Safe Haskell	None
Language	Haskell2010

Proarrow.Object.Exponential

Documentation

class Monoidal k => Closed k where Source Comments #

Minimal complete definition

withObExp, curry, uncurry

Associated Types

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

Methods

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

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

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

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

Instances

Instances details

Closed BOOL Source Comments #

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 Comments #

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

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

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

Closed KIND Source Comments #

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 Comments #

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

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

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

Closed CONSTRAINT Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Constraint

Associated Types

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

Methods

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

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

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

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

Closed LINEAR Source Comments #

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 Comments #

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

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

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

Closed () Source Comments #

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 Comments #

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

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

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

Closed Type Source Comments #

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 Comments #

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

uncurry :: (Ob b, Ob c) => (a ~> (b ~~> c)) -> (a ** b) ~> c Source Comments #

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

(TracedMonoidal k, Ob (Unit :: k)) => Closed (INT k) Source Comments #

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 Comments #

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

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

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

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

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 Comments #

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

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

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

BiCCC k => Closed (FK k) Source Comments #

Instance details

Defined in Proarrow.Helper.CCC

Methods

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

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

uncurry :: forall (b :: FK k) (c :: FK k) (a :: FK k). (Ob b, Ob c) => (a ~> (b ~~> c)) -> (a ** b) ~> c Source Comments #

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

(CategoryOf j, CategoryOf k) => Closed (PROD (PRO j k)) Source Comments #

Instance details

Defined in Proarrow.Object.Exponential

Methods

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

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

uncurry :: forall (b :: PROD (PRO j k)) (c :: PROD (PRO j k)) (a :: PROD (PRO j k)). (Ob b, Ob c) => (a ~> (b ~~> c)) -> (a ** b) ~> c Source Comments #

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

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

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 Comments #

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 Comments #

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

(^^^) :: 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 Comments #

Closed (KLEISLI (Cont r)) Source Comments #

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 Comments #

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 Comments #

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

(^^^) :: 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 Comments #

(Monoidal j, Monoidal k) => Closed (PRO j k) Source Comments #

Instance details

Defined in Proarrow.Profunctor.Day

Methods

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

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

uncurry :: forall (b :: PRO j k) (c :: PRO j k) (a :: PRO j k). (Ob b, Ob c) => (a ~> (b ~~> c)) -> (a ** b) ~> c Source Comments #

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

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

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 Comments #

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

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

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

Closed (Type -> Type) Source Comments #

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) = HaskRan j h

Methods

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

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

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

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

(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 Comments #

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 Comments #

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 Comments #

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

(^^^) :: 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 Comments #

curry' :: forall {k} (a :: k) (b :: k) (c :: k). Closed k => Obj a -> Obj b -> ((a ** b) ~> c) -> a ~> (b ~~> c) Source Comments #

uncurry' :: forall {k} (b :: k) (c :: k) (a :: k). Closed k => Obj b -> Obj c -> (a ~> (b ~~> c)) -> (a ** b) ~> c Source Comments #

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

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

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

eval :: forall {k} (a :: k) (b :: k). (Closed k, Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Comments #

data ExponentialFunctor (a :: k) (b :: (OPPOSITE k, k)) where Source Comments #

Constructors

ExponentialFunctor :: forall {k} (c :: k) (d :: k) (a :: k). (Ob c, Ob d) => (a ~> (c ~~> d)) -> ExponentialFunctor a '('OP c, d)

Instances

Instances details

Closed k => Profunctor (ExponentialFunctor :: k -> (OPPOSITE k, k) -> Type) Source Comments #
Instance details Defined in Proarrow.Object.Exponential Methods dimap :: forall (c :: k) (a :: k) (b :: (OPPOSITE k, k)) (d :: (OPPOSITE k, k)). (c ~> a) -> (b ~> d) -> ExponentialFunctor a b -> ExponentialFunctor c d Source Comments # (\\) :: forall (a :: k) (b :: (OPPOSITE k, k)) r. ((Ob a, Ob b) => r) -> ExponentialFunctor a b -> r Source Comments #
Closed k => Representable (ExponentialFunctor :: k -> (OPPOSITE k, k) -> Type) Source Comments #
Instance details Defined in Proarrow.Object.Exponential Methods index :: forall (a :: k) (b :: (OPPOSITE k, k)). ExponentialFunctor a b -> a ~> ((ExponentialFunctor :: k -> (OPPOSITE k, k) -> Type) % b) Source Comments # tabulate :: forall (b :: (OPPOSITE k, k)) (a :: k). Ob b => (a ~> ((ExponentialFunctor :: k -> (OPPOSITE k, k) -> Type) % b)) -> ExponentialFunctor a b Source Comments # repMap :: forall (a :: (OPPOSITE k, k)) (b :: (OPPOSITE k, k)). (a ~> b) -> ((ExponentialFunctor :: k -> (OPPOSITE k, k) -> Type) % a) ~> ((ExponentialFunctor :: k -> (OPPOSITE k, k) -> Type) % b) Source Comments #
type (ExponentialFunctor :: k -> (OPPOSITE k, k) -> Type) % ('('OP a, b) :: (OPPOSITE k, k)) Source Comments #
Instance details Defined in Proarrow.Object.Exponential type (ExponentialFunctor :: k -> (OPPOSITE k, k) -> Type) % ('('OP a, b) :: (OPPOSITE k, k)) = a ~~> b

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

Instances

Instances details

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

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

Instances

Instances details

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

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