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|
{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies #-}
-----------------------------------------------------------------------------
-- |
-- Module : Control.Comonad.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.Comonad.Trans.Adjoint
( Adjoint
, runAdjoint
, adjoint
, AdjointT(..)
) where
import Prelude hiding (sequence)
import Control.Applicative
import Control.Comonad
import Control.Comonad.Trans.Class
import Data.Functor.Adjunction
import Data.Functor.Identity
import Data.Distributive
type Adjoint f g = AdjointT f g Identity
newtype AdjointT f g w a = AdjointT { runAdjointT :: f (w (g a)) }
adjoint :: Functor f => f (g a) -> Adjoint f g a
adjoint = AdjointT . fmap Identity
runAdjoint :: Functor f => Adjoint f g a -> f (g a)
runAdjoint = fmap runIdentity . runAdjointT
instance (Adjunction f g, Functor w) => Functor (AdjointT f g w) where
fmap f (AdjointT g) = AdjointT $ fmap (fmap (fmap f)) g
b <$ (AdjointT g) = AdjointT $ fmap (fmap (b <$)) g
instance (Adjunction f g, Extend w) => Extend (AdjointT f g w) where
extend f (AdjointT m) = AdjointT $ fmap (extend $ leftAdjunct (f . AdjointT)) m
instance (Adjunction f g, Comonad w) => Comonad (AdjointT f g w) where
extract = rightAdjunct extract . runAdjointT
{-
instance (Adjunction f g, Monad m) => Applicative (AdjointT f g m) where
pure = AdjointT . leftAdjunct return
(<*>) = ap
-}
instance (Adjunction f g, Distributive g) => ComonadTrans (AdjointT f g) where
lower = counit . fmap distribute . runAdjointT
|
