Moduleprofunctors-5.6.3Haskell2010

Data.Profunctor

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/

5 types
7 classes
2 values

Packageprofunctors-5.6.3
Exports14
LanguageHaskell2010
LicenceBSD-3-Clause
SourceProfunctor.hs

Profunctors

1 declaration

classclass 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

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
```

Instances37Profunctor, …

Monad m => Profunctor (Kleisli m)Defined in profunctors-5.6.3 · Data.Profunctor.Unsafe
Profunctor TaggedDefined in profunctors-5.6.3 · Data.Profunctor.Unsafe
Profunctor (CopastroSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Profunctor (CotambaraSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Profunctor (PastroSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Profunctor (Environment p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Profunctor (FreeMapping p)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
Profunctor (Copastro p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Profunctor (Cotambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Profunctor (Pastro p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Profunctor (Baz t)Defined in profunctors-5.6.3 · Data.Profunctor.Traversing
Profunctor (Bazaar a)Defined in profunctors-5.6.3 · Data.Profunctor.Traversing
Profunctor (FreeTraversing p)Defined in profunctors-5.6.3 · Data.Profunctor.Traversing
Profunctor (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Profunctor (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Profunctor p => Profunctor (TambaraSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Profunctor p => Profunctor (Closure p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Profunctor p => Profunctor (CofreeMapping p)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
Profunctor p => Profunctor (Tambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Profunctor p => Profunctor (CofreeTraversing p)Defined in profunctors-5.6.3 · Data.Profunctor.Traversing
Functor f => Profunctor (Costar f)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Functor f => Profunctor (Star f)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Functor w => Profunctor (Cokleisli w)Defined in profunctors-5.6.3 · Data.Profunctor.Unsafe
Profunctor (->)Defined in profunctors-5.6.3 · Data.Profunctor.Unsafe
Profunctor (Forget r)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Contravariant f => Profunctor (Clown f)Defined in profunctors-5.6.3 · Data.Profunctor.Unsafe
Functor f => Profunctor (Joker f)Defined in profunctors-5.6.3 · Data.Profunctor.Unsafe
Arrow p => Profunctor (WrappedArrow p)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Profunctor p => Profunctor (Codensity p)Defined in profunctors-5.6.3 · Data.Profunctor.Ran
(Profunctor p, Profunctor q) => Profunctor (Product p q)Defined in profunctors-5.6.3 · Data.Profunctor.Unsafe
(Profunctor p, Profunctor q) => Profunctor (Sum p q)Defined in profunctors-5.6.3 · Data.Profunctor.Unsafe
(Functor f, Profunctor p) => Profunctor (Tannen f p)Defined in profunctors-5.6.3 · Data.Profunctor.Unsafe
(Functor f, Profunctor p) => Profunctor (Cayley f p)Defined in profunctors-5.6.3 · Data.Profunctor.Cayley
(Profunctor p, Profunctor q) => Profunctor (Procompose p q)Defined in profunctors-5.6.3 · Data.Profunctor.Composition
(Profunctor p, Profunctor q) => Profunctor (Rift p q)Defined in profunctors-5.6.3 · Data.Profunctor.Composition
(Profunctor p, Profunctor q) => Profunctor (Ran p q)Defined in profunctors-5.6.3 · Data.Profunctor.Ran
(Profunctor p, Functor f, Functor g) => Profunctor (Biff p f g)Defined in profunctors-5.6.3 · Data.Profunctor.Unsafe

Profunctorial Strength

classclass Profunctor p => Strong (p :: Type -> Type -> Type) where

Generalizing Star of a strong Functor

Note: Every Functor in Haskell is strong with respect to (,).

This describes profunctor strength with respect to the product structure of Hask.

