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 :: Type -> Type -> Type) 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 :: k -> Type) d (c :: k) = Star {
- runStar :: d -> f c
}
newtype Costar (f :: k -> Type) (d :: k) c = Costar {
- runCostar :: f d -> c
}
newtype WrappedArrow (p :: k -> k1 -> Type) (a :: k) (b :: k1) = WrapArrow {
- unwrapArrow :: p a b
}
newtype Forget r a (b :: k) = Forget {
- runForget :: a -> r
}
type (:->) (p :: k -> k1 -> Type) (q :: k -> k1 -> Type) = forall (a :: k) (b :: k1). p a b -> q a b

Documentation

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

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 Source #

Map over both arguments at the same time.

dimap f g ≡ lmap f . rmap g

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

Map the first argument contravariantly.

lmap f ≡ dimap f id

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

Map the second argument covariantly.

rmap ≡ dimap id

Instances

Instances details

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

newtype Star (f :: k -> Type) d (c :: k) Source #

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) Source #

Instance details

Defined in Data.Profunctor.Types

Methods

id :: Star f a a #

(.) :: Star f b c -> Star f a b -> Star f a c #

Applicative f => Choice (Star f) Source #

Instance details

Defined in Data.Profunctor.Choice

Methods

left' :: Star f a b -> Star f (Either a c) (Either b c) Source #

right' :: Star f a b -> Star f (Either c a) (Either c b) Source #

Traversable f => Cochoice (Star f) Source #

Instance details

Defined in Data.Profunctor.Choice

Methods

unleft :: Star f (Either a d) (Either b d) -> Star f a b Source #

unright :: Star f (Either d a) (Either d b) -> Star f a b Source #

Distributive f => Closed (Star f) Source #

Instance details

Defined in Data.Profunctor.Closed

Methods

closed :: Star f a b -> Star f (x -> a) (x -> b) Source #

(Applicative m, Distributive m) => Mapping (Star m) Source #

Instance details

Defined in Data.Profunctor.Mapping

Methods

map' :: Functor f => Star m a b -> Star m (f a) (f b) Source #

roam :: ((a -> b) -> s -> t) -> Star m a b -> Star m s t Source #

Functor f => Representable (Star f) Source #

Instance details

Defined in Data.Profunctor.Rep

Associated Types

type Rep (Star f)
Instance details Defined in Data.Profunctor.Rep type Rep (Star f) = f

Methods

tabulate :: (d -> Rep (Star f) c) -> Star f d c Source #

Functor m => Strong (Star m) Source #

Instance details

Defined in Data.Profunctor.Strong

Methods

first' :: Star m a b -> Star m (a, c) (b, c) Source #

second' :: Star m a b -> Star m (c, a) (c, b) Source #

Applicative m => Traversing (Star m) Source #

Instance details

Defined in Data.Profunctor.Traversing

Methods

traverse' :: Traversable f => Star m a b -> Star m (f a) (f b) Source #

wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> Star m a b -> Star m s t Source #

Functor f => Profunctor (Star f) Source #

Instance details

Defined in Data.Profunctor.Types

Methods

dimap :: (a -> b) -> (c -> d) -> Star f b c -> Star f a d Source #

lmap :: (a -> b) -> Star f b c -> Star f a c Source #

rmap :: (b -> c) -> Star f a b -> Star f a c Source #

(#.) :: forall a b c q. Coercible c b => q b c -> Star f a b -> Star f a c Source #

(.#) :: forall a b c q. Coercible b a => Star f b c -> q a b -> Star f a c Source #

Functor f => Sieve (Star f) f Source #

Instance details

Defined in Data.Profunctor.Sieve

Methods

sieve :: Star f a b -> a -> f b Source #

Contravariant f => Contravariant (Star f a) Source #

Instance details

Defined in Data.Profunctor.Types

Methods

contramap :: (a' -> a0) -> Star f a a0 -> Star f a a' #

(>$) :: b -> Star f a b -> Star f a a0 #

Alternative f => Alternative (Star f a) Source #

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] #

Applicative f => Applicative (Star f a) Source #

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 #

Functor f => Functor (Star f a) Source #

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 #

Monad f => Monad (Star f a) Source #

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 #

MonadPlus f => MonadPlus (Star f a) Source #

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) Source #

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) Source #

Instance details

Defined in Data.Profunctor.Rep

type Rep (Star f) = f

newtype Costar (f :: k -> Type) (d :: k) c Source #

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

Applicative f => Cochoice (Costar f) Source #

Instance details

Defined in Data.Profunctor.Choice

Methods

unleft :: Costar f (Either a d) (Either b d) -> Costar f a b Source #

unright :: Costar f (Either d a) (Either d b) -> Costar f a b Source #

Functor f => Closed (Costar f) Source #

Instance details

Defined in Data.Profunctor.Closed

Methods

closed :: Costar f a b -> Costar f (x -> a) (x -> b) Source #

Functor f => Corepresentable (Costar f) Source #

Instance details

Defined in Data.Profunctor.Rep

Associated Types

type Corep (Costar f)
Instance details Defined in Data.Profunctor.Rep type Corep (Costar f) = f

Methods

cotabulate :: (Corep (Costar f) d -> c) -> Costar f d c Source #

Functor f => Costrong (Costar f) Source #

Instance details

Defined in Data.Profunctor.Strong

Methods

unfirst :: Costar f (a, d) (b, d) -> Costar f a b Source #

unsecond :: Costar f (d, a) (d, b) -> Costar f a b Source #

Functor f => Profunctor (Costar f) Source #

Instance details

Defined in Data.Profunctor.Types

Methods

dimap :: (a -> b) -> (c -> d) -> Costar f b c -> Costar f a d Source #

lmap :: (a -> b) -> Costar f b c -> Costar f a c Source #

rmap :: (b -> c) -> Costar f a b -> Costar f a c Source #

(#.) :: forall a b c q. Coercible c b => q b c -> Costar f a b -> Costar f a c Source #

(.#) :: forall a b c q. Coercible b a => Costar f b c -> q a b -> Costar f a c Source #

Functor f => Cosieve (Costar f) f Source #

Instance details

Defined in Data.Profunctor.Sieve

Methods

cosieve :: Costar f a b -> f a -> b Source #

Applicative (Costar f a) Source #

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 #

Functor (Costar f a) Source #

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 #

Monad (Costar f a) Source #

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 #

Distributive (Costar f d) Source #

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) Source #

Instance details

Defined in Data.Profunctor.Rep

type Corep (Costar f) = f

newtype WrappedArrow (p :: k -> k1 -> Type) (a :: k) (b :: k1) Source #

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

newtype Forget r a (b :: k) Source #

Forget has a polymorphic kind since 5.6.

Constructors

Forget
Fields runForget :: a -> r

Instances

Instances details

Monoid r => Choice (Forget r :: Type -> Type -> Type) Source #

Instance details

Defined in Data.Profunctor.Choice

Methods

left' :: Forget r a b -> Forget r (Either a c) (Either b c) Source #

right' :: Forget r a b -> Forget r (Either c a) (Either c b) Source #

Cochoice (Forget r :: Type -> Type -> Type) Source #

Instance details

Defined in Data.Profunctor.Choice

Methods

unleft :: Forget r (Either a d) (Either b d) -> Forget r a b Source #

unright :: Forget r (Either d a) (Either d b) -> Forget r a b Source #

Representable (Forget r :: Type -> Type -> Type) Source #

Instance details

Defined in Data.Profunctor.Rep

Associated Types

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