Safe Haskell	None
Language	Haskell2010

Data.Profunctor.Cartesian

Contents

Cartesian p iff forall x. Applicative (p x)
Utilities
About distributivy laws between Cartesian and Cocartesian

Synopsis

class Profunctor p => Cartesian (p :: Type -> Type -> Type) where
- proUnit :: p a ()
- proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> p a1 b1 -> p a2 b2 -> p a b
- (***) :: p a b -> p a' b' -> p (a, a') (b, b')
- (&&&) :: p a b -> p a b' -> p a (b, b')
- proPower :: forall (n :: Nat) a b. KnownNat n => p a b -> p (Finite n -> a) (Finite n -> b)
prodDay :: forall (r :: Type -> Type -> Type) (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Cartesian r => (p :-> r) -> (q :-> r) -> Day (,) p q :-> r
class Profunctor p => Cocartesian (p :: Type -> Type -> Type) where
- proEmpty :: p Void b
- proSum :: (a -> Either a1 a2) -> (Either b1 b2 -> b) -> p a1 b1 -> p a2 b2 -> p a b
- (+++) :: p a b -> p a' b' -> p (Either a a') (Either b b')
- (|||) :: p a b -> p a' b -> p (Either a a') b
- proTimes :: forall (n :: Nat) a b. KnownNat n => p a b -> p (Finite n, a) (Finite n, b)
sumDay :: forall (r :: Type -> Type -> Type) (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Cocartesian r => (p :-> r) -> (q :-> r) -> Day Either p q :-> r
pureDefault :: Cartesian p => b -> p a b
proUnitDefault :: Applicative (p a) => p a ()
liftA2Default :: Cartesian p => (a -> b -> c) -> p x a -> p x b -> p x c
fanoutDefault :: (Profunctor p, Applicative (p a)) => p a b1 -> p a b2 -> p a (b1, b2)
describeFinite :: forall (n :: Nat) p. (KnownNat n, Cartesian p, Cocartesian p) => p (Finite n) (Finite n)
describeFiniteBits :: (FiniteBits a, Cartesian p, Cocartesian p) => p a a

Documentation

class Profunctor p => Cartesian (p :: Type -> Type -> Type) where Source #

Minimal complete definition

proUnit, (proProduct | (***) | (&&&))

Methods

proUnit :: p a () Source #

Unit of the product.

The type of proUnit can be understood as proUnit' :: p () () treated to have more generally-typed p a () using lmap.

const () :: a -> ()
proUnit' :: p () ()
lmap (const ()) proUnit' :: p a ()

proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> p a1 b1 -> p a2 b2 -> p a b Source #

(***) :: p a b -> p a' b' -> p (a, a') (b, b') Source #

Product of two profunctors

(&&&) :: p a b -> p a b' -> p a (b, b') Source #

Alternative way to define the product (pronounced "fan-out")

proPower :: forall (n :: Nat) a b. KnownNat n => p a b -> p (Finite n -> a) (Finite n -> b) Source #

Function from finite types can be constructed as iterated product.

There is a default implementaion, but it can be more efficient implementation.

