Safe Haskell	None
Language	Haskell2010

Data.Profunctor.Cocartesian.Free

Contents

The free Cocartesian profunctors
- Distributive Cartesian on FreeCocartesian p
Newtype wrapper
Utility functions handling product (,) and coproduct Either of

Synopsis

data FreeCocartesian (p :: Type -> Type -> Type) a b
- = Neutral (a -> Void)
- | Cons (Day Either p (FreeCocartesian p) a b)
liftF :: p a b -> FreeCocartesian p a b
foldFree :: forall (q :: Type -> Type -> Type) (p :: Type -> Type -> Type). Cocartesian q => (p :-> q) -> FreeCocartesian p :-> q
emptyF :: forall (p :: Type -> Type -> Type) b. FreeCocartesian p Void b
sumF :: forall (p :: Type -> Type -> Type) a b a' b'. FreeCocartesian p a b -> FreeCocartesian p a' b' -> FreeCocartesian p (Either a a') (Either b b')
multF :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type) (r :: Type -> Type -> Type) a b a' b'. ProductOp p q r -> FreeCocartesian p a b -> FreeCocartesian q a' b' -> FreeCocartesian r (a, a') (b, b')
newtype ForgetCocartesian (p :: Type -> Type -> Type) a b = ForgetCocartesian {
- recallCocartesian :: p a b
}
assocEither :: Either (Either a b) c -> Either a (Either b c)
unassocEither :: Either a (Either b c) -> Either (Either a b) c
distL :: (a, Either b1 b2) -> Either (a, b1) (a, b2)
undistL :: Either (a, b1) (a, b2) -> (a, Either b1 b2)
distR :: (Either a1 a2, b) -> Either (a1, b) (a2, b)
undistR :: Either (a1, b) (a2, b) -> (Either a1 a2, b)

The free `Cocartesian` profunctors

data FreeCocartesian (p :: Type -> Type -> Type) a b 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

Constructors

Neutral (a -> Void)
Cons (Day Either p (FreeCocartesian p) a b)

Instances

Instances details

ProfunctorMonad FreeCocartesian Source #
Instance details Defined in Data.Profunctor.Cocartesian.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 FreeCocartesian Source #
Instance details Defined in Data.Profunctor.Cocartesian.Free Methods promap :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Profunctor p => (p :-> q) -> FreeCocartesian p :-> FreeCocartesian q #
Cartesian p => Cartesian (FreeCocartesian p) Source #
Instance details Defined in Data.Profunctor.Cocartesian.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.Cocartesian.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 (FreeCocartesian p) Source #
Instance details Defined in Data.Profunctor.Cocartesian.Free Methods dimap :: (a -> b) -> (c -> d) -> FreeCocartesian p b c -> FreeCocartesian p a d # lmap :: (a -> b) -> FreeCocartesian p b c -> FreeCocartesian p a c # rmap :: (b -> c) -> FreeCocartesian p a b -> FreeCocartesian p a c # (#.) :: forall a b c q. Coercible c b => q b c -> FreeCocartesian p a b -> FreeCocartesian p a c # (.#) :: forall a b c q. Coercible b a => FreeCocartesian p b c -> q a b -> FreeCocartesian p a c #
Cartesian p => Applicative (FreeCocartesian p a) Source #
Instance details Defined in Data.Profunctor.Cocartesian.Free Methods pure :: a0 -> FreeCocartesian p a a0 # (<>) :: FreeCocartesian p a (a0 -> b) -> FreeCocartesian p a a0 -> FreeCocartesian p a b # liftA2 :: (a0 -> b -> c) -> FreeCocartesian p a a0 -> FreeCocartesian p a b -> FreeCocartesian p a c # (>) :: FreeCocartesian p a a0 -> FreeCocartesian p a b -> FreeCocartesian p a b # (<*) :: FreeCocartesian p a a0 -> FreeCocartesian p a b -> FreeCocartesian p a a0 #
Functor (FreeCocartesian p a) Source #
Instance details Defined in Data.Profunctor.Cocartesian.Free Methods fmap :: (a0 -> b) -> FreeCocartesian p a a0 -> FreeCocartesian p a b # (<$) :: a0 -> FreeCocartesian p a b -> FreeCocartesian p a a0 #

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

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

emptyF :: forall (p :: Type -> Type -> Type) b. FreeCocartesian p Void b Source #

sumF :: forall (p :: Type -> Type -> Type) a b a' b'. FreeCocartesian p a b -> FreeCocartesian p a' b' -> FreeCocartesian p (Either a a') (Either b b') Source #

Distributive `Cartesian` on `FreeCocartesian p`

multF :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type) (r :: Type -> Type -> Type) a b a' b'. ProductOp p q r -> FreeCocartesian p a b -> FreeCocartesian q a' b' -> FreeCocartesian r (a, a') (b, b') Source #

Newtype wrapper

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.Cocartesian.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.Cocartesian.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.Cocartesian.Free Methods fmap :: (a0 -> b) -> ForgetCocartesian p a a0 -> ForgetCocartesian p a b # (<$) :: a0 -> ForgetCocartesian p a b -> ForgetCocartesian p a a0 #