Copyright	(C) 2011-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell2010

Data.Profunctor.Types

Description

For a good explanation of profunctors in Haskell see Dan Piponi's article:

http://blog.sigfpe.com/2011/07/profunctors-in-haskell.html

For more information on strength and costrength, see:

http://comonad.com/reader/2008/deriving-strength-from-laziness/

Synopsis

class Profunctor p where
- dimap :: (a -> b) -> (c -> d) -> p b c -> p a d
- lmap :: (a -> b) -> p b c -> p a c
- rmap :: (b -> c) -> p a b -> p a c
newtype Star f d c = Star {
- runStar :: d -> f c
}
newtype Costar f d c = Costar {
- runCostar :: f d -> c
}
newtype WrappedArrow p a b = WrapArrow {
- unwrapArrow :: p a b
}
newtype Forget r a b = Forget {
- runForget :: a -> r
}
type (:->) p q = forall a b. p a b -> q a b

Documentation

class Profunctor p where #

Formally, the class Profunctor represents a profunctor from Hask -> Hask.

Intuitively it is a bifunctor where the first argument is contravariant and the second argument is covariant.

You can define a Profunctor by either defining dimap or by defining both lmap and rmap.

If you supply dimap, you should ensure that:

dimap id id ≡ id

If you supply lmap and rmap, ensure:

lmap id ≡ id
rmap id ≡ id

If you supply both, you should also ensure:

dimap f g ≡ lmap f . rmap g

These ensure by parametricity:

dimap (f . g) (h . i) ≡ dimap g h . dimap f i
lmap (f . g) ≡ lmap g . lmap f
rmap (f . g) ≡ rmap f . rmap g

Minimal complete definition

dimap | lmap, rmap

Methods

dimap :: (a -> b) -> (c -> d) -> p b c -> p a d #

Map over both arguments at the same time.

dimap f g ≡ lmap f . rmap g

lmap :: (a -> b) -> p b c -> p a c #

Map the first argument contravariantly.

lmap f ≡ dimap f id

rmap :: (b -> c) -> p a b -> p a c #

Map the second argument covariantly.

