Safe Haskell	None
Language	GHC2024

Proarrow.Object.Exponential

Documentation

class Monoidal k => Closed k where Source Github #

Minimal complete definition

withObExp, curry, apply

Associated Types

type (a :: k) ~~> (b :: k) :: k infixr 2 Source Github #

Methods

withObExp :: forall (a :: k) (b :: k) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: k) (b :: k) (c :: k). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: k) (b :: k). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: k) (b :: k) (x :: k) (y :: k). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

Instances

Instances details

Closed Nat Source Github #

Instance details

Defined in Proarrow.Category.Instance.ZX

Associated Types

type (x :: Nat) ~~> (y :: Nat)
Instance details Defined in Proarrow.Category.Instance.ZX type (x :: Nat) ~~> (y :: Nat) = ExpSA x y

Methods

withObExp :: forall (a :: Nat) (b :: Nat) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: Nat) (b :: Nat) (c :: Nat). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: Nat) (b :: Nat). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: Nat) (b :: Nat) (x :: Nat) (y :: Nat). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

Closed BOOL Source Github #

Instance details

Defined in Proarrow.Category.Instance.Bool

Associated Types

type (a :: BOOL) ~~> (b :: BOOL)
Instance details Defined in Proarrow.Category.Instance.Bool type (a :: BOOL) ~~> (b :: BOOL) = ExpSA a b

Methods

withObExp :: forall (a :: BOOL) (b :: BOOL) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: BOOL) (b :: BOOL) (c :: BOOL). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: BOOL) (b :: BOOL). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: BOOL) (b :: BOOL) (x :: BOOL) (y :: BOOL). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

Closed KIND Source Github #

Instance details

Defined in Proarrow.Category.Instance.Cat

Associated Types

type ('K a :: KIND) ~~> ('K b :: KIND)
Instance details Defined in Proarrow.Category.Instance.Cat type ('K a :: KIND) ~~> ('K b :: KIND) = 'K (OPPOSITE a, b)

Methods

withObExp :: forall (a :: KIND) (b :: KIND) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: KIND) (b :: KIND) (c :: KIND). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: KIND) (b :: KIND). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: KIND) (b :: KIND) (x :: KIND) (y :: KIND). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

Closed CONSTRAINT Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

Associated Types

type (a :: CONSTRAINT) ~~> (b :: CONSTRAINT)
Instance details Defined in Proarrow.Category.Instance.Constraint type (a :: CONSTRAINT) ~~> (b :: CONSTRAINT) = 'CNSTRNT (UN 'CNSTRNT a :=> UN 'CNSTRNT b)

Methods

withObExp :: forall (a :: CONSTRAINT) (b :: CONSTRAINT) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: CONSTRAINT) (b :: CONSTRAINT) (c :: CONSTRAINT). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: CONSTRAINT) (b :: CONSTRAINT). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: CONSTRAINT) (b :: CONSTRAINT) (x :: CONSTRAINT) (y :: CONSTRAINT). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

Closed FINREL Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Associated Types

type (x :: FINREL) ~~> (y :: FINREL)
Instance details Defined in Proarrow.Category.Instance.FinRel type (x :: FINREL) ~~> (y :: FINREL) = ExpSA x y

Methods

withObExp :: forall (a :: FINREL) (b :: FINREL) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: FINREL) (b :: FINREL) (c :: FINREL). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: FINREL) (b :: FINREL). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: FINREL) (b :: FINREL) (x :: FINREL) (y :: FINREL). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

Closed FINSET Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinSet

Associated Types

type ('FS a :: FINSET) ~~> ('FS b :: FINSET)
Instance details Defined in Proarrow.Category.Instance.FinSet type ('FS a :: FINSET) ~~> ('FS b :: FINSET) = 'FS (Exp b a)

Methods

withObExp :: forall (a :: FINSET) (b :: FINSET) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: FINSET) (b :: FINSET) (c :: FINSET). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: FINSET) (b :: FINSET). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: FINSET) (b :: FINSET) (x :: FINSET) (y :: FINSET). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

