module Pandora.Paradigm.Schemes.UT where import Pandora.Core.Functor (type (:.), type (:=), type (~>)) import Pandora.Pattern.Category (($)) import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Contravariant (Contravariant) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Extractable (Extractable (extract)) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run)) newtype UT ct cu t u a = UT (u :. t := a) 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 ct cu t u a -> Primary (UT ct cu t u) a run ~(UT (u :. t) := a x) = (u :. t) := a Primary (UT ct cu t u) a x instance Pointable t => Liftable (UT Covariant Covariant t) where lift :: Covariant u => u ~> t <.:> u lift :: u ~> (t <.:> u) lift u a x = ((u :. t) := a) -> UT Covariant Covariant t u a forall k k k k (ct :: k) (cu :: k) (t :: k -> k) (u :: k -> *) (a :: k). ((u :. t) := a) -> UT ct cu t u a UT (((u :. t) := a) -> UT Covariant Covariant t u a) -> ((u :. t) := a) -> UT Covariant Covariant t u a forall (m :: * -> * -> *) a b. Category m => m a b -> m a b $ a |-> t forall (t :: * -> *) a. Pointable t => a |-> t point (a |-> t) -> u a -> (u :. t) := a forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b <$> u a x instance Extractable t => Lowerable (UT Covariant Covariant t) where lower :: Covariant u => t <.:> u ~> u lower :: (t <.:> u) ~> u lower (UT (u :. t) := a x) = a <-| t forall (t :: * -> *) a. Extractable t => a <-| t extract (a <-| t) -> ((u :. t) := a) -> u a forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b <$> (u :. t) := a x