{-# 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)
import Text.Read (Read(..), readListDefault, readListPrecDefault)

-- | Lifted product of functors.
data Product f g a = Pair (f a) (g a)
  deriving ( Data     -- ^ @since 4.9.0.0
           , Generic  -- ^ @since 4.9.0.0
           , Generic1 -- ^ @since 4.9.0.0
           )

-- | @since 4.9.0.0
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

-- | @since 4.9.0.0
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

-- | @since 4.9.0.0
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

-- | @since 4.9.0.0
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

-- | @since 4.9.0.0
instance (Eq1 f, Eq1 g, Eq a) => Eq (Product f g a)
    where (==) = eq1

-- | @since 4.9.0.0
instance (Ord1 f, Ord1 g, Ord a) => Ord (Product f g a) where
    compare = compare1

-- | @since 4.9.0.0
instance (Read1 f, Read1 g, Read a) => Read (Product f g a) where
    readPrec = readPrec1

    readListPrec = readListPrecDefault
    readList     = readListDefault

-- | @since 4.9.0.0
instance (Show1 f, Show1 g, Show a) => Show (Product f g a) where
    showsPrec = showsPrec1

-- | @since 4.9.0.0
instance (Functor f, Functor g) => Functor (Product f g) where
    fmap f (Pair x y) = Pair (fmap f x) (fmap f y)

-- | @since 4.9.0.0
instance (Foldable f, Foldable g) => Foldable (Product f g) where
    foldMap f (Pair x y) = foldMap f x `mappend` foldMap f y

-- | @since 4.9.0.0
instance (Traversable f, Traversable g) => Traversable (Product f g) where
    traverse f (Pair x y) = liftA2 Pair (traverse f x) (traverse f y)

-- | @since 4.9.0.0
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)

-- | @since 4.9.0.0
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)

-- | @since 4.9.0.0
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

-- | @since 4.9.0.0
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)

-- | @since 4.9.0.0
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

-- | @since 4.9.0.0
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)