Comonad: Dual of a Monad

gistfile1.hs

{-# LANGUAGE NoImplicitPrelude #-}
{-# LANGUAGE RebindableSyntax #-}
module Comonad where

import Prelude (Functor(..))

class Functor m => Monad m where
  return :: a -> m a
  join   :: m (m a) -> m a

infixl 1 >>=
(>>=) :: Monad m => m a -> (a -> m b) -> m b
m >>= f = join (fmap f m)

class Functor w => Comonad w where
  extract   :: w a -> a
  duplicate :: w a -> w (w a)

infixl 1 =>>
(=>>) :: Comonad w => w a -> (w a -> b) -> w b
w =>> f = fmap f (duplicate w)