Functors

The first constructor type class we will encounter in this chapter is perhaps the simplest of all: Functor. This type class generalizes the higher-order map :: (a -> b) -> ([a] -> [b]).

Recall the definition of map:

Prelude
map :: (a -> b) -> ([a] -> [b])
map f [] = []
map f (x:xs) = f x : map f xs

The second pair of parentheses in the type signature of map can be dropped without changing the meaning. Nevertheless, I like to add them to emphasize that map lifts a function, (a -> b), on elements to a function, ([a] -> [b]), on lists.

The idea is that map transforms the elements of the list without changing the structure of the list itself:

*Main> map show [1,2,3,4]
["1","2","3","4"]

The Functor type class generalizes this idea from lists to other type constructors of the * -> * kind:

Prelude
class Functor f where
  fmap :: (a -> b) -> (f a -> f b)
  (<$...