    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Data.Bifunctor.Product
    -- Copyright   :  (C) 2008-2013 Jesse Selover,
    -- License     :  BSD-style (see the file LICENSE)
    --
    -- Maintainer  :  Edward Kmett <ekmett@gmail.com>
    -- Stability   :  provisional
    -- Portability :  portable
    --
    -- The product of two bifunctors.
    ----------------------------------------------------------------------------
    module Data.Bifunctor.Product
      ( Product(..)
      ) where

    import Control.Applicative
    import Data.Biapplicative
    import Data.Functor.Apply
    import Data.Bifoldable
    import Data.Bitraversable
    import Data.Monoid hiding (Product, (<>))
    import Data.Semigroup hiding (Product)
    import Data.Semigroup.Bifoldable
    import Data.Semigroup.Bitraversable

    -- | Form the product of two bifunctors
    data Product f g a b = Pair (f a b) (g a b) deriving (Eq,Ord,Show,Read)

    instance (Bifunctor f, Bifunctor g) => Bifunctor (Product f g) where
      first f (Pair x y) = Pair (first f x) (first f y)
      {-# INLINE first #-}
      second g (Pair x y) = Pair (second g x) (second g y)
      {-# INLINE second #-}
      bimap f g (Pair x y) = Pair (bimap f g x) (bimap f g y)
      {-# INLINE bimap #-}

    instance (Biapplicative f, Biapplicative g) => Biapplicative (Product f g) where
      bipure a b = Pair (bipure a b) (bipure a b)
      {-# INLINE bipure #-}
      Pair w x <<*>> Pair y z = Pair (w <<*>> y) (x <<*>> z)
      {-# INLINE (<<*>>) #-}

    instance (Bifoldable f, Bifoldable g) => Bifoldable (Product f g) where
      bifoldMap f g (Pair x y) = bifoldMap f g x `mappend` bifoldMap f g y
      {-# INLINE bifoldMap #-}

    instance (Bitraversable f, Bitraversable g) => Bitraversable (Product f g) where
      bitraverse f g (Pair x y) = Pair <$> bitraverse f g x <*> bitraverse f g y
      {-# INLINE bitraverse #-}

    instance (Bifoldable1 f, Bifoldable1 g) => Bifoldable1 (Product f g) where
      bifoldMap1 f g (Pair x y) = bifoldMap1 f g x <> bifoldMap1 f g y
      {-# INLINE bifoldMap1 #-}

    instance (Bitraversable1 f, Bitraversable1 g) => Bitraversable1 (Product f g) where
      bitraverse1 f g (Pair x y) = Pair <$> bitraverse1 f g x <.> bitraverse1 f g y
      {-# INLINE bitraverse1 #-}