Copyright	(C) 2014-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	portable
Safe Haskell	Safe
Language	Haskell2010

Data.Profunctor.Monad

Description

Synopsis

class ProfunctorFunctor t where
- promap :: Profunctor p => (p :-> q) -> t p :-> t q
class ProfunctorFunctor t => ProfunctorMonad t where
- proreturn :: Profunctor p => p :-> t p
- projoin :: Profunctor p => t (t p) :-> t p
class ProfunctorFunctor t => ProfunctorComonad t where
- proextract :: Profunctor p => t p :-> p
- produplicate :: Profunctor p => t p :-> t (t p)

Documentation

class ProfunctorFunctor t where Source #

ProfunctorFunctor has a polymorphic kind since 5.6 .

Methods

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

Laws:

promap f . promap g ≡ promap (f . g)
promap id ≡ id

Instances

Instances details

ProfunctorFunctor ( Ran p :: ( Type -> Type -> Type ) -> k -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Ran Methods promap :: forall (p0 :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p0 => (p0 :-> q) -> Ran p p0 :-> Ran p q Source #
ProfunctorFunctor ( Procompose p :: ( Type -> Type -> Type ) -> Type -> k -> Type ) Source #
Instance details Defined in Data.Profunctor.Composition Methods promap :: forall (p0 :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p0 => (p0 :-> q) -> Procompose p p0 :-> Procompose p q Source #
ProfunctorFunctor ( Rift p :: ( Type -> Type -> Type ) -> Type -> k -> Type ) Source #
Instance details Defined in Data.Profunctor.Composition Methods promap :: forall (p0 :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p0 => (p0 :-> q) -> Rift p p0 :-> Rift p q Source #
ProfunctorFunctor Copastro Source #
Instance details Defined in Data.Profunctor.Strong Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> Copastro p :-> Copastro q Source #
ProfunctorFunctor Cotambara Source #
Instance details Defined in Data.Profunctor.Strong Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> Cotambara p :-> Cotambara q Source #
ProfunctorFunctor Pastro Source #
Instance details Defined in Data.Profunctor.Strong Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> Pastro p :-> Pastro q Source #
ProfunctorFunctor Tambara Source #
Instance details Defined in Data.Profunctor.Strong Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> Tambara p :-> Tambara q Source #
ProfunctorFunctor Environment Source #
Instance details Defined in Data.Profunctor.Closed Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> Environment p :-> Environment q Source #
ProfunctorFunctor Closure Source #
Instance details Defined in Data.Profunctor.Closed Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> Closure p :-> Closure q Source #
ProfunctorFunctor CopastroSum Source #
Instance details Defined in Data.Profunctor.Choice Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> CopastroSum p :-> CopastroSum q Source #
ProfunctorFunctor CotambaraSum Source #
Instance details Defined in Data.Profunctor.Choice Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> CotambaraSum p :-> CotambaraSum q Source #
ProfunctorFunctor PastroSum Source #
Instance details Defined in Data.Profunctor.Choice Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> PastroSum p :-> PastroSum q Source #
ProfunctorFunctor TambaraSum Source #
Instance details Defined in Data.Profunctor.Choice Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> TambaraSum p :-> TambaraSum q Source #
ProfunctorFunctor FreeTraversing Source #
Instance details Defined in Data.Profunctor.Traversing Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> FreeTraversing p :-> FreeTraversing q Source #
ProfunctorFunctor CofreeTraversing Source #
Instance details Defined in Data.Profunctor.Traversing Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> CofreeTraversing p :-> CofreeTraversing q Source #
ProfunctorFunctor FreeMapping Source #
Instance details Defined in Data.Profunctor.Mapping Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> FreeMapping p :-> FreeMapping q Source #
ProfunctorFunctor CofreeMapping Source #
Instance details Defined in Data.Profunctor.Mapping Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> CofreeMapping p :-> CofreeMapping q Source #
ProfunctorFunctor Coyoneda Source #
Instance details Defined in Data.Profunctor.Yoneda Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> Coyoneda p :-> Coyoneda q Source #
ProfunctorFunctor Yoneda Source #
Instance details Defined in Data.Profunctor.Yoneda Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> Yoneda p :-> Yoneda q Source #
ProfunctorFunctor ( Sum p :: ( Type -> Type -> Type ) -> Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Monad Methods promap :: forall (p0 :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p0 => (p0 :-> q) -> Sum p p0 :-> Sum p q Source #
ProfunctorFunctor ( Product p :: ( Type -> Type -> Type ) -> Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Monad Methods promap :: forall (p0 :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p0 => (p0 :-> q) -> Product p p0 :-> Product p q Source #
Functor f => ProfunctorFunctor ( Tannen f :: ( Type -> Type -> Type ) -> Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Monad Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> Tannen f p :-> Tannen f q Source #
Functor f => ProfunctorFunctor ( Cayley f :: ( Type -> Type -> Type ) -> Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Cayley Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> Cayley f p :-> Cayley f q Source #

