n">a</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="nb">()</span>
+ <span class="n">sequenceA_</span> <span class="o">=</span> <span class="n">traverse_</span> <span class="n">id</span>
+    
+ <span class="n">traverse_</span> <span class="o">::</span> <span class="p">(</span><span class="kt">Applicative</span> <span class="n">f</span><span class="p">,</span> <span class="kt">Foldable</span> <span class="n">t</span><span class="p">,</span> <span class="kt">Functor</span> <span class="n">t</span><span class="p">)</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="nb">()</span>
+ <span class="n">traverse_</span> <span class="n">f</span> <span class="n">c</span> <span class="o">=</span> <span class="n">sequenceA_</span> <span class="p">(</span><span class="n">fmap</span> <span class="n">f</span> <span class="n">c</span><span class="p">)</span>
+</code></pre></div>    </div>
+
+    <p>The additional constraint for implementing <code class="language-plaintext highlighter-rouge">traverse_</code> in terms of <code class="language-plaintext highlighter-rouge">sequenceA_</code> is the requirement of the <code class="language-plaintext highlighter-rouge">Foldable</code> instance <code class="language-plaintext highlighter-rouge">t</code> to be a <code class="language-plaintext highlighter-rouge">Functor</code> as well.</p>
+  </li>
+</ol>
+
+<h1 id="tocAnchor-1-27">Traversable</h1>
+
+<h2 id="tocAnchor-1-27-1">Intuition</h2>
+
+<div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">traverse</span> <span class="o">::</span> <span class="kt">Applicative</span> <span class="n">f</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="p">(</span><span class="n">t</span> <span class="n">b</span><span class="p">)</span>
+<span class="n">sequenceA</span> <span class="o">::</span> <span class="kt">Applicative</span> <span class="n">f</span> <span class="o">=&gt;</span> <span class="n">t</span> <span class="p">(</span><span class="n">f</span> <span class="n">a</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="p">(</span><span class="n">t</span> <span class="n">a</span><span class="p">)</span>
+</code></pre></div></div>
+
+<h3 id="exercises-17">Exercises</h3>
+
+<ol>
+  <li>
+    <p>There are at least two natural ways to turn a tree of lists into a list of trees. What are they, and why?</p>
+
+    <p>Note: I’m not really sure whether my solution is <em>natural</em>, I think the question is rather ambiguous in the sense that it’s not clear whether the trees in the final list of trees can have lists as their values, i.e. <code class="language-plaintext highlighter-rouge">Tree [Int] -&gt; [Tree [Int]]</code> is valid or only <code class="language-plaintext highlighter-rouge">Tree [Int] -&gt; [Tree Int]</code> is, but let me know if you think otherwise.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <p>One way is to put each <code class="language-plaintext highlighter-rouge">Node</code>, <code class="language-plaintext highlighter-rouge">Leaf</code> or <code class="language-plaintext highlighter-rouge">Empty</code> in a list in-order, this way the structure of the tree can be recovered from the list, here is a quick sketch (<code class="language-plaintext highlighter-rouge">[]</code> is an arbitrary list):</p>
+
+    <p><img src="/img/typoclassopedia/tree.jpg" alt="tree to list" /></p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="kr">let</span> <span class="n">tree</span> <span class="o">=</span> <span class="kt">Node</span> <span class="p">(</span><span class="kt">Node</span> <span class="p">(</span><span class="kt">Leaf</span> <span class="kt">[]</span><span class="p">)</span> <span class="kt">Empty</span><span class="p">)</span> <span class="kt">[]</span> <span class="p">(</span><span class="kt">Leaf</span> <span class="kt">[]</span><span class="p">)</span>
+ <span class="kr">let</span> <span class="n">list</span> <span class="o">=</span> <span class="p">[</span><span class="kt">Node</span> <span class="kt">Empty</span> <span class="kt">[]</span> <span class="kt">Empty</span><span class="p">,</span> <span class="kt">Node</span> <span class="kt">Empty</span> <span class="kt">[]</span> <span class="kt">Empty</span><span class="p">,</span> <span class="kt">Leaf</span> <span class="kt">[]</span><span class="p">,</span> <span class="kt">Empty</span><span class="p">,</span> <span class="kt">Leaf</span> <span class="kt">[]</span><span class="p">]</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>Give a natural way to turn a list of trees into a tree of lists.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <p>To recover the original tree from the list of trees, whenever we encounter a <code class="language-plaintext highlighter-rouge">Node</code> in the list, we catch the next three values as left, value, and right nodes of the original node.</p>