rmap ≡ dimap id

Instances

Instances details

Monad m => Profunctor (Kleisli m) #
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Kleisli m b c -> Kleisli m a d # lmap :: (a -> b) -> Kleisli m b c -> Kleisli m a c # rmap :: (b -> c) -> Kleisli m a b -> Kleisli m a c # (#.) :: forall a b c q. Coercible c b => q b c -> Kleisli m a b -> Kleisli m a c # (.#) :: forall a b c q. Coercible b a => Kleisli m b c -> q a b -> Kleisli m a c #
Profunctor (Tagged :: Type -> Type -> Type) #
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Tagged b c -> Tagged a d # lmap :: (a -> b) -> Tagged b c -> Tagged a c # rmap :: (b -> c) -> Tagged a b -> Tagged a c # (#.) :: forall a b c q. Coercible c b => q b c -> Tagged a b -> Tagged a c # (.#) :: forall a b c q. Coercible b a => Tagged b c -> q a b -> Tagged a c #
Profunctor (Copastro p) #
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Copastro p b c -> Copastro p a d # lmap :: (a -> b) -> Copastro p b c -> Copastro p a c # rmap :: (b -> c) -> Copastro p a b -> Copastro p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Copastro p a b -> Copastro p a c # (.#) :: forall a b c q. Coercible b a => Copastro p b c -> q a b -> Copastro p a c #
Profunctor (Cotambara p) #
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Cotambara p b c -> Cotambara p a d # lmap :: (a -> b) -> Cotambara p b c -> Cotambara p a c # rmap :: (b -> c) -> Cotambara p a b -> Cotambara p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Cotambara p a b -> Cotambara p a c # (.#) :: forall a b c q. Coercible b a => Cotambara p b c -> q a b -> Cotambara p a c #
Profunctor (Pastro p) #
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Pastro p b c -> Pastro p a d # lmap :: (a -> b) -> Pastro p b c -> Pastro p a c # rmap :: (b -> c) -> Pastro p a b -> Pastro p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Pastro p a b -> Pastro p a c # (.#) :: forall a b c q. Coercible b a => Pastro p b c -> q a b -> Pastro p a c #
Profunctor p => Profunctor (Tambara p) #
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Tambara p b c -> Tambara p a d # lmap :: (a -> b) -> Tambara p b c -> Tambara p a c # rmap :: (b -> c) -> Tambara p a b -> Tambara p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Tambara p a b -> Tambara p a c # (.#) :: forall a b c q. Coercible b a => Tambara p b c -> q a b -> Tambara p a c #
Profunctor (Environment p) #
Instance details Defined in Data.Profunctor.Closed Methods dimap :: (a -> b) -> (c -> d) -> Environment p b c -> Environment p a d # lmap :: (a -> b) -> Environment p b c -> Environment p a c # rmap :: (b -> c) -> Environment p a b -> Environment p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Environment p a b -> Environment p a c # (.#) :: forall a b c q. Coercible b a => Environment p b c -> q a b -> Environment p a c #
Profunctor p => Profunctor (Closure p) #
Instance details Defined in Data.Profunctor.Closed Methods dimap :: (a -> b) -> (c -> d) -> Closure p b c -> Closure p a d # lmap :: (a -> b) -> Closure p b c -> Closure p a c # rmap :: (b -> c) -> Closure p a b -> Closure p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Closure p a b -> Closure p a c # (.#) :: forall a b c q. Coercible b a => Closure p b c -> q a b -> Closure p a c #
Profunctor (CopastroSum p) #
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> CopastroSum p b c -> CopastroSum p a d # lmap :: (a -> b) -> CopastroSum p b c -> CopastroSum p a c # rmap :: (b -> c) -> CopastroSum p a b -> CopastroSum p a c # (#.) :: forall a b c q. Coercible c b => q b c -> CopastroSum p a b -> CopastroSum p a c # (.#) :: forall a b c q. Coercible b a => CopastroSum p b c -> q a b -> CopastroSum p a c #
Profunctor (CotambaraSum p) #
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> CotambaraSum p b c -> CotambaraSum p a d # lmap :: (a -> b) -> CotambaraSum p b c -> CotambaraSum p a c # rmap :: (b -> c) -> CotambaraSum p a b -> CotambaraSum p a c # (#.) :: forall a b c q. Coercible c b => q b c -> CotambaraSum p a b -> CotambaraSum p a c # (.#) :: forall a b c q. Coercible b a => CotambaraSum p b c -> q a b -> CotambaraSum p a c #
Profunctor (PastroSum p) #
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> PastroSum p b c -> PastroSum p a d # lmap :: (a -> b) -> PastroSum p b c -> PastroSum p a c # rmap :: (b -> c) -> PastroSum p a b -> PastroSum p a c # (#.) :: forall a b c q. Coercible c b => q b c -> PastroSum p a b -> PastroSum p a c # (.#) :: forall a b c q. Coercible b a => PastroSum p b c -> q a b -> PastroSum p a c #
Profunctor p => Profunctor (TambaraSum p) #
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> TambaraSum p b c -> TambaraSum p a d # lmap :: (a -> b) -> TambaraSum p b c -> TambaraSum p a c # rmap :: (b -> c) -> TambaraSum p a b -> TambaraSum p a c # (#.) :: forall a b c q. Coercible c b => q b c -> TambaraSum p a b -> TambaraSum p a c # (.#) :: forall a b c q. Coercible b a => TambaraSum p b c -> q a b -> TambaraSum p a c #
Profunctor (FreeTraversing p) #