class ProfunctorFunctor t => ProfunctorMonad t where Source #

Laws:

promap f . proreturn ≡ proreturn . f
projoin . proreturn ≡ id
projoin . promap proreturn ≡ id
projoin . projoin ≡ projoin . promap projoin

Methods

proreturn :: Profunctor p => p :-> t p Source #

projoin :: Profunctor p => t (t p) :-> t p Source #

Instances

Instances details

ProfunctorMonad Copastro Source #
Instance details Defined in Data.Profunctor.Strong Methods proreturn :: forall (p :: Type -> Type -> Type ). Profunctor p => p :-> Copastro p Source # projoin :: forall (p :: Type -> Type -> Type ). Profunctor p => Copastro ( Copastro p) :-> Copastro p Source #
ProfunctorMonad Pastro Source #
Instance details Defined in Data.Profunctor.Strong Methods proreturn :: forall (p :: Type -> Type -> Type ). Profunctor p => p :-> Pastro p Source # projoin :: forall (p :: Type -> Type -> Type ). Profunctor p => Pastro ( Pastro p) :-> Pastro p Source #
ProfunctorMonad Environment Source #
Instance details Defined in Data.Profunctor.Closed Methods proreturn :: forall (p :: Type -> Type -> Type ). Profunctor p => p :-> Environment p Source # projoin :: forall (p :: Type -> Type -> Type ). Profunctor p => Environment ( Environment p) :-> Environment p Source #
ProfunctorMonad CopastroSum Source #
Instance details Defined in Data.Profunctor.Choice Methods proreturn :: forall (p :: Type -> Type -> Type ). Profunctor p => p :-> CopastroSum p Source # projoin :: forall (p :: Type -> Type -> Type ). Profunctor p => CopastroSum ( CopastroSum p) :-> CopastroSum p Source #
ProfunctorMonad PastroSum Source #
Instance details Defined in Data.Profunctor.Choice Methods proreturn :: forall (p :: Type -> Type -> Type ). Profunctor p => p :-> PastroSum p Source # projoin :: forall (p :: Type -> Type -> Type ). Profunctor p => PastroSum ( PastroSum p) :-> PastroSum p Source #
ProfunctorMonad FreeTraversing Source #
Instance details Defined in Data.Profunctor.Traversing Methods proreturn :: forall (p :: Type -> Type -> Type ). Profunctor p => p :-> FreeTraversing p Source # projoin :: forall (p :: Type -> Type -> Type ). Profunctor p => FreeTraversing ( FreeTraversing p) :-> FreeTraversing p Source #
ProfunctorMonad FreeMapping Source #
Instance details Defined in Data.Profunctor.Mapping Methods proreturn :: forall (p :: Type -> Type -> Type ). Profunctor p => p :-> FreeMapping p Source # projoin :: forall (p :: Type -> Type -> Type ). Profunctor p => FreeMapping ( FreeMapping p) :-> FreeMapping p Source #
ProfunctorMonad Coyoneda Source #
Instance details Defined in Data.Profunctor.Yoneda Methods proreturn :: forall (p :: Type -> Type -> Type ). Profunctor p => p :-> Coyoneda p Source # projoin :: forall (p :: Type -> Type -> Type ). Profunctor p => Coyoneda ( Coyoneda p) :-> Coyoneda p Source #
ProfunctorMonad Yoneda Source #
Instance details Defined in Data.Profunctor.Yoneda Methods proreturn :: forall (p :: Type -> Type -> Type ). Profunctor p => p :-> Yoneda p Source # projoin :: forall (p :: Type -> Type -> Type ). Profunctor p => Yoneda ( Yoneda p) :-> Yoneda p Source #
ProfunctorMonad ( Sum p) Source #
Instance details Defined in Data.Profunctor.Monad Methods proreturn :: forall (p0 :: Type -> Type -> Type ). Profunctor p0 => p0 :-> Sum p p0 Source # projoin :: forall (p0 :: Type -> Type -> Type ). Profunctor p0 => Sum p ( Sum p p0) :-> Sum p p0 Source #
Monad f => ProfunctorMonad ( Tannen f :: ( Type -> Type -> Type ) -> Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Monad Methods proreturn :: forall (p :: Type -> Type -> Type ). Profunctor p => p :-> Tannen f p Source # projoin :: forall (p :: Type -> Type -> Type ). Profunctor p => Tannen f ( Tannen f p) :-> Tannen f p Source #
Category p => ProfunctorMonad ( Procompose p :: ( Type -> Type -> Type ) -> Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Composition Methods proreturn :: forall (p0 :: Type -> Type -> Type ). Profunctor p0 => p0 :-> Procompose p p0 Source # projoin :: forall (p0 :: Type -> Type -> Type ). Profunctor p0 => Procompose p ( Procompose p p0) :-> Procompose p p0 Source #
( Functor f, Monad f) => ProfunctorMonad ( Cayley f :: ( Type -> Type -> Type ) -> Type -> Type -> Type ) Source #	Cayley transforms Monads in `Hask` into monads on `Prof`
Instance details Defined in Data.Profunctor.Cayley Methods proreturn :: forall (p :: Type -> Type -> Type ). Profunctor p => p :-> Cayley f p Source # projoin :: forall (p :: Type -> Type -> Type ). Profunctor p => Cayley f ( Cayley f p) :-> Cayley f p Source #