Instances

Instances details

Cartesian Counting Source #
Instance details Defined in Data.Profunctor.Counting Methods proUnit :: Counting a () Source # proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> Counting a1 b1 -> Counting a2 b2 -> Counting a b Source # (***) :: Counting a b -> Counting a' b' -> Counting (a, a') (b, b') Source # (&&&) :: Counting a b -> Counting a b' -> Counting a (b, b') Source # proPower :: forall (n :: Nat) a b. KnownNat n => Counting a b -> Counting (Finite n -> a) (Finite n -> b) Source #
Cartesian Exhaust Source #
Instance details Defined in Data.Profunctor.Exhaust Methods proUnit :: Exhaust a () Source # proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> Exhaust a1 b1 -> Exhaust a2 b2 -> Exhaust a b Source # (***) :: Exhaust a b -> Exhaust a' b' -> Exhaust (a, a') (b, b') Source # (&&&) :: Exhaust a b -> Exhaust a b' -> Exhaust a (b, b') Source # proPower :: forall (n :: Nat) a b. KnownNat n => Exhaust a b -> Exhaust (Finite n -> a) (Finite n -> b) Source #
Cartesian FinFn Source #
Instance details Defined in Data.Profunctor.FinFn Methods proUnit :: FinFn a () Source # proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> FinFn a1 b1 -> FinFn a2 b2 -> FinFn a b Source # (***) :: FinFn a b -> FinFn a' b' -> FinFn (a, a') (b, b') Source # (&&&) :: FinFn a b -> FinFn a b' -> FinFn a (b, b') Source # proPower :: forall (n :: Nat) a b. KnownNat n => FinFn a b -> FinFn (Finite n -> a) (Finite n -> b) Source #
Cartesian p => Cartesian (ForgetCocartesian p) Source #
Instance details Defined in Data.Profunctor.Cartesian.Free Methods proUnit :: ForgetCocartesian p a () Source # proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> ForgetCocartesian p a1 b1 -> ForgetCocartesian p a2 b2 -> ForgetCocartesian p a b Source # (***) :: ForgetCocartesian p a b -> ForgetCocartesian p a' b' -> ForgetCocartesian p (a, a') (b, b') Source # (&&&) :: ForgetCocartesian p a b -> ForgetCocartesian p a b' -> ForgetCocartesian p a (b, b') Source # proPower :: forall (n :: Nat) a b. KnownNat n => ForgetCocartesian p a b -> ForgetCocartesian p (Finite n -> a) (Finite n -> b) Source #
Cartesian (FreeCartesian p) Source #
Instance details Defined in Data.Profunctor.Cartesian.Free Methods proUnit :: FreeCartesian p a () Source # proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> FreeCartesian p a1 b1 -> FreeCartesian p a2 b2 -> FreeCartesian p a b Source # (***) :: FreeCartesian p a b -> FreeCartesian p a' b' -> FreeCartesian p (a, a') (b, b') Source # (&&&) :: FreeCartesian p a b -> FreeCartesian p a b' -> FreeCartesian p a (b, b') Source # proPower :: forall (n :: Nat) a b. KnownNat n => FreeCartesian p a b -> FreeCartesian p (Finite n -> a) (Finite n -> b) Source #
Cartesian p => Cartesian (FreeCocartesian p) Source #
Instance details Defined in Data.Profunctor.Cartesian.Free Methods proUnit :: FreeCocartesian p a () Source # proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> FreeCocartesian p a1 b1 -> FreeCocartesian p a2 b2 -> FreeCocartesian p a b Source # (***) :: FreeCocartesian p a b -> FreeCocartesian p a' b' -> FreeCocartesian p (a, a') (b, b') Source # (&&&) :: FreeCocartesian p a b -> FreeCocartesian p a b' -> FreeCocartesian p a (b, b') Source # proPower :: forall (n :: Nat) a b. KnownNat n => FreeCocartesian p a b -> FreeCocartesian p (Finite n -> a) (Finite n -> b) Source #