Instance details Defined in Data.Profunctor.Traversing Methods dimap :: (a -> b) -> (c -> d) -> FreeTraversing p b c -> FreeTraversing p a d # lmap :: (a -> b) -> FreeTraversing p b c -> FreeTraversing p a c # rmap :: (b -> c) -> FreeTraversing p a b -> FreeTraversing p a c # (#.) :: forall a b c q. Coercible c b => q b c -> FreeTraversing p a b -> FreeTraversing p a c # (.#) :: forall a b c q. Coercible b a => FreeTraversing p b c -> q a b -> FreeTraversing p a c #
Profunctor p => Profunctor (CofreeTraversing p) #
Instance details Defined in Data.Profunctor.Traversing Methods dimap :: (a -> b) -> (c -> d) -> CofreeTraversing p b c -> CofreeTraversing p a d # lmap :: (a -> b) -> CofreeTraversing p b c -> CofreeTraversing p a c # rmap :: (b -> c) -> CofreeTraversing p a b -> CofreeTraversing p a c # (#.) :: forall a b c q. Coercible c b => q b c -> CofreeTraversing p a b -> CofreeTraversing p a c # (.#) :: forall a b c q. Coercible b a => CofreeTraversing p b c -> q a b -> CofreeTraversing p a c #
Profunctor (FreeMapping p) #
Instance details Defined in Data.Profunctor.Mapping Methods dimap :: (a -> b) -> (c -> d) -> FreeMapping p b c -> FreeMapping p a d # lmap :: (a -> b) -> FreeMapping p b c -> FreeMapping p a c # rmap :: (b -> c) -> FreeMapping p a b -> FreeMapping p a c # (#.) :: forall a b c q. Coercible c b => q b c -> FreeMapping p a b -> FreeMapping p a c # (.#) :: forall a b c q. Coercible b a => FreeMapping p b c -> q a b -> FreeMapping p a c #
Profunctor p => Profunctor (CofreeMapping p) #
Instance details Defined in Data.Profunctor.Mapping Methods dimap :: (a -> b) -> (c -> d) -> CofreeMapping p b c -> CofreeMapping p a d # lmap :: (a -> b) -> CofreeMapping p b c -> CofreeMapping p a c # rmap :: (b -> c) -> CofreeMapping p a b -> CofreeMapping p a c # (#.) :: forall a b c q. Coercible c b => q b c -> CofreeMapping p a b -> CofreeMapping p a c # (.#) :: forall a b c q. Coercible b a => CofreeMapping p b c -> q a b -> CofreeMapping p a c #
Profunctor (Coyoneda p) #
Instance details Defined in Data.Profunctor.Yoneda Methods dimap :: (a -> b) -> (c -> d) -> Coyoneda p b c -> Coyoneda p a d # lmap :: (a -> b) -> Coyoneda p b c -> Coyoneda p a c # rmap :: (b -> c) -> Coyoneda p a b -> Coyoneda p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Coyoneda p a b -> Coyoneda p a c # (.#) :: forall a b c q. Coercible b a => Coyoneda p b c -> q a b -> Coyoneda p a c #
Profunctor (Yoneda p) #
Instance details Defined in Data.Profunctor.Yoneda Methods dimap :: (a -> b) -> (c -> d) -> Yoneda p b c -> Yoneda p a d # lmap :: (a -> b) -> Yoneda p b c -> Yoneda p a c # rmap :: (b -> c) -> Yoneda p a b -> Yoneda p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Yoneda p a b -> Yoneda p a c # (.#) :: forall a b c q. Coercible b a => Yoneda p b c -> q a b -> Yoneda p a c #
Profunctor ((->) :: Type -> Type -> Type) #
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> (b -> c) -> a -> d # lmap :: (a -> b) -> (b -> c) -> a -> c # rmap :: (b -> c) -> (a -> b) -> a -> c # (#.) :: forall a b c q. Coercible c b => q b c -> (a -> b) -> a -> c # (.#) :: forall a b c q. Coercible b a => (b -> c) -> q a b -> a -> c #
Functor w => Profunctor (Cokleisli w) #
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Cokleisli w b c -> Cokleisli w a d # lmap :: (a -> b) -> Cokleisli w b c -> Cokleisli w a c # rmap :: (b -> c) -> Cokleisli w a b -> Cokleisli w a c # (#.) :: forall a b c q. Coercible c b => q b c -> Cokleisli w a b -> Cokleisli w a c # (.#) :: forall a b c q. Coercible b a => Cokleisli w b c -> q a b -> Cokleisli w a c #
Profunctor (Forget r :: Type -> Type -> Type) #
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Forget r b c -> Forget r a d # lmap :: (a -> b) -> Forget r b c -> Forget r a c # rmap :: (b -> c) -> Forget r a b -> Forget r a c # (#.) :: forall a b c q. Coercible c b => q b c -> Forget r a b -> Forget r a c # (.#) :: forall a b c q. Coercible b a => Forget r b c -> q a b -> Forget r a c #
Functor f => Profunctor (Costar f) #
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Costar f b c -> Costar f a d # lmap :: (a -> b) -> Costar f b c -> Costar f a c # rmap :: (b -> c) -> Costar f a b -> Costar f a c # (#.) :: forall a b c q. Coercible c b => q b c -> Costar f a b -> Costar f a c # (.#) :: forall a b c q. Coercible b a => Costar f b c -> q a b -> Costar f a c #
Functor f => Profunctor (Star f) #
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Star f b c -> Star f a d # lmap :: (a -> b) -> Star f b c -> Star f a c # rmap :: (b -> c) -> Star f a b -> Star f a c # (#.) :: forall a b c q. Coercible c b => q b c -> Star f a b -> Star f a c # (.#) :: forall a b c q. Coercible b a => Star f b c -> q a b -> Star f a c #
Functor f => Profunctor (Joker f :: Type -> Type -> Type) #
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Joker f b c -> Joker f a d # lmap :: (a -> b) -> Joker f b c -> Joker f a c # rmap :: (b -> c) -> Joker f a b -> Joker f a c # (#.) :: forall a b c q. Coercible c b => q b c -> Joker f a b -> Joker f a c # (.#) :: forall a b c q. Coercible b a => Joker f b c -> q a b -> Joker f a c #
