Haskell语言学习笔记（61）Distributive

Distributive

class Functor g => Distributive g where
  distribute  :: Functor f => f (g a) -> g (f a)
  distribute  = collect id

  collect     :: Functor f => (a -> g b) -> f a -> g (f b)
  collect f   = distribute . fmap f

  distributeM :: Monad m => m (g a) -> g (m a)
  distributeM = fmap unwrapMonad . distribute . WrapMonad

  collectM    :: Monad m => (a -> g b) -> m a -> g (m b)
  collectM f  = distributeM . liftM f

cotraverse :: (Distributive g, Functor f) => (f a -> b) -> f (g a) -> g b
cotraverse f = fmap f . distribute

comapM :: (Distributive g, Monad m) => (m a -> b) -> m (g a) -> g b
comapM f = fmap f . distributeM

((->)e) 是个 Distributive

instance Distributive ((->)e) where
  distribute a e = fmap ($e) a
  collect f q e = fmap (flip f e) q

Prelude Data.Distributive> distribute [(+1),(+2)] 1
[2,3]
Prelude Data.Distributive> collect (^) [1,2] 3
[1,8]