Safe Haskell	None
Language	GHC2024

Proarrow.Profunctor.Representable

Contents

Orphan instances

Documentation

class Profunctor p => Representable (p :: j +-> k) where Source Github #

Associated Types

type (p :: j +-> k) % (a :: j) :: k infixl 8 Source Github #

Methods

index :: forall (a :: k) (b :: j). p a b -> a ~> (p % b) Source Github #

tabulate :: forall (b :: j) (a :: k). Ob b => (a ~> (p % b)) -> p a b Source Github #

repMap :: forall (a :: j) (b :: j). (a ~> b) -> (p % a) ~> (p % b) Source Github #

Instances

Instances details

Representable Booleans Source Github #

Instance details

Defined in Proarrow.Category.Instance.Bool

Associated Types

type Booleans % (x :: BOOL)
Instance details Defined in Proarrow.Category.Instance.Bool type Booleans % (x :: BOOL) = x

Methods

index :: forall (a :: BOOL) (b :: BOOL). Booleans a b -> a ~> (Booleans % b) Source Github #

tabulate :: forall (b :: BOOL) (a :: BOOL). Ob b => (a ~> (Booleans % b)) -> Booleans a b Source Github #

repMap :: forall (a :: BOOL) (b :: BOOL). (a ~> b) -> (Booleans % a) ~> (Booleans % b) Source Github #

Functor m => Representable (Kleisli m :: Type -> Type -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Arrow

Methods

index :: Kleisli m a b -> a ~> (Kleisli m % b) Source Github #

tabulate :: Ob b => (a ~> (Kleisli m % b)) -> Kleisli m a b Source Github #

repMap :: (a ~> b) -> (Kleisli m % a) ~> (Kleisli m % b) Source Github #

ArrowApply arr => Representable (Arr arr :: Type -> Type -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Arrow

Methods

index :: Arr arr a b -> a ~> (Arr arr % b) Source Github #

tabulate :: Ob b => (a ~> (Arr arr % b)) -> Arr arr a b Source Github #

repMap :: (a ~> b) -> (Arr arr % a) ~> (Arr arr % b) Source Github #

CategoryOf k => Representable (Id :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Identity

Methods

index :: forall (a :: k) (b :: k). Id a b -> a ~> ((Id :: k -> k -> Type) % b) Source Github #

tabulate :: forall (b :: k) (a :: k). Ob b => (a ~> ((Id :: k -> k -> Type) % b)) -> Id a b Source Github #

repMap :: forall (a :: k) (b :: k). (a ~> b) -> ((Id :: k -> k -> Type) % a) ~> ((Id :: k -> k -> Type) % b) Source Github #

Representable (->) Source Github #

Instance details

Defined in Proarrow.Profunctor.Representable

Associated Types

type (->) % (a :: Type)
Instance details Defined in Proarrow.Profunctor.Representable type (->) % (a :: Type) = a

Methods

index :: (a -> b) -> a ~> ((->) % b) Source Github #

tabulate :: Ob b => (a ~> ((->) % b)) -> a -> b Source Github #

repMap :: (a ~> b) -> ((->) % a) ~> ((->) % b) Source Github #

(HasTerminalObject k, CategoryOf j) => Representable (TerminalProfunctor :: k -> j -> Type) Source Github #

Instance details

Defined in Proarrow.Object.Terminal

Methods

index :: forall (a :: k) (b :: j). TerminalProfunctor a b -> a ~> ((TerminalProfunctor :: k -> j -> Type) % b) Source Github #

tabulate :: forall (b :: j) (a :: k). Ob b => (a ~> ((TerminalProfunctor :: k -> j -> Type) % b)) -> TerminalProfunctor a b Source Github #

repMap :: forall (a :: j) (b :: j). (a ~> b) -> ((TerminalProfunctor :: k -> j -> Type) % a) ~> ((TerminalProfunctor :: k -> j -> Type) % b) Source Github #

(Ob r, SymMonoidal k, Closed k) => Representable (Reader ('OP r) :: k -> k -> Type) Source Github #

The reader monad given the Promonad instance.

Instance details

Defined in Proarrow.Promonad.Reader

Methods

index :: forall (a :: k) (b :: k). Reader ('OP r) a b -> a ~> (Reader ('OP r) % b) Source Github #

tabulate :: forall (b :: k) (a :: k). Ob b => (a ~> (Reader ('OP r) % b)) -> Reader ('OP r) a b Source Github #

repMap :: forall (a :: k) (b :: k). (a ~> b) -> (Reader ('OP r) % a) ~> (Reader ('OP r) % b) Source Github #

(Ob w, Monoidal k) => Representable (Writer w :: k -> k -> Type) Source Github #

The writer monad given the Promonad instance.

