fix: use fenced blocks for code

_posts/2017-09-27-typoclassopedia-exercise-answers.md

@@ -1,20 +1,20 @@
 ---
 layout: post
 title:  "Typoclassopedia: Exercise solutions"
-date:   2017-09-27 12:12:12
+date:   2017-09-27 
 permalink: typoclassopedia-exercise-solutions/
 categories: programming
 ---
 
-I wanted to get proficient in Haskell so I decided to follow [An [Essential] Haskell Reading List][http://www.stephendiehl.com/posts/essential_haskell.html], there I stumbled upon Typoclassopedia, 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!
+I wanted to get proficient in Haskell so I decided to follow [An [Essential] Haskell Reading List](http://www.stephendiehl.com/posts/essential_haskell.html), there I stumbled upon [Typoclassopedia](https://wiki.haskell.org/Typeclassopedia), 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!
 
 In each section below, I left some reference material for the exercises and then the solutions.
 
 Functor
 ==========
-### Instances
+## Instances
 
-{% highlight haskell %}
+```haskell
 instance Functor [] where
   fmap :: (a -> b) -> [a] -> [b]
   fmap _ []     = []
@@ -25,30 +25,30 @@ instance Functor Maybe where
   fmap :: (a -> b) -> Maybe a -> Maybe b
   fmap _ Nothing  = Nothing
   fmap g (Just a) = Just (g a)
-{% endhighlight %}
+```
 
 > ((,) 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,). 
 
 > ((->) e) (which can be thought of as (e ->); see above), the type of functions which take a value of type e as a parameter, is a Functor. As a container, (e -> a) represents a (possibly infinite) set of values of a, indexed by values of e. Alternatively, and more usefully, ((->) 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 ((->) e) is sometimes referred to as the reader monad; more on this later. 
 
-#### Exercises
+### Exercises
 
  1. Implement `Functor` instances for `Either e` and `((->) e)`.
 
     **Solution**:
-{% highlight haskell %}
+    ```haskell
     instance Functor (Either e) where
       fmap _ (Left e) = Left e
       fmap g (Right a) = Right (g a)
       
     instance Functor ((->) e) where
       fmap g f = g . f
-{% endhighlight %}
+    ```
 
-2. Implement `Functor` instances for `((,) e)` and for `Pair`, defined as `data Pair a = Pair a a`. Explain their similarities and differences.
+ 2. Implement `Functor` instances for `((,) e)` and for `Pair`, defined as below. Explain their similarities and differences.
 
     **Solution**:
-{% highlight haskell %}
+    ```haskell
     instance Functor ((,) e) where
       fmap g (a, b) = (a, g b) 
       
@@ -56,39 +56,39 @@ instance Functor ((,) e) where
     data Pair a = Pair a a
     instance Functor Pair where
       fmap g (Pair a b) = Pair (g a) (g b)
-{% endhighlight %}
+    ```
 
     Their similarity is in the fact that they both represent types of two values.
     Their difference is that `((,) e)` (tuples of two) can have values of different types (kind of `(,)` is `* -> *`) while both values of `Pair` have the same type `a`, so `Pair` has kind `*`.
 
 3. Implement a `Functor` instance for the type `ITree`, defined as
 
-{% highlight haskell %}
+    ```haskell
     data ITree a = Leaf (Int -> a)
                 | Node [ITree a]
-{% endhighlight %}
+    ```
 
     **Solution**:
-{% highlight haskell %}
+    ```haskell
     instance Functor ITree where
       fmap g (Leaf f) = Leaf (g . f)
       fmap g (Node xs) = Node (fmap (fmap g) xs)
-{% endhighlight %}
+    ```
 
     To test this instance, I defined a function to apply the tree to an `Int`:
 
-{% highlight haskell %}
+    ```haskell
     applyTree :: ITree a -> Int -> [a]
     applyTree (Leaf g) i = [g i]
     applyTree (Node []) _ = []
     applyTree (Node (x:xs)) i = applyTree x i ++ applyTree (Node xs) i
-{% endhighlight %}
+    ```
 
     This is not a standard tree traversing algorithm, I just wanted it to be simple for testing.
 
     Now test the instance:
 
-{% highlight haskell %}
+    ```haskell
     λ: let t = Node [Node [Leaf (+5), Leaf (+1)], Leaf (*2)]
     λ: applyTree t 1
     [6,2,2]
@@ -96,7 +96,7 @@ Now test the instance:
     [6,2,2]
     λ: applyTree (fmap (+10) t) 1
     [16, 12, 12]
-{% endhighlight %}
+    ```
 
 4. Give an example of a type of kind `* -> *` which cannot be made an instance of `Functor` (without using `undefined`).
 
@@ -112,27 +112,27 @@ If false, give a counterexample; if true, prove it by exhibiting some appropriat
 
     It's true, and can be proved by the following function:
 
-{% highlight haskell %}
+    ```haskell
     ffmap :: (Functor f, Functor j) => (a -> b) -> f (j a) -> f (j b)
     ffmap g = fmap (fmap g)
-{% endhighlight %}
+    ```
 
     You can test this on arbitrary compositions of `Functor`s:
 
-{% highlight haskell %}
+    ```haskell
     main = do
       let result :: Maybe (Either String Int) = ffmap (+ 2) (Just . Right $ 5)
       print result -- (Just (Right 7))
-{% endhighlight %}
+    ```
 
-### Functor Laws
+## Functor Laws
 
-{% highlight haskell %}
+```haskell
 fmap id = id
 fmap (g . h) = (fmap g) . (fmap h)
-{% endhighlight %}
+```
 
-#### Exercises
+### Exercises
 
 1. 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. 
 
@@ -140,29 +140,29 @@ fmap (g . h) = (fmap g) . (fmap h)
 
     This is easy, consider this instance:
 
-{% highlight haskell %}
+    ```haskell
     instance Functor [] where
       fmap _ [] = [1]
       fmap g (x:xs) = g x: fmap g xs
-{% endhighlight %}
+    ```
 
     Then, you can test the first and second laws:
 
-{% highlight haskell %}
+    ```haskell
     λ: fmap id [] -- [1], breaks the first law
     λ: fmap ((+1) . (+2)) [1,2] -- [4, 5], second law holds
     λ: fmap (+1) . fmap (+2) $ [1,2] -- [4, 5]
-{% endhighlight %}
+    ```
 
-1. Which laws are violated by the evil Functor instance for list shown above: both laws, or the first law alone? Give specific counterexamples. 
+2. Which laws are violated by the evil Functor instance for list shown above: both laws, or the first law alone? Give specific counterexamples. 
 
-{% highlight haskell %}
+    ```haskell
     -- Evil Functor instance
     instance Functor [] where
       fmap :: (a -> b) -> [a] -> [b]
       fmap _ [] = []
       fmap g (x:xs) = g x : g x : fmap g xs
-{% endhighlight %}
+    ```
 
     **Solution**:
 

_sass/_base.scss

@@ -138,7 +138,7 @@ code {
     font-size: 15px;
     border: 1px solid $grey-color-light;
     border-radius: 3px;
-    background-color: #eef;
+    background-color: white;
 }
 
 code {