Safe Haskell	Safe
Language	Haskell2010

Ala.Product

Synopsis

data Product (f :: k -> *) (g :: k -> *) (a :: k) :: forall k. (k -> *) -> (k -> *) -> k -> * = Pair (f a) (g a)

Documentation

data Product (f :: k -> *) (g :: k -> *) (a :: k) :: forall k. (k -> *) -> (k -> *) -> k -> * #

Lifted product of functors.

Constructors

Pair (f a) (g a)

Instances

Generic1 (Product f g :: k -> *)
Instance details Defined in Data.Functor.Product Associated Types type Rep1 (Product f g) :: k -> * # Methods from1 :: Product f g a -> Rep1 (Product f g) a # to1 :: Rep1 (Product f g) a -> Product f g a #
MFunctor (Product f :: (* -> ) -> -> *)
Instance details Defined in Control.Monad.Morph Methods hoist :: Monad m => (forall a. m a -> n a) -> Product f m b -> Product f n b #
(Monad f, Monad g) => Monad (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods (>>=) :: Product f g a -> (a -> Product f g b) -> Product f g b # (>>) :: Product f g a -> Product f g b -> Product f g b # return :: a -> Product f g a # fail :: String -> Product f g a #
(Functor f, Functor g) => Functor (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods fmap :: (a -> b) -> Product f g a -> Product f g b # (<$) :: a -> Product f g b -> Product f g a #
(MonadFix f, MonadFix g) => MonadFix (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods mfix :: (a -> Product f g a) -> Product f g a #
(Applicative f, Applicative g) => Applicative (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods pure :: a -> Product f g a # (<>) :: Product f g (a -> b) -> Product f g a -> Product f g b # liftA2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c # (>) :: Product f g a -> Product f g b -> Product f g b # (<*) :: Product f g a -> Product f g b -> Product f g a #
(Foldable f, Foldable g) => Foldable (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods fold :: Monoid m => Product f g m -> m # foldMap :: Monoid m => (a -> m) -> Product f g a -> m # foldr :: (a -> b -> b) -> b -> Product f g a -> b # foldr' :: (a -> b -> b) -> b -> Product f g a -> b # foldl :: (b -> a -> b) -> b -> Product f g a -> b # foldl' :: (b -> a -> b) -> b -> Product f g a -> b # foldr1 :: (a -> a -> a) -> Product f g a -> a # foldl1 :: (a -> a -> a) -> Product f g a -> a # toList :: Product f g a -> [a] # null :: Product f g a -> Bool # length :: Product f g a -> Int # elem :: Eq a => a -> Product f g a -> Bool # maximum :: Ord a => Product f g a -> a # minimum :: Ord a => Product f g a -> a # sum :: Num a => Product f g a -> a # product :: Num a => Product f g a -> a #
(Traversable f, Traversable g) => Traversable (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods traverse :: Applicative f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b) # sequenceA :: Applicative f0 => Product f g (f0 a) -> f0 (Product f g a) # mapM :: Monad m => (a -> m b) -> Product f g a -> m (Product f g b) # sequence :: Monad m => Product f g (m a) -> m (Product f g a) #
(Alternative f, Alternative g) => Alternative (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods empty :: Product f g a # (<\|>) :: Product f g a -> Product f g a -> Product f g a # some :: Product f g a -> Product f g [a] # many :: Product f g a -> Product f g [a] #
(Distributive f, Distributive g) => Distributive (Product f g)
Instance details Defined in Data.Distributive Methods distribute :: Functor f0 => f0 (Product f g a) -> Product f g (f0 a) # collect :: Functor f0 => (a -> Product f g b) -> f0 a -> Product f g (f0 b) # distributeM :: Monad m => m (Product f g a) -> Product f g (m a) # collectM :: Monad m => (a -> Product f g b) -> m a -> Product f g (m b) #
(Contravariant f, Contravariant g) => Contravariant (Product f g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Product f g b -> Product f g a # (>$) :: b -> Product f g b -> Product f g a #