Contravariant f => Profunctor (Clown f :: Type -> Type -> Type) #
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Clown f b c -> Clown f a d # lmap :: (a -> b) -> Clown f b c -> Clown f a c # rmap :: (b -> c) -> Clown f a b -> Clown f a c # (#.) :: forall a b c q. Coercible c b => q b c -> Clown f a b -> Clown f a c # (.#) :: forall a b c q. Coercible b a => Clown f b c -> q a b -> Clown f a c #
Arrow p => Profunctor (WrappedArrow p) #
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> WrappedArrow p b c -> WrappedArrow p a d # lmap :: (a -> b) -> WrappedArrow p b c -> WrappedArrow p a c # rmap :: (b -> c) -> WrappedArrow p a b -> WrappedArrow p a c # (#.) :: forall a b c q. Coercible c b => q b c -> WrappedArrow p a b -> WrappedArrow p a c # (.#) :: forall a b c q. Coercible b a => WrappedArrow p b c -> q a b -> WrappedArrow p a c #
Profunctor p => Profunctor (Codensity p) #
Instance details Defined in Data.Profunctor.Ran Methods dimap :: (a -> b) -> (c -> d) -> Codensity p b c -> Codensity p a d # lmap :: (a -> b) -> Codensity p b c -> Codensity p a c # rmap :: (b -> c) -> Codensity p a b -> Codensity p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Codensity p a b -> Codensity p a c # (.#) :: forall a b c q. Coercible b a => Codensity p b c -> q a b -> Codensity p a c #
(Profunctor p, Profunctor q) => Profunctor (Sum p q) #
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Sum p q b c -> Sum p q a d # lmap :: (a -> b) -> Sum p q b c -> Sum p q a c # rmap :: (b -> c) -> Sum p q a b -> Sum p q a c # (#.) :: forall a b c q0. Coercible c b => q0 b c -> Sum p q a b -> Sum p q a c # (.#) :: forall a b c q0. Coercible b a => Sum p q b c -> q0 a b -> Sum p q a c #
(Profunctor p, Profunctor q) => Profunctor (Product p q) #
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Product p q b c -> Product p q a d # lmap :: (a -> b) -> Product p q b c -> Product p q a c # rmap :: (b -> c) -> Product p q a b -> Product p q a c # (#.) :: forall a b c q0. Coercible c b => q0 b c -> Product p q a b -> Product p q a c # (.#) :: forall a b c q0. Coercible b a => Product p q b c -> q0 a b -> Product p q a c #
(Functor f, Profunctor p) => Profunctor (Tannen f p) #
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Tannen f p b c -> Tannen f p a d # lmap :: (a -> b) -> Tannen f p b c -> Tannen f p a c # rmap :: (b -> c) -> Tannen f p a b -> Tannen f p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Tannen f p a b -> Tannen f p a c # (.#) :: forall a b c q. Coercible b a => Tannen f p b c -> q a b -> Tannen f p a c #
(Profunctor p, Profunctor q) => Profunctor (Rift p q) #
Instance details Defined in Data.Profunctor.Composition Methods dimap :: (a -> b) -> (c -> d) -> Rift p q b c -> Rift p q a d # lmap :: (a -> b) -> Rift p q b c -> Rift p q a c # rmap :: (b -> c) -> Rift p q a b -> Rift p q a c # (#.) :: forall a b c q0. Coercible c b => q0 b c -> Rift p q a b -> Rift p q a c # (.#) :: forall a b c q0. Coercible b a => Rift p q b c -> q0 a b -> Rift p q a c #
(Profunctor p, Profunctor q) => Profunctor (Procompose p q) #
Instance details Defined in Data.Profunctor.Composition Methods dimap :: (a -> b) -> (c -> d) -> Procompose p q b c -> Procompose p q a d # lmap :: (a -> b) -> Procompose p q b c -> Procompose p q a c # rmap :: (b -> c) -> Procompose p q a b -> Procompose p q a c # (#.) :: forall a b c q0. Coercible c b => q0 b c -> Procompose p q a b -> Procompose p q a c # (.#) :: forall a b c q0. Coercible b a => Procompose p q b c -> q0 a b -> Procompose p q a c #
(Profunctor p, Profunctor q) => Profunctor (Ran p q) #
Instance details Defined in Data.Profunctor.Ran Methods dimap :: (a -> b) -> (c -> d) -> Ran p q b c -> Ran p q a d # lmap :: (a -> b) -> Ran p q b c -> Ran p q a c # rmap :: (b -> c) -> Ran p q a b -> Ran p q a c # (#.) :: forall a b c q0. Coercible c b => q0 b c -> Ran p q a b -> Ran p q a c # (.#) :: forall a b c q0. Coercible b a => Ran p q b c -> q0 a b -> Ran p q a c #
(Functor f, Profunctor p) => Profunctor (Cayley f p) #
Instance details Defined in Data.Profunctor.Cayley Methods dimap :: (a -> b) -> (c -> d) -> Cayley f p b c -> Cayley f p a d # lmap :: (a -> b) -> Cayley f p b c -> Cayley f p a c # rmap :: (b -> c) -> Cayley f p a b -> Cayley f p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Cayley f p a b -> Cayley f p a c # (.#) :: forall a b c q. Coercible b a => Cayley f p b c -> q a b -> Cayley f p a c #
(Profunctor p, Functor f, Functor g) => Profunctor (Biff p f g) #
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Biff p f g b c -> Biff p f g a d # lmap :: (a -> b) -> Biff p f g b c -> Biff p f g a c # rmap :: (b -> c) -> Biff p f g a b -> Biff p f g a c # (#.) :: forall a b c q. Coercible c b => q b c -> Biff p f g a b -> Biff p f g a c # (.#) :: forall a b c q. Coercible b a => Biff p f g b c -> q a b -> Biff p f g a c #

