module Pandora.Paradigm.Primary.Functor.Maybe where

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 ((<*>), apply))
import Pandora.Pattern.Functor.Traversable (Traversable ((->>)))
import Pandora.Pattern.Functor.Bindable (Bindable ((>>=)))
import Pandora.Pattern.Functor.Monad (Monad)
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.Semilattice (Infimum ((/\)), Supremum ((\/)))
import Pandora.Pattern.Object.Lattice (Lattice)
import Pandora.Paradigm.Primary.Object.Boolean (Boolean (True, False))
import Pandora.Paradigm.Primary.Object.Ordering (Ordering (Less, Equal, Greater))
import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run))
import Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic (Monadic (wrap), (:>) (TM))
import Pandora.Paradigm.Controlflow.Effect.Adaptable (Adaptable (adapt))
import Pandora.Paradigm.Schemes.UT (UT (UT))

data Maybe a = Nothing | Just a

instance Covariant Maybe where
        f <$> Just x = Just $ f x
        _ <$> Nothing = Nothing

instance Pointable Maybe where
        point = Just

instance Avoidable Maybe where
        empty = Nothing

instance Applicative Maybe where
        Just f <*> x = f <$> x
        Nothing <*> _ = Nothing

instance Alternative Maybe where
        Nothing <+> y = y
        Just x <+> _ = Just x

instance Traversable Maybe where
        Nothing ->> _ = point Nothing
        Just x ->> f = Just <$> f x

instance Bindable Maybe where
        Just x >>= f = f x
        Nothing >>= _ = Nothing

instance Monad Maybe where

instance Setoid a => Setoid (Maybe a) where
        Just x == Just y = x == y
        Nothing == Nothing = True
        _ == _ = False

instance Chain a => Chain (Maybe a) where
        Just x <=> Just y = x <=> y
        Nothing <=> Nothing = Equal
        Nothing <=> Just _ = Less
        Just _ <=> Nothing = Greater

instance Semigroup a => Semigroup (Maybe a) where
        Just x + Just y = Just $ x + y
        Nothing + x = x
        x + Nothing = x

instance Semigroup a => Monoid (Maybe a) where
        zero = Nothing

instance Infimum a => Infimum (Maybe a) where
        Just x /\ Just y = Just $ x /\ y
        _ /\ Nothing = Nothing
        Nothing /\ _ = Nothing

instance Supremum a => Supremum (Maybe a) where
        Just x \/ Just y = Just $ x \/ y
        x \/ Nothing = x
        Nothing \/ x = x

instance Lattice a => Lattice (Maybe a) where

maybe :: b -> (a -> b) -> Maybe a -> b
maybe x _ Nothing = x
maybe _ f (Just y) = f y

-- type instance Schematic Monad Maybe u = UT Covariant Covariant Maybe u
type instance Schematic Monad Maybe = UT Covariant Covariant Maybe

instance Interpreted Maybe where
        type Primary Maybe a = Maybe a
        run x = x

instance Monadic Maybe where
        wrap x = TM . UT . point $ x

type Optional = Adaptable Maybe

instance Covariant u => Covariant (UT Covariant Covariant Maybe u) where
        f <$> UT x = UT $ f <$$> x

instance Applicative u => Applicative (UT Covariant Covariant Maybe u) where
        UT f <*> UT x = UT $ apply <$> f <*> x

instance Pointable u => Pointable (UT Covariant Covariant Maybe u) where
        point = UT . point . point

instance (Pointable u, Bindable u) => Bindable (UT Covariant Covariant Maybe u) where
        UT x >>= f = UT $ x >>= maybe (point Nothing) (run . f)

instance Monad u => Monad (UT Covariant Covariant Maybe u) where

nothing :: Optional t => t a
nothing = adapt Nothing