Data.Profunctor.Cayley

Documentation

newtype Cayley f p a b

Static arrows. Lifted by Applicative.

Cayley has a polymorphic kind since 5.6.

Constructors

Cayley

Fields

• runCayley :: f (p a b)

Instances

(Applicative f, Category p) => Category (Cayley f p :: k -> k -> Type)

Defined in Data.Profunctor.Cayley

Methods

id :: forall (a :: k0). Cayley f p a a

(.) :: forall (b :: k0) (c :: k0) (a :: k0). Cayley f p b c -> Cayley f p a b -> Cayley f p a c

Functor f => ProfunctorFunctor (Cayley f :: (Type -> Type -> Type) -> Type -> Type -> Type)

Defined in Data.Profunctor.Cayley

Methods

promap :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Profunctor p => (p :-> q) -> Cayley f p :-> Cayley f q

Comonad f => ProfunctorComonad (Cayley f :: (Type -> Type -> Type) -> Type -> Type -> Type)

Cayley transforms Comonads in Hask into comonads on Prof

Defined in Data.Profunctor.Cayley

Methods

proextract :: forall (p :: Type -> Type -> Type). Profunctor p => Cayley f p :-> p

produplicate :: forall (p :: Type -> Type -> Type). Profunctor p => Cayley f p :-> Cayley f (Cayley f p)

(Functor f, Monad f) => ProfunctorMonad (Cayley f :: (Type -> Type -> Type) -> Type -> Type -> Type)

Cayley transforms Monads in Hask into monads on Prof

Defined in Data.Profunctor.Cayley

Methods

proreturn :: forall (p :: Type -> Type -> Type). Profunctor p => p :-> Cayley f p

projoin :: forall (p :: Type -> Type -> Type). Profunctor p => Cayley f (Cayley f p) :-> Cayley f p

(Applicative f, Arrow p) => Arrow (Cayley f p)

Defined in Data.Profunctor.Cayley

Methods

arr :: (b -> c) -> Cayley f p b c

first :: Cayley f p b c -> Cayley f p (b, d) (c, d)

second :: Cayley f p b c -> Cayley f p (d, b) (d, c)

(***) :: Cayley f p b c -> Cayley f p b' c' -> Cayley f p (b, b') (c, c')

(&&&) :: Cayley f p b c -> Cayley f p b c' -> Cayley f p b (c, c')

(Applicative f, ArrowZero p) => ArrowZero (Cayley f p)

Defined in Data.Profunctor.Cayley

Methods

zeroArrow :: Cayley f p b c

(Applicative f, ArrowPlus p) => ArrowPlus (Cayley f p)

Defined in Data.Profunctor.Cayley

Methods

(<+>) :: Cayley f p b c -> Cayley f p b c -> Cayley f p b c

(Applicative f, ArrowChoice p) => ArrowChoice (Cayley f p)

Defined in Data.Profunctor.Cayley

Methods

left :: Cayley f p b c -> Cayley f p (Either b d) (Either c d)

right :: Cayley f p b c -> Cayley f p (Either d b) (Either d c)

(+++) :: Cayley f p b c -> Cayley f p b' c' -> Cayley f p (Either b b') (Either c c')

(|||) :: Cayley f p b d -> Cayley f p c d -> Cayley f p (Either b c) d

(Applicative f, ArrowLoop p) => ArrowLoop (Cayley f p)

Defined in Data.Profunctor.Cayley

Methods

loop :: Cayley f p (b, d) (c, d) -> Cayley f p b c

(Functor f, Profunctor p) => Profunctor (Cayley f p)

Defined in Data.Profunctor.Cayley

Methods

dimap :: (a -> b) -> (c -> d) -> Cayley f p b c -> Cayley f p a d

lmap :: (a -> b) -> Cayley f p b c -> Cayley f p a c

rmap :: (b -> c) -> Cayley f p a b -> Cayley f p a c

(#.) :: forall a b c q. Coercible c b => q b c -> Cayley f p a b -> Cayley f p a c

(.#) :: forall a b c q. Coercible b a => Cayley f p b c -> q a b -> Cayley f p a c

(Functor f, Costrong p) => Costrong (Cayley f p)

Defined in Data.Profunctor.Cayley

Methods

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

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

(Functor f, Strong p) => Strong (Cayley f p)

Defined in Data.Profunctor.Cayley

Methods

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

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

(Functor f, Closed p) => Closed (Cayley f p)

Defined in Data.Profunctor.Cayley

Methods

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

(Functor f, Cochoice p) => Cochoice (Cayley f p)

Defined in Data.Profunctor.Cayley

Methods

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

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

(Functor f, Choice p) => Choice (Cayley f p)

Defined in Data.Profunctor.Cayley

Methods

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

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

(Functor f, Traversing p) => Traversing (Cayley f p)

Defined in Data.Profunctor.Cayley

Methods

traverse' :: Traversable f0 => Cayley f p a b -> Cayley f p (f0 a) (f0 b)

wander :: (forall (f0 :: Type -> Type). Applicative f0 => (a -> f0 b) -> s -> f0 t) -> Cayley f p a b -> Cayley f p s t

(Functor f, Mapping p) => Mapping (Cayley f p)

Defined in Data.Profunctor.Cayley

Methods

map' :: Functor f0 => Cayley f p a b -> Cayley f p (f0 a) (f0 b)

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

mapCayley :: (forall a. f a -> g a) -> Cayley f p x y -> Cayley g p x y