Cartesian (FreeBicartesian p) Source #
Instance details Defined in Data.Profunctor.Cartesian.FreeBicartesian Methods proUnit :: FreeBicartesian p a () Source # proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> FreeBicartesian p a1 b1 -> FreeBicartesian p a2 b2 -> FreeBicartesian p a b Source # (***) :: FreeBicartesian p a b -> FreeBicartesian p a' b' -> FreeBicartesian p (a, a') (b, b') Source # (&&&) :: FreeBicartesian p a b -> FreeBicartesian p a b' -> FreeBicartesian p a (b, b') Source # proPower :: forall (n :: Nat) a b. KnownNat n => FreeBicartesian p a b -> FreeBicartesian p (Finite n -> a) (Finite n -> b) Source #
Profunctor p => Cartesian (FreeBicartesianD p) Source #
Instance details Defined in Data.Profunctor.Cartesian.FreeBicartesian Methods proUnit :: FreeBicartesianD p a () Source # proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> FreeBicartesianD p a1 b1 -> FreeBicartesianD p a2 b2 -> FreeBicartesianD p a b Source # (***) :: FreeBicartesianD p a b -> FreeBicartesianD p a' b' -> FreeBicartesianD p (a, a') (b, b') Source # (&&&) :: FreeBicartesianD p a b -> FreeBicartesianD p a b' -> FreeBicartesianD p a (b, b') Source # proPower :: forall (n :: Nat) a b. KnownNat n => FreeBicartesianD p a b -> FreeBicartesianD p (Finite n -> a) (Finite n -> b) Source #
Cartesian (Encoding a) Source #
Instance details Defined in Data.Profunctor.UniconEncoding Methods proUnit :: Encoding a a0 () Source # proProduct :: (a0 -> (a1, a2)) -> ((b1, b2) -> b) -> Encoding a a1 b1 -> Encoding a a2 b2 -> Encoding a a0 b Source # (***) :: Encoding a a0 b -> Encoding a a' b' -> Encoding a (a0, a') (b, b') Source # (&&&) :: Encoding a a0 b -> Encoding a a0 b' -> Encoding a a0 (b, b') Source # proPower :: forall (n :: Nat) a0 b. KnownNat n => Encoding a a0 b -> Encoding a (Finite n -> a0) (Finite n -> b) Source #
Cartesian p => Cartesian (Coyoneda p) Source #
Instance details Defined in Data.Profunctor.Cartesian Methods proUnit :: Coyoneda p a () Source # proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> Coyoneda p a1 b1 -> Coyoneda p a2 b2 -> Coyoneda p a b Source # (***) :: Coyoneda p a b -> Coyoneda p a' b' -> Coyoneda p (a, a') (b, b') Source # (&&&) :: Coyoneda p a b -> Coyoneda p a b' -> Coyoneda p a (b, b') Source # proPower :: forall (n :: Nat) a b. KnownNat n => Coyoneda p a b -> Coyoneda p (Finite n -> a) (Finite n -> b) Source #
Cartesian p => Cartesian (Yoneda p) Source #
Instance details Defined in Data.Profunctor.Cartesian Methods proUnit :: Yoneda p a () Source # proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> Yoneda p a1 b1 -> Yoneda p a2 b2 -> Yoneda p a b Source # (***) :: Yoneda p a b -> Yoneda p a' b' -> Yoneda p (a, a') (b, b') Source # (&&&) :: Yoneda p a b -> Yoneda p a b' -> Yoneda p a (b, b') Source # proPower :: forall (n :: Nat) a b. KnownNat n => Yoneda p a b -> Yoneda p (Finite n -> a) (Finite n -> b) Source #
Monoid r => Cartesian (Forget r :: Type -> Type -> Type) Source #
Instance details Defined in Data.Profunctor.Cartesian Methods proUnit :: Forget r a () Source # proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> Forget r a1 b1 -> Forget r a2 b2 -> Forget r a b Source # (***) :: Forget r a b -> Forget r a' b' -> Forget r (a, a') (b, b') Source # (&&&) :: Forget r a b -> Forget r a b' -> Forget r a (b, b') Source # proPower :: forall (n :: Nat) a b. KnownNat n => Forget r a b -> Forget r (Finite n -> a) (Finite n -> b) Source #
