Data.Functor.Prod

Generalize the standard two-functor Product to the product of n-functors. Intuitively, this means:

Product f g a ~~ (f a, g a)

Prod '[]        a ~~  Const () a
Prod '[f]       a ~~ (f a)
Prod '[f, g]    a ~~ (f a, g a)
Prod '[f, g, h] a ~~ (f a, g a, h a)
    ⋮

n-tuples of functors.

data Prod :: [k -> Type] -> k -> Type where

Product of n functors.

Constructors

Unit :: Prod '[] a

Cons :: f a -> Prod fs a -> Prod (f ': fs) a

Instances

(Functor f, Functor (Prod fs)) => Functor (Prod (f ': fs))

Inductively defined instance: Functor (Prod (f ': fs)).

Defined in Data.Functor.Prod

Methods

fmap :: (a -> b) -> Prod (f ': fs) a -> Prod (f ': fs) b

(<$) :: a -> Prod (f ': fs) b -> Prod (f ': fs) a

Functor (Prod ([] :: [Type -> Type]))

Inductively defined instance: Functor (Prod '[]).

Defined in Data.Functor.Prod

Methods

fmap :: (a -> b) -> Prod [] a -> Prod [] b

(<$) :: a -> Prod [] b -> Prod [] a

(Applicative f, Applicative (Prod fs)) => Applicative (Prod (f ': fs))

Inductively defined instance: Applicative (Prod (f ': fs)).

Defined in Data.Functor.Prod

Methods

pure :: a -> Prod (f ': fs) a

(<*>) :: Prod (f ': fs) (a -> b) -> Prod (f ': fs) a -> Prod (f ': fs) b

liftA2 :: (a -> b -> c) -> Prod (f ': fs) a -> Prod (f ': fs) b -> Prod (f ': fs) c

(*>) :: Prod (f ': fs) a -> Prod (f ': fs) b -> Prod (f ': fs) b

(<*) :: Prod (f ': fs) a -> Prod (f ': fs) b -> Prod (f ': fs) a

Applicative (Prod ([] :: [Type -> Type]))

Inductively defined instance: Applicative (Prod '[]).

Defined in Data.Functor.Prod

Methods

pure :: a -> Prod [] a

(<*>) :: Prod [] (a -> b) -> Prod [] a -> Prod [] b

liftA2 :: (a -> b -> c) -> Prod [] a -> Prod [] b -> Prod [] c

(*>) :: Prod [] a -> Prod [] b -> Prod [] b

(<*) :: Prod [] a -> Prod [] b -> Prod [] a

(Foldable f, Foldable (Prod fs)) => Foldable (Prod (f ': fs))

Inductively defined instance: Foldable (Prod (f ': fs)).

Defined in Data.Functor.Prod

Methods

fold :: Monoid m => Prod (f ': fs) m -> m

foldMap :: Monoid m => (a -> m) -> Prod (f ': fs) a -> m

foldr :: (a -> b -> b) -> b -> Prod (f ': fs) a -> b

foldr' :: (a -> b -> b) -> b -> Prod (f ': fs) a -> b

foldl :: (b -> a -> b) -> b -> Prod (f ': fs) a -> b

foldl' :: (b -> a -> b) -> b -> Prod (f ': fs) a -> b

foldr1 :: (a -> a -> a) -> Prod (f ': fs) a -> a

foldl1 :: (a -> a -> a) -> Prod (f ': fs) a -> a

toList :: Prod (f ': fs) a -> [a]

null :: Prod (f ': fs) a -> Bool

length :: Prod (f ': fs) a -> Int

elem :: Eq a => a -> Prod (f ': fs) a -> Bool

maximum :: Ord a => Prod (f ': fs) a -> a

minimum :: Ord a => Prod (f ': fs) a -> a

sum :: Num a => Prod (f ': fs) a -> a

product :: Num a => Prod (f ': fs) a -> a

Foldable (Prod ([] :: [Type -> Type]))

Inductively defined instance: Foldable (Prod '[]).