http://www.riec.tohoku.ac.jp/~asada/papers/arrStrMnd.pdf

Methods

first' :: p a b -> p (a, c) (b, c)

Laws:

first' ≡ dimap swap swap . second'
lmap fst ≡ rmap fst . first'
lmap (second' f) . first' ≡ rmap (second' f) . first'
first' . first' ≡ dimap assoc unassoc . first' where
  assoc ((a,b),c) = (a,(b,c))
  unassoc (a,(b,c)) = ((a,b),c)

second' :: p a b -> p (c, a) (c, b)

Laws:

second' ≡ dimap swap swap . first'
lmap snd ≡ rmap snd . second'
lmap (first' f) . second' ≡ rmap (first' f) . second'
second' . second' ≡ dimap unassoc assoc . second' where
  assoc ((a,b),c) = (a,(b,c))
  unassoc (a,(b,c)) = ((a,b),c)

Instances20Strong, …

Monad m => Strong (Kleisli m)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Strong (FreeMapping p)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
Strong (Pastro p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Strong (FreeTraversing p)Defined in profunctors-5.6.3 · Data.Profunctor.Traversing
Strong p => Strong (Closure p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Strong p => Strong (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Strong p => Strong (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Profunctor p => Strong (CofreeMapping p)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
Profunctor p => Strong (Tambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Profunctor p => Strong (CofreeTraversing p)Defined in profunctors-5.6.3 · Data.Profunctor.Traversing
Functor m => Strong (Star m)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Strong (->)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Strong (Forget r)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Contravariant f => Strong (Clown f)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Arrow p => Strong (WrappedArrow p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Arrow is Strong Category
(Strong p, Strong q) => Strong (Product p q)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
(Strong p, Strong q) => Strong (Sum p q)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
(Functor f, Strong p) => Strong (Tannen f p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
(Functor f, Strong p) => Strong (Cayley f p)Defined in profunctors-5.6.3 · Data.Profunctor.Cayley
(Strong p, Strong q) => Strong (Procompose p q)Defined in profunctors-5.6.3 · Data.Profunctor.Composition

valueuncurry' :: Strong p => p a (b -> c) -> p (a, b) c

classclass Profunctor p => Choice (p :: Type -> Type -> Type) where

The generalization of Costar of Functor that is strong with respect to Either.

Note: This is also a notion of strength, except with regards to another monoidal structure that we can choose to equip Hask with: the cocartesian coproduct.

Methods

left' :: p a b -> p (Either a c) (Either b c)

Laws:

left' ≡ dimap swapE swapE . right' where
  swapE :: Either a b -> Either b a
  swapE = either Right Left
rmap Left ≡ lmap Left . left'
lmap (right f) . left' ≡ rmap (right f) . left'
left' . left' ≡ dimap assocE unassocE . left' where
  assocE :: Either (Either a b) c -> Either a (Either b c)
  assocE (Left (Left a)) = Left a
  assocE (Left (Right b)) = Right (Left b)
  assocE (Right c) = Right (Right c)
  unassocE :: Either a (Either b c) -> Either (Either a b) c
  unassocE (Left a) = Left (Left a)
  unassocE (Right (Left b)) = Left (Right b)
  unassocE (Right (Right c)) = Right c

right' :: p a b -> p (Either c a) (Either c b)

Laws:

right' ≡ dimap swapE swapE . left' where
  swapE :: Either a b -> Either b a
  swapE = either Right Left
rmap Right ≡ lmap Right . right'
lmap (left f) . right' ≡ rmap (left f) . right'
right' . right' ≡ dimap unassocE assocE . right' where
  assocE :: Either (Either a b) c -> Either a (Either b c)
  assocE (Left (Left a)) = Left a
  assocE (Left (Right b)) = Right (Left b)
  assocE (Right c) = Right (Right c)
  unassocE :: Either a (Either b c) -> Either (Either a b) c
  unassocE (Left a) = Left (Left a)
  unassocE (Right (Left b)) = Left (Right b)
  unassocE (Right (Right c)) = Right c

Instances22Choice, …

Monad m => Choice (Kleisli m)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Choice TaggedDefined in profunctors-5.6.3 · Data.Profunctor.Choice
Choice (PastroSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Choice (FreeMapping p)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
Choice (FreeTraversing p)Defined in profunctors-5.6.3 · Data.Profunctor.Traversing
Choice p => Choice (Tambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Choice p => Choice (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Choice p => Choice (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Profunctor p => Choice (TambaraSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Profunctor p => Choice (CofreeMapping p)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
Profunctor p => Choice (CofreeTraversing p)Defined in profunctors-5.6.3 · Data.Profunctor.Traversing
Comonad w => Choice (Cokleisli w)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
extract approximates costrength
Applicative f => Choice (Star f)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Monoid r => Choice (Forget r)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Choice (->)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Functor f => Choice (Joker f)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
ArrowChoice p => Choice (WrappedArrow p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
(Choice p, Choice q) => Choice (Product p q)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
(Choice p, Choice q) => Choice (Sum p q)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
(Functor f, Choice p) => Choice (Tannen f p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
(Functor f, Choice p) => Choice (Cayley f p)Defined in profunctors-5.6.3 · Data.Profunctor.Cayley
(Choice p, Choice q) => Choice (Procompose p q)Defined in profunctors-5.6.3 · Data.Profunctor.Composition

Closed

classclass Profunctor p => Closed (p :: Type -> Type -> Type) where

A strong profunctor allows the monoidal structure to pass through.

