Prefixed.hs

{-# OPTIONS_GHC -fno-warn-orphans #-}
{-# LANGUAGE UndecidableInstances #-}

module Pandora.Paradigm.Structure.Modification.Prefixed where

import Pandora.Core.Functor (type (:.), type (:=))
import Pandora.Pattern.Semigroupoid ((.))
import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)), (<-|-|-))
import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)), (-<<-<<-))
import Pandora.Paradigm.Primary.Algebraic (extract)
import Pandora.Paradigm.Primary.Algebraic.Product ((:*:))
import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (||=)))
import Pandora.Paradigm.Structure.Ability.Morphable (Morphable (Morphing, morphing), Morph (Into), premorph)
import Pandora.Paradigm.Structure.Ability.Nonempty (Nonempty)

newtype Prefixed t k a = Prefixed (t :. (:*:) k := a)

instance Interpreted (->) (Prefixed t k) where
	type Primary (Prefixed t k) a = t :. (:*:) k := a
	run ~(Prefixed x) = x
	unite = Prefixed

-- TODO: Try to generalize (->) here
instance Covariant (->) (->) t => Covariant (->) (->) (Prefixed t k) where
	(<-|-) f = (||=) (f <-|-|-)

instance Traversable (->) (->) t => Traversable (->) (->) (Prefixed t k) where
	f <<- Prefixed x = Prefixed <-|- f -<<-<<- x

instance Covariant (->) (->) t => Morphable (Into t) (Prefixed t k) where
	type Morphing (Into t) (Prefixed t k) = t
	morphing (run . premorph -> prefixed) = extract <-|- prefixed

type instance Nonempty (Prefixed t k) = Prefixed (Nonempty t) k