{-# LANGUAGE UndecidableInstances #-} module Pandora.Paradigm.Primary.Transformer.Instruction where import Pandora.Core.Functor (type (:.), type (>>>)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category ((<--), (<---), (<----), (<-----), (<------)) import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|--), (<-|---), (<-|-|-))) import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)), (<<-<<-)) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\))) import Pandora.Paradigm.Algebraic.Exponential (type (-->)) import Pandora.Paradigm.Algebraic.Product ((:*:)((:*:))) import Pandora.Paradigm.Algebraic.One (One (One)) import Pandora.Paradigm.Algebraic (point) import Pandora.Core.Interpreted ((<~), (<~~~)) data Instruction t a = Enter a | Instruct (t :. Instruction t >>> a) instance Covariant (->) (->) t => Covariant (->) (->) (Instruction t) where a -> b f <-|- :: (a -> b) -> Instruction t a -> Instruction t b <-|- Enter a x = b -> Instruction t b forall (t :: * -> *) a. a -> Instruction t a Enter (b -> Instruction t b) -> b -> Instruction t b forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) <-- a -> b f a x a -> b f <-|- Instruct (t :. Instruction t) >>> a xs = ((t :. Instruction t) >>> b) -> Instruction t b forall (t :: * -> *) a. ((t :. Instruction t) >>> a) -> Instruction t a Instruct (((t :. Instruction t) >>> b) -> Instruction t b) -> ((t :. Instruction t) >>> b) -> Instruction t b forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) <------ a -> b f (a -> b) -> ((t :. Instruction t) >>> a) -> (t :. Instruction t) >>> b forall (source :: * -> * -> *) (target :: * -> * -> *) (t :: * -> *) (u :: * -> *) a b. (Covariant source target t, Covariant source (Betwixt source target) u, Covariant (Betwixt source target) target t) => source a b -> target (t (u a)) (t (u b)) <-|-|- (t :. Instruction t) >>> a xs instance (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => Semimonoidal (-->) (:*:) (:*:) (Instruction t) where mult :: (Instruction t a :*: Instruction t b) --> Instruction t (a :*: b) mult = ((Instruction t a :*: Instruction t b) -> Instruction t (a :*: b)) -> (Instruction t a :*: Instruction t b) --> Instruction t (a :*: b) forall (v :: * -> * -> *) a e. v a e -> Straight v a e Straight (((Instruction t a :*: Instruction t b) -> Instruction t (a :*: b)) -> (Instruction t a :*: Instruction t b) --> Instruction t (a :*: b)) -> ((Instruction t a :*: Instruction t b) -> Instruction t (a :*: b)) -> (Instruction t a :*: Instruction t b) --> Instruction t (a :*: b) forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) <-- \case Enter a x :*: Enter b y -> (a :*: b) -> Instruction t (a :*: b) forall (t :: * -> *) a. a -> Instruction t a Enter ((a :*: b) -> Instruction t (a :*: b)) -> (a :*: b) -> Instruction t (a :*: b) forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) <--- a x a -> b -> a :*: b forall s a. s -> a -> s :*: a :*: b y Enter a x :*: Instruct (t :. Instruction t) >>> b y -> (a x a -> b -> a :*: b forall s a. s -> a -> s :*: a :*:) (b -> a :*: b) -> Instruction t b -> Instruction t (a :*: b) forall (source :: * -> * -> *) (target :: * -> * -> *) (t :: * -> *) a b. Covariant source target t => source a b -> target (t a) (t b) <-|- ((t :. Instruction t) >>> b) -> Instruction t b forall (t :: * -> *) a. ((t :. Instruction t) >>> a) -> Instruction t a Instruct (t :. Instruction t) >>> b y Instruct (t :. Instruction t) >>> a x :*: Enter b y -> (a -> b -> a :*: b forall s a. s -> a -> s :*: a :*: b y) (a -> a :*: b) -> Instruction t a -> Instruction t (a :*: b) forall (source :: * -> * -> *) (target :: * -> * -> *) (t :: * -> *) a b. Covariant source target t => source a b -> target (t a) (t b) <-|- ((t :. Instruction t) >>> a) -> Instruction t a forall (t :: * -> *) a. ((t :. Instruction t) >>> a) -> Instruction t a Instruct (t :. Instruction t) >>> a