{-# LANGUAGE DeriveDataTypeable #-}{-# LANGUAGE DeriveGeneric #-}{-# LANGUAGE PolyKinds #-}{-# LANGUAGE Safe #-}{-# LANGUAGE StandaloneDeriving #-}------------------------------------------------------------------------------- |-- Module : Data.Functor.Product-- Copyright : (c) Ross Paterson 2010-- License : BSD-style (see the file LICENSE)---- Maintainer : libraries@haskell.org-- Stability : stable-- Portability : portable---- Products, lifted to functors.---- @since 4.9.0.0-----------------------------------------------------------------------------moduleData.Functor.Product (Product (..),)whereimportControl.Applicative importGHC.Internal.Control.Monad (MonadPlus (..))importGHC.Internal.Control.Monad.Fix (MonadFix (..))importControl.Monad.Zip (MonadZip (mzipWith ))importGHC.Internal.Data.Data (Data )importData.Functor.Classes importGHC.Generics (Generic ,Generic1 )importPrelude -- $setup-- >>> import Prelude-- | Lifted product of functors.---- ==== __Examples__---- >>> fmap (+1) (Pair [1, 2, 3] (Just 0))-- Pair [2,3,4] (Just 1)---- >>> Pair "Hello, " (Left 'x') <> Pair "World" (Right 'y')-- Pair "Hello, World" (Right 'y')dataProduct f g a =Pair (f a )(g a )deriving(Typeable (Product f g a)
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forall m a. Monoid m => (a -> m) -> f a -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap a -> m
f f a
x m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` (a -> m) -> g a -> m
forall m a. Monoid m => (a -> m) -> g a -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap a -> m
f g a
y -- | @since 4.9.0.0instance(Traversable f ,Traversable g )=>Traversable (Product f g )wheretraverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> Product f g a -> f (Product f g b)
traverse a -> f b
f (Pair f a
x g a
y )=(f b -> g b -> Product f g b)
-> f (f b) -> f (g b) -> f (Product f g b)
forall a b c. (a -> b -> c) -> f a -> f b -> f c
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 f b -> g b -> Product f g b
forall {k} (f :: k -> *) (g :: k -> *) (a :: k).
f a -> g a -> Product f g a
Pair ((a -> f b) -> f a -> f (f b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> f a -> f (f b)
traverse a -> f b
f f a
x )((a -> f b) -> g a -> f (g b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> g a -> f (g b)
traverse a -> f b
f g a
y )-- | @since 4.9.0.0instance(Applicative f ,Applicative g )=>Applicative (Product f g )wherepure :: forall a. a -> Product f g a
pure a
x =f a -> g a -> Product f g a
forall {k} (f :: k -> *) (g :: k -> *) (a :: k).
f a -> g a -> Product f g a
Pair (a -> f a
forall a. a -> f a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
x )(a -> g a
forall a. a -> g a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
x )Pair f (a -> b)
f g (a -> b)
g <*> :: forall a b. Product f g (a -> b) -> Product f g a -> Product f g b
<*> Pair f a
x g a
y =f b -> g b -> Product f g b
forall {k} (f :: k -> *) (g :: k -> *) (a :: k).
f a -> g a -> Product f g a
Pair (f (a -> b)
f f (a -> b) -> f a -> f b
forall a b. f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f a
x )(g (a -> b)
g g (a -> b) -> g a -> g b
forall a b. g (a -> b) -> g a -> g b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> g a
y )liftA2 :: forall a b c.
(a -> b -> c) -> Product f g a -> Product f g b -> Product f g c
liftA2 a -> b -> c
f (Pair f a
a g a
b )(Pair f b
x g b
y )=f c -> g c -> Product f g c
forall {k} (f :: k -> *) (g :: k -> *) (a :: k).
f a -> g a -> Product f g a
Pair ((a -> b -> c) -> f a -> f b -> f c
forall a b c. (a -> b -> c) -> f a -> f b -> f c
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 a -> b -> c
f f a
a f b
x )((a -> b -> c) -> g a -> g b -> g c
forall a b c. (a -> b -> c) -> g a -> g b -> g c
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 a -> b -> c
f g a
b g b
y )-- | @since 4.9.0.0instance(Alternative f ,Alternative g )=>Alternative (Product f g )whereempty :: forall a. Product f g a
empty =f a -> g a -> Product f g a
forall {k} (f :: k -> *) (g :: k -> *) (a :: k).
f a -> g a -> Product f g a
Pair f a
forall a. f a
forall (f :: * -> *) a. Alternative f => f a
empty g a
forall a. g a
forall (f :: * -> *) a. Alternative f => f a
empty Pair f a
x1 g a
y1 <|> :: forall a. Product f g a -> Product f g a -> Product f g a
<|> Pair f a
x2 g a
y2 =f a -> g a -> Product f g a
forall {k} (f :: k -> *) (g :: k -> *) (a :: k).
f a -> g a -> Product f g a
Pair (f a
x1 f a -> f a -> f a
forall a. f a -> f a -> f a
forall (f :: * -> *) a. Alternative f => f a -> f a -> f a
<|> f a
x2 )(g a
y1 g a -> g a -> g a
forall a. g a -> g a -> g a
forall (f :: * -> *) a. Alternative f => f a -> f a -> f a
<|> g a
y2 )-- | @since 4.9.0.0instance(Monad f ,Monad g )=>Monad (Product f g )wherePair f a
m g a
n >>= :: forall a b. Product f g a -> (a -> Product f g b) -> Product f g b
>>= a -> Product f g b
f =f b -> g b -> Product f g b
forall {k} (f :: k -> *) (g :: k -> *) (a :: k).
f a -> g a -> Product f g a
Pair (f a
m f a -> (a -> f b) -> f b
forall a b. f a -> (a -> f b) -> f b
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= Product f g b -> f b
forall {k} {f :: k -> *} {g :: k -> *} {a :: k}.
