Monad equivalence

gistfile1.hs

{-# LANGUAGE UndecidableInstances, FlexibleInstances #-}

import Prelude hiding (return, join, (=<<))

-- A Monad can be defined either with (>>=) + return, or with
-- fmap + join + return

class Return r where
  return :: a -> r a

class Return m => MonadBind m where
  (=<<) :: (a -> m b) -> m a -> m b

class (Return m, Functor m) => MonadJoin m where
  join  :: m (m a) -> m a

instance MonadBind m => Functor m where
  fmap = (=<<) . (return .)

instance MonadBind m => MonadJoin m where
  join = (=<<) id

instance MonadJoin m => MonadBind m where
  (=<<) = (join .) . fmap