Instance details

Defined in Proarrow.Promonad.Writer

Methods

index :: forall (a :: k) (b :: k). Writer w a b -> a ~> (Writer w % b) Source Github #

tabulate :: forall (b :: k) (a :: k). Ob b => (a ~> (Writer w % b)) -> Writer w a b Source Github #

repMap :: forall (a :: k) (b :: k). (a ~> b) -> (Writer w % a) ~> (Writer w % b) Source Github #

Representable (Costar ((,) a) :: Type -> Type -> Type) Source Github #

The right adjoint of (,) a is ((->) a).

Instance details

Defined in Proarrow.Adjunction

Methods

index :: Costar ((,) a) a0 b -> a0 ~> (Costar ((,) a) % b) Source Github #

tabulate :: Ob b => (a0 ~> (Costar ((,) a) % b)) -> Costar ((,) a) a0 b Source Github #

repMap :: (a0 ~> b) -> (Costar ((,) a) % a0) ~> (Costar ((,) a) % b) Source Github #

Representable p => Representable (Adj p :: k -> j -> Type) Source Github #

Instance details

Defined in Proarrow.Adjunction

Methods

index :: forall (a :: k) (b :: j). Adj p a b -> a ~> (Adj p % b) Source Github #

tabulate :: forall (b :: j) (a :: k). Ob b => (a ~> (Adj p % b)) -> Adj p a b Source Github #

repMap :: forall (a :: j) (b :: j). (a ~> b) -> (Adj p % a) ~> (Adj p % b) Source Github #

Corepresentable p => Representable (CorepStar p :: k -> j -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Representable

Methods

index :: forall (a :: k) (b :: j). CorepStar p a b -> a ~> (CorepStar p % b) Source Github #

tabulate :: forall (b :: j) (a :: k). Ob b => (a ~> (CorepStar p % b)) -> CorepStar p a b Source Github #

repMap :: forall (a :: j) (b :: j). (a ~> b) -> (CorepStar p % a) ~> (CorepStar p % b) Source Github #

FunctorForRep f => Representable (Rep f :: k -> j -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Representable

Methods

index :: forall (a :: k) (b :: j). Rep f a b -> a ~> (Rep f % b) Source Github #

tabulate :: forall (b :: j) (a :: k). Ob b => (a ~> (Rep f % b)) -> Rep f a b Source Github #

repMap :: forall (a :: j) (b :: j). (a ~> b) -> (Rep f % a) ~> (Rep f % b) Source Github #

Functor f => Representable (Star f :: k -> j -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Star

Methods

index :: forall (a :: k) (b :: j). Star f a b -> a ~> (Star f % b) Source Github #

tabulate :: forall (b :: j) (a :: k). Ob b => (a ~> (Star f % b)) -> Star f a b Source Github #

repMap :: forall (a :: j) (b :: j). (a ~> b) -> (Star f % a) ~> (Star f % b) Source Github #

Representable p => Representable (Wrapped p :: k -> j -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Wrapped

Methods

index :: forall (a :: k) (b :: j). Wrapped p a b -> a ~> (Wrapped p % b) Source Github #

tabulate :: forall (b :: j) (a :: k). Ob b => (a ~> (Wrapped p % b)) -> Wrapped p a b Source Github #

repMap :: forall (a :: j) (b :: j). (a ~> b) -> (Wrapped p % a) ~> (Wrapped p % b) Source Github #

(forall (b :: j). Ob b => TermUniversal l b, Corepresentable l) => Representable (AsLeftAdjoint l :: k -> j -> Type) Source Github #

Instance details

Defined in Proarrow.Universal

Methods

index :: forall (a :: k) (b :: j). AsLeftAdjoint l a b -> a ~> (AsLeftAdjoint l % b) Source Github #

tabulate :: forall (b :: j) (a :: k). Ob b => (a ~> (AsLeftAdjoint l % b)) -> AsLeftAdjoint l a b Source Github #

repMap :: forall (a :: j) (b :: j). (a ~> b) -> (AsLeftAdjoint l % a) ~> (AsLeftAdjoint l % b) Source Github #

Representable r => Representable (AsRightAdjoint r :: k -> j -> Type) Source Github #

Instance details

Defined in Proarrow.Universal

Methods

index :: forall (a :: k) (b :: j). AsRightAdjoint r a b -> a ~> (AsRightAdjoint r % b) Source Github #

tabulate :: forall (b :: j) (a :: k). Ob b => (a ~> (AsRightAdjoint r % b)) -> AsRightAdjoint r a b Source Github #

repMap :: forall (a :: j) (b :: j). (a ~> b) -> (AsRightAdjoint r % a) ~> (AsRightAdjoint r % b) Source Github #

