profunctors-5.2.1: Profunctors

Copyright(C) 2014-2015 Edward Kmett
LicenseBSD-style (see the file LICENSE)
MaintainerEdward Kmett <ekmett@gmail.com>
Stabilityprovisional
PortabilityRank2Types
Safe HaskellSafe
LanguageHaskell2010

Data.Profunctor.Choice

Contents

Description

 

Synopsis

Strength

class Profunctor p => Choice p 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.

Minimal complete definition

left' | right'

Methods

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

Laws:

left'dimap swapE swapE . right' where
  swapE :: Either a b -> Either b a
  swapE = either Right Left
rmap Leftlmap 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) Source #

Laws:

right'dimap swapE swapE . left' where
  swapE :: Either a b -> Either b a
  swapE = either Right Left
rmap Rightlmap 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)

Instances

Choice (->) Source # 

Methods

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

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

Monad m => Choice (Kleisli m) Source # 

Methods

left' :: Kleisli m a b -> Kleisli m (Either a c) (Either b c) Source #

right' :: Kleisli m a b -> Kleisli m (Either c a) (Either c b) Source #

Comonad w => Choice (Cokleisli w) Source #

extract approximates costrength

Methods

left' :: Cokleisli w a b -> Cokleisli w (Either a c) (Either b c) Source #

right' :: Cokleisli w a b -> Cokleisli w (Either c a) (Either c b) Source #

Choice (Tagged *) Source # 

Methods

left' :: Tagged * a b -> Tagged * (Either a c) (Either b c) Source #

right' :: Tagged * a b -> Tagged * (Either c a) (Either c b) Source #

Monoid r => Choice (Forget r) Source # 

Methods

left' :: Forget r a b -> Forget r (Either a c) (Either b c) Source #

right' :: Forget r a b -> Forget r (Either c a) (Either c b) Source #

ArrowChoice p => Choice (WrappedArrow p) Source # 

Methods

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

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

Traversable w => Choice (Costar w) Source # 

Methods

left' :: Costar w a b -> Costar w (Either a c) (Either b c) Source #

right' :: Costar w a b -> Costar w (Either c a) (Either c b) Source #

Applicative f => Choice (Star f) Source # 

Methods

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

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

Choice p => Choice (Tambara p) Source # 

Methods

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

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

Choice (PastroSum p) Source # 

Methods

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

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

Profunctor p => Choice (TambaraSum p) Source # 

Methods

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

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

Choice (FreeTraversing p) Source # 

Methods

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

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

Profunctor p => Choice (CofreeTraversing p) Source # 
Choice (FreeMapping p) Source # 

Methods

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

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

Profunctor p => Choice (CofreeMapping p) Source # 

Methods

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

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

Choice p => Choice (Coyoneda p) Source # 

Methods

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

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

Choice p => Choice (Yoneda p) Source # 

Methods

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

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

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

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 #

(Choice p, Choice q) => Choice (Procompose p q) Source # 

Methods

left' :: Procompose p q a b -> Procompose p q (Either a c) (Either b c) Source #

right' :: Procompose p q a b -> Procompose p q (Either c a) (Either c b) Source #

Functor f => Choice (Joker * * f) Source # 

Methods

left' :: Joker * * f a b -> Joker * * f (Either a c) (Either b c) Source #

right' :: Joker * * f a b -> Joker * * f (Either c a) (Either c b) Source #

(Choice p, Choice q) => Choice (Product * * p q) Source # 

Methods

left' :: Product * * p q a b -> Product * * p q (Either a c) (Either b c) Source #

right' :: Product * * p q a b -> Product * * p q (Either c a) (Either c b) Source #

(Functor f, Choice p) => Choice (Tannen * * * f p) Source # 

Methods

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

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

newtype TambaraSum p a b Source #

TambaraSum is cofreely adjoins strength with respect to Either.

Note: this is not dual to Tambara. It is Tambara with respect to a different tensor.

Constructors

TambaraSum 

Fields

Instances

ProfunctorComonad TambaraSum Source # 
ProfunctorFunctor TambaraSum Source # 

Methods

promap :: Profunctor p => (p :-> q) -> TambaraSum p :-> TambaraSum q Source #

ProfunctorAdjunction PastroSum TambaraSum Source # 
Profunctor p => Profunctor (TambaraSum p) Source # 

Methods

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

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

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

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

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

Profunctor p => Choice (TambaraSum p) Source # 

Methods

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

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

Category * p => Category * (TambaraSum p) Source # 

Methods

id :: cat a a #

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

Profunctor p => Functor (TambaraSum p a) Source # 

Methods

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

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

data PastroSum p a b where Source #

PastroSum -| TambaraSum

PastroSum freely constructs strength with respect to Either.

Constructors

PastroSum :: (Either y z -> b) -> p x y -> (a -> Either x z) -> PastroSum p a b 

Instances

ProfunctorMonad PastroSum Source # 
ProfunctorFunctor PastroSum Source # 

Methods

promap :: Profunctor p => (p :-> q) -> PastroSum p :-> PastroSum q Source #

ProfunctorAdjunction PastroSum TambaraSum Source # 
Profunctor (PastroSum p) Source # 

Methods

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

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

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

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

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

Choice (PastroSum p) Source # 

Methods

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

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

Costrength

class Profunctor p => Cochoice p where Source #

Minimal complete definition

unleft | unright

Methods

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

Laws:

unleftunright . 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 . unleftunleft . 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 Source #

Laws:

unrightunleft . 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 . unrightunright . 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)

Instances

Cochoice (->) Source # 

Methods

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

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

Applicative f => Cochoice (Costar f) Source # 

Methods

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

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

Traversable f => Cochoice (Star f) Source # 

Methods

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

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

Cochoice (CopastroSum p) Source # 

Methods

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

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

Cochoice (CotambaraSum p) Source # 

Methods

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

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

Cochoice p => Cochoice (Coyoneda p) Source # 

Methods

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

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

Cochoice p => Cochoice (Yoneda p) Source # 

Methods

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

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

(Cochoice p, Cochoice q) => Cochoice (Product * * p q) Source # 

Methods

unleft :: Product * * p q (Either a d) (Either b d) -> Product * * p q a b Source #

unright :: Product * * p q (Either d a) (Either d b) -> Product * * p q a b Source #

(Functor f, Cochoice p) => Cochoice (Tannen * * * f p) Source # 

Methods

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

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

data CotambaraSum q a b where Source #

CotambaraSum cofreely constructs costrength with respect to Either (aka Choice)

Constructors

CotambaraSum :: Cochoice r => (r :-> q) -> r a b -> CotambaraSum q a b 

newtype CopastroSum p a b Source #

CopastroSum -| CotambaraSum

CopastroSum freely constructs costrength with respect to Either (aka Choice)

Constructors

CopastroSum 

Fields