Product f g a -> f a
fstP (Product f g b -> f b) -> (a -> Product f g b) -> a -> f b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> Product f g b
f )(g a
n g a -> (a -> g b) -> g b
forall a b. g a -> (a -> g b) -> g b
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= Product f g b -> g b
forall {k} {f :: k -> *} {g :: k -> *} {a :: k}.
Product f g a -> g a
sndP (Product f g b -> g b) -> (a -> Product f g b) -> a -> g b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> Product f g b
f )wherefstP :: Product f g a -> f a
fstP (Pair f a
a g a
_)=f a
a sndP :: Product f g a -> g a
sndP (Pair f a
_g a
b )=g a
b -- | @since 4.9.0.0instance(MonadPlus f ,MonadPlus g )=>MonadPlus (Product f g )wheremzero :: forall a. Product f g a
mzero =f a -> g a -> Product f g a
forall {k} (f :: k -> *) (g :: k -> *) (a :: k).
f a -> g a -> Product f g a
Pair f a
forall a. f a
forall (m :: * -> *) a. MonadPlus m => m a
mzero g a
forall a. g a
forall (m :: * -> *) a. MonadPlus m => m a
mzero Pair f a
x1 g a
y1 mplus :: forall a. Product f g a -> Product f g a -> Product f g a
`mplus` Pair f a
x2 g a
y2 =f a -> g a -> Product f g a
forall {k} (f :: k -> *) (g :: k -> *) (a :: k).
f a -> g a -> Product f g a
Pair (f a
x1 f a -> f a -> f a
forall a. f a -> f a -> f a
forall (m :: * -> *) a. MonadPlus m => m a -> m a -> m a
`mplus` f a
x2 )(g a
y1 g a -> g a -> g a
forall a. g a -> g a -> g a
forall (m :: * -> *) a. MonadPlus m => m a -> m a -> m a
`mplus` g a
y2 )-- | @since 4.9.0.0instance(MonadFix f ,MonadFix g )=>MonadFix (Product f g )wheremfix :: forall a. (a -> Product f g a) -> Product f g a
mfix a -> Product f g a
f =f a -> g a -> Product f g a
forall {k} (f :: k -> *) (g :: k -> *) (a :: k).
f a -> g a -> Product f g a
Pair ((a -> f a) -> f a
forall a. (a -> f a) -> f a
forall (m :: * -> *) a. MonadFix m => (a -> m a) -> m a
mfix (Product f g a -> f a
forall {k} {f :: k -> *} {g :: k -> *} {a :: k}.
Product f g a -> f a
fstP (Product f g a -> f a) -> (a -> Product f g a) -> a -> f a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> Product f g a
f ))((a -> g a) -> g a
forall a. (a -> g a) -> g a
forall (m :: * -> *) a. MonadFix m => (a -> m a) -> m a
mfix (Product f g a -> g a
forall {k} {f :: k -> *} {g :: k -> *} {a :: k}.
Product f g a -> g a
sndP (Product f g a -> g a) -> (a -> Product f g a) -> a -> g a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> Product f g a
f ))wherefstP :: Product f g a -> f a
fstP (Pair f a
a g a
_)=f a
a sndP :: Product f g a -> g a
sndP (Pair f a
_g a
b )=g a
b -- | @since 4.9.0.0instance(MonadZip f ,MonadZip g )=>MonadZip (Product f g )wheremzipWith :: forall a b c.
(a -> b -> c) -> Product f g a -> Product f g b -> Product f g c
mzipWith a -> b -> c
f (Pair f a
x1 g a
y1 )(Pair f b
x2 g b
y2 )=f c -> g c -> Product f g c
forall {k} (f :: k -> *) (g :: k -> *) (a :: k).
f a -> g a -> Product f g a
Pair ((a -> b -> c) -> f a -> f b -> f c
forall a b c. (a -> b -> c) -> f a -> f b -> f c
forall (m :: * -> *) a b c.
MonadZip m =>
(a -> b -> c) -> m a -> m b -> m c
mzipWith a -> b -> c
f f a
x1 f b
x2 )((a -> b -> c) -> g a -> g b -> g c
forall a b c. (a -> b -> c) -> g a -> g b -> g c
forall (m :: * -> *) a b c.
MonadZip m =>
(a -> b -> c) -> m a -> m b -> m c
mzipWith a -> b -> c
f g a
y1 g b
y2 )-- | @since 4.16.0.0instance(Semigroup (f a ),Semigroup (g a ))=>Semigroup (Product f g a )wherePair f a
x1 g a
y1 <> :: Product f g a -> Product f g a -> Product f g a
<> Pair f a
x2 g a
y2 =f a -> g a -> Product f g a
forall {k} (f :: k -> *) (g :: k -> *) (a :: k).
f a -> g a -> Product f g a
Pair (f a
x1 f a -> f a -> f a
forall a. Semigroup a => a -> a -> a
<> f a
x2 )(g a
y1 g a -> g a -> g a
forall a. Semigroup a => a -> a -> a
<> g a
y2 )-- | @since 4.16.0.0instance(Monoid (f a ),Monoid (g a ))=>Monoid (Product f g a )wheremempty :: Product f g a
mempty =f a -> g a -> Product f g a
forall {k} (f :: k -> *) (g :: k -> *) (a :: k).
f a -> g a -> Product f g a
Pair f a
forall a. Monoid a => a
mempty g a
forall a. Monoid a => a
mempty