Functor

• is a structure which supports the map method.
  • Examples: Lists and binary trees.
• is a design pattern inspired by the definition from category theory (mapping between categories)
• allows one to apply a function to values inside a generic type without changing the structure of the generic type.

Functors form a base for more complex abstraction like monads

In Haskell this idea can be captured in a type class:

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

In Haskell, lists are a simple example of a functor. We may implement fmap as:

fmap f []     = []
fmap f (x:xs) = (f x) : fmap f xs