Closed LINEAR Source Github #

Instance details

Defined in Proarrow.Category.Instance.Linear

Associated Types

type (a :: LINEAR) ~~> (b :: LINEAR)
Instance details Defined in Proarrow.Category.Instance.Linear type (a :: LINEAR) ~~> (b :: LINEAR) = 'L (UN 'L a %1 -> UN 'L b)

Methods

withObExp :: forall (a :: LINEAR) (b :: LINEAR) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: LINEAR) (b :: LINEAR) (c :: LINEAR). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: LINEAR) (b :: LINEAR). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: LINEAR) (b :: LINEAR) (x :: LINEAR) (y :: LINEAR). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

Closed () Source Github #

Instance details

Defined in Proarrow.Object.Exponential

Associated Types

type '() ~~> '()
Instance details Defined in Proarrow.Object.Exponential type '() ~~> '() = '()

Methods

withObExp :: forall (a :: ()) (b :: ()) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: ()) (b :: ()) (c :: ()). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: ()) (b :: ()). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: ()) (b :: ()) (x :: ()) (y :: ()). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

Closed Type Source Github #

Instance details

Defined in Proarrow.Object.Exponential

Associated Types

type (a :: Type) ~~> (b :: Type)
Instance details Defined in Proarrow.Object.Exponential type (a :: Type) ~~> (b :: Type) = a -> b

Methods

withObExp :: (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall a b x y. (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

HasPushouts k => Closed (COSPAN k) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Cospan

Methods

withObExp :: forall (a :: COSPAN k) (b :: COSPAN k) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: COSPAN k) (b :: COSPAN k) (c :: COSPAN k). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: COSPAN k) (b :: COSPAN k). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: COSPAN k) (b :: COSPAN k) (x :: COSPAN k) (y :: COSPAN k). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

TracedMonoidal k => Closed (INT k) Source Github #

Instance details

Defined in Proarrow.Category.Instance.IntConstruction

Methods

withObExp :: forall (a :: INT k) (b :: INT k) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: INT k) (b :: INT k) (c :: INT k). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: INT k) (b :: INT k). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: INT k) (b :: INT k) (x :: INT k) (y :: INT k). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

Num a => Closed (MatK a) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Mat

Methods

withObExp :: forall (a0 :: MatK a) (b :: MatK a) r. (Ob a0, Ob b) => (Ob (a0 ~~> b) => r) -> r Source Github #

curry :: forall (a0 :: MatK a) (b :: MatK a) (c :: MatK a). (Ob a0, Ob b) => ((a0 ** b) ~> c) -> a0 ~> (b ~~> c) Source Github #

apply :: forall (a0 :: MatK a) (b :: MatK a). (Ob a0, Ob b) => ((a0 ~~> b) ** a0) ~> b Source Github #

(^^^) :: forall (a0 :: MatK a) (b :: MatK a) (x :: MatK a) (y :: MatK a). (b ~> y) -> (x ~> a0) -> (a0 ~~> b) ~> (x ~~> y) Source Github #

HasPullbacks k => Closed (SPAN k) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Span

Methods

withObExp :: forall (a :: SPAN k) (b :: SPAN k) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: SPAN k) (b :: SPAN k) (c :: SPAN k). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: SPAN k) (b :: SPAN k). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: SPAN k) (b :: SPAN k) (x :: SPAN k) (y :: SPAN k). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

(CategoryOf j, CategoryOf k) => Closed (PROD (j +-> k)) Source Github #

Instance details

Defined in Proarrow.Profunctor.Exponential

Methods

withObExp :: forall (a :: PROD (j +-> k)) (b :: PROD (j +-> k)) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: PROD (j +-> k)) (b :: PROD (j +-> k)) (c :: PROD (j +-> k)). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: PROD (j +-> k)) (b :: PROD (j +-> k)). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: PROD (j +-> k)) (b :: PROD (j +-> k)) (x :: PROD (j +-> k)) (y :: PROD (j +-> k)). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

CategoryOf k1 => Closed (PROD (k1 -> Type)) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Nat

Methods

withObExp :: forall (a :: PROD (k1 -> Type)) (b :: PROD (k1 -> Type)) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: PROD (k1 -> Type)) (b :: PROD (k1 -> Type)) (c :: PROD (k1 -> Type)). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: PROD (k1 -> Type)) (b :: PROD (k1 -> Type)). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: PROD (k1 -> Type)) (b :: PROD (k1 -> Type)) (x :: PROD (k1 -> Type)) (y :: PROD (k1 -> Type)). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