Applicative f => Cartesian (Star f) Source #
Instance details Defined in Data.Profunctor.Cartesian Methods proUnit :: Star f a () Source # proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> Star f a1 b1 -> Star f a2 b2 -> Star f a b Source # (***) :: Star f a b -> Star f a' b' -> Star f (a, a') (b, b') Source # (&&&) :: Star f a b -> Star f a b' -> Star f a (b, b') Source # proPower :: forall (n :: Nat) a b. KnownNat n => Star f a b -> Star f (Finite n -> a) (Finite n -> b) Source #
Cartesian (->) Source #
Instance details Defined in Data.Profunctor.Cartesian Methods proUnit :: a -> () Source # proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> (a1 -> b1) -> (a2 -> b2) -> a -> b Source # (***) :: (a -> b) -> (a' -> b') -> (a, a') -> (b, b') Source # (&&&) :: (a -> b) -> (a -> b') -> a -> (b, b') Source # proPower :: forall (n :: Nat) a b. KnownNat n => (a -> b) -> (Finite n -> a) -> (Finite n -> b) Source #
Divisible f => Cartesian (Clown f :: Type -> Type -> Type) Source #
Instance details Defined in Data.Profunctor.Cartesian Methods proUnit :: Clown f a () Source # proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> Clown f a1 b1 -> Clown f a2 b2 -> Clown f a b Source # (***) :: Clown f a b -> Clown f a' b' -> Clown f (a, a') (b, b') Source # (&&&) :: Clown f a b -> Clown f a b' -> Clown f a (b, b') Source # proPower :: forall (n :: Nat) a b. KnownNat n => Clown f a b -> Clown f (Finite n -> a) (Finite n -> b) Source #
Applicative f => Cartesian (Joker f :: Type -> Type -> Type) Source #
Instance details Defined in Data.Profunctor.Cartesian Methods proUnit :: Joker f a () Source # proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> Joker f a1 b1 -> Joker f a2 b2 -> Joker f a b Source # (***) :: Joker f a b -> Joker f a' b' -> Joker f (a, a') (b, b') Source # (&&&) :: Joker f a b -> Joker f a b' -> Joker f a (b, b') Source # proPower :: forall (n :: Nat) a b. KnownNat n => Joker f a b -> Joker f (Finite n -> a) (Finite n -> b) Source #
(Cartesian p, Cartesian q) => Cartesian (Product p q) Source #
Instance details Defined in Data.Profunctor.Cartesian Methods proUnit :: Product p q a () Source # proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> Product p q a1 b1 -> Product p q a2 b2 -> Product p q a b Source # (***) :: Product p q a b -> Product p q a' b' -> Product p q (a, a') (b, b') Source # (&&&) :: Product p q a b -> Product p q a b' -> Product p q a (b, b') Source # proPower :: forall (n :: Nat) a b. KnownNat n => Product p q a b -> Product p q (Finite n -> a) (Finite n -> b) Source #
(Cartesian p, Cartesian q) => Cartesian (Procompose p q) Source #
Instance details Defined in Data.Profunctor.Cartesian Methods proUnit :: Procompose p q a () Source # proProduct :: (a -> (a1, a2)) -> ((b1, b2) -> b) -> Procompose p q a1 b1 -> Procompose p q a2 b2 -> Procompose p q a b Source # (***) :: Procompose p q a b -> Procompose p q a' b' -> Procompose p q (a, a') (b, b') Source # (&&&) :: Procompose p q a b -> Procompose p q a b' -> Procompose p q a (b, b') Source # proPower :: forall (n :: Nat) a b. KnownNat n => Procompose p q a b -> Procompose p q (Finite n -> a) (Finite n -> b) Source #

