{-# LANGUAGE UndecidableInstances #-} module Pandora.Paradigm.Primary.Transformer.Reverse where import Pandora.Pattern.Category ((.), ($), (#)) import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-))) import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<))) import Pandora.Pattern.Functor.Extractable (Extractable (extract)) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Applicative (Applicative ((<*>))) import Pandora.Pattern.Functor.Traversable (Traversable ((->>))) import Pandora.Pattern.Functor.Distributive (Distributive ((>>-))) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\))) import Pandora.Paradigm.Primary.Transformer.Backwards (Backwards (Backwards)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite)) newtype Reverse t a = Reverse (t a) instance Covariant t => Covariant (Reverse t) where a -> b f <$> :: (a -> b) -> Reverse t a -> Reverse t b <$> Reverse t a x = t b -> Reverse t b forall k (t :: k -> *) (a :: k). t a -> Reverse t a Reverse (t b -> Reverse t b) -> t b -> Reverse t b forall (m :: * -> * -> *) a b. Category m => 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 <$> t a x instance Covariant_ t (->) (->) => Covariant_ (Reverse t) (->) (->) where a -> b f -<$>- :: (a -> b) -> Reverse t a -> Reverse t b -<$>- Reverse t a x = t b -> Reverse t b forall k (t :: k -> *) (a :: k). t a -> Reverse t a Reverse (t b -> Reverse t b) -> t b -> Reverse t b forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) # a -> b f (a -> b) -> t a -> t b forall (t :: * -> *) (source :: * -> * -> *) (target :: * -> * -> *) a b. Covariant_ t source target => source a b -> target (t a) (t b) -<$>- t a x instance Pointable t (->) => Pointable (Reverse t) (->) where point :: a -> Reverse t a point = t a -> Reverse t a forall k (t :: k -> *) (a :: k). t a -> Reverse t a Reverse (t a -> Reverse t a) -> (a -> t a) -> a -> Reverse t a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . a -> t a forall (t :: * -> *) (source :: * -> * -> *) a. Pointable t source => source a (t a) point instance Extractable t (->) => Extractable (Reverse t) (->) where extract :: Reverse t a -> a extract (Reverse t a x) = t a -> a forall (t :: * -> *) (source :: * -> * -> *) a. Extractable t source => source (t a) a extract t a x instance Applicative t => Applicative (Reverse t) where Reverse t (a -> b) f <*> :: Reverse t (a -> b) -> Reverse t a -> Reverse t b <*> Reverse t a x = t b -> Reverse t b forall k (t :: k -> *) (a :: k). t a -> Reverse t a Reverse (t b -> Reverse t b) -> t b -> Reverse t b forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) # t (a -> b) f t (a -> b) -> t a -> t b forall (t :: * -> *) a b. Applicative t => t (a -> b) -> t a -> t b <*> t a x instance Traversable t => Traversable (Reverse t) where Reverse t a x ->> :: Reverse t a -> (a -> u b) -> (u :. Reverse t) := b ->> a -> u b f = t b -> Reverse t b forall k (t :: k -> *) (a :: k). t a -> Reverse t a Reverse (t b -> Reverse t b) -> u (t b) -> (u :. Reverse t) := b forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b <$> Backwards u (t b) -> Primary (Backwards u) (t b) forall (t :: * -> *) a. Interpreted t => t a -> Primary t a run (t a x t a -> (a -> Backwards u b) -> Backwards u (t b) forall (t :: * -> *) (u :: * -> *) a b. (Traversable t, Pointable u (->), Applicative u) => t a -> (a -> u b) -> (u :. t) := b ->> u b -> Backwards u b forall k (t :: k -> *) (a :: k). t a -> Backwards t a Backwards (u b -> Backwards u b) -> (a -> u b) -> a -> Backwards u b forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . a -> u b f) instance Distributive t => Distributive (Reverse t) where u a x >>- :: u a -> (a -> Reverse t b) -> (Reverse t :. u) := b >>- a -> Reverse t b f = t (u b) -> (Reverse t :. u) := b forall k (t :: k -> *) (a :: k). t a -> Reverse t a Reverse (t (u b) -> (Reverse t :. u) := b) -> t (u b) -> (Reverse t :. u) := b forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) $ u a x u a -> (a -> t b) -> t (u b) forall (t :: * -> *) (u :: * -> *) a b. (Distributive t, Covariant u) => u a -> (a -> t b) -> (t :. u) := b >>- Reverse t b -> t b forall (t :: * -> *) a. Interpreted t => t a -> Primary t a run (Reverse t b -> t b) -> (a -> Reverse t b) -> a -> t b forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . a -> Reverse t b f instance Contravariant t => Contravariant (Reverse t) where a -> b f >$< :: (a -> b) -> Reverse t b -> Reverse t a >$< Reverse t b x = t a -> Reverse t a forall k (t :: k -> *) (a :: k). t a -> Reverse t a Reverse (t a -> Reverse t a) -> t a -> Reverse t a forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) # a -> b f (a -> b) -> t b -> t a forall (t :: * -> *) a b. Contravariant t => (a -> b) -> t b -> t a >$< t b x instance Interpreted (Reverse t) where type Primary (Reverse t) a = t a run :: Reverse t a -> Primary (Reverse t) a run ~(Reverse t a x) = t a Primary (Reverse t) a x unite :: Primary (Reverse t) a -> Reverse t a unite = Primary (Reverse t) a -> Reverse t a forall k (t :: k -> *) (a :: k). t a -> Reverse t a Reverse instance Liftable Reverse where lift :: u ~> Reverse u lift = u a -> Reverse u a forall k (t :: k -> *) (a :: k). t a -> Reverse t a Reverse instance Lowerable Reverse where lower :: Reverse u ~> u lower = Reverse u a -> u a forall (t :: * -> *) a. Interpreted t => t a -> Primary t a run instance Hoistable Reverse where u ~> v f /|\ :: (u ~> v) -> Reverse u ~> Reverse v /|\ Reverse u a x = v a -> Reverse v a forall k (t :: k -> *) (a :: k). t a -> Reverse t a Reverse (v a -> Reverse v a) -> v a -> Reverse v a forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) # u a -> v a u ~> v f u a x