{-# LANGUAGE UndecidableInstances #-} module Pandora.Paradigm.Structure.Ability.Comprehension where import Pandora.Core.Functor (type (:=)) import Pandora.Core.Morphism ((%)) import Pandora.Pattern.Category ((.), ($)) import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Applicative (Applicative ((<*>))) import Pandora.Pattern.Functor.Avoidable (Avoidable (empty)) import Pandora.Pattern.Functor.Traversable (Traversable ((->>))) import Pandora.Pattern.Functor.Bindable (Bindable ((>>=))) import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Paradigm.Schemes.TU (TU (TU), type (<:.>)) import Pandora.Paradigm.Primary.Transformer.Construction (Construction (Construct)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite)) newtype Comprehension t a = Comprehension (t <:.> Construction t := a) instance Interpreted (Comprehension t) where type Primary (Comprehension t) a = t <:.> Construction t := a run :: Comprehension t a -> Primary (Comprehension t) a run ~(Comprehension (t <:.> Construction t) := a x) = Primary (Comprehension t) a (t <:.> Construction t) := a x unite :: Primary (Comprehension t) a -> Comprehension t a unite = Primary (Comprehension t) a -> Comprehension t a forall (t :: * -> *) a. ((t <:.> Construction t) := a) -> Comprehension t a Comprehension instance Covariant (t <:.> Construction t) => Covariant (Comprehension t) where a -> b f <$> :: (a -> b) -> Comprehension t a -> Comprehension t b <$> Comprehension (t <:.> Construction t) := a x = ((t <:.> Construction t) := b) -> Comprehension t b forall (t :: * -> *) a. ((t <:.> Construction t) := a) -> Comprehension t a Comprehension (((t <:.> Construction t) := b) -> Comprehension t b) -> ((t <:.> Construction t) := b) -> Comprehension t b forall (m :: * -> * -> *) a b. Category m => m a b -> m a b $ a -> b f (a -> b) -> ((t <:.> Construction t) := a) -> (t <:.> Construction t) := b forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b <$> (t <:.> Construction t) := a x instance (Avoidable t, Pointable t) => Pointable (Comprehension t) where point :: a |-> Comprehension t point = ((t <:.> Construction t) := a) -> Comprehension t a forall (t :: * -> *) a. ((t <:.> Construction t) := a) -> Comprehension t a Comprehension (((t <:.> Construction t) := a) -> Comprehension t a) -> (a -> (t <:.> Construction t) := a) -> a |-> Comprehension t forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . ((t :. Construction t) := a) -> (t <:.> Construction t) := a forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k) (a :: k). ((t :. u) := a) -> TU ct cu t u a TU (((t :. Construction t) := a) -> (t <:.> Construction t) := a) -> (a -> (t :. Construction t) := a) -> a -> (t <:.> Construction t) := a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . Construction t a |-> t forall (t :: * -> *) a. Pointable t => a |-> t point (Construction t a |-> t) -> (a -> Construction t a) -> a -> (t :. Construction t) := a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . a -> ((t :. Construction t) := a) -> Construction t a forall (t :: * -> *) a. a -> ((t :. Construction t) := a) -> Construction t a Construct (a -> ((t :. Construction t) := a) -> Construction t a) -> ((t :. Construction t) := a) -> a -> Construction t a forall a b c. (a -> b -> c) -> b -> a -> c % (t :. Construction t) := a forall (t :: * -> *) a. Avoidable t => t a empty instance Traversable (t <:.> Construction t) => Traversable (Comprehension t) where Comprehension (t <:.> Construction t) := a x ->> :: Comprehension t a -> (a -> u b) -> (u :. Comprehension t) := b ->> a -> u b f = ((t <:.> Construction t) := b) -> Comprehension t b forall (t :: * -> *) a. ((t <:.> Construction t) := a) -> Comprehension t a Comprehension (((t <:.> Construction t) := b) -> Comprehension t b) -> u ((t <:.> Construction t) := b) -> (u :. Comprehension t) := b forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b <$> ((t <:.> Construction t) := a x ((t <:.> Construction t) := a) -> (a -> u b) -> u ((t <:.> Construction t) := b) forall (t :: * -> *) (u :: * -> *) a b. (Traversable t, Pointable u, Applicative u) => t a -> (a -> u b) -> (u :. t) := b ->> a -> u b f) instance (forall a . Semigroup (t <:.