module Data.Functor.Extension.Kan (Ran (..), Lan (..)) where import "morphisms" Control.Morphism ((.), ($)) import Control.Functor.Contravariant (Contravariant ((>$<))) import Control.Functor.Covariant (Covariant ((<$>))) newtype Ran (t :: * -> *) (u :: * -> *) (b :: *) (a :: *) = Ran { ran :: (a -> t b) -> u b } instance Covariant (Ran t u b) where f <$> Ran x = Ran $ x . (. f) newtype Lan (t :: * -> *) (u :: * -> *) (b :: *) (a :: *) = Lan { lan :: (t b -> a) -> u b } instance Contravariant (Lan t u b) where f >$< Lan x = Lan $ x . (f .)