Haskell: Functors

higher order function: transform functions to functions

Functors 的作用在于 Preserve structures. 例如 map 可以处理 [a] -> [b] 的问题，而 Functor 则可以处理 Maybe a -> Maybe b 甚至自定义的类型 Node a -> Node b.

1 2	class Functor f where fmap :: (a -> b) -> f a -> f b

例如，当 f = Maybe 时，其实现为

instance Functor Maybe where
    fmap :: (a -> b) -> Maybe a -> Maybe b
    fmap f Nothing = Nothing
    fmap f (Just x) = Just (f x)

当然 f = [] 也可以，那就是正常的 map

调用 Functor 有简单的形式：<$>：

reverse . tail  $       "hello"       ==>  "olle"
reverse . tail <$> Just "hello"       ==>  Just "olle"
-- which is the same as
fmap (reverse . tail) (Just "hello")  ==>  Just "olle"

Kinds

Kinds 是 Types 的 Type．如 Maybe :: * -> *，而 Int :: *，Maybe Int :: *．