Haskell Language Functor Class Definition of Functor and Laws
Example
class Functor f where
fmap :: (a -> b) -> f a -> f b
One way of looking at it is that fmap lifts a function of values into a function of values in a context f.
A correct instance of Functor should satisfy the functor laws, though these are not enforced by the compiler:
fmap id = id -- identity
fmap f . fmap g = fmap (f . g) -- composition
There's a commonly-used infix alias for fmap called <$>.
infixl 4 <$>
(<$>) :: Functor f => (a -> b) -> f a -> f b
(<$>) = fmap