(Representable f, Representable g) => Representable (Product f g)
Instance details Defined in Data.Functor.Rep Associated Types type Rep (Product f g) :: * # Methods tabulate :: (Rep (Product f g) -> a) -> Product f g a # index :: Product f g a -> Rep (Product f g) -> a #
(ToJSON1 f, ToJSON1 g) => ToJSON1 (Product f g)
Instance details Defined in Data.Aeson.Types.ToJSON Methods liftToJSON :: (a -> Value) -> ([a] -> Value) -> Product f g a -> Value # liftToJSONList :: (a -> Value) -> ([a] -> Value) -> [Product f g a] -> Value # liftToEncoding :: (a -> Encoding) -> ([a] -> Encoding) -> Product f g a -> Encoding # liftToEncodingList :: (a -> Encoding) -> ([a] -> Encoding) -> [Product f g a] -> Encoding #
(FromJSON1 f, FromJSON1 g) => FromJSON1 (Product f g)
Instance details Defined in Data.Aeson.Types.FromJSON Methods liftParseJSON :: (Value -> Parser a) -> (Value -> Parser [a]) -> Value -> Parser (Product f g a) # liftParseJSONList :: (Value -> Parser a) -> (Value -> Parser [a]) -> Value -> Parser [Product f g a] #
(MonadPlus f, MonadPlus g) => MonadPlus (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods mzero :: Product f g a # mplus :: Product f g a -> Product f g a -> Product f g a #
(Eq1 f, Eq1 g) => Eq1 (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods liftEq :: (a -> b -> Bool) -> Product f g a -> Product f g b -> Bool #
(Ord1 f, Ord1 g) => Ord1 (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods liftCompare :: (a -> b -> Ordering) -> Product f g a -> Product f g b -> Ordering #
(Read1 f, Read1 g) => Read1 (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Product f g a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Product f g a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Product f g a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Product f g a] #
(Show1 f, Show1 g) => Show1 (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Product f g a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Product f g a] -> ShowS #
(MonadZip f, MonadZip g) => MonadZip (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods mzip :: Product f g a -> Product f g b -> Product f g (a, b) # mzipWith :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c # munzip :: Product f g (a, b) -> (Product f g a, Product f g b) #
(Functor f, Functor g, Compactable f, Compactable g) => Compactable (Product f g)
Instance details Defined in Control.Compactable Methods compact :: Product f g (Maybe a) -> Product f g a # separate :: Product f g (Either l r) -> (Product f g l, Product f g r) # filter :: (a -> Bool) -> Product f g a -> Product f g a # partition :: (a -> Bool) -> Product f g a -> (Product f g a, Product f g a) # fmapMaybe :: Functor (Product f g) => (a -> Maybe b) -> Product f g a -> Product f g b # fmapEither :: Functor (Product f g) => (a -> Either l r) -> Product f g a -> (Product f g l, Product f g r) # applyMaybe :: Applicative (Product f g) => Product f g (a -> Maybe b) -> Product f g a -> Product f g b # applyEither :: Applicative (Product f g) => Product f g (a -> Either l r) -> Product f g a -> (Product f g l, Product f g r) # bindMaybe :: Monad (Product f g) => Product f g a -> (a -> Product f g (Maybe b)) -> Product f g b # bindEither :: Monad (Product f g) => Product f g a -> (a -> Product f g (Either l r)) -> (Product f g l, Product f g r) # traverseMaybe :: (Applicative g0, Traversable (Product f g)) => (a -> g0 (Maybe b)) -> Product f g a -> g0 (Product f g b) # traverseEither :: (Applicative g0, Traversable (Product f g)) => (a -> g0 (Either l r)) -> Product f g a -> g0 (Product f g l, Product f g r) #
(Compactable f, Alternative f, Monad f, Compactable g, Alternative g, Monad g) => CompactFold (Product f g)
