Copyright	(c) Justin Le 2019
License	BSD3
Maintainer	justin@jle.im
Stability	experimental
Portability	non-portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Functor.Contravariant.Divisible.Free

Description

Provides free structures for the various typeclasses of the Divisible hierarchy.

Since: 0.3.0.0

Synopsis

newtype Div f a where
- Div {
  - unDiv :: [Coyoneda f a]
  }
- pattern Conquer :: Div f a
- pattern Divide :: (a -> (b, c)) -> f b -> Div f c -> Div f a
hoistDiv :: forall f g. (f ~> g) -> Div f ~> Div g
liftDiv :: f ~> Div f
runDiv :: forall f g. Divisible g => (f ~> g) -> Div f ~> g
divListF :: forall f. Contravariant f => Div f ~> ListF f
listFDiv :: ListF f ~> Div f
newtype Div1 f a where
- Div1 {
  - unDiv1 :: NonEmpty (Coyoneda f a)
  }
- pattern Div1_ :: (a -> (b, c)) -> f b -> Div f c -> Div1 f a
hoistDiv1 :: (f ~> g) -> Div1 f ~> Div1 g
liftDiv1 :: f ~> Div1 f
toDiv :: Div1 f ~> Div f
runDiv1 :: Divise g => (f ~> g) -> Div1 f ~> g
div1NonEmptyF :: Contravariant f => Div1 f ~> NonEmptyF f
nonEmptyFDiv1 :: NonEmptyF f ~> Div1 f
data Dec :: (Type -> Type) -> Type -> Type where
- Lose :: (a -> Void) -> Dec f a
- Choose :: (a -> Either b c) -> f b -> Dec f c -> Dec f a
hoistDec :: forall f g. (f ~> g) -> Dec f ~> Dec g
liftDec :: f ~> Dec f
runDec :: forall f g. Conclude g => (f ~> g) -> Dec f ~> g
data Dec1 :: (Type -> Type) -> Type -> Type where
- Dec1 :: (a -> Either b c) -> f b -> Dec f c -> Dec1 f a
hoistDec1 :: forall f g. (f ~> g) -> Dec1 f ~> Dec1 g
liftDec1 :: f ~> Dec1 f
toDec :: Dec1 f a -> Dec f a
runDec1 :: Decide g => (f ~> g) -> Dec1 f ~> g

Documentation

newtype Div f a Source #

The free Divisible. Used to sequence multiple contravariant consumers, splitting out the input across all consumers.

This type is essentially ListF; the only reason why it has to exist separately outside of ListF is because the current typeclass hierarchy isn't compatible with both the covariant Interpret instance (requiring Plus) and the contravariant Interpret instance (requiring Divisible).

The wrapping in Coyoneda is also to provide a usable Associative instance for the contravariant Day.

Constructors

Div
Fields unDiv :: [Coyoneda f a]

Bundled Patterns

pattern Conquer :: Div f a

Pattern matching on an empty Div.

Before v0.3.3.0, this used to be the concrete constructor of Div. After, it is now an abstract pattern.

pattern Divide :: (a -> (b, c)) -> f b -> Div f c -> Div f a

Pattern matching on a non-empty Div, exposing the raw f instead of having it wrapped in a Coyoneda. This is the analogue of Pure and essentially treats the "cons" of the Div as a contravariant day convolution.

Before v0.3.3.0, this used to be the concrete constructor of Div. After, it is now an abstract pattern.

