Synopsis

# 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

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 detailsDefined in Data.Profunctor.Unsafe Methodsdimap :: (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 # Instance detailsDefined in Data.Profunctor.Mapping Methodsdimap :: (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 # Instance detailsDefined in Data.Profunctor.Mapping Methodsdimap :: (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 # Instance detailsDefined in Data.Profunctor.Choice Methodsdimap :: (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 # Instance detailsDefined in Data.Profunctor.Choice Methodsdimap :: (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 # Instance detailsDefined in Data.Profunctor.Choice Methodsdimap :: (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 # Instance detailsDefined in Data.Profunctor.Choice Methodsdimap :: (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) Instance detailsDefined in Data.Profunctor.Closed Methodsdimap :: (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 # Instance detailsDefined in Data.Profunctor.Closed Methodsdimap :: (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) Instance detailsDefined in Data.Profunctor.Strong Methodsdimap :: (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 # Instance detailsDefined in Data.Profunctor.Strong Methodsdimap :: (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 # Instance detailsDefined in Data.Profunctor.Strong Methodsdimap :: (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 # Instance detailsDefined in Data.Profunctor.Strong Methodsdimap :: (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) Instance detailsDefined in Data.Profunctor.Unsafe Methodsdimap :: (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) Instance detailsDefined in Data.Profunctor.Unsafe Methodsdimap :: (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 detailsDefined in Data.Profunctor.Unsafe Methodsdimap :: (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) Instance detailsDefined in Data.Profunctor.Types Methodsdimap :: (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) Instance detailsDefined in Data.Profunctor.Types Methodsdimap :: (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) Instance detailsDefined in Data.Profunctor.Types Methodsdimap :: (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) Instance detailsDefined in Data.Profunctor.Unsafe Methodsdimap :: (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 detailsDefined in Data.Profunctor.Unsafe Methodsdimap :: (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 detailsDefined in Data.Profunctor.Types Methodsdimap :: (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) Instance detailsDefined in Data.Profunctor.Unsafe Methodsdimap :: (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 detailsDefined in Data.Profunctor.Unsafe Methodsdimap :: (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 detailsDefined in Data.Profunctor.Unsafe Methodsdimap :: (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) Instance detailsDefined in Data.Profunctor.Unsafe Methodsdimap :: (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 Source #

type J p a = p a a Source #

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

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