bifunctors-5.6.2: Bifunctors

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) #

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) # |
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 #
BifunctorComonad (Product p :: (k -> k1 -> Type) -> k -> k1 -> Type) # |
Instance details Defined in Data.Bifunctor.Product Methods biextract :: forall (p0 :: k -> k1 -> Type). Product p p0 :-> p0 # biextend :: forall (p0 :: k -> k1 -> Type) (q :: k -> k1 -> Type). (Product p p0 :-> q) -> Product p p0 :-> Product p q # biduplicate :: forall (p0 :: k -> k1 -> Type). Product p p0 :-> Product p (Product p p0) #
(Category p, Category q) => Category (Product p q :: k -> k -> Type) # |
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) # |
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-BwJEHVBCec7K8po0blH047" '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) # | 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) # |
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) # |
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) # |
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) # |
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) # |
Instance details Defined in Data.Bifunctor.Product Methods zeroArrow :: Product p q b c #
(Bifoldable f, Bifoldable g) => Bifoldable (Product f g) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
Instance details Defined in Data.Bifunctor.Product Methods bipure :: a -> b -> Product f g a b # (<<*>>) :: Product f g (a -> b) (c -> d) -> Product f g a c -> Product f g b d # biliftA2 :: (a -> b -> c) -> (d -> e -> f0) -> Product f g a d -> Product f g b e -> Product f g c f0 # (*>>) :: Product f g a b -> Product f g c d -> Product f g c d # (<<*) :: Product f g a b -> Product f g c d -> Product f g a b #
(Foldable (f a), Foldable (g a)) => Foldable (Product f g a) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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-BwJEHVBCec7K8po0blH047" '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) # |
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) # |
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) # |
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) # |
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) # |
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-BwJEHVBCec7K8po0blH047" '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) # |
Instance details Defined in Data.Bifunctor.Product type Rep (Product f g a b) = D1 ('MetaData "Product" "Data.Bifunctor.Product" "bifunctors-5.6.2-BwJEHVBCec7K8po0blH047" '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))))