prodDay :: forall (r :: Type -> Type -> Type) (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Cartesian r => (p :-> r) -> (q :-> r) -> Day (,) p q :-> r Source #

class Profunctor p => Cocartesian (p :: Type -> Type -> Type) where Source #

Minimal complete definition

proEmpty, (proSum | (+++) | (|||))

Methods

proEmpty :: p Void b Source #

Unit of the sum.

The type of proEmpty can be understood as proEmpty' :: p Void Void treated to have more generally-typed p Void b using rmap.

absurd    :: Void -> b
proEmpty' :: p Void Void
rmap absurd proEmpty' :: p Void b

proSum :: (a -> Either a1 a2) -> (Either b1 b2 -> b) -> p a1 b1 -> p a2 b2 -> p a b Source #

(+++) :: p a b -> p a' b' -> p (Either a a') (Either b b') Source #

Sum of two profunctors

(|||) :: p a b -> p a' b -> p (Either a a') b Source #

Alternative way to define the sum (pronounced "fan-in")

proTimes :: forall (n :: Nat) a b. KnownNat n => p a b -> p (Finite n, a) (Finite n, b) Source #

Pairing with finite types can be constructed as iterated sum.

There is a default implementaion, but it can be more efficient implementation.

Instances

Instances details

Cocartesian Counting Source #
Instance details Defined in Data.Profunctor.Counting Methods proEmpty :: Counting Void b Source # proSum :: (a -> Either a1 a2) -> (Either b1 b2 -> b) -> Counting a1 b1 -> Counting a2 b2 -> Counting a b Source # (+++) :: Counting a b -> Counting a' b' -> Counting (Either a a') (Either b b') Source # (\|\|\|) :: Counting a b -> Counting a' b -> Counting (Either a a') b Source # proTimes :: forall (n :: Nat) a b. KnownNat n => Counting a b -> Counting (Finite n, a) (Finite n, b) Source #
Cocartesian Exhaust Source #
Instance details Defined in Data.Profunctor.Exhaust Methods proEmpty :: Exhaust Void b Source # proSum :: (a -> Either a1 a2) -> (Either b1 b2 -> b) -> Exhaust a1 b1 -> Exhaust a2 b2 -> Exhaust a b Source # (+++) :: Exhaust a b -> Exhaust a' b' -> Exhaust (Either a a') (Either b b') Source # (\|\|\|) :: Exhaust a b -> Exhaust a' b -> Exhaust (Either a a') b Source # proTimes :: forall (n :: Nat) a b. KnownNat n => Exhaust a b -> Exhaust (Finite n, a) (Finite n, b) Source #
Cocartesian FinFn Source #
Instance details Defined in Data.Profunctor.FinFn Methods proEmpty :: FinFn Void b Source # proSum :: (a -> Either a1 a2) -> (Either b1 b2 -> b) -> FinFn a1 b1 -> FinFn a2 b2 -> FinFn a b Source # (+++) :: FinFn a b -> FinFn a' b' -> FinFn (Either a a') (Either b b') Source # (\|\|\|) :: FinFn a b -> FinFn a' b -> FinFn (Either a a') b Source # proTimes :: forall (n :: Nat) a b. KnownNat n => FinFn a b -> FinFn (Finite n, a) (Finite n, b) Source #
Cocartesian p => Cocartesian (ForgetCartesian p) Source #
Instance details Defined in Data.Profunctor.Cartesian.Free Methods proEmpty :: ForgetCartesian p Void b Source # proSum :: (a -> Either a1 a2) -> (Either b1 b2 -> b) -> ForgetCartesian p a1 b1 -> ForgetCartesian p a2 b2 -> ForgetCartesian p a b Source # (+++) :: ForgetCartesian p a b -> ForgetCartesian p a' b' -> ForgetCartesian p (Either a a') (Either b b') Source # (\|\|\|) :: ForgetCartesian p a b -> ForgetCartesian p a' b -> ForgetCartesian p (Either a a') b Source # proTimes :: forall (n :: Nat) a b. KnownNat n => ForgetCartesian p a b -> ForgetCartesian p (Finite n, a) (Finite n, b) Source #
Profunctor p => Cocartesian (FreeCocartesian p) Source #
Instance details Defined in Data.Profunctor.Cartesian.Free Methods proEmpty :: FreeCocartesian p Void b Source # proSum :: (a -> Either a1 a2) -> (Either b1 b2 -> b) -> FreeCocartesian p a1 b1 -> FreeCocartesian p a2 b2 -> FreeCocartesian p a b Source # (+++) :: FreeCocartesian p a b -> FreeCocartesian p a' b' -> FreeCocartesian p (Either a a') (Either b b') Source # (\|\|\|) :: FreeCocartesian p a b -> FreeCocartesian p a' b -> FreeCocartesian p (Either a a') b Source # proTimes :: forall (n :: Nat) a b. KnownNat n => FreeCocartesian p a b -> FreeCocartesian p (Finite n, a) (Finite n, b) Source #
