Copyright	(C) 2008-2016 Jesse Selover Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	portable
Safe Haskell	Safe
Language	Haskell2010

Data.Bifunctor.Product

Description

The product of two bifunctors.

Synopsis

data Product (f :: k -> k1 -> Type) (g :: k -> k1 -> Type) (a :: k) (b :: k1) = Pair (f a b) (g a b)

Documentation

data Product (f :: k -> k1 -> Type) (g :: k -> k1 -> Type) (a :: k) (b :: k1) Source #

Form the product of two bifunctors

Constructors

Pair (f a b) (g a b)

Instances

Instances details

BifunctorFunctor (Product p :: (k2 -> k3 -> Type) -> k2 -> k3 -> Type) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

bifmap :: forall (p0 :: k2 -> k3 -> Type) (q :: k2 -> k3 -> Type). (p0 :-> q) -> Product p p0 :-> Product p q Source #

BifunctorComonad (Product p :: (k -> k1 -> Type) -> k -> k1 -> Type) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

biextract :: forall (p0 :: k -> k1 -> Type). Product p p0 :-> p0 Source #

biextend :: forall (p0 :: k -> k1 -> Type) (q :: k -> k1 -> Type). (Product p p0 :-> q) -> Product p p0 :-> Product p q Source #

biduplicate :: forall (p0 :: k -> k1 -> Type). Product p p0 :-> Product p (Product p p0) Source #

(Category p, Category q) => Category (Product p q :: k -> k -> Type) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

id :: forall (a :: k). Product p q a a #

(.) :: forall (b :: k) (c :: k) (a :: k). Product p q b c -> Product p q a b -> Product p q a c #

Generic1 (Product f g a :: k1 -> Type) Source #

Instance details

Defined in Data.Bifunctor.Product

Associated Types

type Rep1 (Product f g a :: k1 -> Type)

Instance details

Defined in Data.Bifunctor.Product

type Rep1 (Product f g a :: k1 -> Type) = D1 ('MetaData "Product" "Data.Bifunctor.Product" "bifunctors-5.6.2-EFCED5cRXUbF5ynLhzsEHB" 'False) (C1 ('MetaCons "Pair" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 (f a)) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 (g a))))

Methods

from1 :: forall (a0 :: k1). Product f g a a0 -> Rep1 (Product f g a) a0 #

to1 :: forall (a0 :: k1). Rep1 (Product f g a) a0 -> Product f g a a0 #

(Swap p, Swap q) => Swap (Product p q) Source #

Since: 5.6.1

Instance details

Defined in Data.Bifunctor.Product

Methods

swap :: Product p q a b -> Product p q b a #

(Arrow p, Arrow q) => Arrow (Product p q) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

arr :: (b -> c) -> Product p q b c #

first :: Product p q b c -> Product p q (b, d) (c, d) #

second :: Product p q b c -> Product p q (d, b) (d, c) #

(***) :: Product p q b c -> Product p q b' c' -> Product p q (b, b') (c, c') #

(&&&) :: Product p q b c -> Product p q b c' -> Product p q b (c, c') #

(ArrowChoice p, ArrowChoice q) => ArrowChoice (Product p q) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

left :: Product p q b c -> Product p q (Either b d) (Either c d) #

right :: Product p q b c -> Product p q (Either d b) (Either d c) #

(+++) :: Product p q b c -> Product p q b' c' -> Product p q (Either b b') (Either c c') #

(|||) :: Product p q b d -> Product p q c d -> Product p q (Either b c) d #

(ArrowLoop p, ArrowLoop q) => ArrowLoop (Product p q) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

loop :: Product p q (b, d) (c, d) -> Product p q b c #

(ArrowPlus p, ArrowPlus q) => ArrowPlus (Product p q) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

(<+>) :: Product p q b c -> Product p q b c -> Product p q b c #

(ArrowZero p, ArrowZero q) => ArrowZero (Product p q) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

zeroArrow :: Product p q b c #

(Bifoldable f, Bifoldable g) => Bifoldable (Product f g) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

bifold :: Monoid m => Product f g m m -> m #

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Product f g a b -> m #

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Product f g a b -> c #

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Product f g a b -> c #

(Bifoldable1 f, Bifoldable1 g) => Bifoldable1 (Product f g) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

bifold1 :: Semigroup m => Product f g m m -> m #

bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Product f g a b -> m #

(Bifunctor f, Bifunctor g) => Bifunctor (Product f g) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

bimap :: (a -> b) -> (c -> d) -> Product f g a c -> Product f g b d #

first :: (a -> b) -> Product f g a c -> Product f g b c #

second :: (b -> c) -> Product f g a b -> Product f g a c #

(Bitraversable f, Bitraversable g) => Bitraversable (Product f g) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> Product f g a b -> f0 (Product f g c d) #

(Eq2 f, Eq2 g) => Eq2 (Product f g) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Product f g a c -> Product f g b d -> Bool #

(Ord2 f, Ord2 g) => Ord2 (Product f g) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Product f g a c -> Product f g b d -> Ordering #

(Read2 f, Read2 g) => Read2 (Product f g) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Product f g a b) #

liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Product f g a b] #

liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Product f g a b) #

liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Product f g a b] #

(Show2 f, Show2 g) => Show2 (Product f g) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Product f g a b -> ShowS #

liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Product f g a b] -> ShowS #

(Biapplicative f, Biapplicative g) => Biapplicative (Product f g) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

bipure :: a -> b -> Product f g a b Source #

(<<*>>) :: Product f g (a -> b) (c -> d) -> Product f g a c -> Product f g b d Source #

biliftA2 :: (a -> b -> c) -> (d -> e -> f0) -> Product f g a d -> Product f g b e -> Product f g c f0 Source #

