profunctors-5.2.1: Profunctors

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

Data.Profunctor.Closed

Description

 

Synopsis

Documentation

class Profunctor p => Closed p where #

A strong profunctor allows the monoidal structure to pass through.

A closed profunctor allows the closed structure to pass through.

Minimal complete definition

closed

Methods

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

Instances

Closed (->) # 

Methods

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

(Distributive f, Monad f) => Closed (Kleisli f) # 

Methods

closed :: Kleisli f a b -> Kleisli f (x -> a) (x -> b) #

Functor f => Closed (Cokleisli f) # 

Methods

closed :: Cokleisli f a b -> Cokleisli f (x -> a) (x -> b) #

Closed (Tagged *) # 

Methods

closed :: Tagged * a b -> Tagged * (x -> a) (x -> b) #

Functor f => Closed (Costar f) # 

Methods

closed :: Costar f a b -> Costar f (x -> a) (x -> b) #

Distributive f => Closed (Star f) # 

Methods

closed :: Star f a b -> Star f (x -> a) (x -> b) #

Closed (Environment p) # 

Methods

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

Profunctor p => Closed (Closure p) # 

Methods

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

Closed (FreeMapping p) # 

Methods

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

Profunctor p => Closed (CofreeMapping p) # 

Methods

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

Closed p => Closed (Coyoneda p) # 

Methods

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

Closed p => Closed (Yoneda p) # 

Methods

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

(Closed p, Closed q) => Closed (Procompose p q) # 

Methods

closed :: Procompose p q a b -> Procompose p q (x -> a) (x -> b) #

(Closed p, Closed q) => Closed (Product * * p q) # 

Methods

closed :: Product * * p q a b -> Product * * p q (x -> a) (x -> b) #

(Functor f, Closed p) => Closed (Tannen * * * f p) # 

Methods

closed :: Tannen * * * f p a b -> Tannen * * * f p (x -> a) (x -> b) #

newtype Closure p a b #

Closure adjoins a Closed structure to any Profunctor.

Analogous to Tambara for Strong.

Constructors

Closure 

Fields

Instances

ProfunctorComonad Closure # 
ProfunctorFunctor Closure # 

Methods

promap :: Profunctor p => (p :-> q) -> Closure p :-> Closure q #

ProfunctorAdjunction Environment Closure # 
Arrow p => Arrow (Closure p) # 

Methods

arr :: (b -> c) -> Closure p b c #

first :: Closure p b c -> Closure p (b, d) (c, d) #

second :: Closure p b c -> Closure p (d, b) (d, c) #

(***) :: Closure p b c -> Closure p b' c' -> Closure p (b, b') (c, c') #

(&&&) :: Closure p b c -> Closure p b c' -> Closure p b (c, c') #

ArrowZero p => ArrowZero (Closure p) # 

Methods

zeroArrow :: Closure p b c #

ArrowPlus p => ArrowPlus (Closure p) # 

Methods

(<+>) :: Closure p b c -> Closure p b c -> Closure p b c #

ArrowLoop p => ArrowLoop (Closure p) # 

Methods

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

Profunctor p => Profunctor (Closure p) # 

Methods

dimap :: (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 #

(#.) :: Coercible * c b => (b -> c) -> Closure p a b -> Closure p a c #

(.#) :: Coercible * b a => Closure p b c -> (a -> b) -> Closure p a c #

Strong p => Strong (Closure p) # 

Methods

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

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

Profunctor p => Closed (Closure p) # 

Methods

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

Category * p => Category * (Closure p) # 

Methods

id :: cat a a #

(.) :: cat b c -> cat a b -> cat a c #

Profunctor p => Functor (Closure p a) # 

Methods

fmap :: (a -> b) -> Closure p a a -> Closure p a b #

(<$) :: a -> Closure p a b -> Closure p a a #

(Profunctor p, Arrow p) => Applicative (Closure p a) # 

Methods

pure :: a -> Closure p a a #

(<*>) :: Closure p a (a -> b) -> Closure p a a -> Closure p a b #

(*>) :: Closure p a a -> Closure p a b -> Closure p a b #

(<*) :: Closure p a a -> Closure p a b -> Closure p a a #

(Profunctor p, ArrowPlus p) => Alternative (Closure p a) # 

Methods

empty :: Closure p a a #

(<|>) :: Closure p a a -> Closure p a a -> Closure p a a #

some :: Closure p a a -> Closure p a [a] #

many :: Closure p a a -> Closure p a [a] #

(Profunctor p, Arrow p, Monoid b) => Monoid (Closure p a b) # 

Methods

mempty :: Closure p a b #

mappend :: Closure p a b -> Closure p a b -> Closure p a b #

mconcat :: [Closure p a b] -> Closure p a b #

close :: Closed p => (p :-> q) -> p :-> Closure q #

unclose :: Profunctor q => (p :-> Closure q) -> p :-> q #

data Environment p a b where #

Constructors

Environment :: ((z -> y) -> b) -> p x y -> (a -> z -> x) -> Environment p a b 

Instances

ProfunctorMonad Environment # 
ProfunctorFunctor Environment # 

Methods

promap :: Profunctor p => (p :-> q) -> Environment p :-> Environment q #

ProfunctorAdjunction Environment Closure # 
Profunctor (Environment p) # 

Methods

dimap :: (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 #

(#.) :: Coercible * c b => (b -> c) -> Environment p a b -> Environment p a c #

(.#) :: Coercible * b a => Environment p b c -> (a -> b) -> Environment p a c #

Closed (Environment p) # 

Methods

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

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