Cocartesian (FreeBicartesian p) Source #
Instance details Defined in Data.Profunctor.Cartesian.FreeBicartesian Methods proEmpty :: FreeBicartesian p Void b Source # proSum :: (a -> Either a1 a2) -> (Either b1 b2 -> b) -> FreeBicartesian p a1 b1 -> FreeBicartesian p a2 b2 -> FreeBicartesian p a b Source # (+++) :: FreeBicartesian p a b -> FreeBicartesian p a' b' -> FreeBicartesian p (Either a a') (Either b b') Source # (\|\|\|) :: FreeBicartesian p a b -> FreeBicartesian p a' b -> FreeBicartesian p (Either a a') b Source # proTimes :: forall (n :: Nat) a b. KnownNat n => FreeBicartesian p a b -> FreeBicartesian p (Finite n, a) (Finite n, b) Source #
Profunctor p => Cocartesian (FreeBicartesianD p) Source #
Instance details Defined in Data.Profunctor.Cartesian.FreeBicartesian Methods proEmpty :: FreeBicartesianD p Void b Source # proSum :: (a -> Either a1 a2) -> (Either b1 b2 -> b) -> FreeBicartesianD p a1 b1 -> FreeBicartesianD p a2 b2 -> FreeBicartesianD p a b Source # (+++) :: FreeBicartesianD p a b -> FreeBicartesianD p a' b' -> FreeBicartesianD p (Either a a') (Either b b') Source # (\|\|\|) :: FreeBicartesianD p a b -> FreeBicartesianD p a' b -> FreeBicartesianD p (Either a a') b Source # proTimes :: forall (n :: Nat) a b. KnownNat n => FreeBicartesianD p a b -> FreeBicartesianD p (Finite n, a) (Finite n, b) Source #
Cocartesian (Encoding a) Source #
Instance details Defined in Data.Profunctor.UniconEncoding Methods proEmpty :: Encoding a Void b Source # proSum :: (a0 -> Either a1 a2) -> (Either b1 b2 -> b) -> Encoding a a1 b1 -> Encoding a a2 b2 -> Encoding a a0 b Source # (+++) :: Encoding a a0 b -> Encoding a a' b' -> Encoding a (Either a0 a') (Either b b') Source # (\|\|\|) :: Encoding a a0 b -> Encoding a a' b -> Encoding a (Either a0 a') b Source # proTimes :: forall (n :: Nat) a0 b. KnownNat n => Encoding a a0 b -> Encoding a (Finite n, a0) (Finite n, b) Source #
Cocartesian p => Cocartesian (Coyoneda p) Source #
Instance details Defined in Data.Profunctor.Cartesian Methods proEmpty :: Coyoneda p Void b Source # proSum :: (a -> Either a1 a2) -> (Either b1 b2 -> b) -> Coyoneda p a1 b1 -> Coyoneda p a2 b2 -> Coyoneda p a b Source # (+++) :: Coyoneda p a b -> Coyoneda p a' b' -> Coyoneda p (Either a a') (Either b b') Source # (\|\|\|) :: Coyoneda p a b -> Coyoneda p a' b -> Coyoneda p (Either a a') b Source # proTimes :: forall (n :: Nat) a b. KnownNat n => Coyoneda p a b -> Coyoneda p (Finite n, a) (Finite n, b) Source #
Cocartesian p => Cocartesian (Yoneda p) Source #
Instance details Defined in Data.Profunctor.Cartesian Methods proEmpty :: Yoneda p Void b Source # proSum :: (a -> Either a1 a2) -> (Either b1 b2 -> b) -> Yoneda p a1 b1 -> Yoneda p a2 b2 -> Yoneda p a b Source # (+++) :: Yoneda p a b -> Yoneda p a' b' -> Yoneda p (Either a a') (Either b b') Source # (\|\|\|) :: Yoneda p a b -> Yoneda p a' b -> Yoneda p (Either a a') b Source # proTimes :: forall (n :: Nat) a b. KnownNat n => Yoneda p a b -> Yoneda p (Finite n, a) (Finite n, b) Source #
Cocartesian (Forget r :: Type -> Type -> Type) Source #
Instance details Defined in Data.Profunctor.Cartesian Methods proEmpty :: Forget r Void b Source # proSum :: (a -> Either a1 a2) -> (Either b1 b2 -> b) -> Forget r a1 b1 -> Forget r a2 b2 -> Forget r a b Source # (+++) :: Forget r a b -> Forget r a' b' -> Forget r (Either a a') (Either b b') Source # (\|\|\|) :: Forget r a b -> Forget r a' b -> Forget r (Either a a') b Source # proTimes :: forall (n :: Nat) a b. KnownNat n => Forget r a b -> Forget r (Finite n, a) (Finite n, b) Source #
Functor f => Cocartesian (Star f) Source #
Instance details Defined in Data.Profunctor.Cartesian Methods proEmpty :: Star f Void b Source # proSum :: (a -> Either a1 a2) -> (Either b1 b2 -> b) -> Star f a1 b1 -> Star f a2 b2 -> Star f a b Source # (+++) :: Star f a b -> Star f a' b' -> Star f (Either a a') (Either b b') Source # (\|\|\|) :: Star f a b -> Star f a' b -> Star f (Either a a') b Source # proTimes :: forall (n :: Nat) a b. KnownNat n => Star f a b -> Star f (Finite n, a) (Finite n, b) Source #
