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|
{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies #-}
-----------------------------------------------------------------------------
-- |
-- Module : Control.Monad.Trans.Adjoint
-- Copyright : (C) 2011 Edward Kmett
-- License : BSD-style (see the file LICENSE)
--
-- Maintainer : Edward Kmett <ekmett@gmail.com>
-- Stability : provisional
-- Portability : MPTCs, fundeps
--
----------------------------------------------------------------------------
module Control.Monad.Trans.Adjoint
( Adjoint
, runAdjoint
, adjoint
, AdjointT(..)
) where
import Prelude hiding (sequence)
import Control.Applicative
import Control.Monad (ap, liftM)
import Control.Monad.Trans.Class
import Data.Traversable
import Data.Functor.Adjunction
import Data.Functor.Identity
type Adjoint f g = AdjointT f g Identity
newtype AdjointT f g m a = AdjointT { runAdjointT :: g (m (f a)) }
adjoint :: Functor g => g (f a) -> Adjoint f g a
adjoint = AdjointT . fmap Identity
runAdjoint :: Functor g => Adjoint f g a -> g (f a)
runAdjoint = fmap runIdentity . runAdjointT
instance (Adjunction f g, Monad m) => Functor (AdjointT f g m) where
fmap f (AdjointT g) = AdjointT $ fmap (liftM (fmap f)) g
b <$ (AdjointT g) = AdjointT $ fmap (liftM (b <$)) g
instance (Adjunction f g, Monad m) => Applicative (AdjointT f g m) where
pure = AdjointT . leftAdjunct return
(<*>) = ap
instance (Adjunction f g, Monad m) => Monad (AdjointT f g m) where
return = AdjointT . leftAdjunct return
AdjointT m >>= f = AdjointT $ fmap (>>= rightAdjunct (runAdjointT . f)) m
-- | Exploiting this instance requires that we have the missing Traversables for Identity, (,)e and IdentityT
instance (Adjunction f g, Traversable f) => MonadTrans (AdjointT f g) where
lift = AdjointT . fmap sequence . unit
|