Defined in Data.Functor.Prod

Methods

fold :: Monoid m => Prod [] m -> m

foldMap :: Monoid m => (a -> m) -> Prod [] a -> m

foldr :: (a -> b -> b) -> b -> Prod [] a -> b

foldr' :: (a -> b -> b) -> b -> Prod [] a -> b

foldl :: (b -> a -> b) -> b -> Prod [] a -> b

foldl' :: (b -> a -> b) -> b -> Prod [] a -> b

foldr1 :: (a -> a -> a) -> Prod [] a -> a

foldl1 :: (a -> a -> a) -> Prod [] a -> a

toList :: Prod [] a -> [a]

null :: Prod [] a -> Bool

length :: Prod [] a -> Int

elem :: Eq a => a -> Prod [] a -> Bool

maximum :: Ord a => Prod [] a -> a

minimum :: Ord a => Prod [] a -> a

sum :: Num a => Prod [] a -> a

product :: Num a => Prod [] a -> a

(Traversable f, Traversable (Prod fs)) => Traversable (Prod (f ': fs))

Inductively defined instance: Traversable (Prod (f ': fs)).

Defined in Data.Functor.Prod

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Prod (f ': fs) a -> f0 (Prod (f ': fs) b)

sequenceA :: Applicative f0 => Prod (f ': fs) (f0 a) -> f0 (Prod (f ': fs) a)

mapM :: Monad m => (a -> m b) -> Prod (f ': fs) a -> m (Prod (f ': fs) b)

sequence :: Monad m => Prod (f ': fs) (m a) -> m (Prod (f ': fs) a)

Traversable (Prod ([] :: [Type -> Type]))

Inductively defined instance: Traversable (Prod '[]).

Defined in Data.Functor.Prod

Methods

traverse :: Applicative f => (a -> f b) -> Prod [] a -> f (Prod [] b)

sequenceA :: Applicative f => Prod [] (f a) -> f (Prod [] a)

mapM :: Monad m => (a -> m b) -> Prod [] a -> m (Prod [] b)

sequence :: Monad m => Prod [] (m a) -> m (Prod [] a)

(Eq1 f, Eq1 (Prod fs)) => Eq1 (Prod (f ': fs))

Inductively defined instance: Eq1 (Prod (f ': fs)).

Defined in Data.Functor.Prod

Methods

liftEq :: (a -> b -> Bool) -> Prod (f ': fs) a -> Prod (f ': fs) b -> Bool

Eq1 (Prod ([] :: [Type -> Type]))

Inductively defined instance: Eq1 (Prod '[]).

Defined in Data.Functor.Prod

Methods

liftEq :: (a -> b -> Bool) -> Prod [] a -> Prod [] b -> Bool

(Ord1 f, Ord1 (Prod fs)) => Ord1 (Prod (f ': fs))

Inductively defined instance: Ord1 (Prod (f ': fs)).

Defined in Data.Functor.Prod

Methods

liftCompare :: (a -> b -> Ordering) -> Prod (f ': fs) a -> Prod (f ': fs) b -> Ordering

Ord1 (Prod ([] :: [Type -> Type]))

Inductively defined instance: Ord1 (Prod '[]).

Defined in Data.Functor.Prod

Methods

liftCompare :: (a -> b -> Ordering) -> Prod [] a -> Prod [] b -> Ordering

(Show1 f, Show1 (Prod fs)) => Show1 (Prod (f ': fs))

Inductively defined instance: Show1 (Prod (f ': fs)).

Defined in Data.Functor.Prod

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Prod (f ': fs) a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Prod (f ': fs) a] -> ShowS

Show1 (Prod ([] :: [Type -> Type]))

Inductively defined instance: Show1 (Prod '[]).

Defined in Data.Functor.Prod

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Prod [] a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Prod [] a] -> ShowS

(Alternative f, Alternative (Prod fs)) => Alternative (Prod (f ': fs))

Inductively defined instance: Alternative (Prod (f ': fs)).

Defined in Data.Functor.Prod

Methods

empty :: Prod (f ': fs) a

(<|>) :: Prod (f ': fs) a -> Prod (f ': fs) a -> Prod (f ': fs) a

some :: Prod (f ': fs) a -> Prod (f ': fs) [a]

many :: Prod (f ': fs) a -> Prod (f ': fs) [a]

Alternative (Prod ([] :: [Type -> Type]))

Inductively defined instance: Alternative (Prod '[]).

Defined in Data.Functor.Prod

Methods

empty :: Prod [] a

(<|>) :: Prod [] a -> Prod [] a -> Prod [] a

some :: Prod [] a -> Prod [] [a]

many :: Prod [] a -> Prod [] [a]

(Eq1 f, Eq a, Eq1 (Prod fs)) => Eq (Prod (f ': fs) a)

Inductively defined instance: Eq (Prod (f ': fs)).

