module Pandora.Paradigm.Schemes.UT where import Pandora.Core.Functor (type (:.), type (:=), type (~>)) import Pandora.Pattern.Category ((.), ($)) import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$>)), Covariant_ ((-<$>-)), (-<$$>-)) import Pandora.Pattern.Functor.Contravariant (Contravariant) import Pandora.Pattern.Functor.Applicative (Applicative ((<*>), (<**>))) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Bindable (Bindable ((>>=), join)) import Pandora.Pattern.Functor.Extractable (Extractable (extract)) import Pandora.Pattern.Functor.Traversable (Traversable ((->>))) import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite)) newtype UT ct cu t u a = UT (u :. t := a) infixr 3 <.:>, >.:>, <.:<, >.:< type (<.:>) = UT Covariant Covariant type (>.:>) = UT Contravariant Covariant type (<.:<) = UT Covariant Contravariant type (>.:<) = UT Contravariant Contravariant instance Interpreted (UT ct cu t u) where type Primary (UT ct cu t u) a = u :. t := a run ~(UT x) = x unite = UT instance (Covariant t, Covariant u) => Covariant (t <.:> u) where f <$> UT x = UT $ f <$$> x instance (Covariant_ t (->) (->), Covariant_ u (->) (->)) => Covariant_ (t <.:> u) (->) (->) where f -<$>- UT x = UT $ f -<$$>- x instance (Applicative t, Applicative u) => Applicative (t <.:> u) where UT f <*> UT x = UT $ f <**> x instance (Pointable t (->), Pointable u (->)) => Pointable (t <.:> u) (->) where point = UT . point . point instance (Traversable t, Bindable t, Applicative u, Monad u) => Bindable (t <.:> u) where UT x >>= f = UT $ x >>= \i -> join <$> i ->> run . f instance (Extractable t (->), Extractable u (->)) => Extractable (t <.:> u) (->) where extract = extract . extract . run instance Pointable t (->) => Liftable (UT Covariant Covariant t) where lift :: Covariant_ u (->) (->) => u ~> t <.:> u lift x = UT $ point @_ @(->) -<$>- x instance Extractable t (->) => Lowerable (UT Covariant Covariant t) where lower :: Covariant_ u (->) (->) => t <.:> u ~> u lower (UT x) = extract @_ @(->) -<$>- x