class ProfunctorFunctor t => ProfunctorComonad t where Source #

Laws:

proextract . promap f ≡ f . proextract
proextract . produplicate ≡ id
promap proextract . produplicate ≡ id
produplicate . produplicate ≡ promap produplicate . produplicate

Methods

proextract :: Profunctor p => t p :-> p Source #

produplicate :: Profunctor p => t p :-> t (t p) Source #

Instances

Instances details

ProfunctorComonad Cotambara Source #
Instance details Defined in Data.Profunctor.Strong Methods proextract :: forall (p :: Type -> Type -> Type ). Profunctor p => Cotambara p :-> p Source # produplicate :: forall (p :: Type -> Type -> Type ). Profunctor p => Cotambara p :-> Cotambara ( Cotambara p) Source #
ProfunctorComonad Tambara Source #
Instance details Defined in Data.Profunctor.Strong Methods proextract :: forall (p :: Type -> Type -> Type ). Profunctor p => Tambara p :-> p Source # produplicate :: forall (p :: Type -> Type -> Type ). Profunctor p => Tambara p :-> Tambara ( Tambara p) Source #
ProfunctorComonad Closure Source #
Instance details Defined in Data.Profunctor.Closed Methods proextract :: forall (p :: Type -> Type -> Type ). Profunctor p => Closure p :-> p Source # produplicate :: forall (p :: Type -> Type -> Type ). Profunctor p => Closure p :-> Closure ( Closure p) Source #
ProfunctorComonad CotambaraSum Source #
Instance details Defined in Data.Profunctor.Choice Methods proextract :: forall (p :: Type -> Type -> Type ). Profunctor p => CotambaraSum p :-> p Source # produplicate :: forall (p :: Type -> Type -> Type ). Profunctor p => CotambaraSum p :-> CotambaraSum ( CotambaraSum p) Source #
ProfunctorComonad TambaraSum Source #
Instance details Defined in Data.Profunctor.Choice Methods proextract :: forall (p :: Type -> Type -> Type ). Profunctor p => TambaraSum p :-> p Source # produplicate :: forall (p :: Type -> Type -> Type ). Profunctor p => TambaraSum p :-> TambaraSum ( TambaraSum p) Source #
ProfunctorComonad CofreeTraversing Source #
Instance details Defined in Data.Profunctor.Traversing Methods proextract :: forall (p :: Type -> Type -> Type ). Profunctor p => CofreeTraversing p :-> p Source # produplicate :: forall (p :: Type -> Type -> Type ). Profunctor p => CofreeTraversing p :-> CofreeTraversing ( CofreeTraversing p) Source #
ProfunctorComonad CofreeMapping Source #
Instance details Defined in Data.Profunctor.Mapping Methods proextract :: forall (p :: Type -> Type -> Type ). Profunctor p => CofreeMapping p :-> p Source # produplicate :: forall (p :: Type -> Type -> Type ). Profunctor p => CofreeMapping p :-> CofreeMapping ( CofreeMapping p) Source #
