{-# LANGUAGE UndecidableInstances #-} module Pandora.Paradigm.Structure.Modification.Prefixed where import Pandora.Core.Functor (type (:.), type (:=)) import Pandora.Pattern.Category ((.), ($)) import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$>))) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Traversable (Traversable ((->>), (->>>))) import Pandora.Pattern.Object.Monoid (Monoid (zero)) import Pandora.Paradigm.Primary.Functor.Product (Product ((:*:))) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite)) newtype Prefixed t k a = Prefixed (t :. Product k := a) instance Interpreted (Prefixed t k) where type Primary (Prefixed t k) a = t :. Product k := a run :: Prefixed t k a -> Primary (Prefixed t k) a run ~(Prefixed (t :. Product k) := a x) = (t :. Product k) := a Primary (Prefixed t k) a x unite :: Primary (Prefixed t k) a -> Prefixed t k a unite = Primary (Prefixed t k) a -> Prefixed t k a forall (t :: * -> *) k a. ((t :. Product k) := a) -> Prefixed t k a Prefixed instance Covariant t => Covariant (Prefixed t k) where a -> b f <$> :: (a -> b) -> Prefixed t k a -> Prefixed t k b <$> Prefixed (t :. Product k) := a x = ((t :. Product k) := b) -> Prefixed t k b forall (t :: * -> *) k a. ((t :. Product k) := a) -> Prefixed t k a Prefixed (((t :. Product k) := b) -> Prefixed t k b) -> ((t :. Product k) := b) -> Prefixed t k b forall (m :: * -> * -> *). Category m => m ~~> m $ a -> b f (a -> b) -> ((t :. Product k) := a) -> (t :. Product k) := b forall (t :: * -> *) (u :: * -> *) a b. (Covariant t, Covariant u) => (a -> b) -> ((t :. u) := a) -> (t :. u) := b <$$> (t :. Product k) := a x instance Traversable t => Traversable (Prefixed t k) where Prefixed (t :. Product k) := a x ->> :: Prefixed t k a -> (a -> u b) -> (u :. Prefixed t k) := b ->> a -> u b f = ((t :. Product k) := b) -> Prefixed t k b forall (t :: * -> *) k a. ((t :. Product k) := a) -> Prefixed t k a Prefixed (((t :. Product k) := b) -> Prefixed t k b) -> u ((t :. Product k) := b) -> (u :. Prefixed t k) := b forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b <$> (t :. Product k) := a x ((t :. Product k) := a) -> (a -> u b) -> u ((t :. Product k) := b) forall (t :: * -> *) (u :: * -> *) (v :: * -> *) a b. (Traversable t, Pointable u, Applicative u, Traversable v) => ((v :. t) := a) -> (a -> u b) -> (u :. (v :. t)) := b ->>> a -> u b f instance (Monoid k, Pointable t) => Pointable (Prefixed t k) where point :: a :=> Prefixed t k point = ((t :. Product k) := a) -> Prefixed t k a forall (t :: * -> *) k a. ((t :. Product k) := a) -> Prefixed t k a Prefixed (((t :. Product k) := a) -> Prefixed t k a) -> (a -> (t :. Product k) := a) -> a :=> Prefixed t k forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . Product k a :=> t forall (t :: * -> *) a. Pointable t => a :=> t point (Product k a :=> t) -> (a -> Product k a) -> a -> (t :. Product k) := a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . k -> a -> Product k a forall s a. s -> a -> Product s a (:*:) k forall a. Monoid a => a zero