A closed profunctor allows the closed structure to pass through.

Methods

closed :: p a b -> p (x -> a) (x -> b)

Laws:

lmap (. f) . closed ≡ rmap (. f) . closed
closed . closed ≡ dimap uncurry curry . closed
dimap const ($()) . closed ≡ id

Instances17Closed, …

Closed TaggedDefined in profunctors-5.6.3 · Data.Profunctor.Closed
Closed (Environment p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Closed (FreeMapping p)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
Closed p => Closed (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Closed p => Closed (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Profunctor p => Closed (Closure p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Profunctor p => Closed (CofreeMapping p)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
(Distributive f, Monad f) => Closed (Kleisli f)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Distributive f => Closed (Star f)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Functor f => Closed (Cokleisli f)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Functor f => Closed (Costar f)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Closed (->)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
(Closed p, Closed q) => Closed (Product p q)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
(Closed p, Closed q) => Closed (Sum p q)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
(Functor f, Closed p) => Closed (Tannen f p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
(Functor f, Closed p) => Closed (Cayley f p)Defined in profunctors-5.6.3 · Data.Profunctor.Cayley
(Closed p, Closed q) => Closed (Procompose p q)Defined in profunctors-5.6.3 · Data.Profunctor.Composition

valuecurry' :: Closed p => p (a, b) c -> p a (b -> c)

classclass (Traversing p, Closed p) => Mapping (p :: Type -> Type -> Type) where

Methods

map' :: Functor f => p a b -> p (f a) (f b)

Laws:

map' . rmap f ≡ rmap (fmap f) . map'
map' . map' ≡ dimap Compose getCompose . map'
dimap Identity runIdentity . map' ≡ id

roam :: ((a -> b) -> s -> t) -> p a b -> p s t

Instances10Mapping, …

Mapping (FreeMapping p)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
Mapping p => Mapping (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Mapping p => Mapping (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Profunctor p => Mapping (CofreeMapping p)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
(Monad m, Distributive m) => Mapping (Kleisli m)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
Mapping (->)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
(Applicative m, Distributive m) => Mapping (Star m)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
(Functor f, Mapping p) => Mapping (Tannen f p)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
(Functor f, Mapping p) => Mapping (Cayley f p)Defined in profunctors-5.6.3 · Data.Profunctor.Cayley
(Mapping p, Mapping q) => Mapping (Procompose p q)Defined in profunctors-5.6.3 · Data.Profunctor.Composition

Profunctorial Costrength

classclass Profunctor p => Costrong (p :: Type -> Type -> Type) where

Analogous to ArrowLoop, loop = unfirst

Methods

unfirst :: p (a, d) (b, d) -> p a b

Laws:

unfirst ≡ unsecond . dimap swap swap
lmap (,()) ≡ unfirst . rmap (,())
unfirst . lmap (second f) ≡ unfirst . rmap (second f)
unfirst . unfirst = unfirst . dimap assoc unassoc where
  assoc ((a,b),c) = (a,(b,c))
  unassoc (a,(b,c)) = ((a,b),c)

unsecond :: p (d, a) (d, b) -> p a b

Laws:

unsecond ≡ unfirst . dimap swap swap
lmap ((),) ≡ unsecond . rmap ((),)
unsecond . lmap (first f) ≡ unsecond . rmap (first f)
unsecond . unsecond = unsecond . dimap unassoc assoc where
  assoc ((a,b),c) = (a,(b,c))
  unassoc (a,(b,c)) = ((a,b),c)

Instances15Costrong, …

MonadFix m => Costrong (Kleisli m)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Costrong TaggedDefined in profunctors-5.6.3 · Data.Profunctor.Strong
Costrong (Copastro p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Costrong (Cotambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Costrong p => Costrong (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Costrong p => Costrong (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Functor f => Costrong (Cokleisli f)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Functor f => Costrong (Costar f)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Costrong (->)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
ArrowLoop p => Costrong (WrappedArrow p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
(Costrong p, Costrong q) => Costrong (Product p q)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
(Costrong p, Costrong q) => Costrong (Sum p q)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
