Moduleprofunctors-5.6.3Haskell2010

Data.Profunctor.Choice

4 types
2 classes
4 values

Packageprofunctors-5.6.3
Exports10
LanguageHaskell2010
LicenceBSD-3-Clause
SourceChoice.hs

Strength

5 declarations

classclass Profunctor p => Choice (p :: Type -> Type -> Type) 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.

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

Instances22Choice, …

Monad m => Choice (Kleisli m)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Choice TaggedDefined in profunctors-5.6.3 · Data.Profunctor.Choice
Choice (PastroSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Choice (FreeMapping p)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
Choice (FreeTraversing p)Defined in profunctors-5.6.3 · Data.Profunctor.Traversing
Choice p => Choice (Tambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Choice p => Choice (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Choice p => Choice (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Profunctor p => Choice (TambaraSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Profunctor p => Choice (CofreeMapping p)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
Profunctor p => Choice (CofreeTraversing p)Defined in profunctors-5.6.3 · Data.Profunctor.Traversing
Comonad w => Choice (Cokleisli w)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
extract approximates costrength
Applicative f => Choice (Star f)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Monoid r => Choice (Forget r)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Choice (->)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Functor f => Choice (Joker f)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
ArrowChoice p => Choice (WrappedArrow p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
(Choice p, Choice q) => Choice (Product p q)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
(Choice p, Choice q) => Choice (Sum p q)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
(Functor f, Choice p) => Choice (Tannen f p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
(Functor f, Choice p) => Choice (Cayley f p)Defined in profunctors-5.6.3 · Data.Profunctor.Cayley
(Choice p, Choice q) => Choice (Procompose p q)Defined in profunctors-5.6.3 · Data.Profunctor.Composition

newtypenewtype TambaraSum (p :: Type -> Type -> Type) a b

TambaraSum is cofreely adjoins strength with respect to Either.

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

Constructors

TambaraSum
- runTambaraSum :: forall c. p (Either a c) (Either b c)

Instances7ProfunctorComonad, ProfunctorAdjunction, ProfunctorFunctor, Category, Choice, Profunctor, …

ProfunctorComonad TambaraSumDefined in profunctors-5.6.3 · Data.Profunctor.Choice
ProfunctorAdjunction PastroSum TambaraSumDefined in profunctors-5.6.3 · Data.Profunctor.Choice
ProfunctorFunctor TambaraSumDefined in profunctors-5.6.3 · Data.Profunctor.Choice
Category p => Category (TambaraSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Profunctor p => Choice (TambaraSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Profunctor p => Profunctor (TambaraSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Profunctor p => Functor (TambaraSum p a)Defined in profunctors-5.6.3 · Data.Profunctor.Choice

valuetambaraSum :: Choice p => p :-> q -> p :-> TambaraSum q

tambaraSum . untambaraSum ≡ id
untambaraSum . tambaraSum ≡ id

valueuntambaraSum :: Profunctor q => p :-> TambaraSum q -> p :-> q

tambaraSum . untambaraSum ≡ id
untambaraSum . tambaraSum ≡ id

datadata PastroSum (p :: Type -> Type -> Type) 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

Instances6ProfunctorMonad, ProfunctorAdjunction, ProfunctorFunctor, Choice, Profunctor, Functor

ProfunctorMonad PastroSumDefined in profunctors-5.6.3 · Data.Profunctor.Choice
ProfunctorAdjunction PastroSum TambaraSumDefined in profunctors-5.6.3 · Data.Profunctor.Choice
ProfunctorFunctor PastroSumDefined in profunctors-5.6.3 · Data.Profunctor.Choice
Choice (PastroSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Profunctor (PastroSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Functor (PastroSum p a)Defined in profunctors-5.6.3 · Data.Profunctor.Choice

Costrength

5 declarations

classclass Profunctor p => Cochoice (p :: Type -> Type -> Type) where

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

Instances12Cochoice, …

Cochoice (CopastroSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Cochoice (CotambaraSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Cochoice p => Cochoice (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Cochoice p => Cochoice (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Applicative f => Cochoice (Costar f)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Traversable f => Cochoice (Star f)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Cochoice (->)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Cochoice (Forget r)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
(Cochoice p, Cochoice q) => Cochoice (Product p q)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
(Cochoice p, Cochoice q) => Cochoice (Sum p q)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
(Functor f, Cochoice p) => Cochoice (Tannen f p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
(Functor f, Cochoice p) => Cochoice (Cayley f p)Defined in profunctors-5.6.3 · Data.Profunctor.Cayley

datadata CotambaraSum (q :: Type -> Type -> Type) 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

Instances6ProfunctorComonad, ProfunctorAdjunction, ProfunctorFunctor, Cochoice, Profunctor, Functor

ProfunctorComonad CotambaraSumDefined in profunctors-5.6.3 · Data.Profunctor.Choice
ProfunctorAdjunction CopastroSum CotambaraSumDefined in profunctors-5.6.3 · Data.Profunctor.Choice
ProfunctorFunctor CotambaraSumDefined in profunctors-5.6.3 · Data.Profunctor.Choice
Cochoice (CotambaraSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Profunctor (CotambaraSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Functor (CotambaraSum p a)Defined in profunctors-5.6.3 · Data.Profunctor.Choice

valuecotambaraSum :: Cochoice p => p :-> q -> p :-> CotambaraSum q

cotambaraSum . uncotambaraSum ≡ id
uncotambaraSum . cotambaraSum ≡ id

valueuncotambaraSum :: Profunctor q => p :-> CotambaraSum q -> p :-> q

cotambaraSum . uncotambaraSum ≡ id
uncotambaraSum . cotambaraSum ≡ id

newtypenewtype CopastroSum (p :: Type -> Type -> Type) a b

CopastroSum -| CotambaraSum

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

Constructors

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

Instances6ProfunctorMonad, ProfunctorAdjunction, ProfunctorFunctor, Cochoice, Profunctor, Functor

ProfunctorMonad CopastroSumDefined in profunctors-5.6.3 · Data.Profunctor.Choice
ProfunctorAdjunction CopastroSum CotambaraSumDefined in profunctors-5.6.3 · Data.Profunctor.Choice
ProfunctorFunctor CopastroSumDefined in profunctors-5.6.3 · Data.Profunctor.Choice
Cochoice (CopastroSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Profunctor (CopastroSum p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Functor (CopastroSum p a)Defined in profunctors-5.6.3 · Data.Profunctor.Choice