module Pandora.Paradigm.Schemes.UTU where

import Pandora.Core.Functor (type (:.), type (>>>))
import Pandora.Core.Interpreted (Interpreted (Primary, run, unite))
import Pandora.Pattern.Functor.Covariant (Covariant)
import Pandora.Pattern.Functor.Contravariant (Contravariant)

newtype UTU ct cu t u u' a = UTU (u :. t :. u' >>> a)

type (<.<:>.>) = UTU Covariant Covariant Covariant
type (>.<:>.>) = UTU Contravariant Covariant Covariant
type (<.<:>.<) = UTU Covariant Covariant Contravariant
type (>.<:>.<) = UTU Contravariant Covariant Contravariant
type (<.>:<.>) = UTU Covariant Contravariant Covariant
type (>.>:<.>) = UTU Contravariant Contravariant Covariant
type (<.>:<.<) = UTU Covariant Contravariant Contravariant
type (>.>:<.<) = UTU Contravariant Contravariant Contravariant

instance Interpreted (->) (UTU ct cu t u u') where
	type Primary (UTU ct cu t u u') a = u :. t :. u' >>> a
	run :: ((->) < UTU ct cu t u u' a) < Primary (UTU ct cu t u u') a
run ~(UTU (u :. (t :. u')) >>> a
x) = (u :. (t :. u')) >>> a
Primary (UTU ct cu t u u') a
x
	unite :: ((->) < Primary (UTU ct cu t u u') a) < UTU ct cu t u u' a
unite = ((->) < Primary (UTU ct cu t u u') a) < UTU ct cu t u u' a
forall k k k k k (ct :: k) (cu :: k) (t :: k -> k) (u :: k -> *)
       (u' :: k -> k) (a :: k).
((u :. (t :. u')) >>> a) -> UTU ct cu t u u' a
UTU