(Functor f, Costrong p) => Costrong (Tannen f p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
(Functor f, Costrong p) => Costrong (Cayley f p)Defined in profunctors-5.6.3 · Data.Profunctor.Cayley
(Corepresentable p, Corepresentable q) => Costrong (Procompose p q)Defined in profunctors-5.6.3 · Data.Profunctor.Composition

classclass Profunctor p => Cochoice (p :: Type -> Type -> Type) where

Methods

unleft :: p (Either a d) (Either b d) -> p a b

Laws:

unleft ≡ unright . dimap swapE swapE where
  swapE :: Either a b -> Either b a
  swapE = either Right Left
rmap (either id absurd) ≡ unleft . lmap (either id absurd)
unfirst . rmap (second f) ≡ unfirst . lmap (second f)
unleft . unleft ≡ unleft . dimap assocE unassocE where
  assocE :: Either (Either a b) c -> Either a (Either b c)
  assocE (Left (Left a)) = Left a
  assocE (Left (Right b)) = Right (Left b)
  assocE (Right c) = Right (Right c)
  unassocE :: Either a (Either b c) -> Either (Either a b) c
  unassocE (Left a) = Left (Left a)
  unassocE (Right (Left b)) = Left (Right b)
  unassocE (Right (Right c)) = Right c

unright :: p (Either d a) (Either d b) -> p a b

Laws:

unright ≡ unleft . dimap swapE swapE where
  swapE :: Either a b -> Either b a
  swapE = either Right Left
rmap (either absurd id) ≡ unright . lmap (either absurd id)
unsecond . rmap (first f) ≡ unsecond . lmap (first f)
unright . unright ≡ unright . dimap unassocE assocE where
  assocE :: Either (Either a b) c -> Either a (Either b c)
  assocE (Left (Left a)) = Left a
  assocE (Left (Right b)) = Right (Left b)
  assocE (Right c) = Right (Right c)
  unassocE :: Either a (Either b c) -> Either (Either a b) c
  unassocE (Left a) = Left (Left a)
  unassocE (Right (Left b)) = Left (Right b)
  unassocE (Right (Right c)) = Right c

Instances12Cochoice, …

Cochoice (CopastroSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Cochoice (CotambaraSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Cochoice p => Cochoice (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Cochoice p => Cochoice (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Applicative f => Cochoice (Costar f)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Traversable f => Cochoice (Star f)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Cochoice (->)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Cochoice (Forget r)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
(Cochoice p, Cochoice q) => Cochoice (Product p q)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
(Cochoice p, Cochoice q) => Cochoice (Sum p q)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
(Functor f, Cochoice p) => Cochoice (Tannen f p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
(Functor f, Cochoice p) => Cochoice (Cayley f p)Defined in profunctors-5.6.3 · Data.Profunctor.Cayley

Common Profunctors

newtypenewtype Star (f :: k -> Type) d (c :: k)

Lift a Functor into a Profunctor (forwards).

Star has a polymorphic kind since 5.6.

Constructors

Star
- runStar :: d -> f c

Instances18Category, Choice, Cochoice, Closed, Mapping, Strong, …

Monad f => Category (Star f)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Applicative f => Choice (Star f)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Traversable f => Cochoice (Star f)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Distributive f => Closed (Star f)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
(Applicative m, Distributive m) => Mapping (Star m)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
Functor m => Strong (Star m)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Functor f => Profunctor (Star f)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Applicative m => Traversing (Star m)Defined in profunctors-5.6.3 · Data.Profunctor.Traversing
Functor f => Representable (Star f)Defined in profunctors-5.6.3 · Data.Profunctor.Rep
Functor f => Sieve (Star f) fDefined in profunctors-5.6.3 · Data.Profunctor.Sieve
Monad f => Monad (Star f a)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Functor f => Functor (Star f a)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Applicative f => Applicative (Star f a)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Alternative f => Alternative (Star f a)Defined in profunctors-5.6.3 · Data.Profunctor.Types
MonadPlus f => MonadPlus (Star f a)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Contravariant f => Contravariant (Star f a)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Distributive f => Distributive (Star f a)Defined in profunctors-5.6.3 · Data.Profunctor.Types
type Rep (Star f) = fDefined in profunctors-5.6.3 · Data.Profunctor.Rep

newtypenewtype Costar (f :: k -> Type) (d :: k) c

Lift a Functor into a Profunctor (backwards).