Representable p => Representable (FromAdjunction p :: k -> j -> Type) Source Github #

Instance details

Defined in Proarrow.Universal

Methods

index :: forall (a :: k) (b :: j). FromAdjunction p a b -> a ~> (FromAdjunction p % b) Source Github #

tabulate :: forall (b :: j) (a :: k). Ob b => (a ~> (FromAdjunction p % b)) -> FromAdjunction p a b Source Github #

repMap :: forall (a :: j) (b :: j). (a ~> b) -> (FromAdjunction p % a) ~> (FromAdjunction p % b) Source Github #

(Ob a, MonoidalAction m k) => Representable (Action a :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Action

Methods

index :: forall (a0 :: k) (b :: k). Action a a0 b -> a0 ~> ((Action a :: k -> k -> Type) % b) Source Github #

tabulate :: forall (b :: k) (a0 :: k). Ob b => (a0 ~> ((Action a :: k -> k -> Type) % b)) -> Action a a0 b Source Github #

repMap :: forall (a0 :: k) (b :: k). (a0 ~> b) -> ((Action a :: k -> k -> Type) % a0) ~> ((Action a :: k -> k -> Type) % b) Source Github #

(HasBinaryProducts k, Representable p, Representable q) => Representable (p :*: q :: k -> j -> Type) Source Github #

Instance details

Defined in Proarrow.Object.BinaryProduct

Methods

index :: forall (a :: k) (b :: j). (p :*: q) a b -> a ~> ((p :*: q) % b) Source Github #

tabulate :: forall (b :: j) (a :: k). Ob b => (a ~> ((p :*: q) % b)) -> (p :*: q) a b Source Github #

repMap :: forall (a :: j) (b :: j). (a ~> b) -> ((p :*: q) % a) ~> ((p :*: q) % b) Source Github #

(HasLimits j2 k, Representable d) => Representable (Ran ('OP j2) d :: k -> j1 -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Ran

Methods

index :: forall (a :: k) (b :: j1). Ran ('OP j2) d a b -> a ~> (Ran ('OP j2) d % b) Source Github #

tabulate :: forall (b :: j1) (a :: k). Ob b => (a ~> (Ran ('OP j2) d % b)) -> Ran ('OP j2) d a b Source Github #

repMap :: forall (a :: j1) (b :: j1). (a ~> b) -> (Ran ('OP j2) d % a) ~> (Ran ('OP j2) d % b) Source Github #

(Representable p, Representable q) => Representable (p :.: q :: k -> j2 -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Composition

Methods

index :: forall (a :: k) (b :: j2). (p :.: q) a b -> a ~> ((p :.: q) % b) Source Github #

tabulate :: forall (b :: j2) (a :: k). Ob b => (a ~> ((p :.: q) % b)) -> (p :.: q) a b Source Github #

repMap :: forall (a :: j2) (b :: j2). (a ~> b) -> ((p :.: q) % a) ~> ((p :.: q) % b) Source Github #

(Representable p, Representable q) => Representable (p :&&&: q :: (i, j2) -> j1 -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

index :: forall (a :: (i, j2)) (b :: j1). (p :&&&: q) a b -> a ~> ((p :&&&: q) % b) Source Github #

tabulate :: forall (b :: j1) (a :: (i, j2)). Ob b => (a ~> ((p :&&&: q) % b)) -> (p :&&&: q) a b Source Github #

repMap :: forall (a :: j1) (b :: j1). (a ~> b) -> ((p :&&&: q) % a) ~> ((p :&&&: q) % b) Source Github #

Monoidal k => Representable (Tensor :: k -> LIST k -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Promonoidal

Methods

index :: forall (a :: k) (b :: LIST k). Tensor a b -> a ~> ((Tensor :: k -> LIST k -> Type) % b) Source Github #

tabulate :: forall (b :: LIST k) (a :: k). Ob b => (a ~> ((Tensor :: k -> LIST k -> Type) % b)) -> Tensor a b Source Github #

repMap :: forall (a :: LIST k) (b :: LIST k). (a ~> b) -> ((Tensor :: k -> LIST k -> Type) % a) ~> ((Tensor :: k -> LIST k -> Type) % b) Source Github #

(Closed k, SymMonoidal k, Ob r) => Representable (Corep (Not r) :: k -> OPPOSITE k -> Type) Source Github #

The Op-Op adjunction, giving rise to the continuation monad.