Instance details Defined in Control.Compactable Methods compactFold :: Foldable g0 => Product f g (g0 a) -> Product f g a # separateFold :: Bifoldable g0 => Product f g (g0 a b) -> (Product f g a, Product f g b) # fmapFold :: (Functor (Product f g), Foldable g0) => (a -> g0 b) -> Product f g a -> Product f g b # fmapBifold :: (Functor (Product f g), Bifoldable g0) => (a -> g0 l r) -> Product f g a -> (Product f g l, Product f g r) # applyFold :: (Applicative (Product f g), Foldable g0) => Product f g (a -> g0 b) -> Product f g a -> Product f g b # applyBifold :: (Applicative (Product f g), Bifoldable g0) => Product f g (a -> g0 l r) -> Product f g a -> (Product f g l, Product f g r) # bindFold :: (Monad (Product f g), Foldable g0) => Product f g a -> (a -> Product f g (g0 b)) -> Product f g b # bindBifold :: (Monad (Product f g), Bifoldable g0) => Product f g a -> (a -> Product f g (g0 l r)) -> (Product f g l, Product f g r) # traverseFold :: (Applicative h, Foldable g0, Traversable (Product f g)) => (a -> h (g0 b)) -> Product f g a -> h (Product f g b) # traverseBifold :: (Applicative h, Bifoldable g0, Traversable (Product f g)) => (a -> h (g0 l r)) -> Product f g a -> h (Product f g l, Product f g r) #
(Divisible f, Divisible g) => Divisible (Product f g)
Instance details Defined in Data.Functor.Contravariant.Divisible Methods divide :: (a -> (b, c)) -> Product f g b -> Product f g c -> Product f g a # conquer :: Product f g a #
(Decidable f, Decidable g) => Decidable (Product f g)
Instance details Defined in Data.Functor.Contravariant.Divisible Methods lose :: (a -> Void) -> Product f g a # choose :: (a -> Either b c) -> Product f g b -> Product f g c -> Product f g a #
(NFData1 f, NFData1 g) => NFData1 (Product f g)	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a -> ()) -> Product f g a -> () #
(Hashable1 f, Hashable1 g) => Hashable1 (Product f g)
Instance details Defined in Data.Hashable.Class Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> Product f g a -> Int #
(Apply f, Apply g) => Apply (Product f g)
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Product f g (a -> b) -> Product f g a -> Product f g b # (.>) :: Product f g a -> Product f g b -> Product f g b # (<.) :: Product f g a -> Product f g b -> Product f g a # liftF2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c #
(Traversable1 f, Traversable1 g) => Traversable1 (Product f g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b) # sequence1 :: Apply f0 => Product f g (f0 b) -> f0 (Product f g b) #
(Pointed p, Pointed q) => Pointed (Product p q)
Instance details Defined in Data.Pointed Methods point :: a -> Product p q a #
(Foldable1 f, Foldable1 g) => Foldable1 (Product f g)
Instance details Defined in Data.Semigroup.Foldable.Class Methods fold1 :: Semigroup m => Product f g m -> m # foldMap1 :: Semigroup m => (a -> m) -> Product f g a -> m # toNonEmpty :: Product f g a -> NonEmpty a #
(Plus f, Plus g) => Plus (Product f g)
Instance details Defined in Data.Functor.Plus Methods zero :: Product f g a #
(Alt f, Alt g) => Alt (Product f g)
Instance details Defined in Data.Functor.Alt Methods (<!>) :: Product f g a -> Product f g a -> Product f g a # some :: Applicative (Product f g) => Product f g a -> Product f g [a] # many :: Applicative (Product f g) => Product f g a -> Product f g [a] #
(Bind f, Bind g) => Bind (Product f g)
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Product f g a -> (a -> Product f g b) -> Product f g b # join :: Product f g (Product f g a) -> Product f g a #
(Eq1 f, Eq1 g, Eq a) => Eq (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods (==) :: Product f g a -> Product f g a -> Bool # (/=) :: Product f g a -> Product f g a -> Bool #
(Typeable a, Typeable f, Typeable g, Typeable k, Data (f a), Data (g a)) => Data (Product f g a)
