Validation.hs

module Pandora.Paradigm.Primary.Functor.Validation where

import Pandora.Pattern.Semigroupoid ((.))
import Pandora.Pattern.Category (($), (#))
import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))
import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult))
import Pandora.Pattern.Functor.Monoidal (Monoidal (unit))
import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)))
import Pandora.Pattern.Functor.Bivariant (Bivariant ((<->)))
import Pandora.Pattern.Object.Setoid (Setoid ((==)))
import Pandora.Pattern.Object.Chain (Chain ((<=>)))
import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))
import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->))
import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))
import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:) (Option, Adoption))
import Pandora.Paradigm.Primary.Algebraic.One (One (One))
import Pandora.Paradigm.Primary.Algebraic (point)
import Pandora.Pattern.Morphism.Flip (Flip (Flip))
import Pandora.Pattern.Morphism.Straight (Straight (Straight))
import Pandora.Paradigm.Primary.Object.Boolean (Boolean (False))
import Pandora.Paradigm.Primary.Object.Ordering (Ordering (Less, Greater))

data Validation e a = Flaws e | Validated a

instance Covariant (->) (->) (Validation e) where
	_ <$> Flaws e = Flaws e
	f <$> Validated x = Validated $ f x
	_ <$> Flaws e = Flaws e
	f <$> Validated x = Validated $ f x
	_ <$> Flaws e = Flaws e
	f <$> Validated x = Validated $ f x

instance Covariant (->) (->) (Flip Validation a) where
	f <$> Flip (Flaws e) = Flip . Flaws $ f e
	_ <$> Flip (Validated x) = Flip $ Validated x
	f <$> Flip (Flaws e) = Flip . Flaws $ f e
	_ <$> Flip (Validated x) = Flip $ Validated x
	f <$> Flip (Flaws e) = Flip . Flaws $ f e
	_ <$> Flip (Validated x) = Flip $ Validated x

instance Semigroup e => Semimonoidal (-->) (:*:) (:*:) (Validation e) where
	mult = Straight $ \case
		Validated x :*: Validated y -> Validated $ x :*: y
		Flaws x :*: Flaws y -> Flaws $ x + y
		Validated _ :*: Flaws y -> Flaws y
		Flaws x :*: Validated _ -> Flaws x

instance Semigroup e => Monoidal (-->) (->) (:*:) (:*:) (Validation e) where
	unit _ = Straight $ Validated . ($ One)

instance Semigroup e => Semimonoidal (-->) (:*:) (:+:) (Validation e) where
	mult = Straight $ \case
		Flaws _ :*: y -> Adoption <$> y
		Validated x :*: _ -> Option <$> Validated x

instance Traversable (->) (->) (Validation e) where
	f <<- Validated x = Validated <$> f x
	_ <<- Flaws e = point $ Flaws e

instance Bivariant (->) (->) (->) Validation where
	f <-> g = validation # Flaws . f # Validated . g

instance (Setoid e, Setoid a) => Setoid (Validation e a) where
	Validated x == Validated y = x == y
	Flaws x == Flaws y = x == y
	_ == _ = False

instance (Chain e, Chain a) => Chain (Validation e a) where
	Validated x <=> Validated y = x <=> y
	Flaws x <=> Flaws y = x <=> y
	Flaws _ <=> Validated _ = Less
	Validated _ <=> Flaws _ = Greater

instance (Semigroup e, Semigroup a) => Semigroup (Validation e a) where
	Validated x + Validated y = Validated $ x + y
	Flaws x + Flaws y = Flaws $ x + y
	Flaws _ + Validated y = Validated y
	Validated x + Flaws _ = Validated x

validation :: (e -> r) -> (a -> r) -> Validation e a -> r
validation f _ (Flaws x) = f x
validation _ s (Validated x) = s x