-- | @PolyKinds@ variant of base's `Data.Functor.Product.Product`.
--
-- Note that to some extent base's `Product` is already poly-kinded,
-- but it has problematic type class instances which are not poly-kinded.
-- Furthermore, the mere existence of the non poly-kinded instances disallows
-- orphan instances declaration of proper poly-kinded instances.
--
-- If/when `Product` from base will be fixed
-- (see https://gitlab.haskell.org/ghc/ghc/issues/17015 for more details)
-- this module will be removed and its uses will be replaced with `Product` from base.

{-# LANGUAGE DeriveDataTypeable, PolyKinds, Safe #-}

module Data.Functor.Product.PolyKinds (Product(..)) where

import Control.Applicative
import Control.Monad (MonadPlus(..))
import Control.Monad.Fix (MonadFix(..))
import Control.Monad.Zip (MonadZip(mzipWith))
import Data.Data (Data)
import Data.Functor.Classes
import GHC.Generics (Generic, Generic1)

import Prelude.Compat

-- | A @PolyKinds@ variant of 'Data.Functor.Product.Product'.
--
-- Note that the original 'Data.Functor.Product.Product' is poly-kinded
-- in its type, but not in its instances such as 'Eq'.
data Product f g a = Pair (f a) (g a)
    deriving (Data, Generic, Generic1, Eq, Ord, Read, Show)

instance (Eq1 f, Eq1 g) => Eq1 (Product f g) where
    liftEq eq (Pair x1 y1) (Pair x2 y2) = liftEq eq x1 x2 && liftEq eq y1 y2

instance (Ord1 f, Ord1 g) => Ord1 (Product f g) where
    liftCompare comp (Pair x1 y1) (Pair x2 y2) =
        liftCompare comp x1 x2 <> liftCompare comp y1 y2

instance (Read1 f, Read1 g) => Read1 (Product f g) where
    liftReadPrec rp rl =
        readData $
        readBinaryWith (liftReadPrec rp rl) (liftReadPrec rp rl) "Pair" Pair

    liftReadListPrec = liftReadListPrecDefault
    liftReadList     = liftReadListDefault

instance (Show1 f, Show1 g) => Show1 (Product f g) where
    liftShowsPrec sp sl d (Pair x y) =
        showsBinaryWith (liftShowsPrec sp sl) (liftShowsPrec sp sl) "Pair" d x y

instance (Functor f, Functor g) => Functor (Product f g) where
    fmap f (Pair x y) = Pair (fmap f x) (fmap f y)
    a <$ (Pair x y) = Pair (a <$ x) (a <$ y)

instance (Foldable f, Foldable g) => Foldable (Product f g) where
    foldMap f (Pair x y) = foldMap f x <> foldMap f y

instance (Traversable f, Traversable g) => Traversable (Product f g) where
    traverse f (Pair x y) = liftA2 Pair (traverse f x) (traverse f y)

instance (Applicative f, Applicative g) => Applicative (Product f g) where
    pure x = Pair (pure x) (pure x)
    Pair f g <*> Pair x y = Pair (f <*> x) (g <*> y)
    liftA2 f (Pair a b) (Pair x y) = Pair (liftA2 f a x) (liftA2 f b y)

instance (Alternative f, Alternative g) => Alternative (Product f g) where
    empty = Pair empty empty
    Pair x1 y1 <|> Pair x2 y2 = Pair (x1 <|> x2) (y1 <|> y2)

instance (Monad f, Monad g) => Monad (Product f g) where
    Pair m n >>= f =
        Pair (m >>= fstP . f) (n >>= sndP . f)
        where
            fstP (Pair a _) = a
            sndP (Pair _ b) = b

instance (MonadPlus f, MonadPlus g) => MonadPlus (Product f g) where
    mzero = Pair mzero mzero
    Pair x1 y1 `mplus` Pair x2 y2 = Pair (x1 `mplus` x2) (y1 `mplus` y2)

instance (MonadFix f, MonadFix g) => MonadFix (Product f g) where
    mfix f =
        Pair (mfix (fstP . f)) (mfix (sndP . f))
        where
            fstP (Pair a _) = a
            sndP (Pair _ b) = b

instance (MonadZip f, MonadZip g) => MonadZip (Product f g) where
    mzipWith f (Pair x1 y1) (Pair x2 y2) = Pair (mzipWith f x1 x2) (mzipWith f y1 y2)