+  </li>
+  <li>
+    <p>What is the type of <code class="language-plaintext highlighter-rouge">traverse . traverse</code>? What does it do?</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="p">(</span><span class="n">traverse</span> <span class="o">.</span> <span class="n">traverse</span><span class="p">)</span> <span class="o">::</span> <span class="kt">Applicative</span> <span class="n">f</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="p">(</span><span class="n">t2</span> <span class="n">a</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="p">(</span><span class="n">t</span> <span class="p">(</span><span class="n">t2</span> <span class="n">b</span><span class="p">))</span>
+</code></pre></div>    </div>
+
+    <p>It traverses on a deeper level, retaining the structure of the first level.</p>
+  </li>
+  <li>
+    <p>Implement <code class="language-plaintext highlighter-rouge">traverse</code> in terms of <code class="language-plaintext highlighter-rouge">sequenceA</code>, and vice versa.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="n">sequenceA</span> <span class="o">=</span> <span class="n">traverse</span> <span class="n">id</span>
+    
+ <span class="n">traverseA</span> <span class="n">f</span> <span class="n">c</span> <span class="o">=</span> <span class="n">sequenceA</span> <span class="p">(</span><span class="n">fmap</span> <span class="n">f</span> <span class="n">c</span><span class="p">)</span>
+</code></pre></div>    </div>
+  </li>
+</ol>
+
+<h2 id="tocAnchor-1-27-2">Instances and examples</h2>
+
+<h3 id="exercises-18">Exercises</h3>
+
+<ol>
+  <li>
+    <p>Implement <code class="language-plaintext highlighter-rouge">fmap</code> and <code class="language-plaintext highlighter-rouge">foldMap</code> using only the <code class="language-plaintext highlighter-rouge">Traversable</code> methods. (Note that the <code class="language-plaintext highlighter-rouge">Traversable</code> module provides these implementations as <code class="language-plaintext highlighter-rouge">fmapDefault</code> and <code class="language-plaintext highlighter-rouge">foldMapDefault</code>.)</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="kr">newtype</span> <span class="kt">Id</span> <span class="n">a</span> <span class="o">=</span> <span class="kt">Id</span> <span class="p">{</span> <span class="n">getId</span> <span class="o">::</span> <span class="n">a</span> <span class="p">}</span>
+    
+ <span class="kr">instance</span> <span class="kt">Functor</span> <span class="kt">Id</span> <span class="kr">where</span>
+   <span class="n">fmap</span> <span class="n">f</span> <span class="p">(</span><span class="kt">Id</span> <span class="n">x</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Id</span> <span class="p">(</span><span class="n">f</span> <span class="n">x</span><span class="p">)</span>
+    
+ <span class="kr">instance</span> <span class="kt">Applicative</span> <span class="kt">Id</span> <span class="kr">where</span>
+   <span class="n">pure</span> <span class="n">x</span> <span class="o">=</span> <span class="kt">Id</span> <span class="n">x</span>
+   <span class="p">(</span><span class="kt">Id</span> <span class="n">f</span><span class="p">)</span> <span class="o">&lt;*&gt;</span> <span class="p">(</span><span class="kt">Id</span> <span class="n">x</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Id</span> <span class="p">(</span><span class="n">f</span> <span class="n">x</span><span class="p">)</span>
+    
+ <span class="n">fmapDefault</span> <span class="o">::</span> <span class="kt">Traversable</span> <span class="n">t</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">b</span>
+ <span class="n">fmapDefault</span> <span class="n">f</span> <span class="o">=</span> <span class="n">getId</span> <span class="o">.</span> <span class="n">traverse</span> <span class="p">(</span><span class="kt">Id</span> <span class="o">.</span> <span class="n">f</span><span class="p">)</span>
+    
