Data.Profunctor.Yoneda

Documentation

newtype Yoneda p a b

This is the cofree profunctor given a data constructor of kind * -> * -> *

Constructors

Yoneda

Fields

• runYoneda :: forall x y. (x -> a) -> (b -> y) -> p x y

Instances

ProfunctorComonad Yoneda

Methods

proextract :: Profunctor p => Yoneda p :-> p

produplicate :: Profunctor p => Yoneda p :-> Yoneda (Yoneda p)

ProfunctorMonad Yoneda

Methods

proreturn :: Profunctor p => p :-> Yoneda p

projoin :: Profunctor p => Yoneda (Yoneda p) :-> Yoneda p

ProfunctorFunctor Yoneda

Methods

promap :: Profunctor p => (p :-> q) -> Yoneda p :-> Yoneda q

Profunctor (Yoneda p)

Methods

dimap :: (a -> b) -> (c -> d) -> Yoneda p b c -> Yoneda p a d

lmap :: (a -> b) -> Yoneda p b c -> Yoneda p a c

rmap :: (b -> c) -> Yoneda p a b -> Yoneda p a c

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

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

Costrong p => Costrong (Yoneda p)

Methods

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

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

Strong p => Strong (Yoneda p)

Methods

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

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

Cochoice p => Cochoice (Yoneda p)

Methods

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

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

Choice p => Choice (Yoneda p)

Methods

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

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

Closed p => Closed (Yoneda p)

Methods

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

Traversing p => Traversing (Yoneda p)

Methods

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

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

Mapping p => Mapping (Yoneda p)

Methods

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

(Category * p, Profunctor p) => Category * (Yoneda p)

Methods

id :: cat a a

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

Functor (Yoneda p a)

Methods

fmap :: (a -> b) -> Yoneda p a a -> Yoneda p a b

(<$) :: a -> Yoneda p a b -> Yoneda p a a

extractYoneda :: Yoneda p a b -> p a b

projoin . extractYoneda ≡ id
extractYoneda . projoin ≡ id
projoin ≡ extractYoneda

duplicateYoneda :: Yoneda p a b -> Yoneda (Yoneda p) a b

projoin . duplicateYoneda ≡ id
duplicateYoneda . projoin ≡ id
duplicateYoneda = proreturn

data Coyoneda p a b where

Constructors

Coyoneda :: (a -> x) -> (y -> b) -> p x y -> Coyoneda p a b

Instances

ProfunctorComonad Coyoneda

Methods

proextract :: Profunctor p => Coyoneda p :-> p

produplicate :: Profunctor p => Coyoneda p :-> Coyoneda (Coyoneda p)

ProfunctorMonad Coyoneda

Methods

proreturn :: Profunctor p => p :-> Coyoneda p

projoin :: Profunctor p => Coyoneda (Coyoneda p) :-> Coyoneda p

ProfunctorFunctor Coyoneda

Methods

promap :: Profunctor p => (p :-> q) -> Coyoneda p :-> Coyoneda q

Profunctor (Coyoneda p)

Methods

dimap :: (a -> b) -> (c -> d) -> Coyoneda p b c -> Coyoneda p a d

lmap :: (a -> b) -> Coyoneda p b c -> Coyoneda p a c

rmap :: (b -> c) -> Coyoneda p a b -> Coyoneda p a c

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

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

Costrong p => Costrong (Coyoneda p)

Methods

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

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

Strong p => Strong (Coyoneda p)

Methods

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

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

Cochoice p => Cochoice (Coyoneda p)

Methods

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

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

Choice p => Choice (Coyoneda p)

Methods

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

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

Closed p => Closed (Coyoneda p)

Methods

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

Traversing p => Traversing (Coyoneda p)

Methods

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

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

Mapping p => Mapping (Coyoneda p)

Methods

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

(Category * p, Profunctor p) => Category * (Coyoneda p)

Methods

id :: cat a a

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

returnCoyoneda :: p a b -> Coyoneda p a b

returnCoyoneda . proextract ≡ id
proextract . returnCoyoneda ≡ id
produplicate ≡ returnCoyoneda

joinCoyoneda :: Coyoneda (Coyoneda p) a b -> Coyoneda p a b

joinCoyoneda . produplicate ≡ id
produplicate . joinCoyoneda ≡ id
joinCoyoneda ≡ proextract