Instance details

Defined in Proarrow.Object.Exponential

Methods

index :: forall (a :: k) (b :: OPPOSITE k). Corep (Not r) a b -> a ~> (Corep (Not r) % b) Source Github #

tabulate :: forall (b :: OPPOSITE k) (a :: k). Ob b => (a ~> (Corep (Not r) % b)) -> Corep (Not r) a b Source Github #

repMap :: forall (a :: OPPOSITE k) (b :: OPPOSITE k). (a ~> b) -> (Corep (Not r) % a) ~> (Corep (Not r) % b) Source Github #

Corepresentable p => Representable (Op p :: OPPOSITE j -> OPPOSITE k -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Representable

Methods

index :: forall (a :: OPPOSITE j) (b :: OPPOSITE k). Op p a b -> a ~> (Op p % b) Source Github #

tabulate :: forall (b :: OPPOSITE k) (a :: OPPOSITE j). Ob b => (a ~> (Op p % b)) -> Op p a b Source Github #

repMap :: forall (a :: OPPOSITE k) (b :: OPPOSITE k). (a ~> b) -> (Op p % a) ~> (Op p % b) Source Github #

Representable p => Representable (Coprod p :: COPROD k -> COPROD j -> Type) Source Github #

Instance details

Defined in Proarrow.Object.BinaryCoproduct

Methods

index :: forall (a :: COPROD k) (b :: COPROD j). Coprod p a b -> a ~> (Coprod p % b) Source Github #

tabulate :: forall (b :: COPROD j) (a :: COPROD k). Ob b => (a ~> (Coprod p % b)) -> Coprod p a b Source Github #

repMap :: forall (a :: COPROD j) (b :: COPROD j). (a ~> b) -> (Coprod p % a) ~> (Coprod p % b) Source Github #

Representable p => Representable (Prod p :: PROD k -> PROD j -> Type) Source Github #

Instance details

Defined in Proarrow.Object.BinaryProduct

Methods

index :: forall (a :: PROD k) (b :: PROD j). Prod p a b -> a ~> (Prod p % b) Source Github #

tabulate :: forall (b :: PROD j) (a :: PROD k). Ob b => (a ~> (Prod p % b)) -> Prod p a b Source Github #

repMap :: forall (a :: PROD j) (b :: PROD j). (a ~> b) -> (Prod p % a) ~> (Prod p % b) Source Github #

Representable p => Representable (List p :: LIST k -> LIST j -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.List

Methods

index :: forall (a :: LIST k) (b :: LIST j). List p a b -> a ~> (List p % b) Source Github #

tabulate :: forall (b :: LIST j) (a :: LIST k). Ob b => (a ~> (List p % b)) -> List p a b Source Github #

repMap :: forall (a :: LIST j) (b :: LIST j). (a ~> b) -> (List p % a) ~> (List p % b) Source Github #

(Representable p, Representable q) => Representable (p :|||: q :: k -> COPRODUCT i j -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Fam

Methods

index :: forall (a :: k) (b :: COPRODUCT i j). (p :|||: q) a b -> a ~> ((p :|||: q) % b) Source Github #

tabulate :: forall (b :: COPRODUCT i j) (a :: k). Ob b => (a ~> ((p :|||: q) % b)) -> (p :|||: q) a b Source Github #

repMap :: forall (a :: COPRODUCT i j) (b :: COPRODUCT i j). (a ~> b) -> ((p :|||: q) % a) ~> ((p :|||: q) % b) Source Github #

(Representable l, Representable r, HasBinaryProducts k) => Representable (l :&&: r :: k -> (x, y) -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Fam

Methods

index :: forall (a :: k) (b :: (x, y)). (l :&&: r) a b -> a ~> ((l :&&: r) % b) Source Github #

tabulate :: forall (b :: (x, y)) (a :: k). Ob b => (a ~> ((l :&&: r) % b)) -> (l :&&: r) a b Source Github #

repMap :: forall (a :: (x, y)) (b :: (x, y)). (a ~> b) -> ((l :&&: r) % a) ~> ((l :&&: r) % b) Source Github #

(Representable p, forall (a :: k). ob a => ob (p % a)) => Representable (Sub p :: SUBCAT ob -> SUBCAT ob -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Sub

Methods

index :: forall (a :: SUBCAT ob) (b :: SUBCAT ob). Sub p a b -> a ~> ((Sub p :: SUBCAT ob -> SUBCAT ob -> Type) % b) Source Github #

tabulate :: forall (b :: SUBCAT ob) (a :: SUBCAT ob). Ob b => (a ~> ((Sub p :: SUBCAT ob -> SUBCAT ob -> Type) % b)) -> Sub p a b Source Github #

repMap :: forall (a :: SUBCAT ob) (b :: SUBCAT ob). (a ~> b) -> ((Sub p :: SUBCAT ob -> SUBCAT ob -> Type) % a) ~> ((Sub p :: SUBCAT ob -> SUBCAT ob -> Type) % b) Source Github #

HasLimits j k => Representable (LimitAdj j :: COREPK b k -> REPK a k -> Type) Source Github #