+ <span class="n">foldMapDefault</span> <span class="o">::</span> <span class="p">(</span><span class="kt">Monoid</span> <span class="n">m</span><span class="p">,</span> <span class="kt">Traversable</span> <span class="n">t</span><span class="p">)</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">m</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">t</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">m</span>
+ <span class="n">foldMapDefault</span> <span class="n">f</span> <span class="o">=</span> <span class="n">getConst</span> <span class="o">.</span> <span class="n">traverse</span> <span class="p">(</span><span class="kt">Const</span> <span class="o">.</span> <span class="n">f</span><span class="p">)</span>
+</code></pre></div>    </div>
+
+    <p>See the <a href="https://www.stackage.org/haddock/lts-9.9/base-4.9.1.0/src/Data-Functor-Const.html#Const">Const</a> Functor’s definition for intuition.</p>
+  </li>
+  <li>
+    <p>Implement <code class="language-plaintext highlighter-rouge">Traversable</code> instances for <code class="language-plaintext highlighter-rouge">[]</code>, <code class="language-plaintext highlighter-rouge">Maybe</code>, <code class="language-plaintext highlighter-rouge">((,) a)</code>, and <code class="language-plaintext highlighter-rouge">Either a</code>.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="kr">instance</span> <span class="kt">Traversable</span> <span class="kt">[]</span> <span class="kr">where</span>
+   <span class="n">traverse</span> <span class="o">::</span> <span class="kt">Applicative</span> <span class="n">f</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="p">[</span><span class="n">b</span><span class="p">]</span>
+   <span class="n">traverse</span> <span class="kr">_</span> <span class="kt">[]</span> <span class="o">=</span> <span class="n">pure</span> <span class="kt">[]</span>
+   <span class="n">traverse</span> <span class="n">f</span> <span class="p">(</span><span class="n">x</span><span class="o">:</span><span class="n">xs</span><span class="p">)</span> <span class="o">=</span> <span class="p">(</span><span class="o">:</span><span class="p">)</span> <span class="o">&lt;$&gt;</span> <span class="n">f</span> <span class="n">x</span> <span class="o">&lt;*&gt;</span> <span class="kt">Main</span><span class="o">.</span><span class="n">traverse</span> <span class="n">f</span> <span class="n">xs</span>
+      
+ <span class="kr">instance</span> <span class="kt">Traversable</span> <span class="kt">Maybe</span> <span class="kr">where</span>
+   <span class="n">traverse</span> <span class="o">::</span> <span class="kt">Applicative</span> <span class="n">f</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Maybe</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="p">(</span><span class="kt">Maybe</span> <span class="n">b</span><span class="p">)</span>
+      
+   <span class="n">traverse</span> <span class="kr">_</span> <span class="kt">Nothing</span> <span class="o">=</span> <span class="n">pure</span> <span class="kt">Nothing</span>
+   <span class="n">traverse</span> <span class="n">f</span> <span class="p">(</span><span class="kt">Just</span> <span class="n">x</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Just</span> <span class="o">&lt;$&gt;</span> <span class="n">f</span> <span class="n">x</span>
+      
+ <span class="kr">instance</span> <span class="kt">Traversable</span> <span class="p">((,)</span> <span class="n">c</span><span class="p">)</span> <span class="kr">where</span>
+   <span class="n">traverse</span> <span class="o">::</span> <span class="kt">Applicative</span> <span class="n">f</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
+      
+   <span class="n">traverse</span> <span class="n">f</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="o">=</span> <span class="p">(,)</span> <span class="n">c</span> <span class="o">&lt;$&gt;</span> <span class="n">f</span> <span class="n">a</span>
+      
+ <span class="kr">instance</span> <span class="kt">Traversable</span> <span class="p">(</span><span class="kt">Either</span> <span class="n">c</span><span class="p">)</span> <span class="kr">where</span>
+   <span class="n">traverse</span> <span class="o">::</span> <span class="kt">Applicative</span> <span class="n">f</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Either</span> <span class="n">c</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="p">(</span><span class="kt">Either</span> <span class="n">c</span> <span class="n">b</span><span class="p">)</span>
+      