newtype Star f d c #

Lift a Functor into a Profunctor (forwards).

Star has a polymorphic kind since 5.6.

Constructors

Star
Fields runStar :: d -> f c

Instances

Instances details

Monad f => Category (Star f :: Type -> Type -> Type) #
Instance details Defined in Data.Profunctor.Types Methods id :: forall (a :: k). Star f a a # (.) :: forall (b :: k) (c :: k) (a :: k). Star f b c -> Star f a b -> Star f a c #
Functor f => Profunctor (Star f) #
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Star f b c -> Star f a d # lmap :: (a -> b) -> Star f b c -> Star f a c # rmap :: (b -> c) -> Star f a b -> Star f a c # (#.) :: forall a b c q. Coercible c b => q b c -> Star f a b -> Star f a c # (.#) :: forall a b c q. Coercible b a => Star f b c -> q a b -> Star f a c #
Functor m => Strong (Star m) #
Instance details Defined in Data.Profunctor.Strong Methods first' :: Star m a b -> Star m (a, c) (b, c) # second' :: Star m a b -> Star m (c, a) (c, b) #
Distributive f => Closed (Star f) #
Instance details Defined in Data.Profunctor.Closed Methods closed :: Star f a b -> Star f (x -> a) (x -> b) #
Traversable f => Cochoice (Star f) #
Instance details Defined in Data.Profunctor.Choice Methods unleft :: Star f (Either a d) (Either b d) -> Star f a b # unright :: Star f (Either d a) (Either d b) -> Star f a b #
Applicative f => Choice (Star f) #
Instance details Defined in Data.Profunctor.Choice Methods left' :: Star f a b -> Star f (Either a c) (Either b c) # right' :: Star f a b -> Star f (Either c a) (Either c b) #
Applicative m => Traversing (Star m) #
Instance details Defined in Data.Profunctor.Traversing Methods traverse' :: Traversable f => Star m a b -> Star m (f a) (f b) # wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> Star m a b -> Star m s t #
(Applicative m, Distributive m) => Mapping (Star m) #
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => Star m a b -> Star m (f a) (f b) # roam :: ((a -> b) -> s -> t) -> Star m a b -> Star m s t #
Functor f => Representable (Star f) #
Instance details Defined in Data.Profunctor.Rep Associated Types type Rep (Star f) :: Type -> Type # Methods tabulate :: (d -> Rep (Star f) c) -> Star f d c #
Functor f => Sieve (Star f) f #
Instance details Defined in Data.Profunctor.Sieve Methods sieve :: Star f a b -> a -> f b #
Monad f => Monad (Star f a) #
Instance details Defined in Data.Profunctor.Types Methods (>>=) :: Star f a a0 -> (a0 -> Star f a b) -> Star f a b # (>>) :: Star f a a0 -> Star f a b -> Star f a b # return :: a0 -> Star f a a0 #
Functor f => Functor (Star f a) #
Instance details Defined in Data.Profunctor.Types Methods fmap :: (a0 -> b) -> Star f a a0 -> Star f a b # (<$) :: a0 -> Star f a b -> Star f a a0 #
Applicative f => Applicative (Star f a) #
Instance details Defined in Data.Profunctor.Types Methods pure :: a0 -> Star f a a0 # (<>) :: Star f a (a0 -> b) -> Star f a a0 -> Star f a b # liftA2 :: (a0 -> b -> c) -> Star f a a0 -> Star f a b -> Star f a c # (>) :: Star f a a0 -> Star f a b -> Star f a b # (<*) :: Star f a a0 -> Star f a b -> Star f a a0 #
Contravariant f => Contravariant (Star f a) #
Instance details Defined in Data.Profunctor.Types Methods contramap :: (a0 -> b) -> Star f a b -> Star f a a0 # (>$) :: b -> Star f a b -> Star f a a0 #
Alternative f => Alternative (Star f a) #
Instance details Defined in Data.Profunctor.Types Methods empty :: Star f a a0 # (<\|>) :: Star f a a0 -> Star f a a0 -> Star f a a0 # some :: Star f a a0 -> Star f a [a0] # many :: Star f a a0 -> Star f a [a0] #
MonadPlus f => MonadPlus (Star f a) #
Instance details Defined in Data.Profunctor.Types Methods mzero :: Star f a a0 # mplus :: Star f a a0 -> Star f a a0 -> Star f a a0 #
Distributive f => Distributive (Star f a) #
Instance details Defined in Data.Profunctor.Types Methods distribute :: Functor f0 => f0 (Star f a a0) -> Star f a (f0 a0) # collect :: Functor f0 => (a0 -> Star f a b) -> f0 a0 -> Star f a (f0 b) # distributeM :: Monad m => m (Star f a a0) -> Star f a (m a0) # collectM :: Monad m => (a0 -> Star f a b) -> m a0 -> Star f a (m b) #
type Rep (Star f) #
Instance details Defined in Data.Profunctor.Rep type Rep (Star f) = f