Colimit j -| Limit j

Instance details

Defined in Proarrow.Adjunction

Methods

index :: forall (a0 :: COREPK b k) (b0 :: REPK a k). LimitAdj j a0 b0 -> a0 ~> ((LimitAdj j :: COREPK b k -> REPK a k -> Type) % b0) Source Github #

tabulate :: forall (b0 :: REPK a k) (a0 :: COREPK b k). Ob b0 => (a0 ~> ((LimitAdj j :: COREPK b k -> REPK a k -> Type) % b0)) -> LimitAdj j a0 b0 Source Github #

repMap :: forall (a0 :: REPK a k) (b0 :: REPK a k). (a0 ~> b0) -> ((LimitAdj j :: COREPK b k -> REPK a k -> Type) % a0) ~> ((LimitAdj j :: COREPK b k -> REPK a k -> Type) % b0) Source Github #

(Representable p, Representable q) => Representable (p :**: q :: (k1, k2) -> (j1, j2) -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Representable

Methods

index :: forall (a :: (k1, k2)) (b :: (j1, j2)). (p :**: q) a b -> a ~> ((p :**: q) % b) Source Github #

tabulate :: forall (b :: (j1, j2)) (a :: (k1, k2)). Ob b => (a ~> ((p :**: q) % b)) -> (p :**: q) a b Source Github #

repMap :: forall (a :: (j1, j2)) (b :: (j1, j2)). (a ~> b) -> ((p :**: q) % a) ~> ((p :**: q) % b) Source Github #

repObj :: forall {j} {k} (p :: j +-> k) (a :: j). (Representable p, Ob a) => Obj (p % a) Source Github #

withRepOb :: forall {j} {k} (p :: j +-> k) (a :: j) r. (Representable p, Ob a) => (Ob (p % a) => r) -> r Source Github #

dimapRep :: forall {j} {k} p (a :: k) (b :: j) (c :: k) (d :: j). Representable p => (c ~> a) -> (b ~> d) -> p a b -> p c d Source Github #

trivialRep :: forall {j} {k} p (a :: j). (Representable p, Ob a) => p (p % a) a Source Github #

data CorepStar (p :: k +-> j) (a :: k) (b :: j) where Source Github #

Constructors

CorepStar
Fields :: forall {j} {k} (b :: j) (a :: k) (p :: k +-> j). Ob b => { unCorepStar :: a ~> (p %% b) } -> CorepStar p a b

Instances

Instances details

Corepresentable p => Profunctor (CorepStar p :: k -> j -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Representable Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> CorepStar p a b -> CorepStar p c d Source Github # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> CorepStar p a b -> r Source Github #
Corepresentable p => Representable (CorepStar p :: k -> j -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Representable Methods index :: forall (a :: k) (b :: j). CorepStar p a b -> a ~> (CorepStar p % b) Source Github # tabulate :: forall (b :: j) (a :: k). Ob b => (a ~> (CorepStar p % b)) -> CorepStar p a b Source Github # repMap :: forall (a :: j) (b :: j). (a ~> b) -> (CorepStar p % a) ~> (CorepStar p % b) Source Github #
Corepresentable p => Proadjunction (CorepStar p :: k -> j -> Type) (p :: k +-> j) Source Github #
Instance details Defined in Proarrow.Adjunction Methods unit :: forall (a :: j). Ob a => (p :.: CorepStar p) a a Source Github # counit :: (CorepStar p :.: p) :~> ((~>) :: CAT k) Source Github #
type (CorepStar p :: k -> j -> Type) % (a :: j) Source Github #
Instance details Defined in Proarrow.Profunctor.Representable type (CorepStar p :: k -> j -> Type) % (a :: j) = p %% a

mapCorepStar :: forall {k} {j} (p :: k +-> j) (q :: k +-> j). (Corepresentable p, Corepresentable q) => (p ~> q) -> CorepStar q ~> CorepStar p Source Github #

data RepCostar (p :: k +-> j) (a :: k) (b :: j) where Source Github #

Constructors

RepCostar
Fields :: forall {k} {j} (a :: k) (p :: k +-> j) (b :: j). Ob a => { unRepCostar :: (p % a) ~> b } -> RepCostar p a b

