Safe Haskell	None
Language	Haskell2010

Data.Profunctor.Cartesian.Free

Synopsis

data FreeMonoidal (t :: Type -> Type -> Type) i (p :: Type -> Type -> Type) a b
- = Neutral (a -> i) (i -> b)
- | Cons (Day t p (FreeMonoidal t i p) a b)
type FreeCartesian = FreeMonoidal (,) ()
liftFreeCartesian :: p a b -> FreeCartesian p a b
foldFreeCartesian :: forall (q :: Type -> Type -> Type) (p :: Type -> Type -> Type). Cartesian q => (p :-> q) -> FreeCartesian p :-> q
type FreeCocartesian = FreeMonoidal Either Void
liftFreeCocartesian :: p a b -> FreeCocartesian p a b
foldFreeCocartesian :: forall (q :: Type -> Type -> Type) (p :: Type -> Type -> Type). Cocartesian q => (p :-> q) -> FreeCocartesian p :-> q
newtype ForgetCartesian (p :: Type -> Type -> Type) a b = ForgetCartesian {
- recallCartesian :: p a b
}
newtype ForgetCocartesian (p :: Type -> Type -> Type) a b = ForgetCocartesian {
- recallCocartesian :: p a b
}

Documentation

data FreeMonoidal (t :: Type -> Type -> Type) i (p :: Type -> Type -> Type) a b Source #

Constructs free monoidal profunctor with specified monoid. Each parameters of FreeMonoidal t i p stands for:

t for the monoidal product
i for the unit of the monoidal product t
p for the profunctor generating FreeMonoidal

For example, FreeMonoidal (,) () p is the free Cartesian profunctor.

Constructors

Neutral (a -> i) (i -> b)
Cons (Day t p (FreeMonoidal t i p) a b)

Instances

Instances details

ProfunctorMonad FreeCartesian Source #
Instance details Defined in Data.Profunctor.Cartesian.Free Methods proreturn :: forall (p :: Type -> Type -> Type). Profunctor p => p :-> FreeCartesian p # projoin :: forall (p :: Type -> Type -> Type). Profunctor p => FreeCartesian (FreeCartesian p) :-> FreeCartesian p #
ProfunctorMonad FreeCocartesian Source #
Instance details Defined in Data.Profunctor.Cartesian.Free Methods proreturn :: forall (p :: Type -> Type -> Type). Profunctor p => p :-> FreeCocartesian p # projoin :: forall (p :: Type -> Type -> Type). Profunctor p => FreeCocartesian (FreeCocartesian p) :-> FreeCocartesian p #
ProfunctorFunctor (FreeMonoidal t i :: (Type -> Type -> Type) -> Type -> Type -> Type) Source #
Instance details Defined in Data.Profunctor.Cartesian.Free Methods promap :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Profunctor p => (p :-> q) -> FreeMonoidal t i p :-> FreeMonoidal t i q #
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 #
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 #
Profunctor (FreeMonoidal t i p) Source #
Instance details Defined in Data.Profunctor.Cartesian.Free Methods dimap :: (a -> b) -> (c -> d) -> FreeMonoidal t i p b c -> FreeMonoidal t i p a d # lmap :: (a -> b) -> FreeMonoidal t i p b c -> FreeMonoidal t i p a c # rmap :: (b -> c) -> FreeMonoidal t i p a b -> FreeMonoidal t i p a c # (#.) :: forall a b c q. Coercible c b => q b c -> FreeMonoidal t i p a b -> FreeMonoidal t i p a c # (.#) :: forall a b c q. Coercible b a => FreeMonoidal t i p b c -> q a b -> FreeMonoidal t i p a c #
Functor (FreeMonoidal t i p a) Source #
Instance details Defined in Data.Profunctor.Cartesian.Free Methods fmap :: (a0 -> b) -> FreeMonoidal t i p a a0 -> FreeMonoidal t i p a b # (<$) :: a0 -> FreeMonoidal t i p a b -> FreeMonoidal t i p a a0 #

type FreeCartesian = FreeMonoidal (,) () Source #

Free Cartesian profunctor is FreeMonoidal profunctor with respect to (,).

liftFreeCartesian :: p a b -> FreeCartesian p a b Source #

foldFreeCartesian :: forall (q :: Type -> Type -> Type) (p :: Type -> Type -> Type). Cartesian q => (p :-> q) -> FreeCartesian p :-> q Source #

type FreeCocartesian = FreeMonoidal Either Void Source #

Free Cocartesian profunctor is FreeMonoidal profunctor with respect to Either.