(*>>) :: Product f g a b -> Product f g c d -> Product f g c d Source #

(<<*) :: Product f g a b -> Product f g c d -> Product f g a b Source #

(Foldable (f a), Foldable (g a)) => Foldable (Product f g a) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

fold :: Monoid m => Product f g a m -> m #

foldMap :: Monoid m => (a0 -> m) -> Product f g a a0 -> m #

foldMap' :: Monoid m => (a0 -> m) -> Product f g a a0 -> m #

foldr :: (a0 -> b -> b) -> b -> Product f g a a0 -> b #

foldr' :: (a0 -> b -> b) -> b -> Product f g a a0 -> b #

foldl :: (b -> a0 -> b) -> b -> Product f g a a0 -> b #

foldl' :: (b -> a0 -> b) -> b -> Product f g a a0 -> b #

foldr1 :: (a0 -> a0 -> a0) -> Product f g a a0 -> a0 #

foldl1 :: (a0 -> a0 -> a0) -> Product f g a a0 -> a0 #

toList :: Product f g a a0 -> [a0] #

null :: Product f g a a0 -> Bool #

length :: Product f g a a0 -> Int #

elem :: Eq a0 => a0 -> Product f g a a0 -> Bool #

maximum :: Ord a0 => Product f g a a0 -> a0 #

minimum :: Ord a0 => Product f g a a0 -> a0 #

sum :: Num a0 => Product f g a a0 -> a0 #

product :: Num a0 => Product f g a a0 -> a0 #

(Eq2 f, Eq2 g, Eq a) => Eq1 (Product f g a) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

liftEq :: (a0 -> b -> Bool) -> Product f g a a0 -> Product f g a b -> Bool #

(Ord2 f, Ord2 g, Ord a) => Ord1 (Product f g a) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

liftCompare :: (a0 -> b -> Ordering) -> Product f g a a0 -> Product f g a b -> Ordering #

(Read2 f, Read2 g, Read a) => Read1 (Product f g a) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Product f g a a0) #

liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Product f g a a0] #

liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Product f g a a0) #

liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Product f g a a0] #

(Show2 f, Show2 g, Show a) => Show1 (Product f g a) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> Product f g a a0 -> ShowS #

liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [Product f g a a0] -> ShowS #

(Traversable (f a), Traversable (g a)) => Traversable (Product f g a) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

traverse :: Applicative f0 => (a0 -> f0 b) -> Product f g a a0 -> f0 (Product f g a b) #

sequenceA :: Applicative f0 => Product f g a (f0 a0) -> f0 (Product f g a a0) #

mapM :: Monad m => (a0 -> m b) -> Product f g a a0 -> m (Product f g a b) #

sequence :: Monad m => Product f g a (m a0) -> m (Product f g a a0) #

(Functor (f a), Functor (g a)) => Functor (Product f g a) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

fmap :: (a0 -> b) -> Product f g a a0 -> Product f g a b #

(<$) :: a0 -> Product f g a b -> Product f g a a0 #

Generic (Product f g a b) Source #

Instance details

Defined in Data.Bifunctor.Product

Associated Types

type Rep (Product f g a b)

Instance details

Defined in Data.Bifunctor.Product

type Rep (Product f g a b) = D1 ('MetaData "Product" "Data.Bifunctor.Product" "bifunctors-5.6.2-EFCED5cRXUbF5ynLhzsEHB" 'False) (C1 ('MetaCons "Pair" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a b)) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (g a b))))

Methods

from :: Product f g a b -> Rep (Product f g a b) x #

to :: Rep (Product f g a b) x -> Product f g a b #

(Read (f a b), Read (g a b)) => Read (Product f g a b) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

readsPrec :: Int -> ReadS (Product f g a b) #

readList :: ReadS [Product f g a b] #

readPrec :: ReadPrec (Product f g a b) #

readListPrec :: ReadPrec [Product f g a b] #

(Show (f a b), Show (g a b)) => Show (Product f g a b) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

showsPrec :: Int -> Product f g a b -> ShowS #

show :: Product f g a b -> String #

showList :: [Product f g a b] -> ShowS #

(Eq (f a b), Eq (g a b)) => Eq (Product f g a b) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

(==) :: Product f g a b -> Product f g a b -> Bool #

(/=) :: Product f g a b -> Product f g a b -> Bool #

(Ord (f a b), Ord (g a b)) => Ord (Product f g a b) Source #

Instance details

Defined in Data.Bifunctor.Product

Methods

compare :: Product f g a b -> Product f g a b -> Ordering #

(<) :: Product f g a b -> Product f g a b -> Bool #

(<=) :: Product f g a b -> Product f g a b -> Bool #

(>) :: Product f g a b -> Product f g a b -> Bool #

(>=) :: Product f g a b -> Product f g a b -> Bool #

max :: Product f g a b -> Product f g a b -> Product f g a b #

min :: Product f g a b -> Product f g a b -> Product f g a b #

type Rep1 (Product f g a :: k1 -> Type) Source #

Instance details

Defined in Data.Bifunctor.Product

type Rep1 (Product f g a :: k1 -> Type) = D1 ('MetaData "Product" "Data.Bifunctor.Product" "bifunctors-5.6.2-EFCED5cRXUbF5ynLhzsEHB" 'False) (C1 ('MetaCons "Pair" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 (f a)) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 (g a))))

type Rep (Product f g a b) Source #

Instance details

Defined in Data.Bifunctor.Product

type Rep (Product f g a b) = D1 ('MetaData "Product" "Data.Bifunctor.Product" "bifunctors-5.6.2-EFCED5cRXUbF5ynLhzsEHB" 'False) (C1 ('MetaCons "Pair" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a b)) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (g a b))))