Instances

Instances details

FreeOf Divisible Div Source #	Since: 0.3.0.0
Instance details Defined in Data.HFunctor.Final Associated Types type FreeFunctorBy Div :: (Type -> Type) -> Constraint Source # Methods fromFree :: forall (f :: Type -> Type). Div f ~> Final Divisible f Source # toFree :: forall (f :: Type -> Type). FreeFunctorBy Div f => Final Divisible f ~> Div f Source #
HTraversable Div Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods htraverse :: forall h f g (a :: k1). Applicative h => (forall (x :: k). f x -> h (g x)) -> Div f a -> h (Div g a) Source #
Divisible f => Interpret Div (f :: Type -> Type) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods retract :: Div f ~> f Source # interpret :: forall (g :: k -> Type). (g ~> f) -> Div g ~> f Source #
Contravariant (Div f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods contramap :: (a' -> a) -> Div f a -> Div f a' # (>$) :: b -> Div f b -> Div f a #
Divisible (Div f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods divide :: (a -> (b, c)) -> Div f b -> Div f c -> Div f a # conquer :: Div f a #
Divise (Div f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods divise :: (a -> (b, c)) -> Div f b -> Div f c -> Div f a Source # divised :: Div f a -> Div f b -> Div f (a, b) Source #
Inplicative (Div f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods knot :: a -> Div f a Source #
Inply (Div f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods gather :: (b -> c -> a) -> (a -> (b, c)) -> Div f b -> Div f c -> Div f a Source # gathered :: Div f a -> Div f b -> Div f (a, b) Source #
Invariant (Div f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods invmap :: (a -> b) -> (b -> a) -> Div f a -> Div f b #
Inject Div Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods inject :: forall (f :: k -> Type). f ~> Div f Source #
HFunctor Div Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods hmap :: forall (f :: k -> Type) (g :: k -> Type). (f ~> g) -> Div f ~> Div g Source #
type FreeFunctorBy Div Source #
Instance details Defined in Data.HFunctor.Final type FreeFunctorBy Div = Unconstrained :: (Type -> Type) -> Constraint

hoistDiv :: forall f g. (f ~> g) -> Div f ~> Div g Source #

Map over the undering context in a Div.

liftDiv :: f ~> Div f Source #

Inject a single action in f into a Div f.

runDiv :: forall f g. Divisible g => (f ~> g) -> Div f ~> g Source #

Interpret a Div into a context g, provided g is Divisible.

divListF :: forall f. Contravariant f => Div f ~> ListF f Source #

Div is isomorphic to ListF for contravariant f. This witnesses one way of that isomorphism.

listFDiv :: ListF f ~> Div f Source #

Div is isomorphic to ListF for contravariant f. This witnesses one way of that isomorphism.

newtype Div1 f a Source #

The free Divise: a non-empty version of Div.

This type is essentially NonEmptyF; the only reason why it has to exist separately outside of NonEmptyF is because the current typeclass hierarchy isn't compatible with both the covariant Interpret instance (requiring Plus) and the contravariant Interpret instance (requiring Divisible).

The wrapping in Coyoneda is also to provide a usable Associative instance for the contravariant Day.

Constructors

Div1
Fields unDiv1 :: NonEmpty (Coyoneda f a)

Bundled Patterns

pattern Div1_ :: (a -> (b, c)) -> f b -> Div f c -> Div1 f a

Pattern matching on a Div1, exposing the raw f instead of having it wrapped in a Coyoneda. This is the analogue of Ap1 and essentially treats the "cons" of the Div1 as a contravariant day convolution.

Before v0.3.3.0, this used to be the concrete constructor of Div1. After, it is now an abstract pattern.