x Instruct (t :. Instruction t) >>> a x :*: Instruct (t :. Instruction t) >>> b y -> ((t :. Instruction t) >>> (a :*: b)) -> Instruction t (a :*: b) forall (t :: * -> *) a. ((t :. Instruction t) >>> a) -> Instruction t a Instruct (((t :. Instruction t) >>> (a :*: b)) -> Instruction t (a :*: b)) -> ((t :. Instruction t) >>> (a :*: b)) -> Instruction t (a :*: b) forall (m :: * -> * -> *) a b. Category m => m (m a b) (m 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)) forall (source :: * -> * -> *) (target :: * -> * -> *) (t :: * -> *) a b. Semimonoidal (-->) source target t => source (t a) (t b) --> t (target a b) mult @(-->) ((Instruction t a :*: Instruction t b) --> Instruction t (a :*: b)) -> (Instruction t a :*: Instruction t b) -> Instruction t (a :*: b) forall (m :: * -> * -> *) (t :: * -> *) a. Interpreted m t => (m < t a) < Primary t a <~) ((Instruction t a :*: Instruction t b) -> Instruction t (a :*: b)) -> t (Instruction t a :*: Instruction t b) -> (t :. Instruction t) >>> (a :*: b) forall (source :: * -> * -> *) (target :: * -> * -> *) (t :: * -> *) a b. Covariant source target t => source a b -> target (t a) (t 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)) forall (source :: * -> * -> *) (target :: * -> * -> *) (t :: * -> *) a b. Semimonoidal (-->) source target t => source (t a) (t b) --> t (target a b) mult @(-->) ((((t :. Instruction t) >>> a) :*: ((t :. Instruction t) >>> b)) --> t (Instruction t a :*: Instruction t b)) -> (((t :. Instruction t) >>> a) :*: ((t :. Instruction t) >>> b)) -> t (Instruction t a :*: Instruction t b) forall (m :: * -> * -> *) (t :: * -> *) a. Interpreted m t => (m < t a) < Primary t a <~~~ (t :. Instruction t) >>> a x ((t :. Instruction t) >>> a) -> ((t :. Instruction t) >>> b) -> ((t :. Instruction t) >>> a) :*: ((t :. Instruction t) >>> b) forall s a. s -> a -> s :*: a :*: (t :. Instruction t) >>> b y instance (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => Monoidal (-->) (-->) (:*:) (:*:) (Instruction t) where unit :: Proxy (:*:) -> (Unit (:*:) --> a) --> Instruction t a unit Proxy (:*:) _ = (Straight (->) One a -> Instruction t a) -> Straight (->) (Straight (->) One a) (Instruction t a) forall (v :: * -> * -> *) a e. v a e -> Straight v a e Straight ((Straight (->) One a -> Instruction t a) -> Straight (->) (Straight (->) One a) (Instruction t a)) -> (Straight (->) One a -> Instruction t a) -> Straight (->) (Straight (->) One a) (Instruction t a) forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) <-- a -> Instruction t a forall (t :: * -> *) a. a -> Instruction t a Enter (a -> Instruction t a) -> (Straight (->) One a -> a) -> Straight (->) One a -> Instruction t a forall (m :: * -> * -> *) b c a. Semigroupoid m => m b c -> m a b -> m a c . (Straight (->) One a -> One -> a forall (m :: * -> * -> *) (t :: * -> *) a. Interpreted m t => (m < t a) < Primary t a <~ One One) instance Covariant (->) (->) t => Bindable (->) (Instruction t) where a -> Instruction t b f =<< :: (a -> Instruction t b) -> Instruction t a -> Instruction t b =<< Enter a x = a -> Instruction t b f a x a -> Instruction t b f =<< Instruct (t :. Instruction t) >>> a xs = ((t :. Instruction t) >>> b) -> Instruction t b forall (t :: * -> *) a. ((t :. Instruction t) >>> a) -> Instruction t a Instruct (((t :. Instruction t) >>> b) -> Instruction t b) -> ((t :. Instruction t) >>> b) -> Instruction t b forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) <---- (a -> Instruction t b f (a -> Instruction t b) -> Instruction t a -> Instruction t b forall (source :: * -> * -> *) (t :: * -> *) a b. Bindable source t => source a (t b) -> source (t a) (t b) =<<) (Instruction t a -> Instruction t b) -> ((t :. Instruction t) >>> a) -> (t :. Instruction t) >>> b forall (source :: * -> * -> *) (target :: * -> * -> *) (t :: * -> *) a b. Covariant source target t => source