From 0e3d5a990faa155ddd470d1736272b5b1ad4097f Mon Sep 17 00:00:00 2001 From: Mahdi Dibaiee Date: Sat, 30 Sep 2017 18:48:12 +0330 Subject: [PATCH] post(typoclassopedia): Applicative Laws theme(monospace): use Mononoki for code --- _includes/head.html | 2 +- ...-09-27-typoclassopedia-exercise-answers.md | 52 ++++++++++++++++++ _sass/_base.scss | 8 ++- _sass/_syntax-highlighting.scss | 4 +- css/fonts/mononoki-Regular.ttf | Bin 0 -> 90216 bytes css/fonts/mononoki-Regular.woff | Bin 0 -> 41136 bytes 6 files changed, 61 insertions(+), 5 deletions(-) create mode 100644 css/fonts/mononoki-Regular.ttf create mode 100644 css/fonts/mononoki-Regular.woff diff --git a/_includes/head.html b/_includes/head.html index 3a266d4..1d053da 100644 --- a/_includes/head.html +++ b/_includes/head.html @@ -6,7 +6,7 @@ {% if page.title %}{{ page.title }}{% else %}{{ site.title }}{% endif %} - + diff --git a/_posts/2017-09-27-typoclassopedia-exercise-answers.md b/_posts/2017-09-27-typoclassopedia-exercise-answers.md index 5d645bf..3b81086 100644 --- a/_posts/2017-09-27-typoclassopedia-exercise-answers.md +++ b/_posts/2017-09-27-typoclassopedia-exercise-answers.md @@ -275,3 +275,55 @@ The Functor section links to [Category Theory](https://en.wikibooks.org/wiki/Has fmap (f . g) (Just x) = Just ((f . g) x) = Just (f (g x)) fmap f (fmap g (Just x)) = Just (f (g x)) = Just ((f . g) x) ``` + +Applicative +=========== + +## Laws + +1. The identity law: + + ```haskell + pure id <*> v = v + ``` + +2. Homomorphism: + + ```haskell + pure f <*> pure x = pure (f x) + ``` + + 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. + +3. Interchange: + + ```haskell + u <*> pure y = pure ($ y) <*> u + ``` + + 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. + +4. Composition: + + ```haskell + u <*> (v <*> w) = pure (.) <*> u <*> v <*> w + ``` + + This one is the trickiest law to gain intuition for. In some sense it is expressing a sort of associativity property of (`<*>`). The reader may wish to simply convince themselves that this law is type-correct. + +### Exercises + +(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 + +```haskell +pure f <*> x = pure (flip ($)) <*> x <*> pure f +``` + +**Solution**: + +```haskell +pure f <*> x = pure (($) f) <*> x -- identical +pure f <*> x = pure ($) <*> pure f <*> x -- homomorphism +pure f <*> x = pure (flip ($)) <*> x <*> pure f -- flip arguments +``` + diff --git a/_sass/_base.scss b/_sass/_base.scss index dc81032..5c06995 100644 --- a/_sass/_base.scss +++ b/_sass/_base.scss @@ -224,7 +224,11 @@ pre { font-family: 'Ubuntu Light'; src: url(fonts/Ubuntu-Light_gdi.woff); } +//@font-face { + //font-family: 'Ubuntu Mono'; + //src: url(fonts/UbuntuMono-Regular_gdi.woff); +//} @font-face { - font-family: 'Ubuntu Mono'; - src: url(fonts/UbuntuMono-Regular_gdi.woff); + font-family: Mononoki; + src: url(fonts/mononoki-Regular.woff); } diff --git a/_sass/_syntax-highlighting.scss b/_sass/_syntax-highlighting.scss index c165e65..1742a20 100644 --- a/_sass/_syntax-highlighting.scss +++ b/_sass/_syntax-highlighting.scss @@ -5,7 +5,7 @@ /* 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