Data.Category.CartesianClosed

Documentation

type family Exponential (~>) y z :: *

class (HasTerminalObject ~>, HasBinaryProducts ~>) => CartesianClosed (~>) where

Methods

apply :: Obj ~> y -> Obj ~> z -> BinaryProduct ~> (Exponential ~> y z) y ~> z

tuple :: Obj ~> y -> Obj ~> z -> z ~> Exponential ~> y (BinaryProduct ~> z y)

(^^^) :: (z1 ~> z2) -> (y2 ~> y1) -> Exponential ~> y1 z1 ~> Exponential ~> y2 z2

Instances

CartesianClosed (->)

CartesianClosed Cat

CartesianClosed Boolean

Category ~> => CartesianClosed (Presheaves ~>)

data ExpFunctor (~>)

Constructors

ExpFunctor

Instances

CartesianClosed ~> => Functor (ExpFunctor ~>)

data CatApply y z

Constructors

CatApply

Instances

(Category y, Category z) => Functor (CatApply y z)

data CatTuple y z

Constructors

CatTuple

Instances

(Category y, Category z) => Functor (CatTuple y z)

type Presheaves (~>) = Nat (Op ~>) (->)

data PShExponential (~>) p q

Constructors

PShExponential

Instances

(Dom p ~ Op ~>, Dom q ~ Op ~>, Cod p ~ (->), Cod q ~ (->), Category ~>, Functor p, Functor q) => Functor (PShExponential ~> p q)

data ProductWith (~>) y

Constructors

ProductWith (Obj ~> y)

Instances

HasBinaryProducts ~> => Functor (ProductWith ~> y)

data ExponentialWith (~>) y

Constructors

ExponentialWith (Obj ~> y)

Instances

CartesianClosed ~> => Functor (ExponentialWith ~> y)

curryAdj :: CartesianClosed ~> => Obj ~> y -> Adjunction ~> ~> (ProductWith ~> y) (ExponentialWith ~> y)

curry :: CartesianClosed ~> => Obj ~> x -> Obj ~> y -> Obj ~> z -> ((ProductWith ~> y :% x) ~> z) -> x ~> (ExponentialWith ~> y :% z)

uncurry :: CartesianClosed ~> => Obj ~> x -> Obj ~> y -> Obj ~> z -> (x ~> (ExponentialWith ~> y :% z)) -> (ProductWith ~> y :% x) ~> z

type State (~>) s a = ExponentialWith ~> s :% (ProductWith ~> s :% a)

stateMonadReturn :: CartesianClosed ~> => Obj ~> s -> Obj ~> a -> a ~> State ~> s a

stateMonadJoin :: CartesianClosed ~> => Obj ~> s -> Obj ~> a -> State ~> s (State ~> s a) ~> State ~> s a

type Context (~>) s a = ProductWith ~> s :% (ExponentialWith ~> s :% a)

contextComonadExtract :: CartesianClosed ~> => Obj ~> s -> Obj ~> a -> Context ~> s a ~> a

contextComonadDuplicate :: CartesianClosed ~> => Obj ~> s -> Obj ~> a -> Context ~> s a ~> Context ~> s (Context ~> s a)