Safe Haskell	None
Language	GHC2024

Proarrow.Profunctor.Instance.Initial

Description

The empty profunctor, with no values at all: the initial object of the category of profunctors j +-> k.

Synopsis

data InitialProfunctor (a :: k) (b :: j)

Documentation

data InitialProfunctor (a :: k) (b :: j) Source Github #

The profunctor with no values at all: the initial object of the category of profunctors j +-> k.

Instances

Instances details

(CategoryOf j, CategoryOf k) => Finitary (InitialProfunctor :: k -> j -> Type) Source Github #	The initial profunctor has no elements anywhere.
Instance details Defined in Proarrow.Category.Enriched.Finitary Methods size :: forall (a :: k) (b :: j). (Ob a, Ob b) => Natural Source Github # toIndex :: forall (a :: k) (b :: j). (Ob a, Ob b) => InitialProfunctor a b -> Natural Source Github # fromIndex :: forall (a :: k) (b :: j). (Ob a, Ob b) => Natural -> InitialProfunctor a b Source Github # elements :: forall (a :: k) (b :: j). (Ob a, Ob b) => [InitialProfunctor a b] Source Github #
(Thin j, Thin k) => DecidableProfunctor (InitialProfunctor :: k -> j -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Initial Methods decide :: forall (a :: k) (b :: j). (Ob a, Ob b) => Decision (InitialProfunctor :: k -> j -> Type) a b (Holds (InitialProfunctor :: k -> j -> Type) a b) Source Github # toHolds :: forall (a :: k) (b :: j) r. InitialProfunctor a b -> ((Holds (InitialProfunctor :: k -> j -> Type) a b ~ 'TRU, Ob a, Ob b) => r) -> r Source Github #
(Thin j, Thin k) => ThinProfunctor (InitialProfunctor :: k -> j -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Initial Methods arr :: forall (a :: k) (b :: j). (Ob a, Ob b, HasArrow (InitialProfunctor :: k -> j -> Type) a b) => InitialProfunctor a b Source Github # withArr :: forall (a :: k) (b :: j) r. InitialProfunctor a b -> ((HasArrow (InitialProfunctor :: k -> j -> Type) a b, Ob a, Ob b) => r) -> r Source Github #
(CategoryOf j, CategoryOf k) => Profunctor (InitialProfunctor :: k -> j -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Initial Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> InitialProfunctor a b -> InitialProfunctor c d Source Github # lmap :: forall (c :: k) (a :: k) (b :: j). (c ~> a) -> InitialProfunctor a b -> InitialProfunctor c b Source Github # rmap :: forall (b :: j) (d :: j) (a :: k). (b ~> d) -> InitialProfunctor a b -> InitialProfunctor a d Source Github # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> InitialProfunctor a b -> r Source Github #
Dagger k => DaggerProfunctor (InitialProfunctor :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Initial Methods dagger :: forall (a :: k) (b :: k). InitialProfunctor a b -> InitialProfunctor b a Source Github #
Show (InitialProfunctor a b) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Initial Methods showsPrec :: Int -> InitialProfunctor a b -> ShowS Github # show :: InitialProfunctor a b -> String Github # showList :: [InitialProfunctor a b] -> ShowS Github #
Eq (InitialProfunctor a b) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Initial Methods (==) :: InitialProfunctor a b -> InitialProfunctor a b -> Bool Github # (/=) :: InitialProfunctor a b -> InitialProfunctor a b -> Bool Github #
type HasArrow (InitialProfunctor :: k -> j -> Type) (a :: k) (b :: j) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Initial type HasArrow (InitialProfunctor :: k -> j -> Type) (a :: k) (b :: j) = Bottom
type Holds (InitialProfunctor :: k -> j -> Type) (a :: k) (b :: j) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Initial type Holds (InitialProfunctor :: k -> j -> Type) (a :: k) (b :: j) = 'FLS