+   <span class="n">traverse</span> <span class="kr">_</span> <span class="p">(</span><span class="kt">Left</span> <span class="n">c</span><span class="p">)</span> <span class="o">=</span> <span class="n">pure</span> <span class="p">(</span><span class="kt">Left</span> <span class="n">c</span><span class="p">)</span>
+   <span class="n">traverse</span> <span class="n">f</span> <span class="p">(</span><span class="kt">Right</span> <span class="n">a</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Right</span> <span class="o">&lt;$&gt;</span> <span class="n">f</span> <span class="n">a</span>
+</code></pre></div>    </div>
+  </li>
+  <li>
+    <p>Explain why <code class="language-plaintext highlighter-rouge">Set</code> is <code class="language-plaintext highlighter-rouge">Foldable</code> but not <code class="language-plaintext highlighter-rouge">Traversable</code>.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <p>First, in terms of laws, <code class="language-plaintext highlighter-rouge">Set</code> is not a <code class="language-plaintext highlighter-rouge">Functor</code>, thus it cannot be made into a <code class="language-plaintext highlighter-rouge">Traversable</code> instance, since <code class="language-plaintext highlighter-rouge">Traversable</code> instances require <code class="language-plaintext highlighter-rouge">Functor</code> superclasses.</p>
+
+    <p>Second, on an intuitive level: In <code class="language-plaintext highlighter-rouge">Foldable</code>, the goal is not to keep the shape/structure of the original container, we are trying to reduce the container into some value, and the shape of the final result doesn’t matter, but in <code class="language-plaintext highlighter-rouge">Traversable</code>, we ought to keep the structure of the final result, but we can’t guarantee this while using <code class="language-plaintext highlighter-rouge">Set</code>s, because we can define some transformation <code class="language-plaintext highlighter-rouge">f :: Set a -&gt; Set a</code> which reduces the length of the <code class="language-plaintext highlighter-rouge">Set</code>.</p>
+
+    <p>See <a href="https://stackoverflow.com/questions/35857733/foldable-vs-traversable">Foldable vs. Traversable</a> and <a href="https://stackoverflow.com/questions/19177125/sets-functors-and-eq-confusion">Sets, Functors and Eq confusion</a>. and <a href="https://wiki.haskell.org/Foldable_and_Traversable">Foldable and Traversable</a> for more details.</p>
+  </li>
+  <li>
+    <p>Show that <code class="language-plaintext highlighter-rouge">Traversable</code> functors compose: that is, implement an instance for <code class="language-plaintext highlighter-rouge">Traversable (Compose f g)</code> given <code class="language-plaintext highlighter-rouge">Traversable</code> instances for <code class="language-plaintext highlighter-rouge">f</code> and <code class="language-plaintext highlighter-rouge">g</code>.</p>
+
+    <p><strong>Solution</strong>:</p>
+
+    <div class="language-haskell highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="kr">instance</span> <span class="p">(</span><span class="kt">Traversable</span> <span class="n">f</span><span class="p">,</span> <span class="kt">Traversable</span> <span class="n">g</span><span class="p">)</span> <span class="o">=&gt;</span> <span class="kt">Traversable</span> <span class="p">(</span><span class="kt">Compose</span> <span class="n">f</span> <span class="n">g</span><span class="p">)</span> <span class="kr">where</span>
+   <span class="n">traverse</span> <span class="o">::</span> <span class="p">(</span><span class="kt">Applicative</span> <span class="n">f</span><span class="p">)</span> <span class="o">=&gt;</span> <span class="p">(</span><span class="n">a</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Compose</span> <span class="n">g</span> <span class="n">h</span> <span class="n">a</span> <span class="o">-&gt;</span> <span class="n">f</span> <span class="p">(</span><span class="kt">Compose</span> <span class="n">g</span> <span class="n">h</span> <span class="n">b</span><span class="p">)</span>
+   <span class="n">traverse</span> <span class="n">f</span> <span class="p">(</span><span class="kt">Compose</span> <span class="n">t</span><span class="p">)</span> <span class="o">=</span> <span class="kt">Compose</span> <span class="o">&lt;$&gt;</span> <span class="n">traverse</span> <span class="p">(</span><span class="n">traverse</span> <span class="n">f</span><span class="p">)</span> <span class="n">t</span>
+</code></pre></div>    </div>
+  </li>
+</ol>
+
+
+  </article>
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