#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702
#endif
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.Extend
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
extended f (AdjointT m) = AdjointT $ fmap (extended $ leftAdjunct (f . AdjointT)) m
instance (Adjunction f g, Comonad w) => Comonad (AdjointT f g w) where
extend f (AdjointT m) = AdjointT $ fmap (extend $ leftAdjunct (f . AdjointT)) m
extract = rightAdjunct extract . runAdjointT
instance (Adjunction f g, Distributive g) => ComonadTrans (AdjointT f g) where
lower = counit . fmap distribute . runAdjointT