ProfunctorComonad Coyoneda Source #
Instance details Defined in Data.Profunctor.Yoneda Methods proextract :: forall (p :: Type -> Type -> Type ). Profunctor p => Coyoneda p :-> p Source # produplicate :: forall (p :: Type -> Type -> Type ). Profunctor p => Coyoneda p :-> Coyoneda ( Coyoneda p) Source #
ProfunctorComonad Yoneda Source #
Instance details Defined in Data.Profunctor.Yoneda Methods proextract :: forall (p :: Type -> Type -> Type ). Profunctor p => Yoneda p :-> p Source # produplicate :: forall (p :: Type -> Type -> Type ). Profunctor p => Yoneda p :-> Yoneda ( Yoneda p) Source #
ProfunctorComonad ( Product p) Source #
Instance details Defined in Data.Profunctor.Monad Methods proextract :: forall (p0 :: Type -> Type -> Type ). Profunctor p0 => Product p p0 :-> p0 Source # produplicate :: forall (p0 :: Type -> Type -> Type ). Profunctor p0 => Product p p0 :-> Product p ( Product p p0) Source #
Comonad f => ProfunctorComonad ( Tannen f :: ( Type -> Type -> Type ) -> Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Monad Methods proextract :: forall (p :: Type -> Type -> Type ). Profunctor p => Tannen f p :-> p Source # produplicate :: forall (p :: Type -> Type -> Type ). Profunctor p => Tannen f p :-> Tannen f ( Tannen f p) Source #
Category p => ProfunctorComonad ( Rift p :: ( Type -> Type -> Type ) -> Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Composition Methods proextract :: forall (p0 :: Type -> Type -> Type ). Profunctor p0 => Rift p p0 :-> p0 Source # produplicate :: forall (p0 :: Type -> Type -> Type ). Profunctor p0 => Rift p p0 :-> Rift p ( Rift p p0) Source #
Category p => ProfunctorComonad ( Ran p :: ( Type -> Type -> Type ) -> Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Ran Methods proextract :: forall (p0 :: Type -> Type -> Type ). Profunctor p0 => Ran p p0 :-> p0 Source # produplicate :: forall (p0 :: Type -> Type -> Type ). Profunctor p0 => Ran p p0 :-> Ran p ( Ran p p0) Source #
Comonad f => ProfunctorComonad ( Cayley f :: ( Type -> Type -> Type ) -> Type -> Type -> Type ) Source #	Cayley transforms Comonads in `Hask` into comonads on `Prof`
Instance details Defined in Data.Profunctor.Cayley Methods proextract :: forall (p :: Type -> Type -> Type ). Profunctor p => Cayley f p :-> p Source # produplicate :: forall (p :: Type -> Type -> Type ). Profunctor p => Cayley f p :-> Cayley f ( Cayley f p) Source #