Data.Profunctor.Choice

Strength

class Profunctor p => Choice p where

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)

Laws:

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

Laws:

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

Methods

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

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

Monad m => Choice (Kleisli m)

Methods

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

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

Comonad w => Choice (Cokleisli w)

extract approximates costrength

Methods

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

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

Choice (Tagged *)

Methods

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

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

Monoid r => Choice (Forget r)

Methods

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

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

ArrowChoice p => Choice (WrappedArrow p)

Methods

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

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

Traversable w => Choice (Costar w)

Methods

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

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

Applicative f => Choice (Star f)

Methods

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

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

Choice p => Choice (Tambara p)

Methods

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

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

Choice (PastroSum p)

Methods

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

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

Profunctor p => Choice (TambaraSum p)

Methods

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

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

Choice (FreeTraversing p)

Methods

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

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

Profunctor p => Choice (CofreeTraversing p)

Methods

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

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

Choice (FreeMapping p)

Methods

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

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

Profunctor p => Choice (CofreeMapping p)

Methods

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

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

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)

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

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)

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

Methods

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

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

Functor f => Choice (Joker * * f)

Methods

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

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

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

Methods

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

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

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

Methods

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

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

newtype TambaraSum p a b

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

• runTambaraSum :: forall c. p (Either a c) (Either b c)

Instances

ProfunctorComonad TambaraSum

Methods

proextract :: Profunctor p => TambaraSum p :-> p

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

ProfunctorFunctor TambaraSum

Methods

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

ProfunctorAdjunction PastroSum TambaraSum

Methods

unit :: Profunctor p => p :-> TambaraSum (PastroSum p)

counit :: Profunctor p => PastroSum (TambaraSum p) :-> p

Profunctor p => Profunctor (TambaraSum p)

Methods

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

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

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

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

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

Profunctor p => Choice (TambaraSum p)

Methods

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

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

Category * p => Category * (TambaraSum p)

Methods

id :: cat a a

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

Profunctor p => Functor (TambaraSum p a)

Methods

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

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

tambaraSum :: Choice p => (p :-> q) -> p :-> TambaraSum q

tambaraSum . untambaraSum ≡ id
untambaraSum . tambaraSum ≡ id

untambaraSum :: Profunctor q => (p :-> TambaraSum q) -> p :-> q

tambaraSum . untambaraSum ≡ id
untambaraSum . tambaraSum ≡ id

data PastroSum p a b where

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

Methods

proreturn :: Profunctor p => p :-> PastroSum p

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

ProfunctorFunctor PastroSum

Methods

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

ProfunctorAdjunction PastroSum TambaraSum

Methods

unit :: Profunctor p => p :-> TambaraSum (PastroSum p)

counit :: Profunctor p => PastroSum (TambaraSum p) :-> p

Profunctor (PastroSum p)

Methods

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

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

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

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

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

Choice (PastroSum p)

Methods

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

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

Costrength

class Profunctor p => Cochoice p where

Minimal complete definition

unleft | unright

Methods

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

Laws:

unleft ≡ unright . 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 . unleft ≡ unleft . 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

Laws:

unright ≡ unleft . 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 . unright ≡ unright . 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 (->)

Methods

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

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

Applicative f => Cochoice (Costar f)

Methods

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

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

Traversable f => Cochoice (Star f)

Methods

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

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

Cochoice (CopastroSum p)

Methods

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

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

Cochoice (CotambaraSum p)

Methods

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

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

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

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

Methods

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

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

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

Methods

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

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

data CotambaraSum q a b where

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

Constructors

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

Instances

ProfunctorComonad CotambaraSum

Methods

proextract :: Profunctor p => CotambaraSum p :-> p

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

ProfunctorFunctor CotambaraSum

Methods

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

ProfunctorAdjunction CopastroSum CotambaraSum

Methods

unit :: Profunctor p => p :-> CotambaraSum (CopastroSum p)

counit :: Profunctor p => CopastroSum (CotambaraSum p) :-> p

Profunctor (CotambaraSum p)

Methods

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

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

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

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

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

Cochoice (CotambaraSum p)

Methods

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

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

Functor (CotambaraSum p a)

Methods

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

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

cotambaraSum :: Cochoice p => (p :-> q) -> p :-> CotambaraSum q

cotambaraSum . uncotambaraSum ≡ id
uncotambaraSum . cotambaraSum ≡ id

uncotambaraSum :: Profunctor q => (p :-> CotambaraSum q) -> p :-> q

cotambaraSum . uncotambaraSum ≡ id
uncotambaraSum . cotambaraSum ≡ id

newtype CopastroSum p a b

CopastroSum -| CotambaraSum

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

Constructors

CopastroSum

Fields

• runCopastroSum :: forall r. Cochoice r => (forall x y. p x y -> r x y) -> r a b

Instances

ProfunctorMonad CopastroSum

Methods

proreturn :: Profunctor p => p :-> CopastroSum p

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

ProfunctorFunctor CopastroSum

Methods

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

ProfunctorAdjunction CopastroSum CotambaraSum

Methods

unit :: Profunctor p => p :-> CotambaraSum (CopastroSum p)

counit :: Profunctor p => CopastroSum (CotambaraSum p) :-> p

Profunctor (CopastroSum p)

Methods

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

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

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

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

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

Cochoice (CopastroSum p)

Methods

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

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