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|
{-# LANGUAGE MultiParamTypeClasses #-}
-----------------------------------------------------------------------------
-- |
-- Module : Control.Monad.Trans.Contravariant.Adjoint
-- Copyright : (C) 2011 Edward Kmett
-- License : BSD-style (see the file LICENSE)
--
-- Maintainer : Edward Kmett <ekmett@gmail.com>
-- Stability : provisional
-- Portability : MPTCs, fundeps
--
-- Uses a contravariant adjunction:
--
-- f -| g : Hask^op -> Hask
--
-- to build a 'Comonad' to 'Monad' transformer. Sadly, the dual construction,
-- which builds a 'Comonad' out of a 'Monad', is uninhabited, because any
-- 'Adjunction' of the form
--
-- > f -| g : Hask -> Hask^op
--
-- would trivially admit unsafePerformIO.
--
----------------------------------------------------------------------------
module Control.Monad.Trans.Contravariant.Adjoint
( Adjoint
, runAdjoint
, adjoint
, AdjointT(..)
) where
import Prelude hiding (sequence)
import Control.Applicative
import Control.Comonad
import Control.Monad (ap)
import Data.Functor.Identity
import Data.Functor.Contravariant
import Data.Functor.Contravariant.Adjunction
type Adjoint f g = AdjointT f g Identity
newtype AdjointT f g w a = AdjointT { runAdjointT :: g (w (f a)) }
adjoint :: Contravariant g => g (f a) -> Adjoint f g a
adjoint = AdjointT . contramap runIdentity
runAdjoint :: Contravariant g => Adjoint f g a -> g (f a)
runAdjoint = contramap Identity . runAdjointT
instance (Adjunction f g, Functor w) => Functor (AdjointT f g w) where
fmap f (AdjointT g) = AdjointT $ contramap (fmap (contramap f)) g
instance (Adjunction f g, Comonad w) => Applicative (AdjointT f g w) where
pure = AdjointT . leftAdjunct extract
(<*>) = ap
instance (Adjunction f g, Comonad w) => Monad (AdjointT f g w) where
return = AdjointT . leftAdjunct extract
AdjointT m >>= f = AdjointT $ contramap (extend (rightAdjunct (runAdjointT . f))) m
|