newtype Costar f d c #

Lift a Functor into a Profunctor (backwards).

Costar has a polymorphic kind since 5.6.

Constructors

Costar
Fields runCostar :: f d -> c

Instances

Instances details

Functor f => Profunctor (Costar f) #
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Costar f b c -> Costar f a d # lmap :: (a -> b) -> Costar f b c -> Costar f a c # rmap :: (b -> c) -> Costar f a b -> Costar f a c # (#.) :: forall a b c q. Coercible c b => q b c -> Costar f a b -> Costar f a c # (.#) :: forall a b c q. Coercible b a => Costar f b c -> q a b -> Costar f a c #
Functor f => Costrong (Costar f) #
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Costar f (a, d) (b, d) -> Costar f a b # unsecond :: Costar f (d, a) (d, b) -> Costar f a b #
Functor f => Closed (Costar f) #
Instance details Defined in Data.Profunctor.Closed Methods closed :: Costar f a b -> Costar f (x -> a) (x -> b) #
Applicative f => Cochoice (Costar f) #
Instance details Defined in Data.Profunctor.Choice Methods unleft :: Costar f (Either a d) (Either b d) -> Costar f a b # unright :: Costar f (Either d a) (Either d b) -> Costar f a b #
Functor f => Corepresentable (Costar f) #
Instance details Defined in Data.Profunctor.Rep Associated Types type Corep (Costar f) :: Type -> Type # Methods cotabulate :: (Corep (Costar f) d -> c) -> Costar f d c #
Functor f => Cosieve (Costar f) f #
Instance details Defined in Data.Profunctor.Sieve Methods cosieve :: Costar f a b -> f a -> b #
Monad (Costar f a) #
Instance details Defined in Data.Profunctor.Types Methods (>>=) :: Costar f a a0 -> (a0 -> Costar f a b) -> Costar f a b # (>>) :: Costar f a a0 -> Costar f a b -> Costar f a b # return :: a0 -> Costar f a a0 #
Functor (Costar f a) #
Instance details Defined in Data.Profunctor.Types Methods fmap :: (a0 -> b) -> Costar f a a0 -> Costar f a b # (<$) :: a0 -> Costar f a b -> Costar f a a0 #
Applicative (Costar f a) #
Instance details Defined in Data.Profunctor.Types Methods pure :: a0 -> Costar f a a0 # (<>) :: Costar f a (a0 -> b) -> Costar f a a0 -> Costar f a b # liftA2 :: (a0 -> b -> c) -> Costar f a a0 -> Costar f a b -> Costar f a c # (>) :: Costar f a a0 -> Costar f a b -> Costar f a b # (<*) :: Costar f a a0 -> Costar f a b -> Costar f a a0 #
Distributive (Costar f d) #
Instance details Defined in Data.Profunctor.Types Methods distribute :: Functor f0 => f0 (Costar f d a) -> Costar f d (f0 a) # collect :: Functor f0 => (a -> Costar f d b) -> f0 a -> Costar f d (f0 b) # distributeM :: Monad m => m (Costar f d a) -> Costar f d (m a) # collectM :: Monad m => (a -> Costar f d b) -> m a -> Costar f d (m b) #
type Corep (Costar f) #
Instance details Defined in Data.Profunctor.Rep type Corep (Costar f) = f

newtype WrappedArrow p a b #

Wrap an arrow for use as a Profunctor.