Instances

Instances details

Representable p => Proadjunction (p :: k +-> j) (RepCostar p :: k -> j -> Type) Source Github #
Instance details Defined in Proarrow.Adjunction Methods unit :: forall (a :: k). Ob a => (RepCostar p :.: p) a a Source Github # counit :: (p :.: RepCostar p) :~> ((~>) :: CAT j) Source Github #
(Representable p, Thin j) => ThinProfunctor (RepCostar p :: k -> j -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Representable Methods arr :: forall (a :: k) (b :: j). (Ob a, Ob b, HasArrow (RepCostar p) a b) => RepCostar p a b Source Github # withArr :: forall (a :: k) (b :: j) r. RepCostar p a b -> (HasArrow (RepCostar p) a b => r) -> r Source Github #
Representable p => Profunctor (RepCostar p :: k -> j -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Representable Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> RepCostar p a b -> RepCostar p c d Source Github # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> RepCostar p a b -> r Source Github #
Representable p => Corepresentable (RepCostar p :: k -> j -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Representable Methods coindex :: forall (a :: k) (b :: j). RepCostar p a b -> (RepCostar p %% a) ~> b Source Github # cotabulate :: forall (a :: k) (b :: j). Ob a => ((RepCostar p %% a) ~> b) -> RepCostar p a b Source Github # corepMap :: forall (a :: k) (b :: k). (a ~> b) -> (RepCostar p %% a) ~> (RepCostar p %% b) Source Github #
type (RepCostar p :: k -> j -> Type) %% (a :: k) Source Github #
Instance details Defined in Proarrow.Profunctor.Representable type (RepCostar p :: k -> j -> Type) %% (a :: k) = p % a
type HasArrow (RepCostar p :: k -> j -> Type) (a :: k) (b :: j) Source Github #
Instance details Defined in Proarrow.Profunctor.Representable type HasArrow (RepCostar p :: k -> j -> Type) (a :: k) (b :: j) = HasArrow (Hom j) (p % a) b

mapRepCostar :: forall {k} {j} (p :: k +-> j) (q :: k +-> j). (Representable p, Representable q) => (p ~> q) -> RepCostar q ~> RepCostar p Source Github #

flipRep :: forall {k1} (p :: k1 +-> k1). Representable p => (((~>) :: CAT k1) :~> p) -> RepCostar p :~> ((~>) :: CAT k1) Source Github #

unflipRep :: forall {k1} (p :: k1 +-> k1). Representable p => (RepCostar p :~> ((~>) :: CAT k1)) -> ((~>) :: CAT k1) :~> p Source Github #

flipCorep :: forall {k1} (p :: k1 +-> k1). Corepresentable p => (((~>) :: CAT k1) :~> p) -> CorepStar p :~> ((~>) :: CAT k1) Source Github #

unflipCorep :: forall {k1} (p :: k1 +-> k1). Corepresentable p => (CorepStar p :~> ((~>) :: CAT k1)) -> ((~>) :: CAT k1) :~> p Source Github #

data Rep (f :: j +-> k) (a :: k) (b :: j) where Source Github #

Constructors

Rep
Fields :: forall {j} {k} (f :: j +-> k) (a :: k) (b :: j). Ob b => { unRep :: a ~> (f @ b) } -> Rep f a b

Instances

Instances details

(Cartesian k, SelfAction k, Ob c) => Strong k (Rep (Constant c) :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Optic

Methods

act :: forall (a :: k) (b :: k) (x :: k) (y :: k). (a ~> b) -> Rep (Constant c) x y -> Rep (Constant c) (Act a x) (Act b y) Source Github #

Strong (COPROD Type) (Rep (Constant (First c)) :: Type -> Type -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Optic

Methods

act :: forall (a :: COPROD Type) (b :: COPROD Type) x y. (a ~> b) -> Rep (Constant (First c)) x y -> Rep (Constant (First c)) (Act a x) (Act b y) Source Github #

(Cartesian k, Ob c, Strong (SUBCAT (Any :: k -> Constraint)) ((~>) :: CAT k)) => Strong (SUBCAT (Any :: k -> Constraint)) (Rep (Constant c) :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Optic

Methods

act :: forall (a :: SUBCAT (Any :: k -> Constraint)) (b :: SUBCAT (Any :: k -> Constraint)) (x :: k) (y :: k). (a ~> b) -> Rep (Constant c) x y -> Rep (Constant c) (Act a x) (Act b y) Source Github #

(FunctorForRep f, Thin k) => ThinProfunctor (Rep f :: k -> j -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Representable

Methods

arr :: forall (a :: k) (b :: j). (Ob a, Ob b, HasArrow (Rep f) a b) => Rep f a b Source Github #

withArr :: forall (a :: k) (b :: j) r. Rep f a b -> (HasArrow (Rep f) a b => r) -> r Source Github #

MonoidalProfunctor (Rep Fun) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

par0 :: Rep Fun (Unit :: FINREL) (Unit :: FINSET) Source Github #

par :: forall (x1 :: FINREL) (x2 :: FINSET) (y1 :: FINREL) (y2 :: FINSET). Rep Fun x1 x2 -> Rep Fun y1 y2 -> Rep Fun (x1 ** y1) (x2 ** y2) Source Github #