Closed (KLEISLI (Cont r)) Source Github #

Instance details

Defined in Proarrow.Promonad.Cont

Methods

withObExp :: forall (a :: KLEISLI (Cont r)) (b :: KLEISLI (Cont r)) r0. (Ob a, Ob b) => (Ob (a ~~> b) => r0) -> r0 Source Github #

curry :: forall (a :: KLEISLI (Cont r)) (b :: KLEISLI (Cont r)) (c :: KLEISLI (Cont r)). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: KLEISLI (Cont r)) (b :: KLEISLI (Cont r)). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: KLEISLI (Cont r)) (b :: KLEISLI (Cont r)) (x :: KLEISLI (Cont r)) (y :: KLEISLI (Cont r)). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

(Monoidal j, Monoidal k) => Closed (j +-> k) Source Github #

Instance details

Defined in Proarrow.Profunctor.Day

Methods

withObExp :: forall (a :: j +-> k) (b :: j +-> k) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: j +-> k) (b :: j +-> k) (c :: j +-> k). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: j +-> k) (b :: j +-> k). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: j +-> k) (b :: j +-> k) (x :: j +-> k) (y :: j +-> k). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

CommutativeMonoid m => Closed (MONOIDK m) Source Github #

Instance details

Defined in Proarrow.Monoid

Methods

withObExp :: forall (a :: MONOIDK m) (b :: MONOIDK m) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: MONOIDK m) (b :: MONOIDK m) (c :: MONOIDK m). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: MONOIDK m) (b :: MONOIDK m). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: MONOIDK m) (b :: MONOIDK m) (x :: MONOIDK m) (y :: MONOIDK m). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

(Closed j, Closed k) => Closed (j, k) Source Github #

Instance details

Defined in Proarrow.Object.Exponential

Methods

withObExp :: forall (a :: (j, k)) (b :: (j, k)) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: (j, k)) (b :: (j, k)) (c :: (j, k)). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: (j, k)) (b :: (j, k)). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: (j, k)) (b :: (j, k)) (x :: (j, k)) (y :: (j, k)). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

Closed (Type -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Nat

Associated Types

type (j :: Type -> Type) ~~> (h :: Type -> Type)
Instance details Defined in Proarrow.Category.Instance.Nat type (j :: Type -> Type) ~~> (h :: Type -> Type) = Ran j h

Methods

withObExp :: forall (a :: Type -> Type) (b :: Type -> Type) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: Type -> Type) (b :: Type -> Type) (c :: Type -> Type). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: Type -> Type) (b :: Type -> Type). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: Type -> Type) (b :: Type -> Type) (x :: Type -> Type) (y :: Type -> Type). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

(Ok cs p, Elem Closed cs, Elem Monoidal cs) => Closed (FREE cs p) Source Github #

Instance details

Defined in Proarrow.Object.Exponential

Methods

withObExp :: forall (a :: FREE cs p) (b :: FREE cs p) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: FREE cs p) (b :: FREE cs p) (c :: FREE cs p). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: FREE cs p) (b :: FREE cs p). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: FREE cs p) (b :: FREE cs p) (x :: FREE cs p) (y :: FREE cs p). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

(Bicategory kk, Ob0 kk k, Ob (I :: kk k k), forall (f :: kk k k) (g :: kk k k). (Ob f, Ob g) => RightKanExtension f g) => Closed (ENDO kk k) Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Endo