Cocartesian (->) Source #
Instance details Defined in Data.Profunctor.Cartesian Methods proEmpty :: Void -> b Source # proSum :: (a -> Either a1 a2) -> (Either b1 b2 -> b) -> (a1 -> b1) -> (a2 -> b2) -> a -> b Source # (+++) :: (a -> b) -> (a' -> b') -> Either a a' -> Either b b' Source # (\|\|\|) :: (a -> b) -> (a' -> b) -> Either a a' -> b Source # proTimes :: forall (n :: Nat) a b. KnownNat n => (a -> b) -> (Finite n, a) -> (Finite n, b) Source #
Decidable f => Cocartesian (Clown f :: Type -> Type -> Type) Source #
Instance details Defined in Data.Profunctor.Cartesian Methods proEmpty :: Clown f Void b Source # proSum :: (a -> Either a1 a2) -> (Either b1 b2 -> b) -> Clown f a1 b1 -> Clown f a2 b2 -> Clown f a b Source # (+++) :: Clown f a b -> Clown f a' b' -> Clown f (Either a a') (Either b b') Source # (\|\|\|) :: Clown f a b -> Clown f a' b -> Clown f (Either a a') b Source # proTimes :: forall (n :: Nat) a b. KnownNat n => Clown f a b -> Clown f (Finite n, a) (Finite n, b) Source #
Alternative f => Cocartesian (Joker f :: Type -> Type -> Type) Source #
Instance details Defined in Data.Profunctor.Cartesian Methods proEmpty :: Joker f Void b Source # proSum :: (a -> Either a1 a2) -> (Either b1 b2 -> b) -> Joker f a1 b1 -> Joker f a2 b2 -> Joker f a b Source # (+++) :: Joker f a b -> Joker f a' b' -> Joker f (Either a a') (Either b b') Source # (\|\|\|) :: Joker f a b -> Joker f a' b -> Joker f (Either a a') b Source # proTimes :: forall (n :: Nat) a b. KnownNat n => Joker f a b -> Joker f (Finite n, a) (Finite n, b) Source #
(Cocartesian p, Cocartesian q) => Cocartesian (Product p q) Source #
Instance details Defined in Data.Profunctor.Cartesian Methods proEmpty :: Product p q Void b Source # proSum :: (a -> Either a1 a2) -> (Either b1 b2 -> b) -> Product p q a1 b1 -> Product p q a2 b2 -> Product p q a b Source # (+++) :: Product p q a b -> Product p q a' b' -> Product p q (Either a a') (Either b b') Source # (\|\|\|) :: Product p q a b -> Product p q a' b -> Product p q (Either a a') b Source # proTimes :: forall (n :: Nat) a b. KnownNat n => Product p q a b -> Product p q (Finite n, a) (Finite n, b) Source #
(Cocartesian p, Cocartesian q) => Cocartesian (Procompose p q) Source #
Instance details Defined in Data.Profunctor.Cartesian Methods proEmpty :: Procompose p q Void b Source # proSum :: (a -> Either a1 a2) -> (Either b1 b2 -> b) -> Procompose p q a1 b1 -> Procompose p q a2 b2 -> Procompose p q a b Source # (+++) :: Procompose p q a b -> Procompose p q a' b' -> Procompose p q (Either a a') (Either b b') Source # (\|\|\|) :: Procompose p q a b -> Procompose p q a' b -> Procompose p q (Either a a') b Source # proTimes :: forall (n :: Nat) a b. KnownNat n => Procompose p q a b -> Procompose p q (Finite n, a) (Finite n, b) Source #

sumDay :: forall (r :: Type -> Type -> Type) (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Cocartesian r => (p :-> r) -> (q :-> r) -> Day Either p q :-> r Source #

`Cartesian p` iff `forall x. Applicative (p x)`

pureDefault :: Cartesian p => b -> p a b Source #

proUnitDefault :: Applicative (p a) => p a () Source #

liftA2Default :: Cartesian p => (a -> b -> c) -> p x a -> p x b -> p x c Source #

fanoutDefault :: (Profunctor p, Applicative (p a)) => p a b1 -> p a b2 -> p a (b1, b2) Source #

Utilities

describeFinite :: forall (n :: Nat) p. (KnownNat n, Cartesian p, Cocartesian p) => p (Finite n) (Finite n) Source #

describeFiniteBits :: (FiniteBits a, Cartesian p, Cocartesian p) => p a a Source #

About distributivy laws between `Cartesian` and `Cocartesian`

Documentation

Instances

Instances

Cartesian p iff forall x. Applicative (p x)

Utilities

About distributivy laws between Cartesian and Cocartesian

`Cartesian p` iff `forall x. Applicative (p x)`

About distributivy laws between `Cartesian` and `Cocartesian`