profunctors-5.6.2: Profunctors
Copyright(C) 2014-2015 Edward Kmett
LicenseBSD-style (see the file LICENSE)
MaintainerEdward Kmett <ekmett@gmail.com>
Stabilityexperimental
Portabilityportable
Safe HaskellTrustworthy
LanguageHaskell2010

Data.Profunctor.Cayley

Description

 
Synopsis
  • newtype Cayley (f :: k -> Type) (p :: k1 -> k2 -> k) (a :: k1) (b :: k2) = Cayley {}
  • mapCayley :: forall {k1} {k2} {k3} f g (p :: k2 -> k3 -> k1) (x :: k2) (y :: k3). (forall (a :: k1). f a -> g a) -> Cayley f p x y -> Cayley g p x y

Documentation

newtype Cayley (f :: k -> Type) (p :: k1 -> k2 -> k) (a :: k1) (b :: k2) Source #

Static arrows. Lifted by Applicative.

Cayley has a polymorphic kind since 5.6.

Constructors

Cayley 

Fields

Instances

Instances details
Functor f => ProfunctorFunctor (Cayley f :: (Type -> Type -> Type) -> Type -> Type -> Type) Source # 
Instance details

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 Source #

(Applicative f, Category p) => Category (Cayley f p :: k -> k -> Type) Source # 
Instance details

Defined in Data.Profunctor.Cayley

Methods

id :: forall (a :: k). Cayley f p a a #

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

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

Cayley transforms Comonads in Hask into comonads on Prof

Instance details

Defined in Data.Profunctor.Cayley

Methods

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

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

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

Cayley transforms Monads in Hask into monads on Prof

Instance details

Defined in Data.Profunctor.Cayley

Methods

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

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

(Applicative f, Arrow p) => Arrow (Cayley f p) Source # 
Instance details

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, ArrowChoice p) => ArrowChoice (Cayley f p) Source # 
Instance details

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) Source # 
Instance details

Defined in Data.Profunctor.Cayley

Methods

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

(Applicative f, ArrowPlus p) => ArrowPlus (Cayley f p) Source # 
Instance details

Defined in Data.Profunctor.Cayley

Methods

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

(Applicative f, ArrowZero p) => ArrowZero (Cayley f p) Source # 
Instance details

Defined in Data.Profunctor.Cayley

Methods

zeroArrow :: Cayley f p b c #

(Functor f, Choice p) => Choice (Cayley f p) Source # 
Instance details

Defined in Data.Profunctor.Cayley

Methods

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

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

(Functor f, Cochoice p) => Cochoice (Cayley f p) Source # 
Instance details

Defined in Data.Profunctor.Cayley

Methods

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

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

(Functor f, Closed p) => Closed (Cayley f p) Source # 
Instance details

Defined in Data.Profunctor.Cayley

Methods

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

(Functor f, Mapping p) => Mapping (Cayley f p) Source # 
Instance details

Defined in Data.Profunctor.Cayley

Methods

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

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

(Functor f, Costrong p) => Costrong (Cayley f p) Source # 
Instance details

Defined in Data.Profunctor.Cayley

Methods

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

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

(Functor f, Strong p) => Strong (Cayley f p) Source # 
Instance details

Defined in Data.Profunctor.Cayley

Methods

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

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

(Functor f, Traversing p) => Traversing (Cayley f p) Source # 
Instance details

Defined in Data.Profunctor.Cayley

Methods

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

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

(Functor f, Profunctor p) => Profunctor (Cayley f p) Source # 
Instance details

Defined in Data.Profunctor.Cayley

Methods

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

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

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

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

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

mapCayley :: forall {k1} {k2} {k3} f g (p :: k2 -> k3 -> k1) (x :: k2) (y :: k3). (forall (a :: k1). f a -> g a) -> Cayley f p x y -> Cayley g p x y Source #