WrappedArrow has a polymorphic kind since 5.6.

Constructors

WrapArrow
Fields unwrapArrow :: p a b

Instances

Instances details

Category p => Category (WrappedArrow p :: k -> k -> Type) #
Instance details Defined in Data.Profunctor.Types Methods id :: forall (a :: k0). WrappedArrow p a a # (.) :: forall (b :: k0) (c :: k0) (a :: k0). WrappedArrow p b c -> WrappedArrow p a b -> WrappedArrow p a c #
Arrow p => Arrow (WrappedArrow p) #
Instance details Defined in Data.Profunctor.Types Methods arr :: (b -> c) -> WrappedArrow p b c # first :: WrappedArrow p b c -> WrappedArrow p (b, d) (c, d) # second :: WrappedArrow p b c -> WrappedArrow p (d, b) (d, c) # (***) :: WrappedArrow p b c -> WrappedArrow p b' c' -> WrappedArrow p (b, b') (c, c') # (&&&) :: WrappedArrow p b c -> WrappedArrow p b c' -> WrappedArrow p b (c, c') #
ArrowZero p => ArrowZero (WrappedArrow p) #
Instance details Defined in Data.Profunctor.Types Methods zeroArrow :: WrappedArrow p b c #
ArrowChoice p => ArrowChoice (WrappedArrow p) #
Instance details Defined in Data.Profunctor.Types Methods left :: WrappedArrow p b c -> WrappedArrow p (Either b d) (Either c d) # right :: WrappedArrow p b c -> WrappedArrow p (Either d b) (Either d c) # (+++) :: WrappedArrow p b c -> WrappedArrow p b' c' -> WrappedArrow p (Either b b') (Either c c') # (\|\|\|) :: WrappedArrow p b d -> WrappedArrow p c d -> WrappedArrow p (Either b c) d #
ArrowApply p => ArrowApply (WrappedArrow p) #
Instance details Defined in Data.Profunctor.Types Methods app :: WrappedArrow p (WrappedArrow p b c, b) c #
ArrowLoop p => ArrowLoop (WrappedArrow p) #
Instance details Defined in Data.Profunctor.Types Methods loop :: WrappedArrow p (b, d) (c, d) -> WrappedArrow p b c #
Arrow p => Profunctor (WrappedArrow p) #
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> WrappedArrow p b c -> WrappedArrow p a d # lmap :: (a -> b) -> WrappedArrow p b c -> WrappedArrow p a c # rmap :: (b -> c) -> WrappedArrow p a b -> WrappedArrow p a c # (#.) :: forall a b c q. Coercible c b => q b c -> WrappedArrow p a b -> WrappedArrow p a c # (.#) :: forall a b c q. Coercible b a => WrappedArrow p b c -> q a b -> WrappedArrow p a c #
ArrowLoop p => Costrong (WrappedArrow p) #
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: WrappedArrow p (a, d) (b, d) -> WrappedArrow p a b # unsecond :: WrappedArrow p (d, a) (d, b) -> WrappedArrow p a b #
Arrow p => Strong (WrappedArrow p) #	`Arrow` is `Strong` `Category`
Instance details Defined in Data.Profunctor.Strong Methods first' :: WrappedArrow p a b -> WrappedArrow p (a, c) (b, c) # second' :: WrappedArrow p a b -> WrappedArrow p (c, a) (c, b) #
ArrowChoice p => Choice (WrappedArrow p) #
Instance details Defined in Data.Profunctor.Choice Methods left' :: WrappedArrow p a b -> WrappedArrow p (Either a c) (Either b c) # right' :: WrappedArrow p a b -> WrappedArrow p (Either c a) (Either c b) #

newtype Forget r a b #

Forget has a polymorphic kind since 5.6.