Methods

withObExp :: forall (a :: ENDO kk k) (b :: ENDO kk k) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: ENDO kk k) (b :: ENDO kk k) (c :: ENDO kk k). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: ENDO kk k) (b :: ENDO kk k). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: ENDO kk k) (b :: ENDO kk k) (x :: ENDO kk k) (y :: ENDO kk k). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

uncurry :: forall {k} (b :: k) (c :: k) (a :: k). (Closed k, Ob b, Ob c) => (a ~> (b ~~> c)) -> (a ** b) ~> c Source Github #

comp :: forall {k} (a :: k) (b :: k) (c :: k). (Closed k, Ob a, Ob b, Ob c) => ((b ~~> c) ** (a ~~> b)) ~> (a ~~> c) Source Github #

mkExponential :: forall {k} (a :: k) (b :: k). Closed k => (a ~> b) -> (Unit :: k) ~> (a ~~> b) Source Github #

lower :: forall {k} (a :: k) (b :: k). (Closed k, Ob a, Ob b) => ((Unit :: k) ~> (a ~~> b)) -> a ~> b Source Github #

toEl :: forall {k} (a :: k). (Closed k, Ob a) => a ~> ((Unit :: k) ~~> a) Source Github #

data family ExpRep :: (OPPOSITE k, k) +-> k Source Github #

Instances

Instances details

Closed k => FunctorForRep (ExpRep :: (OPPOSITE k, k) +-> k) Source Github #
Instance details Defined in Proarrow.Object.Exponential Methods fmap :: forall (a :: (OPPOSITE k, k)) (b :: (OPPOSITE k, k)). (a ~> b) -> ((ExpRep :: (OPPOSITE k, k) +-> k) @ a) ~> ((ExpRep :: (OPPOSITE k, k) +-> k) @ b) Source Github #
type (ExpRep :: (OPPOSITE k, k) +-> k) @ ('('OP a, b) :: (OPPOSITE k, k)) Source Github #
Instance details Defined in Proarrow.Object.Exponential type (ExpRep :: (OPPOSITE k, k) +-> k) @ ('('OP a, b) :: (OPPOSITE k, k)) = a ~~> b

class (Cartesian k, Closed k) => CCC k Source Github #

Instances

Instances details

(Cartesian k, Closed k) => CCC k Source Github #
Instance details Defined in Proarrow.Object.Exponential

class (CCC k, HasCoproducts k) => BiCCC k Source Github #

Instances

Instances details

(CCC k, HasCoproducts k) => BiCCC k Source Github #
Instance details Defined in Proarrow.Object.Exponential

ap :: forall {j} {k} (y :: j) (a :: k) (x :: j) p. (Closed j, Cartesian k, MonoidalProfunctor p, Ob y) => p a (x ~~> y) -> p a x -> p a y Source Github #

data family Not (r :: k) :: k +-> OPPOSITE k Source Github #

Instances

Instances details

(Closed k, Ob r) => FunctorForRep (Not r :: k +-> OPPOSITE k) Source Github #
Instance details Defined in Proarrow.Object.Exponential Methods fmap :: forall (a :: k) (b :: k). (a ~> b) -> (Not r @ a) ~> (Not r @ 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 #
type (Not r :: k +-> OPPOSITE k) @ (a :: k) Source Github #
Instance details Defined in Proarrow.Object.Exponential type (Not r :: k +-> OPPOSITE k) @ (a :: k) = 'OP (a ~~> r)
type (Corep (Not r) :: k -> OPPOSITE k -> Type) % ('OP a :: OPPOSITE k) Source Github #
Instance details Defined in Proarrow.Object.Exponential type (Corep (Not r) :: k -> OPPOSITE k -> Type) % ('OP a :: OPPOSITE k) = a ~~> r

swapClosed :: forall {k} (c :: k) (a :: k) (b :: k). (Closed k, SymMonoidal k, Ob b, Ob c) => (a ~> (b ~~> c)) -> b ~> (a ~~> c) Source Github #

data family (a :: k) --> (b :: k) :: k Source Github #

Instances

Instances details

(Ob a, Ob b, Elem Closed cs, Elem Monoidal cs) => IsFreeOb (a --> b :: FREE cs p) Source Github #
Instance details Defined in Proarrow.Object.Exponential Methods withLowerOb :: forall {k} (f :: j +-> k) r. (Representable f, All cs k) => (Ob (Lower f (a --> b)) => r) -> r Source Github #
type Lower (f :: j +-> k) (a --> b :: FREE cs p) Source Github #
Instance details Defined in Proarrow.Object.Exponential type Lower (f :: j +-> k) (a --> b :: FREE cs p) = Lower f a ~~> Lower f b