Defined in Data.Functor.Prod

Methods

(==) :: Prod (f ': fs) a -> Prod (f ': fs) a -> Bool

(/=) :: Prod (f ': fs) a -> Prod (f ': fs) a -> Bool

Eq a => Eq (Prod ([] :: [Type -> Type]) a)

Inductively defined instance: Eq (Prod '[]).

Defined in Data.Functor.Prod

Methods

(==) :: Prod [] a -> Prod [] a -> Bool

(/=) :: Prod [] a -> Prod [] a -> Bool

(Ord1 f, Ord a, Ord1 (Prod fs)) => Ord (Prod (f ': fs) a)

Inductively defined instance: Ord (Prod (f ': fs)).

Defined in Data.Functor.Prod

Methods

compare :: Prod (f ': fs) a -> Prod (f ': fs) a -> Ordering

(<) :: Prod (f ': fs) a -> Prod (f ': fs) a -> Bool

(<=) :: Prod (f ': fs) a -> Prod (f ': fs) a -> Bool

(>) :: Prod (f ': fs) a -> Prod (f ': fs) a -> Bool

(>=) :: Prod (f ': fs) a -> Prod (f ': fs) a -> Bool

max :: Prod (f ': fs) a -> Prod (f ': fs) a -> Prod (f ': fs) a

min :: Prod (f ': fs) a -> Prod (f ': fs) a -> Prod (f ': fs) a

Ord a => Ord (Prod ([] :: [Type -> Type]) a)

Inductively defined instance: Ord (Prod '[]).

Defined in Data.Functor.Prod

Methods

compare :: Prod [] a -> Prod [] a -> Ordering

(<) :: Prod [] a -> Prod [] a -> Bool

(<=) :: Prod [] a -> Prod [] a -> Bool

(>) :: Prod [] a -> Prod [] a -> Bool

(>=) :: Prod [] a -> Prod [] a -> Bool

max :: Prod [] a -> Prod [] a -> Prod [] a

min :: Prod [] a -> Prod [] a -> Prod [] a

(Show1 f, Show a, Show1 (Prod fs)) => Show (Prod (f ': fs) a)

Inductively defined instance: Show (Prod (f ': fs)).

Defined in Data.Functor.Prod

Methods

showsPrec :: Int -> Prod (f ': fs) a -> ShowS

show :: Prod (f ': fs) a -> String

showList :: [Prod (f ': fs) a] -> ShowS

Show a => Show (Prod ([] :: [Type -> Type]) a)

Inductively defined instance: Show (Prod '[]).

Defined in Data.Functor.Prod

Methods

showsPrec :: Int -> Prod [] a -> ShowS

show :: Prod [] a -> String

showList :: [Prod [] a] -> ShowS

zeroTuple :: Prod '[] a

The unit of the product.

oneTuple :: f a -> Prod '[f] a

Lift a functor to a 1-tuple.

fromProduct :: Product f g a -> Prod '[f, g] a

Conversion from a standard Product

toProduct :: Prod '[f, g] a -> Product f g a

Conversion to a standard Product

Flat product of functor products

prod :: Prod ls a -> Prod rs a -> Prod (ls ++ rs) a

Flat product of products.

Lifting functions

uncurryn :: Curried (Prod fs a -> r a) -> Prod fs a -> r a

Like uncurry but using Prod instead of pairs. Can be thought of as a family of functions:

uncurryn :: r a -> Prod '[] a
uncurryn :: (f a -> r a) -> Prod '[f] a
uncurryn :: (f a -> g a -> r a) -> Prod '[f, g] a
uncurryn :: (f a -> g a -> h a -> r a) -> Prod '[f, g, h] a
        ⋮

Type-level helpers

type family l ++ r :: [k] where ...

Type-level, poly-kinded, list-concatenation.

Equations

'[] ++ ys = ys

(x ': xs) ++ ys = x ': (xs ++ ys)

type family Curried t where ...

Prod '[f, g, h] a -> r is the type of the uncurried form of a function f a -> g a -> h a -> r. Curried moves from the former to the later. E.g.

Curried (Prod '[]  a    -> r) = r a
Curried (Prod '[f] a    -> r) = f a -> r a
Curried (Prod '[f, g] a -> r) = f a -> g a -> r a

Equations

Curried (Prod '[] a -> r a) = r a

Curried (Prod (f ': fs) a -> r a) = f a -> Curried (Prod fs a -> r a)