{-# LANGUAGE UndecidableInstances #-} module Pandora.Paradigm.Controlflow.Effect.Transformer.Comonadic (Comonadic (..), (:<) (..)) where import Pandora.Core.Functor (type (~>)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($)) import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) import Pandora.Pattern.Functor.Comonad (Comonad) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\))) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)((:*:))) import Pandora.Paradigm.Primary.Algebraic.One (One (One)) import Pandora.Paradigm.Primary.Algebraic (Extractable_, point) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite)) class Interpreted t => Comonadic t where {-# MINIMAL bring #-} bring :: Extractable_ u => t :< u ~> t infixr 3 :< newtype (:<) t u a = TC { (:<) t u a -> Schematic Comonad t u a tc :: Schematic Comonad t u a } instance Covariant (->) (->) (Schematic Comonad t u) => Covariant (->) (->) (t :< u) where a -> b f -<$>- :: (a -> b) -> (:<) t u a -> (:<) t u b -<$>- TC Schematic Comonad t u a x = Schematic Comonad t u b -> (:<) t u b forall (t :: * -> *) (u :: * -> *) a. Schematic Comonad t u a -> (:<) t u a TC (Schematic Comonad t u b -> (:<) t u b) -> Schematic Comonad t u b -> (:<) t u b forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) $ a -> b f (a -> b) -> Schematic Comonad t u a -> Schematic Comonad t u b forall (source :: * -> * -> *) (target :: * -> * -> *) (t :: * -> *) a b. Covariant source target t => source a b -> target (t a) (t b) -<$>- Schematic Comonad t u a x instance Semimonoidal (->) (:*:) (:*:) (Schematic Comonad t u) => Semimonoidal (->) (:*:) (:*:) (t :< u) where multiply :: ((:<) t u a :*: (:<) t u b) -> (:<) t u (a :*: b) multiply (TC Schematic Comonad t u a f :*: TC Schematic Comonad t u b x) = Schematic Comonad t u (a :*: b) -> (:<) t u (a :*: b) forall (t :: * -> *) (u :: * -> *) a. Schematic Comonad t u a -> (:<) t u a TC (Schematic Comonad t u (a :*: b) -> (:<) t u (a :*: b)) -> Schematic Comonad t u (a :*: b) -> (:<) t u (a :*: b) forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) $ (Schematic Comonad t u a :*: Schematic Comonad t u b) -> Schematic Comonad t u (a :*: b) forall k (p :: * -> * -> *) (source :: * -> * -> *) (target :: k -> k -> k) (t :: k -> *) (a :: k) (b :: k). Semimonoidal p source target t => p (source (t a) (t b)) (t (target a b)) multiply ((Schematic Comonad t u a :*: Schematic Comonad t u b) -> Schematic Comonad t u (a :*: b)) -> (Schematic Comonad t u a :*: Schematic Comonad t u b) -> Schematic Comonad t u (a :*: b) forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) $ Schematic Comonad t u a f Schematic Comonad t u a -> Schematic Comonad t u b -> Schematic Comonad t u a :*: Schematic Comonad t u b forall s a. s -> a -> s :*: a :*: Schematic Comonad t u b x instance Monoidal (->) (->) (:*:) (:*:) (Schematic Comonad t u) => Monoidal (->) (->) (:*:) (:*:) (t :< u) where unit :: Proxy (:*:) -> (Unit (:*:) -> a) -> (:<) t u a unit Proxy (:*:) _ Unit (:*:) -> a f = Schematic Comonad t u a -> (:<) t u a forall (t :: * -> *) (u :: * -> *) a. Schematic Comonad t u a -> (:<) t u a TC (Schematic Comonad t u a -> (:<) t u a) -> (a -> Schematic Comonad t u a) -> a -> (:<) t u a forall (m :: * -> * -> *) b c a. Semigroupoid m => m b c -> m a b -> m a c . a -> Schematic Comonad t u a forall (t :: * -> *) a. Monoidal (->) (->) (:*:) (:*:) t => a -> t a point (a -> (:<) t u a) -> a -> (:<) t u a forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) $ Unit (:*:) -> a f One Unit (:*:) One instance Traversable (->) (->) (Schematic Comonad t u) => Traversable (->) (->) (t :< u) where a -> u b f <<- :: (a -> u b) -> (:<) t u a -> u ((:<) t u b) <<- TC Schematic Comonad t u a x = Schematic Comonad t u b -> (:<) t u b forall (t :: * -> *) (u :: * -> *) a. Schematic Comonad t u a -> (:<) t u a TC (Schematic Comonad t u b -> (:<) t u b) -> u (Schematic Comonad t u b) -> u ((:<) t u b) forall (source :: * -> * -> *) (target :: * -> * -> *) (t :: * -> *) a b. Covariant source target t => source a b -> target (t a) (t b) -<$>- a -> u b f (a -> u b) -> Schematic Comonad t u a -> u (Schematic Comonad t u b) forall (source :: * -> * -> *) (target :: * -> * -> *) (t :: * -> *) (u :: * -> *) a b. (Traversable source target t, Covariant source target u, Monoidal source target (:*:) (:*:) u) => source a (u b) -> target (t a) (u (t b)) <<- Schematic Comonad t u a x instance Distributive (->) (->) (Schematic Comonad t u) => Distributive (->) (->) (t :< u) where a -> (:<) t u b f -<< :: (a -> (:<) t u b) -> u a -> (:<) t u (u b) -<< u a x = Schematic Comonad t u (u b) -> (:<) t u (u b) forall (t :: * -> *) (u :: * -> *) a. Schematic