Haskell语言学习笔记（51）Comonad

Comonad

class Functor w => Comonad w where  extract :: w a -> a  duplicate :: w a -> w (w a)  duplicate = extend id  extend :: (w a -> b) -> w a -> w b  extend f = fmap f . duplicate

Comonad 是个类型类。

比较 Monad 和 Comonad

class Functor m => Monad m where  return :: a -> m a  bind :: (a -> m b) -> (m a -> m b)  join :: m (m a) -> m a  join = bind id  bind f = fmap f . join  (>>=) :: m a -> (a -> m b) -> m b  (>>=) = flip bindclass Functor w => Comonad w where  extract :: w a -> a  extend :: (w a -> b) -> w a -> w b  duplicate :: w a -> w (w a)  duplicate = extend id  extend f = fmap f . duplicate  (=>>) :: w b -> (w b -> a) -> a  (=>>) = flip extend

((,) e) 是个 Comonad

也称作 CoReader(Env) Comonad。

instance Comonad ((,)e) where  duplicate p = (fst p, p)  extract = snd

Prelude Control.Comonad> duplicate (3,4)(3,(3,4))Prelude Control.Comonad> extract (3,4)4Prelude Control.Comonad> extend fst (3,4)(3,3)Prelude Control.Comonad> extend snd (3,4)(3,4)

((->)m) 是个 Comonad

也称作 CoWriter(Traced) Comonad。

instance Monoid m => Comonad ((->)m) where  duplicate f m = f . mappend m  extract f = f mempty

参考链接

Haskell for all: Comonads are objects
Comonads in Haskell