Since: 0.3.3.0

Instances

Instances details

FreeOf Divise Div1 Source #	Since: 0.3.0.0
Instance details Defined in Data.HFunctor.Final Associated Types type FreeFunctorBy Div1 :: (Type -> Type) -> Constraint Source # Methods fromFree :: forall (f :: Type -> Type). Div1 f ~> Final Divise f Source # toFree :: forall (f :: Type -> Type). FreeFunctorBy Div1 f => Final Divise f ~> Div1 f Source #
HTraversable Div1 Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods htraverse :: forall h f g (a :: k1). Applicative h => (forall (x :: k). f x -> h (g x)) -> Div1 f a -> h (Div1 g a) Source #
HTraversable1 Div1 Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods htraverse1 :: forall h f g (a :: k1). Apply h => (forall (x :: k). f x -> h (g x)) -> Div1 f a -> h (Div1 g a) Source #
Divise f => Interpret Div1 (f :: Type -> Type) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods retract :: Div1 f ~> f Source # interpret :: forall (g :: k -> Type). (g ~> f) -> Div1 g ~> f Source #
Contravariant (Div1 f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods contramap :: (a' -> a) -> Div1 f a -> Div1 f a' # (>$) :: b -> Div1 f b -> Div1 f a #
Divise (Div1 f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods divise :: (a -> (b, c)) -> Div1 f b -> Div1 f c -> Div1 f a Source # divised :: Div1 f a -> Div1 f b -> Div1 f (a, b) Source #
Inply (Div1 f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods gather :: (b -> c -> a) -> (a -> (b, c)) -> Div1 f b -> Div1 f c -> Div1 f a Source # gathered :: Div1 f a -> Div1 f b -> Div1 f (a, b) Source #
Invariant (Div1 f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods invmap :: (a -> b) -> (b -> a) -> Div1 f a -> Div1 f b #
Inject Div1 Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods inject :: forall (f :: k -> Type). f ~> Div1 f Source #
HFunctor Div1 Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods hmap :: forall (f :: k -> Type) (g :: k -> Type). (f ~> g) -> Div1 f ~> Div1 g Source #
type FreeFunctorBy Div1 Source #
Instance details Defined in Data.HFunctor.Final type FreeFunctorBy Div1 = Unconstrained :: (Type -> Type) -> Constraint

hoistDiv1 :: (f ~> g) -> Div1 f ~> Div1 g Source #

Map over the underlying context in a Div1.

liftDiv1 :: f ~> Div1 f Source #

Inject a single action in f into a Div f.

toDiv :: Div1 f ~> Div f Source #

A Div1 is a "non-empty" Div; this function "forgets" the non-empty property and turns it back into a normal Div.

runDiv1 :: Divise g => (f ~> g) -> Div1 f ~> g Source #

Interpret a Div1 into a context g, provided g is Divise.

div1NonEmptyF :: Contravariant f => Div1 f ~> NonEmptyF f Source #

Div1 is isomorphic to NonEmptyF for contravariant f. This witnesses one way of that isomorphism.

nonEmptyFDiv1 :: NonEmptyF f ~> Div1 f Source #

Div1 is isomorphic to NonEmptyF for contravariant f. This witnesses one way of that isomorphism.

data Dec :: (Type -> Type) -> Type -> Type where Source #

The free Decide. Used to aggregate multiple possible consumers, directing the input into an appropriate consumer.

Constructors

Lose :: (a -> Void) -> Dec f a
Choose :: (a -> Either b c) -> f b -> Dec f c -> Dec f a

Instances

Instances details

Inject Dec Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods inject :: forall (f :: k -> Type). f ~> Dec f Source #
FreeOf Conclude Dec Source #	Since: 0.3.0.0
Instance details Defined in Data.HFunctor.Final Associated Types type FreeFunctorBy Dec :: (Type -> Type) -> Constraint Source # Methods fromFree :: forall (f :: Type -> Type). Dec f ~> Final Conclude f Source # toFree :: forall (f :: Type -> Type). FreeFunctorBy Dec f => Final Conclude f ~> Dec f Source #
HTraversable Dec Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods htraverse :: forall h f g (a :: k1). Applicative h => (forall (x :: k). f x -> h (g x)) -> Dec f a -> h (Dec g a) Source #
HFunctor Dec Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods hmap :: forall (f :: k -> Type) (g :: k -> Type). (f ~> g) -> Dec f ~> Dec g Source #
Conclude f => Interpret Dec (f :: Type -> Type) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods retract :: Dec f ~> f Source # interpret :: forall (g :: k -> Type). (g ~> f) -> Dec g ~> f Source #
Contravariant (Dec f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods contramap :: (a' -> a) -> Dec f a -> Dec f a' # (>$) :: b -> Dec f b -> Dec f a #
Conclude (Dec f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods conclude :: (a -> Void) -> Dec f a Source #
Decide (Dec f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods decide :: (a -> Either b c) -> Dec f b -> Dec f c -> Dec f a Source #
Inalt (Dec f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods swerve :: (b -> a) -> (c -> a) -> (a -> Either b c) -> Dec f b -> Dec f c -> Dec f a Source # swerved :: Dec f a -> Dec f b -> Dec f (Either a b) Source #
Inplus (Dec f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods reject :: (a -> Void) -> Dec f a Source #
Invariant (Dec f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods invmap :: (a -> b) -> (b -> a) -> Dec f a -> Dec f b #
type FreeFunctorBy Dec Source #
Instance details Defined in Data.HFunctor.Final type FreeFunctorBy Dec = Unconstrained :: (Type -> Type) -> Constraint