Instance details Defined in Data.Functor.Product Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g0. g0 -> c g0) -> Product f g a -> c (Product f g a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product f g a) # toConstr :: Product f g a -> Constr # dataTypeOf :: Product f g a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Product f g a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product f g a)) # gmapT :: (forall b. Data b => b -> b) -> Product f g a -> Product f g a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product f g a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product f g a -> r # gmapQ :: (forall d. Data d => d -> u) -> Product f g a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Product f g a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product f g a -> m (Product f g a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product f g a -> m (Product f g a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product f g a -> m (Product f g a) #
(Ord1 f, Ord1 g, Ord a) => Ord (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods compare :: Product f g a -> Product f g a -> Ordering # (<) :: Product f g a -> Product f g a -> Bool # (<=) :: Product f g a -> Product f g a -> Bool # (>) :: Product f g a -> Product f g a -> Bool # (>=) :: Product f g a -> Product f g a -> Bool # max :: Product f g a -> Product f g a -> Product f g a # min :: Product f g a -> Product f g a -> Product f g a #
(Read1 f, Read1 g, Read a) => Read (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods readsPrec :: Int -> ReadS (Product f g a) # readList :: ReadS [Product f g a] # readPrec :: ReadPrec (Product f g a) # readListPrec :: ReadPrec [Product f g a] #
(Show1 f, Show1 g, Show a) => Show (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods showsPrec :: Int -> Product f g a -> ShowS # show :: Product f g a -> String # showList :: [Product f g a] -> ShowS #
Generic (Product f g a)
Instance details Defined in Data.Functor.Product Associated Types type Rep (Product f g a) :: * -> * # Methods from :: Product f g a -> Rep (Product f g a) x # to :: Rep (Product f g a) x -> Product f g a #
(Hashable1 f, Hashable1 g, Hashable a) => Hashable (Product f g a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Product f g a -> Int # hash :: Product f g a -> Int #
(ToJSON1 f, ToJSON1 g, ToJSON a) => ToJSON (Product f g a)
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSON :: Product f g a -> Value # toEncoding :: Product f g a -> Encoding # toJSONList :: [Product f g a] -> Value # toEncodingList :: [Product f g a] -> Encoding #
(FromJSON1 f, FromJSON1 g, FromJSON a) => FromJSON (Product f g a)
Instance details Defined in Data.Aeson.Types.FromJSON Methods parseJSON :: Value -> Parser (Product f g a) # parseJSONList :: Value -> Parser [Product f g a] #
(NFData1 f, NFData1 g, NFData a) => NFData (Product f g a)	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods rnf :: Product f g a -> () #
Field1 (Product f g a) (Product f' g a) (f a) (f' a)
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (Product f g a) (Product f' g a) (f a) (f' a) #
Field2 (Product f g a) (Product f g' a) (g a) (g' a)
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (Product f g a) (Product f g' a) (g a) (g' a) #
type Rep1 (Product f g :: k -> *)
Instance details Defined in Data.Functor.Product type Rep1 (Product f g :: k -> ) = D1 (MetaData "Product" "Data.Functor.Product" "base" False) (C1 (MetaCons "Pair" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 f) :: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 g)))
type Rep (Product f g)
Instance details Defined in Data.Functor.Rep type Rep (Product f g) = Either (Rep f) (Rep g)
type Rep (Product f g a)
Instance details Defined in Data.Functor.Product type Rep (Product f g a) = D1 (MetaData "Product" "Data.Functor.Product" "base" False) (C1 (MetaCons "Pair" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f a)) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (g a))))