Moduleprofunctors-5.6.3Haskell2010

Data.Profunctor.Yoneda

Synopsis

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

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

Instances13ProfunctorComonad, ProfunctorMonad, ProfunctorFunctor, Category, Choice, Cochoice, …

ProfunctorComonad YonedaDefined in profunctors-5.6.3 · Data.Profunctor.Yoneda
ProfunctorMonad YonedaDefined in profunctors-5.6.3 · Data.Profunctor.Yoneda
ProfunctorFunctor YonedaDefined in profunctors-5.6.3 · Data.Profunctor.Yoneda
(Category p, Profunctor p) => Category (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Choice p => Choice (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Cochoice p => Cochoice (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Closed p => Closed (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Mapping p => Mapping (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Costrong p => Costrong (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Strong p => Strong (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Profunctor (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Traversing p => Traversing (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Functor (Yoneda p a)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda

valueextractYoneda :: Yoneda p a b -> p a b

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

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

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

datadata Coyoneda (p :: Type -> Type -> Type) a b where

Instances13ProfunctorComonad, ProfunctorMonad, ProfunctorFunctor, Category, Choice, Cochoice, …

ProfunctorComonad CoyonedaDefined in profunctors-5.6.3 · Data.Profunctor.Yoneda
ProfunctorMonad CoyonedaDefined in profunctors-5.6.3 · Data.Profunctor.Yoneda
ProfunctorFunctor CoyonedaDefined in profunctors-5.6.3 · Data.Profunctor.Yoneda
(Category p, Profunctor p) => Category (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Choice p => Choice (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Cochoice p => Cochoice (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Closed p => Closed (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Mapping p => Mapping (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Costrong p => Costrong (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Strong p => Strong (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Profunctor (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Traversing p => Traversing (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Functor (Coyoneda p a)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda

valuereturnCoyoneda :: p a b -> Coyoneda p a b

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

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

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