> Construction t := a), Bindable t, Pointable t, Avoidable t) => Applicative (Comprehension t) where Comprehension t (a -> b) fs <*> :: Comprehension t (a -> b) -> Comprehension t a -> Comprehension t b <*> Comprehension t a xs = Comprehension t (a -> b) fs Comprehension t (a -> b) -> ((a -> b) -> Comprehension t b) -> Comprehension t b forall (t :: * -> *) a b. Bindable t => t a -> (a -> t b) -> t b >>= \a -> b f -> Comprehension t a xs Comprehension t a -> (a -> Comprehension t b) -> Comprehension t b forall (t :: * -> *) a b. Bindable t => t a -> (a -> t b) -> t b >>= ((t <:.> Construction t) := b) -> Comprehension t b forall (t :: * -> *) a. ((t <:.> Construction t) := a) -> Comprehension t a Comprehension (((t <:.> Construction t) := b) -> Comprehension t b) -> (a -> (t <:.> Construction t) := b) -> a -> Comprehension t b forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . ((t :. Construction t) := b) -> (t <:.> Construction t) := b forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k) (a :: k). ((t :. u) := a) -> TU ct cu t u a TU (((t :. Construction t) := b) -> (t <:.> Construction t) := b) -> (a -> (t :. Construction t) := b) -> a -> (t <:.> Construction t) := b forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . Construction t b |-> t forall (t :: * -> *) a. Pointable t => a |-> t point (Construction t b |-> t) -> (a -> Construction t b) -> a -> (t :. Construction t) := b forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . b |-> Construction t forall (t :: * -> *) a. Pointable t => a |-> t point (b |-> Construction t) -> (a -> b) -> a -> Construction t b forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . a -> b f instance (forall a . Semigroup (t <:.> Construction t := a), Bindable t) => Bindable (Comprehension t) where Comprehension (TU (t :. Construction t) := a t) >>= :: Comprehension t a -> (a -> Comprehension t b) -> Comprehension t b >>= a -> Comprehension t b f = ((t <:.> Construction t) := b) -> Comprehension t b forall (t :: * -> *) a. ((t <:.> Construction t) := a) -> Comprehension t a Comprehension (((t <:.> Construction t) := b) -> Comprehension t b) -> (((t :. Construction t) := b) -> (t <:.> Construction t) := b) -> ((t :. Construction t) := b) -> Comprehension t b forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . ((t :. Construction t) := b) -> (t <:.> Construction t) := b forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k) (a :: k). ((t :. u) := a) -> TU ct cu t u a TU (((t :. Construction t) := b) -> Comprehension t b) -> ((t :. Construction t) := b) -> Comprehension t b forall (m :: * -> * -> *) a b. Category m => m a b -> m a b $ (t :. Construction t) := a t ((t :. Construction t) := a) -> (Construction t a -> (t :. Construction t) := b) -> (t :. Construction t) := b forall (t :: * -> *) a b. Bindable t => t a -> (a -> t b) -> t b >>= \(Construct a x (t :. Construction t) := a xs) -> ((t <:.> Construction t) := b) -> (t :. Construction t) := b forall (t :: * -> *) a. Interpreted t => t a -> Primary t a run (((t <:.> Construction t) := b) -> (t :. Construction t) := b) -> ((t <:.> Construction t) := b) -> (t :. Construction t) := b forall (m :: * -> * -> *) a b. Category m => m a b -> m a b $ Comprehension t b -> Primary (Comprehension t) b forall (t :: * -> *) a. Interpreted t => t a -> Primary t a run (a -> Comprehension t b f a x) ((t <:.> Construction t) := b) -> ((t <:.> Construction t) := b) -> (t <:.> Construction t) := b forall a. Semigroup a => a -> a -> a + Comprehension t b -> Primary (Comprehension t) b forall (t :: * -> *) a. Interpreted t => t a -> Primary t a run (TU Covariant Covariant t (Construction t) a -> Comprehension t a forall (t :: * -> *) a. ((t <:.> Construction t) := a) -> Comprehension t a Comprehension (((t :. Construction t) := a) -> TU Covariant Covariant t (Construction t) a forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k) (a :: k). ((t :. u) := a) -> TU ct cu t u a TU (t :. Construction t) := a xs) Comprehension t a -> (a -> Comprehension t b) -> Comprehension t b forall (t :: * -> *) a b. Bindable t => t a -> (a -> t b) -> t b >>= a -> Comprehension t b f)