Caution about `Cartesian` instance

Note that FreeCocartesian p have an instance of Cartesian, by distributing product on sums to sum of products of individual profunctors. When it is desirable to disable Cartesian instance of FreeCocartesian p, use ForgetCartesian to ignore Cartesian instance of p.

Because there are some profunctors which are both Cartesian and Cocartesian but do not satisfy distributive laws, using FreeCocartesian with such profunctors might cause a surprising behavior.

For example, Joker [] is not distributive, as Alternative [] is not distributive as shown below.

>>> import Control.Applicative
>>> let x = [id, id]
>>> let y = [1]; z = [2]
>>> x <*> (y <|> z)
[1,2,1,2]
>>> (x <*> y) <|> (x <*> z)
[1,1,2,2]

With such non-distributive Cartesian p, foldFreeCocartesian does not preserve the Cartesian operations. The following equation does not have to hold.

-- Not necessarily holds!
foldFreeCocartesian id (ps *** qs)
 == foldFreeCocartesian id ps *** foldFreeCocartesian id qs

liftFreeCocartesian :: p a b -> FreeCocartesian p a b Source #

foldFreeCocartesian :: forall (q :: Type -> Type -> Type) (p :: Type -> Type -> Type). Cocartesian q => (p :-> q) -> FreeCocartesian p :-> q Source #

newtype ForgetCartesian (p :: Type -> Type -> Type) a b Source #

Forgets Cartesian instance from a Profunctor.

Constructors

ForgetCartesian
Fields recallCartesian :: p a b

Instances

Instances details

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 => Profunctor (ForgetCartesian p) Source #
Instance details Defined in Data.Profunctor.Cartesian.Free Methods dimap :: (a -> b) -> (c -> d) -> ForgetCartesian p b c -> ForgetCartesian p a d # lmap :: (a -> b) -> ForgetCartesian p b c -> ForgetCartesian p a c # rmap :: (b -> c) -> ForgetCartesian p a b -> ForgetCartesian p a c # (#.) :: forall a b c q. Coercible c b => q b c -> ForgetCartesian p a b -> ForgetCartesian p a c # (.#) :: forall a b c q. Coercible b a => ForgetCartesian p b c -> q a b -> ForgetCartesian p a c #
Functor (p a) => Functor (ForgetCartesian p a) Source #
Instance details Defined in Data.Profunctor.Cartesian.Free Methods fmap :: (a0 -> b) -> ForgetCartesian p a a0 -> ForgetCartesian p a b # (<$) :: a0 -> ForgetCartesian p a b -> ForgetCartesian p a a0 #

newtype ForgetCocartesian (p :: Type -> Type -> Type) a b Source #

Forgets Cocartesian instance from a Profunctor.

Constructors

ForgetCocartesian
Fields recallCocartesian :: p a b

Instances

Instances details

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 #
Profunctor p => Profunctor (ForgetCocartesian p) Source #
Instance details Defined in Data.Profunctor.Cartesian.Free Methods dimap :: (a -> b) -> (c -> d) -> ForgetCocartesian p b c -> ForgetCocartesian p a d # lmap :: (a -> b) -> ForgetCocartesian p b c -> ForgetCocartesian p a c # rmap :: (b -> c) -> ForgetCocartesian p a b -> ForgetCocartesian p a c # (#.) :: forall a b c q. Coercible c b => q b c -> ForgetCocartesian p a b -> ForgetCocartesian p a c # (.#) :: forall a b c q. Coercible b a => ForgetCocartesian p b c -> q a b -> ForgetCocartesian p a c #
Functor (p a) => Functor (ForgetCocartesian p a) Source #
Instance details Defined in Data.Profunctor.Cartesian.Free Methods fmap :: (a0 -> b) -> ForgetCocartesian p a a0 -> ForgetCocartesian p a b # (<$) :: a0 -> ForgetCocartesian p a b -> ForgetCocartesian p a a0 #

Documentation

Instances

Caution about Cartesian instance

Instances

Instances

Caution about `Cartesian` instance