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/

Contents

Profunctors
Profunctorial Strength
Closed
Profunctorial Costrength
Common Profunctors

Synopsis

class Profunctor
class Strong
value uncurry'
class Choice
class Closed
value curry'
class Mapping
class Costrong
class Cochoice
newtype Star
newtype Costar
newtype WrappedArrow
newtype Forget
type :->

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

Profunctors

classclass 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

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

Source#

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

Source#

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

Source#

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

Source#

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)

Source#

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

Source#

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)

Source#

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, ArrowZero, ArrowLoop, …

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
ArrowZero p => ArrowZero (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
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)

Source#

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

Source#

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