    {-# LANGUAGE DeriveDataTypeable #-}
    {-# LANGUAGE DeriveGeneric #-}
    {-# LANGUAGE PolyKinds #-}
    {-# LANGUAGE Safe #-}
    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Data.Functor.Product
    -- Copyright   :  (c) Ross Paterson 2010
    -- License     :  BSD-style (see the file LICENSE)
    --
    -- Maintainer  :  libraries@haskell.org
    -- Stability   :  experimental
    -- Portability :  portable
    --
    -- Products, lifted to functors.
    --
    -- @since 4.9.0.0
    -----------------------------------------------------------------------------

    module Data.Functor.Product (
        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.Foldable (Foldable(foldMap))
    import Data.Functor.Classes
    import Data.Monoid (mappend)
    import Data.Traversable (Traversable(traverse))
    import GHC.Generics (Generic, Generic1)

    -- | Lifted product of functors.
    data Product f g a = Pair (f a) (g a)
      deriving (Data, Generic, Generic1)

    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 `mappend` liftCompare comp y1 y2

    instance (Read1 f, Read1 g) => Read1 (Product f g) where
        liftReadsPrec rp rl = readsData $
            readsBinaryWith (liftReadsPrec rp rl) (liftReadsPrec rp rl) "Pair" Pair

    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 (Eq1 f, Eq1 g, Eq a) => Eq (Product f g a)
        where (==) = eq1
    instance (Ord1 f, Ord1 g, Ord a) => Ord (Product f g a) where
        compare = compare1
    instance (Read1 f, Read1 g, Read a) => Read (Product f g a) where
        readsPrec = readsPrec1
    instance (Show1 f, Show1 g, Show a) => Show (Product f g a) where
        showsPrec = showsPrec1

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

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

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

    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)