hoistDec :: forall f g. (f ~> g) -> Dec f ~> Dec g Source #

Map over the underlying context in a Dec.

liftDec :: f ~> Dec f Source #

Inject a single action in f into a Dec f.

runDec :: forall f g. Conclude g => (f ~> g) -> Dec f ~> g Source #

Interpret a Dec into a context g, provided g is Conclude.

data Dec1 :: (Type -> Type) -> Type -> Type where Source #

The free Decide: a non-empty version of Dec.

Constructors

Dec1 :: (a -> Either b c) -> f b -> Dec f c -> Dec1 f a

Instances

Instances details

Inject Dec1 Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods inject :: forall (f :: k -> Type). f ~> Dec1 f Source #
FreeOf Decide Dec1 Source #	Since: 0.3.0.0
Instance details Defined in Data.HFunctor.Final Associated Types type FreeFunctorBy Dec1 :: (Type -> Type) -> Constraint Source # Methods fromFree :: forall (f :: Type -> Type). Dec1 f ~> Final Decide f Source # toFree :: forall (f :: Type -> Type). FreeFunctorBy Dec1 f => Final Decide f ~> Dec1 f Source #
HTraversable Dec1 Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods htraverse :: forall h f g (a :: k1). Applicative h => (forall (x :: k). f x -> h (g x)) -> Dec1 f a -> h (Dec1 g a) Source #
HTraversable1 Dec1 Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods htraverse1 :: forall h f g (a :: k1). Apply h => (forall (x :: k). f x -> h (g x)) -> Dec1 f a -> h (Dec1 g a) Source #
HFunctor Dec1 Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods hmap :: forall (f :: k -> Type) (g :: k -> Type). (f ~> g) -> Dec1 f ~> Dec1 g Source #
Decide f => Interpret Dec1 (f :: Type -> Type) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods retract :: Dec1 f ~> f Source # interpret :: forall (g :: k -> Type). (g ~> f) -> Dec1 g ~> f Source #
Contravariant (Dec1 f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods contramap :: (a' -> a) -> Dec1 f a -> Dec1 f a' # (>$) :: b -> Dec1 f b -> Dec1 f a #
Decide (Dec1 f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods decide :: (a -> Either b c) -> Dec1 f b -> Dec1 f c -> Dec1 f a Source #
Inalt (Dec1 f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods swerve :: (b -> a) -> (c -> a) -> (a -> Either b c) -> Dec1 f b -> Dec1 f c -> Dec1 f a Source # swerved :: Dec1 f a -> Dec1 f b -> Dec1 f (Either a b) Source #
Invariant (Dec1 f) Source #
Instance details Defined in Data.Functor.Contravariant.Divisible.Free Methods invmap :: (a -> b) -> (b -> a) -> Dec1 f a -> Dec1 f b #
type FreeFunctorBy Dec1 Source #
Instance details Defined in Data.HFunctor.Final type FreeFunctorBy Dec1 = Unconstrained :: (Type -> Type) -> Constraint

hoistDec1 :: forall f g. (f ~> g) -> Dec1 f ~> Dec1 g Source #

Map over the undering context in a Dec1.

liftDec1 :: f ~> Dec1 f Source #

Inject a single action in f into a Dec1 f.

toDec :: Dec1 f a -> Dec f a Source #

A Dec1 is a "non-empty" Dec; this function "forgets" the non-empty property and turns it back into a normal Dec.

runDec1 :: Decide g => (f ~> g) -> Dec1 f ~> g Source #

Interpret a Dec1 into a context g, provided g is Decide.