Costar has a polymorphic kind since 5.6.

Constructors

Costar
- runCostar :: f d -> c

Instances11Cochoice, Closed, Costrong, Profunctor, Corepresentable, Cosieve, …

Applicative f => Cochoice (Costar f)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Functor f => Closed (Costar f)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Functor f => Costrong (Costar f)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Functor f => Profunctor (Costar f)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Functor f => Corepresentable (Costar f)Defined in profunctors-5.6.3 · Data.Profunctor.Rep
Functor f => Cosieve (Costar f) fDefined in profunctors-5.6.3 · Data.Profunctor.Sieve
Monad (Costar f a)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Functor (Costar f a)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Applicative (Costar f a)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Distributive (Costar f d)Defined in profunctors-5.6.3 · Data.Profunctor.Types
type Corep (Costar f) = fDefined in profunctors-5.6.3 · Data.Profunctor.Rep

newtypenewtype WrappedArrow (p :: k -> k1 -> Type) (a :: k) (b :: k1)

Wrap an arrow for use as a Profunctor.

WrappedArrow has a polymorphic kind since 5.6.

Constructors

WrapArrow
- unwrapArrow :: p a b

Instances10Category, Arrow, ArrowApply, ArrowChoice, ArrowLoop, ArrowZero, …

Category p => Category (WrappedArrow p)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Arrow p => Arrow (WrappedArrow p)Defined in profunctors-5.6.3 · Data.Profunctor.Types
ArrowApply p => ArrowApply (WrappedArrow p)Defined in profunctors-5.6.3 · Data.Profunctor.Types
ArrowChoice p => ArrowChoice (WrappedArrow p)Defined in profunctors-5.6.3 · Data.Profunctor.Types
ArrowLoop p => ArrowLoop (WrappedArrow p)Defined in profunctors-5.6.3 · Data.Profunctor.Types
ArrowZero p => ArrowZero (WrappedArrow p)Defined in profunctors-5.6.3 · Data.Profunctor.Types
ArrowChoice p => Choice (WrappedArrow p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
ArrowLoop p => Costrong (WrappedArrow p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Arrow p => Strong (WrappedArrow p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Arrow is Strong Category
Arrow p => Profunctor (WrappedArrow p)Defined in profunctors-5.6.3 · Data.Profunctor.Types

newtypenewtype Forget r a (b :: k)

Forget has a polymorphic kind since 5.6.

Constructors

Forget
- runForget :: a -> r

Instances14Choice, Cochoice, Strong, Profunctor, Traversing, Representable, …

Monoid r => Choice (Forget r)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Cochoice (Forget r)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Strong (Forget r)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Profunctor (Forget r)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Monoid m => Traversing (Forget m)Defined in profunctors-5.6.3 · Data.Profunctor.Traversing
Representable (Forget r)Defined in profunctors-5.6.3 · Data.Profunctor.Rep
Sieve (Forget r) (Const r)Defined in profunctors-5.6.3 · Data.Profunctor.Sieve
Functor (Forget r a)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Foldable (Forget r a)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Traversable (Forget r a)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Contravariant (Forget r a)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Semigroup r => Semigroup (Forget r a b)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Via Semigroup r => (a -> r)
Monoid r => Monoid (Forget r a b)Defined in profunctors-5.6.3 · Data.Profunctor.Types
Via Monoid r => (a -> r)
type Rep (Forget r) = Const rDefined in profunctors-5.6.3 · Data.Profunctor.Rep

typetype (:->) (p :: k -> k1 -> Type) (q :: k -> k1 -> Type) = forall (a :: k) (b :: k1). p a b -> q a b

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