module Pandora.Paradigm.Schemes.TUT where import Pandora.Core.Functor (type (:.), type (:=), type (~>)) import Pandora.Pattern.Category (identity, ($)) import Pandora.Pattern.Functor.Covariant (Covariant) import Pandora.Pattern.Functor.Contravariant (Contravariant) import Pandora.Pattern.Functor.Distributive (Distributive ((>>-))) import Pandora.Pattern.Functor.Adjoint (Adjoint ((-|), (|-))) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run)) newtype TUT ct ct' cu t t' u a = TUT (t :. u :. t' := a) type (<:<.>:>) = TUT Covariant Covariant Covariant type (>:<.>:>) = TUT Contravariant Covariant Covariant type (<:<.>:<) = TUT Covariant Covariant Contravariant type (>:<.>:<) = TUT Contravariant Covariant Contravariant type (<:>.<:>) = TUT Covariant Contravariant Covariant type (>:>.<:>) = TUT Contravariant Contravariant Covariant type (<:>.<:<) = TUT Covariant Contravariant Contravariant type (>:>.<:<) = TUT Contravariant Contravariant Contravariant instance Interpreted (TUT ct ct' cu t t' u) where type Primary (TUT ct ct' cu t t' u) a = t :. u :. t' := a run :: TUT ct ct' cu t t' u a -> Primary (TUT ct ct' cu t t' u) a run ~(TUT (t :. (u :. t')) := a x) = (t :. (u :. t')) := a Primary (TUT ct ct' cu t t' u) a x instance (Adjoint t' t, Distributive t) => Liftable (t <:<.>:> t') where lift :: Covariant u => u ~> t <:<.>:> t' := u lift :: u ~> ((t <:<.>:> t') := u) lift u a x = ((t :. (u :. t')) := a) -> TUT Covariant Covariant Covariant t t' u a forall k k k k k k (ct :: k) (ct' :: k) (cu :: k) (t :: k -> *) (t' :: k -> k) (u :: k -> k) (a :: k). ((t :. (u :. t')) := a) -> TUT ct ct' cu t t' u a TUT (((t :. (u :. t')) := a) -> TUT Covariant Covariant Covariant t t' u a) -> ((t :. (u :. t')) := a) -> TUT Covariant Covariant Covariant t t' u a forall (m :: * -> * -> *) a b. Category m => m a b -> m a b $ u a x u a -> (a -> t (t' a)) -> (t :. (u :. t')) := a forall (t :: * -> *) (u :: * -> *) a b. (Distributive t, Covariant u) => u a -> (a -> t b) -> (t :. u) := b >>- (a -> (t' a -> t' a) -> t (t' a) forall (t :: * -> *) (u :: * -> *) a b. Adjoint t u => a -> (t a -> b) -> u b -| t' a -> t' a forall (m :: * -> * -> *) a. Category m => m a a identity) instance (Adjoint t t', Distributive t') => Lowerable (t <:<.>:> t') where lower :: Covariant u => (t <:<.>:> t' := u) ~> u lower :: ((t <:<.>:> t') := u) ~> u lower (TUT (t :. (u :. t')) := a x) = (t :. (u :. t')) := a x ((t :. (u :. t')) := a) -> ((:.) u t' a -> t' (u a)) -> u a forall (t :: * -> *) (u :: * -> *) a b. Adjoint t u => t a -> (a -> u b) -> b |- ((:.) u t' a -> (t' a -> t' a) -> t' (u a) forall (t :: * -> *) (u :: * -> *) a b. (Distributive t, Covariant u) => u a -> (a -> t b) -> (t :. u) := b >>- t' a -> t' a forall (m :: * -> * -> *) a. Category m => m a a identity)