module Pandora.Paradigm.Primary.Transformer.Instruction where import Pandora.Core.Functor (type (:.), type (:=)) import Pandora.Pattern.Category (($)) import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$>))) import Pandora.Pattern.Functor.Avoidable (Avoidable (empty)) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Alternative (Alternative ((<+>))) import Pandora.Pattern.Functor.Applicative (Applicative ((<*>))) import Pandora.Pattern.Functor.Traversable (Traversable ((->>), (->>>))) import Pandora.Pattern.Functor.Bindable (Bindable ((>>=))) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) data Instruction t a = Enter a | Instruct (t :. Instruction t := a) instance Covariant t => Covariant (Instruction t) where a -> b f <$> :: (a -> b) -> Instruction t a -> Instruction t b <$> Enter a x = b -> Instruction t b forall (t :: * -> *) a. a -> Instruction t a Enter (b -> Instruction t b) -> b -> Instruction t b forall (m :: * -> * -> *) a b. Category m => m a b -> m a b $ a -> b f a x a -> b f <$> Instruct (t :. Instruction t) := a xs = ((t :. Instruction t) := b) -> Instruction t b forall (t :: * -> *) a. ((t :. Instruction t) := a) -> Instruction t a Instruct (((t :. Instruction t) := b) -> Instruction t b) -> ((t :. Instruction t) := b) -> Instruction t b forall (m :: * -> * -> *) a b. Category m => m a b -> m a b $ a -> b f (a -> b) -> ((t :. Instruction t) := a) -> (t :. Instruction t) := b forall (t :: * -> *) (u :: * -> *) a b. (Covariant t, Covariant u) => (a -> b) -> ((t :. u) := a) -> (t :. u) := b <$$> (t :. Instruction t) := a xs instance Covariant t => Pointable (Instruction t) where point :: a |-> Instruction t point = a |-> Instruction t forall (t :: * -> *) a. a -> Instruction t a Enter instance Alternative t => Alternative (Instruction t) where Enter a x <+> :: Instruction t a -> Instruction t a -> Instruction t a <+> Instruction t a _ = a -> Instruction t a forall (t :: * -> *) a. a -> Instruction t a Enter a x Instruction t a _ <+> Enter a y = a -> Instruction t a forall (t :: * -> *) a. a -> Instruction t a Enter a y Instruct (t :. Instruction t) := a xs <+> Instruct (t :. Instruction t) := a ys = ((t :. Instruction t) := a) -> Instruction t a forall (t :: * -> *) a. ((t :. Instruction t) := a) -> Instruction t a Instruct (((t :. Instruction t) := a) -> Instruction t a) -> ((t :. Instruction t) := a) -> Instruction t a forall (m :: * -> * -> *) a b. Category m => m a b -> m a b $ (t :. Instruction t) := a xs ((t :. Instruction t) := a) -> ((t :. Instruction t) := a) -> (t :. Instruction t) := a forall (t :: * -> *) a. Alternative t => t a -> t a -> t a <+> (t :. Instruction t) := a ys instance Avoidable t => Avoidable (Instruction t) where empty :: Instruction t a empty = ((t :. Instruction t) := a) -> Instruction t a forall (t :: * -> *) a. ((t :. Instruction t) := a) -> Instruction t a Instruct (t :. Instruction t) := a forall (t :: * -> *) a. Avoidable t => t a empty instance Covariant t => Applicative (Instruction t) where Enter a -> b f <*> :: Instruction t (a -> b) -> Instruction t a -> Instruction t b <*> Enter a y = 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 a b -> m a b $ a -> b f a y Enter a -> b f <*> Instruct (t :. Instruction t) := a y = ((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 a b -> m a b $ a -> b f (a -> b) -> ((t :. Instruction t) := a) -> (t :. Instruction t) := b forall (t :: * -> *) (u :: * -> *) a b. (Covariant t, Covariant u) => (a -> b) -> ((t :. u) := a) -> (t :. u) := b <$$> (t :. Instruction t) := a y Instruct (t :. Instruction t) := (a -> b) f <*> Instruction t a y = ((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 a b -> m a b $ (Instruction t (a -> b) -> Instruction t a -> Instruction t b forall (t :: * -> *) a b. Applicative t => t (a -> b) -> t a -> t b <*> Instruction t a y) (Instruction t (a -> b) -> Instruction t b) -> ((t :. Instruction t) := (a -> b)) -> (t :. Instruction t) := b forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b <$> (t :. Instruction t) := (a -> b) f instance Covariant t => Bindable (Instruction t) where Enter a x >>= :: Instruction t a -> (a -> Instruction t b) -> Instruction t b >>= a -> Instruction t b f = a -> Instruction t b f a x Instruct (t :. Instruction t) := a xs >>= a -> Instruction t b f = ((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 a b -> m a b $ (Instruction t a -> (a -> Instruction t b) -> Instruction t b forall (t :: * -> *) a b. Bindable t => t a -> (a -> t b) -> t b >>= a -> Instruction t b f) (Instruction t a -> Instruction t b) -> ((t :. Instruction t) := a) -> (t :. Instruction t) := b forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b <$> (t :. Instruction t) := a xs instance Traversable t => Traversable (Instruction t) where Enter a x ->> :: Instruction t a -> (a -> u b) -> (u :. Instruction t) := b ->> a -> u b f = b -> Instruction t b forall (t :: * -> *) a. a -> Instruction t a Enter (b -> Instruction t b) -> u b -> (u :. Instruction t) := b forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b <$> a -> u b f a x Instruct (t :. Instruction t) := a xs ->> a -> u b f = ((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 :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b <$> ((t :. Instruction t) := a xs ((t :. Instruction t) := a) -> (a -> u b) -> u ((t :. Instruction t) := 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 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 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 :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b <$> u a x