module Pandora.Paradigm.Primary.Functor.Constant where

import Pandora.Pattern.Semigroupoid ((.))
import Pandora.Pattern.Category ((<--), (<---))
import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))
import Pandora.Pattern.Functor.Contravariant (Contravariant ((>-|-)))
import Pandora.Pattern.Functor.Invariant (Invariant ((<!<)))
import Pandora.Pattern.Object.Setoid (Setoid ((==)))
import Pandora.Pattern.Object.Chain (Chain ((<=>)))
import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))
import Pandora.Pattern.Object.Monoid (Monoid (zero))
import Pandora.Pattern.Object.Ringoid (Ringoid ((*)))
import Pandora.Pattern.Object.Quasiring (Quasiring (one))
import Pandora.Pattern.Object.Semilattice (Infimum ((/\)), Supremum ((\/)))
import Pandora.Pattern.Object.Lattice (Lattice)
import Pandora.Pattern.Object.Group (Group (invert))
import Pandora.Pattern.Operation.Exponential ()
import Pandora.Pattern.Morphism.Flip (Flip (Flip))

newtype Constant a b = Constant a

instance Covariant (->) (->) (Constant a) where
	_ <-|- Constant x = Constant x

instance Covariant (->) (->) (Flip Constant b) where
	f <-|- Flip (Constant x) = Flip . Constant <-- f x

instance Contravariant (->) (->) (Constant a) where
	_ >-|- Constant x = Constant x

instance Invariant (Constant a) where
	_ <!< _ = \(Constant x) -> Constant x

instance Setoid a => Setoid (Constant a b) where
	Constant x == Constant y = x == y

instance Chain a => Chain (Constant a b) where
	Constant x <=> Constant y = x <=> y

instance Semigroup a => Semigroup (Constant a b) where
	Constant x + Constant y = Constant <-- x + y

instance Monoid a => Monoid (Constant a b) where
	 zero = Constant zero

instance Ringoid a => Ringoid (Constant a b) where
	Constant x * Constant y = Constant <--- x * y

instance Quasiring a => Quasiring (Constant a b) where
	 one = Constant one

instance Infimum a => Infimum (Constant a b) where
	Constant x /\ Constant y = Constant <-- x /\ y

instance Supremum a => Supremum (Constant a b) where
	Constant x \/ Constant y = Constant <-- x \/ y

instance Lattice a => Lattice (Constant a b) where

instance Group a => Group (Constant a b) where
	invert (Constant x) = Constant <-- invert x