module Pandora.Paradigm.Schemes.T_U where import Pandora.Pattern.Category (($)) import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Contravariant (Contravariant) import Pandora.Pattern.Functor.Bivariant (Bivariant ((<->))) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite)) newtype T_U ct cu t p u a = T_U (p (t a) (u a)) type (<:.:>) p t = T_U Covariant Covariant t p t type (>:.:>) p t = T_U Contravariant Covariant t p t type (<:.:<) p t = T_U Covariant Contravariant t p t type (>:.:<) p t = T_U Contravariant Contravariant t p t instance Interpreted (T_U ct cu t p u) where type Primary (T_U ct cu t p u) a = p (t a) (u a) run :: T_U ct cu t p u a -> Primary (T_U ct cu t p u) a run ~(T_U p (t a) (u a) x) = p (t a) (u a) Primary (T_U ct cu t p u) a x unite :: Primary (T_U ct cu t p u) a -> T_U ct cu t p u a unite = Primary (T_U ct cu t p u) a -> T_U ct cu t p u a forall k k k k k (ct :: k) (cu :: k) (t :: k -> k) (p :: k -> k -> *) (u :: k -> k) (a :: k). p (t a) (u a) -> T_U ct cu t p u a T_U instance (Bivariant p, Covariant t, Covariant u) => Covariant (T_U Covariant Covariant t p u) where a -> b f <$> :: (a -> b) -> T_U Covariant Covariant t p u a -> T_U Covariant Covariant t p u b <$> (T_U p (t a) (u a) x) = p (t b) (u b) -> T_U Covariant Covariant t p u b forall k k k k k (ct :: k) (cu :: k) (t :: k -> k) (p :: k -> k -> *) (u :: k -> k) (a :: k). p (t a) (u a) -> T_U ct cu t p u a T_U (p (t b) (u b) -> T_U Covariant Covariant t p u b) -> p (t b) (u b) -> T_U Covariant Covariant t p u b forall (m :: * -> * -> *) a b. Category m => m a b -> m a b $ (a -> b f (a -> b) -> t a -> t b forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b <$>) (t a -> t b) -> (u a -> u b) -> p (t a) (u a) -> p (t b) (u b) forall (v :: * -> * -> *) a b c d. Bivariant v => (a -> b) -> (c -> d) -> v a c -> v b d <-> (a -> b f (a -> b) -> u a -> u b forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b <$>) (p (t a) (u a) -> p (t b) (u b)) -> p (t a) (u a) -> p (t b) (u b) forall (m :: * -> * -> *) a b. Category m => m a b -> m a b $ p (t a) (u a) x