a b -> target (t a) (t b) <-|- (t :. Instruction t) >>> a xs instance Monad (->) t => Monad (->) (Instruction t) where instance Traversable (->) (->) t => Traversable (->) (->) (Instruction t) where a -> u b f <<- :: (a -> u b) -> Instruction t a -> u (Instruction t b) <<- Enter a x = b -> Instruction t b forall (t :: * -> *) a. a -> Instruction t a Enter (b -> Instruction t b) -> u b -> u (Instruction t b) forall (source :: * -> * -> *) (target :: * -> * -> *) (t :: * -> *) a b. Covariant source target t => source a b -> target (t a) (t b) <-|- a -> u b f a x a -> u b f <<- Instruct (t :. Instruction t) >>> a xs = ((t :. Instruction t) >>> b) -> Instruction t b forall (t :: * -> *) a. ((t :. Instruction t) >>> a) -> Instruction t a Instruct (((t :. Instruction t) >>> b) -> Instruction t b) -> u ((t :. Instruction t) >>> b) -> u (Instruction t 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) -> ((t :. Instruction t) >>> a) -> u ((t :. Instruction t) >>> b) forall (t :: * -> *) (u :: * -> *) (v :: * -> *) (category :: * -> * -> *) a b. (Traversable category category t, Covariant category category u, Monoidal (Straight category) (Straight category) (:*:) (:*:) u, Traversable category category v) => category a (u b) -> category (v (t a)) (u (v (t b))) <<-<<- (t :. Instruction t) >>> a xs) instance Liftable (->) Instruction where lift :: u a -> Instruction u a lift u a x = ((u :. Instruction u) >>> a) -> Instruction u a forall (t :: * -> *) a. ((t :. Instruction t) >>> a) -> Instruction t a Instruct (((u :. Instruction u) >>> a) -> Instruction u a) -> ((u :. Instruction u) >>> a) -> Instruction u a forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) <---- a -> Instruction u a forall (t :: * -> *) a. a -> Instruction t a Enter (a -> Instruction u a) -> u a -> (u :. Instruction u) >>> a forall (source :: * -> * -> *) (target :: * -> * -> *) (t :: * -> *) a b. Covariant source target t => source a b -> target (t a) (t b) <-|- u a x instance (forall t . Bindable (->) t, forall t . Monoidal (-->) (-->) (:*:) (:*:) t) => Lowerable (->) Instruction where lower :: Instruction u a -> u a lower (Enter a x) = a -> u a forall (t :: * -> *) a. Pointable t => a -> t a point a x lower (Instruct (u :. Instruction u) >>> a xs) = Instruction u a -> u a forall (cat :: * -> * -> *) (t :: (* -> *) -> * -> *) (u :: * -> *) a. (Lowerable cat t, Covariant cat cat u) => cat (t u a) (u a) lower (Instruction u a -> u a) -> ((u :. Instruction u) >>> a) -> u a forall (source :: * -> * -> *) (t :: * -> *) a b. Bindable source t => source a (t b) -> source (t a) (t b) =<< (u :. Instruction u) >>> a xs instance (forall v . Covariant (->) (->) v) => Hoistable (->) Instruction where forall a. u a -> v a _ /|\ :: (forall a. u a -> v a) -> forall a. Instruction u a -> Instruction v a /|\ Enter a x = a -> Instruction v a forall (t :: * -> *) a. a -> Instruction t a Enter a x forall a. u a -> v a f /|\ Instruct (u :. Instruction u) >>> a xs = ((v :. Instruction v) >>> a) -> Instruction v a forall (t :: * -> *) a. ((t :. Instruction t) >>> a) -> Instruction t a Instruct (((v :. Instruction v) >>> a) -> Instruction v a) -> ((v :. Instruction v) >>> a) -> Instruction v a forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b) <---- (forall a. u a -> v a f (forall a. u a -> v a) -> Instruction u a -> Instruction v a forall k (m :: * -> * -> *) (t :: (* -> *) -> k -> *) (u :: * -> *) (v :: * -> *). (Hoistable m t, Covariant m m u) => (forall a. m (u a) (v a)) -> forall (a :: k). m (t u a) (t v a) /|\) (Instruction u a -> Instruction v a) -> v (Instruction u a) -> (v :. Instruction v) >>> a forall (source :: * -> * -> *) (target :: * -> * -> *) (t :: * -> *) a b. Covariant source target t => source a b -> target (t a) (t b) <-|- ((u :. Instruction u) >>> a) -> v (Instruction u a) forall a. u a -> v a f (u :. Instruction u) >>> a xs