Comonad t u a -> (:<) t u a TC (Schematic Comonad t u (u b) -> (:<) t u (u b)) -> Schematic Comonad t u (u b) -> (:<) t u (u b) forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) $ (:<) t u b -> Schematic Comonad t u b forall (t :: * -> *) (u :: * -> *) a. (:<) t u a -> Schematic Comonad t u a tc ((:<) t u b -> Schematic Comonad t u b) -> (a -> (:<) t u b) -> a -> Schematic Comonad t u b forall (m :: * -> * -> *) b c a. Semigroupoid m => m b c -> m a b -> m a c . a -> (:<) t u b f (a -> Schematic Comonad t u b) -> u a -> Schematic Comonad t u (u b) forall (source :: * -> * -> *) (target :: * -> * -> *) (t :: * -> *) (u :: * -> *) a b. (Distributive source target t, Covariant source target u) => source a (t b) -> target (u a) (t (u b)) -<< u a x instance Bindable (->) (Schematic Comonad t u) => Bindable (->) (t :< u) where a -> (:<) t u b f =<< :: (a -> (:<) t u b) -> (:<) t u a -> (:<) t u b =<< TC Schematic Comonad t u a x = Schematic Comonad t u b -> (:<) t u b forall (t :: * -> *) (u :: * -> *) a. Schematic Comonad t u a -> (:<) t u a TC (Schematic Comonad t u b -> (:<) t u b) -> Schematic Comonad t u b -> (:<) t u b forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) $ (:<) t u b -> Schematic Comonad t u b forall (t :: * -> *) (u :: * -> *) a. (:<) t u a -> Schematic Comonad t u a tc ((:<) t u b -> Schematic Comonad t u b) -> (a -> (:<) t u b) -> a -> Schematic Comonad t u b forall (m :: * -> * -> *) b c a. Semigroupoid m => m b c -> m a b -> m a c . a -> (:<) t u b f (a -> Schematic Comonad t u b) -> Schematic Comonad t u a -> Schematic Comonad t u b forall (source :: * -> * -> *) (t :: * -> *) a b. Bindable source t => source a (t b) -> source (t a) (t b) =<< Schematic Comonad t u a x instance Extendable (->) (Schematic Comonad t u) => Extendable (->) (t :< u) where (:<) t u a -> b f <<= :: ((:<) t u a -> b) -> (:<) t u a -> (:<) t u b <<= TC Schematic Comonad t u a x = Schematic Comonad t u b -> (:<) t u b forall (t :: * -> *) (u :: * -> *) a. Schematic Comonad t u a -> (:<) t u a TC (Schematic Comonad t u b -> (:<) t u b) -> Schematic Comonad t u b -> (:<) t u b forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) $ (:<) t u a -> b f ((:<) t u a -> b) -> (Schematic Comonad t u a -> (:<) t u a) -> Schematic Comonad t u a -> b forall (m :: * -> * -> *) b c a. Semigroupoid m => m b c -> m a b -> m a c . Schematic Comonad t u a -> (:<) t u a forall (t :: * -> *) (u :: * -> *) a. Schematic Comonad t u a -> (:<) t u a TC (Schematic Comonad t u a -> b) -> Schematic Comonad t u a -> Schematic Comonad t u b forall (source :: * -> * -> *) (t :: * -> *) a b. Extendable source t => source (t a) b -> source (t a) (t b) <<= Schematic Comonad t u a x instance (Extractable_ (t :< u), Extendable (->) (t :< u)) => Comonad (t :< u) (->) where instance Lowerable (->) (Schematic Comonad t) => Lowerable (->) ((:<) t) where lower :: (:<) t u a -> u a lower (TC Schematic Comonad t u a x) = Schematic Comonad t u a -> u a forall (cat :: * -> * -> *) (t :: (* -> *) -> * -> *) (u :: * -> *) a. (Lowerable cat t, Covariant cat cat u) => cat (t u a) (u a) lower Schematic Comonad t u a x instance Hoistable (Schematic Comonad t) => Hoistable ((:<) t) where u ~> v f /|\ :: (u ~> v) -> (t :< u) ~> (t :< v) /|\ TC Schematic Comonad t u a x = Schematic Comonad t v a -> (:<) t v a forall (t :: * -> *) (u :: * -> *) a. Schematic Comonad t u a -> (:<) t u a TC (Schematic Comonad t v a -> (:<) t v a) -> Schematic Comonad t v a -> (:<) t v a forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) $ u ~> v f (u ~> v) -> Schematic Comonad t u a -> Schematic Comonad t v a forall k (t :: (* -> *) -> k -> *) (u :: * -> *) (v :: * -> *). (Hoistable t, Covariant (->) (->) u) => (u ~> v) -> t u ~> t v /|\ Schematic Comonad t u a x instance (Interpreted (Schematic Comonad t u)) => Interpreted (t :< u) where type Primary (t :< u) a = Primary (Schematic Comonad t u) a run :: (:<) t u a -> Primary (t :< u) a run ~(TC Schematic Comonad t u a x) = Schematic Comonad t u a -> Primary (Schematic Comonad t u) a forall (t :: * -> *) a. Interpreted t => t a -> Primary t a run Schematic Comonad t u a x unite :: Primary (t :< u) a -> (:<) t u a unite = Schematic Comonad t u a -> (:<) t u a forall (t :: * -> *) (u :: * -> *) a. Schematic Comonad t u a -> (:<) t u a TC (Schematic Comonad t u a -> (:<) t u a) -> (Primary (Schematic Comonad t u) a -> Schematic Comonad t u a) -> Primary (Schematic Comonad t u) a -> (:<) t u a forall (m :: * -> * -> *) b c a. Semigroupoid m => m b c -> m a b -> m a c . Primary (Schematic Comonad t u) a -> Schematic Comonad t u a forall (t :: * -> *) a. Interpreted t => Primary t a -> t a unite