MonoidalProfunctor (Rep Forget) Source Github #

Forget is a lax monoidal functor

Instance details

Defined in Proarrow.Category.Instance.Linear

Methods

par0 :: Rep Forget (Unit :: Type) (Unit :: LINEAR) Source Github #

par :: forall x1 (x2 :: LINEAR) y1 (y2 :: LINEAR). Rep Forget x1 x2 -> Rep Forget y1 y2 -> Rep Forget (x1 ** y1) (x2 ** y2) Source Github #

(Monoidal k, Monoid r) => MonoidalProfunctor (Rep (Constant r) :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Monoid

Methods

par0 :: Rep (Constant r) (Unit :: k) (Unit :: k) Source Github #

par :: forall (x1 :: k) (x2 :: k) (y1 :: k) (y2 :: k). Rep (Constant r) x1 x2 -> Rep (Constant r) y1 y2 -> Rep (Constant r) (x1 ** y1) (x2 ** y2) Source Github #

FunctorForRep f => Profunctor (Rep f :: k -> j -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Representable

Methods

dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> Rep f a b -> Rep f c d Source Github #

(\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> Rep f a b -> r Source Github #

Corepresentable (Rep Forget) Source Github #

By creating the left adjoint to the forgetful functor, we obtain the free-forgetful adjunction between Hask and LINEAR

Instance details

Defined in Proarrow.Category.Instance.Linear

Associated Types

type (Rep Forget) %% (a :: Type)
Instance details Defined in Proarrow.Category.Instance.Linear type (Rep Forget) %% (a :: Type) = 'L (Ur a)

Methods

coindex :: forall a (b :: LINEAR). Rep Forget a b -> (Rep Forget %% a) ~> b Source Github #

cotabulate :: forall a (b :: LINEAR). Ob a => ((Rep Forget %% a) ~> b) -> Rep Forget a b Source Github #

corepMap :: (a ~> b) -> (Rep Forget %% a) ~> (Rep Forget %% b) Source Github #

FunctorForRep f => Representable (Rep f :: k -> j -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Representable

Methods

index :: forall (a :: k) (b :: j). Rep f a b -> a ~> (Rep f % b) Source Github #

tabulate :: forall (b :: j) (a :: k). Ob b => (a ~> (Rep f % b)) -> Rep f a b Source Github #

repMap :: forall (a :: j) (b :: j). (a ~> b) -> (Rep f % a) ~> (Rep f % b) Source Github #

FunctorForRep f => HasColimits (Rep f :: i -> a -> Type) k Source Github #

Instance details

Defined in Proarrow.Category.Colimit

Methods

colimit :: forall (d :: k +-> i). Corepresentable d => (Rep f :.: Colimit (Rep f) d) :~> d Source Github #

colimitUniv :: forall (d :: k +-> i) (p :: k +-> a). (Corepresentable d, Profunctor p) => ((Rep f :.: p) :~> d) -> p :~> Colimit (Rep f) d Source Github #

FunctorForRep f => Proadjunction (Rep f :: k -> j -> Type) (Corep f :: j -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Adjunction

Methods

unit :: forall (a :: j). Ob a => (Corep f :.: Rep f) a a Source Github #

counit :: (Rep f :.: Corep f) :~> ((~>) :: CAT k) Source Github #

HasCofree ob => Corepresentable (Rep (CofreeSub ob) :: SUBCAT ob -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Cofree

Methods

coindex :: forall (a :: SUBCAT ob) (b :: k). Rep (CofreeSub ob) a b -> (Rep (CofreeSub ob) %% a) ~> b Source Github #

cotabulate :: forall (a :: SUBCAT ob) (b :: k). Ob a => ((Rep (CofreeSub ob) %% a) ~> b) -> Rep (CofreeSub ob) a b Source Github #

corepMap :: forall (a :: SUBCAT ob) (b :: SUBCAT ob). (a ~> b) -> (Rep (CofreeSub ob) %% a) ~> (Rep (CofreeSub ob) %% b) Source Github #

Num a => MonoidalProfunctor (Rep (App :: MatK a +-> Type) :: Type -> MatK a -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Mat

Methods

par0 :: Rep (App :: MatK a +-> Type) (Unit :: Type) (Unit :: MatK a) Source Github #

par :: forall x1 (x2 :: MatK a) y1 (y2 :: MatK a). Rep (App :: MatK a +-> Type) x1 x2 -> Rep (App :: MatK a +-> Type) y1 y2 -> Rep (App :: MatK a +-> Type) (x1 ** y1) (x2 ** y2) Source Github #

