Profunctor.Monad.Profunctor

Documentation

class Profunctor (p :: Type -> Type -> Type) 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

Monad m => Profunctor (Kleisli m)

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 p => Profunctor (CofreeMapping p)

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 (FreeMapping p)

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 (TambaraSum p)

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 (PastroSum p)

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 (CotambaraSum p)

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 (CopastroSum p)

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 p => Profunctor (Closure p)

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 (Environment p)

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 (Tambara p)

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 (Pastro p)

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 (Cotambara p)

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 (Copastro p)

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 (Tagged :: Type -> Type -> Type)

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 ((->) :: Type -> Type -> Type)

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)

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

Functor f => Profunctor (Star f)

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 (Costar f)

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

Profunctor (Forget r :: Type -> Type -> Type)

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 (Joker f :: Type -> Type -> Type)

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)

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)

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 q) => Profunctor (Sum p q)

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)

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)

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, Functor f, Functor g) => Profunctor (Biff p f g)

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

(=.) :: Profunctor p => (y -> x) -> p x a -> p y a infixl 5

type J p a = p a a

A type synonym to keep type signatures DRY. J for "join".

J :: (* -> * -> *) -> (* -> *)
join :: Monad m => m (m a) -> (m a)