Functor

The Functor type-class gives us a way to generalize function application to arbitrary types. Let's first look at regular function application. Suppose we defined a function of primitive types:

  f :: Num a => a -> a
  f = (^2)

We can apply it directly to the types it was intended for:

  f 5
  f 5.0  –- etc

To apply the f function to a richer type, we need to make that type an instance of Functor and then use the fmap function:

--  fmap   function     Functor
fmap       f            (Just 5)
fmap       (f . read)   getLine

The Functor type-class defines fmap:

class Functor f where
  fmap :: (a -> b) -> f a -> f b

Let's create our own Maybe' type and make it an instance of Functor:

data Maybe' a = Just' a | Nothing'
  deriving (Show)

instance Functor Maybe' where
  fmap _ Nothing' =   Nothing'
  fmap f (Just' x) = Just' (f x)

By making Maybe' a Functor type-class, we are describing how single-parameter functions may be applied to our type, assuming the function types align with...