MonoidalProfunctor (Coprod (Rep Fun)) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

par0 :: Coprod (Rep Fun) (Unit :: COPROD FINREL) (Unit :: COPROD FINSET) Source Github #

par :: forall (x1 :: COPROD FINREL) (x2 :: COPROD FINSET) (y1 :: COPROD FINREL) (y2 :: COPROD FINSET). Coprod (Rep Fun) x1 x2 -> Coprod (Rep Fun) y1 y2 -> Coprod (Rep Fun) (x1 ** y1) (x2 ** y2) Source Github #

(HasCoproducts k, Ob r) => MonoidalProfunctor (Coprod (Rep (Constant r)) :: COPROD k -> COPROD k -> Type) Source Github #

Instance details

Defined in Proarrow.Monoid

Methods

par0 :: Coprod (Rep (Constant r)) (Unit :: COPROD k) (Unit :: COPROD k) Source Github #

par :: forall (x1 :: COPROD k) (x2 :: COPROD k) (y1 :: COPROD k) (y2 :: COPROD k). Coprod (Rep (Constant r)) x1 x2 -> Coprod (Rep (Constant r)) y1 y2 -> Coprod (Rep (Constant r)) (x1 ** y1) (x2 ** y2) Source Github #

HasFree ob => Corepresentable (Rep (Forget ob) :: k -> SUBCAT ob -> Type) Source Github #

By creating the left adjoint to the forgetful functor, we obtain the free-forgetful adjunction.

Instance details

Defined in Proarrow.Profunctor.Free

Methods

coindex :: forall (a :: k) (b :: SUBCAT ob). Rep (Forget ob) a b -> (Rep (Forget ob) %% a) ~> b Source Github #

cotabulate :: forall (a :: k) (b :: SUBCAT ob). Ob a => ((Rep (Forget ob) %% a) ~> b) -> Rep (Forget ob) a b Source Github #

corepMap :: forall (a :: k) (b :: k). (a ~> b) -> (Rep (Forget ob) %% a) ~> (Rep (Forget ob) %% b) Source Github #

type Colimit (Rep f :: i -> a -> Type) (d :: k +-> i) Source Github #

Instance details

Defined in Proarrow.Category.Colimit

type Colimit (Rep f :: i -> a -> Type) (d :: k +-> i) = Corep f :.: d

type (Rep Forget) %% (a :: Type) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Linear

type (Rep Forget) %% (a :: Type) = 'L (Ur a)

type (Rep f :: k -> j -> Type) % (a :: j) Source Github #

Instance details

Defined in Proarrow.Profunctor.Representable

type (Rep f :: k -> j -> Type) % (a :: j) = f @ a

type HasArrow (Rep f :: k -> j -> Type) (a :: k) (b :: j) Source Github #

Instance details

Defined in Proarrow.Profunctor.Representable

type HasArrow (Rep f :: k -> j -> Type) (a :: k) (b :: j) = HasArrow (Hom k) a (f @ b)

type (Rep (Forget ob) :: k -> SUBCAT ob -> Type) %% (a :: k) Source Github #

Instance details

Defined in Proarrow.Profunctor.Free

type (Rep (Forget ob) :: k -> SUBCAT ob -> Type) %% (a :: k) = 'SUB (Free ob % a) :: SUBCAT ob

type (Rep (CofreeSub ob) :: SUBCAT ob -> k -> Type) %% (a :: SUBCAT ob) Source Github #

Instance details

Defined in Proarrow.Profunctor.Cofree

type (Rep (CofreeSub ob) :: SUBCAT ob -> k -> Type) %% (a :: SUBCAT ob) = UN ('SUB :: k -> SUBCAT ob) a

rep :: forall {j} {k} (f :: j +-> k) (a :: k) (b :: j) (a' :: k) (b' :: j). Ob b => Iso (a ~> (f @ b)) (a' ~> (f @ b')) (Rep f a b) (Rep f a' b') Source Github #

type Monad (m :: j +-> j) = (Promonad m, Representable m) Source Github #

return :: forall {j} (m :: j +-> j) (a :: j). (Monad m, Ob a) => a ~> (m % a) Source Github #

bind :: forall {j} (m :: j +-> j) (a :: j) (b :: j). (Monad m, Ob b) => (a ~> (m % b)) -> (m % a) ~> (m % b) Source Github #

Orphan instances

Representable p => Corepresentable (Op p :: OPPOSITE j -> OPPOSITE k -> Type) Source Github #
Instance details Methods coindex :: forall (a :: OPPOSITE j) (b :: OPPOSITE k). Op p a b -> (Op p %% a) ~> b Source Github # cotabulate :: forall (a :: OPPOSITE j) (b :: OPPOSITE k). Ob a => ((Op p %% a) ~> b) -> Op p a b Source Github # corepMap :: forall (a :: OPPOSITE j) (b :: OPPOSITE j). (a ~> b) -> (Op p %% a) ~> (Op p %% b) Source Github #