Constructors

Forget
Fields runForget :: a -> r

Instances

Instances details

Profunctor (Forget r :: Type -> Type -> Type) #
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Forget r b c -> Forget r a d # lmap :: (a -> b) -> Forget r b c -> Forget r a c # rmap :: (b -> c) -> Forget r a b -> Forget r a c # (#.) :: forall a b c q. Coercible c b => q b c -> Forget r a b -> Forget r a c # (.#) :: forall a b c q. Coercible b a => Forget r b c -> q a b -> Forget r a c #
Strong (Forget r :: Type -> Type -> Type) #
Instance details Defined in Data.Profunctor.Strong Methods first' :: Forget r a b -> Forget r (a, c) (b, c) # second' :: Forget r a b -> Forget r (c, a) (c, b) #
Cochoice (Forget r :: Type -> Type -> Type) #
Instance details Defined in Data.Profunctor.Choice Methods unleft :: Forget r (Either a d) (Either b d) -> Forget r a b # unright :: Forget r (Either d a) (Either d b) -> Forget r a b #
Monoid r => Choice (Forget r :: Type -> Type -> Type) #
Instance details Defined in Data.Profunctor.Choice Methods left' :: Forget r a b -> Forget r (Either a c) (Either b c) # right' :: Forget r a b -> Forget r (Either c a) (Either c b) #
Monoid m => Traversing (Forget m :: Type -> Type -> Type) #
Instance details Defined in Data.Profunctor.Traversing Methods traverse' :: Traversable f => Forget m a b -> Forget m (f a) (f b) # wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> Forget m a b -> Forget m s t #
Representable (Forget r :: Type -> Type -> Type) #
Instance details Defined in Data.Profunctor.Rep Associated Types type Rep (Forget r) :: Type -> Type # Methods tabulate :: (d -> Rep (Forget r) c) -> Forget r d c #
Sieve (Forget r :: Type -> Type -> Type) (Const r :: Type -> Type) #
Instance details Defined in Data.Profunctor.Sieve Methods sieve :: Forget r a b -> a -> Const r b #
Functor (Forget r a :: Type -> Type) #
Instance details Defined in Data.Profunctor.Types Methods fmap :: (a0 -> b) -> Forget r a a0 -> Forget r a b # (<$) :: a0 -> Forget r a b -> Forget r a a0 #
Foldable (Forget r a :: Type -> Type) #
Instance details Defined in Data.Profunctor.Types Methods fold :: Monoid m => Forget r a m -> m # foldMap :: Monoid m => (a0 -> m) -> Forget r a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Forget r a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Forget r a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Forget r a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Forget r a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Forget r a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Forget r a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Forget r a a0 -> a0 # toList :: Forget r a a0 -> [a0] # null :: Forget r a a0 -> Bool # length :: Forget r a a0 -> Int # elem :: Eq a0 => a0 -> Forget r a a0 -> Bool # maximum :: Ord a0 => Forget r a a0 -> a0 # minimum :: Ord a0 => Forget r a a0 -> a0 # sum :: Num a0 => Forget r a a0 -> a0 # product :: Num a0 => Forget r a a0 -> a0 #
Traversable (Forget r a :: Type -> Type) #
Instance details Defined in Data.Profunctor.Types Methods traverse :: Applicative f => (a0 -> f b) -> Forget r a a0 -> f (Forget r a b) # sequenceA :: Applicative f => Forget r a (f a0) -> f (Forget r a a0) # mapM :: Monad m => (a0 -> m b) -> Forget r a a0 -> m (Forget r a b) # sequence :: Monad m => Forget r a (m a0) -> m (Forget r a a0) #
Contravariant (Forget r a :: Type -> Type) #
Instance details Defined in Data.Profunctor.Types Methods contramap :: (a0 -> b) -> Forget r a b -> Forget r a a0 # (>$) :: b -> Forget r a b -> Forget r a a0 #
Semigroup r => Semigroup (Forget r a b) #	Via `Semigroup r => (a -> r)` Since: 5.6.2
Instance details Defined in Data.Profunctor.Types Methods (<>) :: Forget r a b -> Forget r a b -> Forget r a b # sconcat :: NonEmpty (Forget r a b) -> Forget r a b # stimes :: Integral b0 => b0 -> Forget r a b -> Forget r a b #
Monoid r => Monoid (Forget r a b) #	Via `Monoid r => (a -> r)` Since: 5.6.2
Instance details Defined in Data.Profunctor.Types Methods mempty :: Forget r a b # mappend :: Forget r a b -> Forget r a b -> Forget r a b # mconcat :: [Forget r a b] -> Forget r a b #
type Rep (Forget r :: Type -> Type -> Type) #
Instance details Defined in Data.Profunctor.Rep type Rep (Forget r :: Type -> Type -> Type) = Const r :: Type -> Type

type (:->) p q = forall a b. p a b -> q a b infixr 0 #

(:->) has a polymorphic kind since 5.6.