{-# LANGUAGE UndecidableInstances #-} module Pandora.Paradigm.Primary.Transformer.Instruction 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.Semimonoidal (Semimonoidal (multiply_)) 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 ((/|\), hoist)) import Pandora.Paradigm.Primary.Algebraic.Exponential () import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)((:*:))) 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 (t :: * -> *) (u :: * -> *) (category :: * -> * -> *) a b. (Covariant u category category, Covariant t category category) => category a b -> category (t (u a)) (t (u b)) -<$$>- (t :. Instruction t) := a xs instance Covariant t (->) (->) => Pointable (Instruction t) (->) where point :: a -> Instruction t a point = a -> Instruction t a forall (t :: * -> *) a. a -> Instruction t a Enter instance (Covariant t (->) (->), Semimonoidal t (->) (:*:) (:*:)) => Semimonoidal (Instruction t) (->) (:*:) (:*:) where multiply_ :: (Instruction t a :*: Instruction t b) -> Instruction t (a :*: b) multiply_ (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 multiply_ (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 (t :: * -> *) (source :: * -> * -> *) (target :: * -> * -> *) a b. Covariant t source target => source a b -> target (t a) (t b) -<$>- ((t :. Instruction t) := b) -> Instruction t b forall (t :: * -> *) a. ((t :. Instruction t) := a) -> Instruction t a Instruct (t :. Instruction t) := b y multiply_ (Instruct (t :. Instruction t) := a x :*: Enter b y) = (a -> b -> a :*: b forall s a. s -> a -> s :*: a :*: b y) (a -> a :*: b) -> Instruction t a -> Instruction t (a :*: b) forall (t :: * -> *) (source :: * -> * -> *) (target :: * -> * -> *) a b. Covariant t source target => source a b -> target (t a) (t b) -<$>- ((t :. Instruction t) := a) -> Instruction t a forall (t :: * -> *) a. ((t :. Instruction t) := a) -> Instruction t a Instruct (t :. Instruction t) := a x multiply_ (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 (t :: k -> *) (p :: * -> * -> *) (source :: * -> * -> *) (target :: k -> k -> k) (a :: k) (b :: k). Semimonoidal t p source target => p (source (t a) (t b)) (t (target a b)) forall (target :: * -> * -> *) a b. Semimonoidal (Instruction t) (->) (:*:) target => (Instruction t a :*: Instruction t b) -> Instruction t (target a b) multiply_ @_ @(->) @(:*:) ((Instruction t a :*: Instruction t b) -> Instruction t (a :*: b)) -> t (Instruction t a :*: Instruction t b) -> (t :. Instruction t) := (a :*: b) forall (t :: * -> *) (source :: * -> * -> *) (target :: * -> * -> *) a b. Covariant t source target => source a b -> target (t a) (t b) -<$>- (((t :. Instruction t) := a) :*: ((t :. Instruction t) := b)) -> t (Instruction t a :*: Instruction t b) forall k (t :: k -> *) (p :: * -> * -> *) (source :: * -> * -> *) (target :: k -> k -> k) (a :: k) (b :: k). Semimonoidal t p source target => p (source (t a) (t b)) (t (target a b)) multiply_ ((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 (->) (->) => 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 (t :: * -> *) (source :: * -> * -> *) a b. Bindable t source => source a (t b) -> source (t a) (t b) =<<) (Instruction t a -> Instruction t b) -> ((t :. Instruction t) := a) -> (t :. Instruction t) := b forall (t :: * -> *) (source :: * -> * -> *) (target :: * -> * -> *) a b. Covariant t source target => source a b -> target (t a) (t b) -<$>- (t :. Instruction t) := a xs instance Monad t => Monad (Instruction t) where instance Traversable t (->) (->) => Traversable (Instruction t) (->) (->) where a -> u b f <<- :: (a -> u b) -> Instruction t a -> u (Instruction t b) <<- Enter a x = b -> Instruction t b forall (t :: * -> *) a. a -> Instruction t a Enter (b -> Instruction t b) -> u b -> u (Instruction t b) forall (t :: * -> *) (source :: * -> * -> *) (target :: * -> * -> *) a b. Covariant t source target => source a b -> target (t a) (t b) -<$>- 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 (t :: * -> *) (source :: * -> * -> *) (target :: * -> * -> *) a b. Covariant t source target => 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 t category category, Covariant u category category, Pointable u category, Semimonoidal u category (:*:) (:*:), Traversable v category category) => category a (u b) -> category (v (t a)) (u (v (t b))) -<<-<<- (t :. Instruction t) := a xs instance Liftable Instruction where lift :: u ~> Instruction u 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 (t :: * -> *) (source :: * -> * -> *) (target :: * -> * -> *) a b. Covariant t source target => source a b -> target (t a) (t b) -<$>- u a x instance (forall t . Bindable t (->), forall t . Pointable t (->)) => Lowerable Instruction where lower :: Instruction u ~> u lower (Enter a x) = a -> u a forall (t :: * -> *) (source :: * -> * -> *) a. Pointable t source => source a (t a) point a x lower (Instruct (u :. Instruction u) := a xs) = Instruction u a -> u a forall (t :: (* -> *) -> * -> *) (u :: * -> *). (Lowerable t, Covariant u (->) (->)) => t u ~> u lower (Instruction u a -> u a) -> ((u :. Instruction u) := a) -> u a forall (t :: * -> *) (source :: * -> * -> *) a b. Bindable t source => source a (t b) -> source (t a) (t b) =<< (u :. Instruction u) := a xs instance (forall v . Covariant v (->) (->)) => Hoistable Instruction where u ~> v _ /|\ :: (u ~> v) -> Instruction u ~> Instruction v /|\ Enter a x = a -> Instruction v a forall (t :: * -> *) a. a -> Instruction t a Enter a x u ~> v 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) $ (u ~> v) -> Instruction u ~> Instruction v forall k (t :: (* -> *) -> k -> *) (u :: * -> *) (v :: * -> *). (Hoistable t, Covariant u (->) (->)) => (u ~> v) -> t u ~> t v hoist u ~> v f (Instruction u a -> Instruction v a) -> v (Instruction u a) -> (v :. Instruction v) := a forall (t :: * -> *) (source :: * -> * -> *) (target :: * -> * -> *) a b. Covariant t source target => source a b -> target (t a) (t b) -<$>- ((u :. Instruction u) := a) -> v (Instruction u a) u ~> v f (u :. Instruction u) := a xs