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