Safe Haskell	None
Language	GHC2024

Proarrow.Category.Instance.Zero

Description

The initial category: the empty kind VOID with no objects (its Ob constraint is Bottom, which nothing satisfies) and no arrows.

Documentation

data VOID Source Github #

Instances

Instances details

Enumerable VOID Source Github #

Instance details

Defined in Proarrow.Category.Enriched.Thin

Methods

withIndex :: forall (a :: VOID) r. Ob a => (KnownIndex a => r) -> r Source Github #

withOb :: forall (a :: VOID) r. KnownIndex a => (Ob a => r) -> r Source Github #

atOb :: forall (i :: Nat). SNat i -> AtOb VOID (At VOID i) Source Github #

Finite VOID Source Github #

Instance details

Defined in Proarrow.Category.Enriched.Thin

Associated Types

type Objects VOID
Instance details Defined in Proarrow.Category.Enriched.Thin type Objects VOID = '[] :: [VOID]

Methods

finite :: IndexedList (Objects VOID) Source Github #

withAtLookup :: forall (i :: Nat) r. SNat i -> (Lookup (Objects VOID) i ~ At VOID i => r) -> r Source Github #

Indexed VOID Source Github #

The empty kind has no inhabitants to number.

Instance details

Defined in Proarrow.Category.Enriched.Thin

Associated Types

type Index (a :: VOID)
Instance details Defined in Proarrow.Category.Enriched.Thin type Index (a :: VOID) = 'Z
type At VOID i
Instance details Defined in Proarrow.Category.Enriched.Thin type At VOID i = 'Nothing :: Maybe VOID

CategoryOf VOID Source Github #

The category with no objects, the initial category.

Instance details

Defined in Proarrow.Category.Instance.Zero

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Zero type (~>) = Zero
type Ob (a :: VOID)
Instance details Defined in Proarrow.Category.Instance.Zero type Ob (a :: VOID) = Bottom

DaggerProfunctor Zero Source Github #

Instance details

Defined in Proarrow.Category.Instance.Zero

Methods

dagger :: forall (a :: VOID) (b :: VOID). Zero a b -> Zero b a Source Github #

Promonad Zero Source Github #

Instance details

Defined in Proarrow.Category.Instance.Zero

Methods

id :: forall (a :: VOID). Ob a => Zero a a Source Github #

(.) :: forall (b :: VOID) (c :: VOID) (a :: VOID). Zero b c -> Zero a b -> Zero a c Source Github #

DecidableProfunctor Zero Source Github #

Instance details

Defined in Proarrow.Category.Enriched.Thin

Associated Types

type Holds Zero (a :: VOID) (b :: VOID)
Instance details Defined in Proarrow.Category.Enriched.Thin type Holds Zero (a :: VOID) (b :: VOID) = 'FLS

Methods

decide :: forall (a :: VOID) (b :: VOID). (Ob a, Ob b) => Decision Zero a b (Holds Zero a b) Source Github #

toHolds :: forall (a :: VOID) (b :: VOID) r. Zero a b -> ((Holds Zero a b ~ 'TRU, Ob a, Ob b) => r) -> r Source Github #

ThinProfunctor Zero Source Github #

Instance details

Defined in Proarrow.Category.Enriched.Thin

Associated Types

type HasArrow Zero (a :: VOID) (b :: VOID)
Instance details Defined in Proarrow.Category.Enriched.Thin type HasArrow Zero (a :: VOID) (b :: VOID) = Holds Zero a b ~ 'TRU

Methods

arr :: forall (a :: VOID) (b :: VOID). (Ob a, Ob b, HasArrow Zero a b) => Zero a b Source Github #

withArr :: forall (a :: VOID) (b :: VOID) r. Zero a b -> ((HasArrow Zero a b, Ob a, Ob b) => r) -> r Source Github #

Profunctor Zero Source Github #

Instance details

Defined in Proarrow.Category.Instance.Zero

Methods

dimap :: forall (c :: VOID) (a :: VOID) (b :: VOID) (d :: VOID). (c ~> a) -> (b ~> d) -> Zero a b -> Zero c d Source Github #

lmap :: forall (c :: VOID) (a :: VOID) (b :: VOID). (c ~> a) -> Zero a b -> Zero c b Source Github #

rmap :: forall (b :: VOID) (d :: VOID) (a :: VOID). (b ~> d) -> Zero a b -> Zero a d Source Github #

(\\) :: forall (a :: VOID) (b :: VOID) r. ((Ob a, Ob b) => r) -> Zero a b -> r Source Github #

CategoryOf k => FunctorForRep (Initiate :: VOID +-> k) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Fam

Methods

fmap :: forall (a :: VOID) (b :: VOID). (a ~> b) -> ((Initiate :: VOID +-> k) @ a) ~> ((Initiate :: VOID +-> k) @ b) Source Github #

CategoryOf k => FunctorForRep (Absurd :: VOID +-> k) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Zero

Methods

fmap :: forall (a :: VOID) (b :: VOID). (a ~> b) -> ((Absurd :: VOID +-> k) @ a) ~> ((Absurd :: VOID +-> k) @ b) Source Github #

type Objects VOID Source Github #

Instance details

Defined in Proarrow.Category.Enriched.Thin

type Objects VOID = '[] :: [VOID]

type (~>) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Zero

type (~>) = Zero

type At VOID i Source Github #

Instance details

Defined in Proarrow.Category.Enriched.Thin

type At VOID i = 'Nothing :: Maybe VOID

type Index (a :: VOID) Source Github #

Instance details

Defined in Proarrow.Category.Enriched.Thin

type Index (a :: VOID) = 'Z

type Ob (a :: VOID) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Zero

type Ob (a :: VOID) = Bottom

type HasArrow Zero (a :: VOID) (b :: VOID) Source Github #

Instance details

Defined in Proarrow.Category.Enriched.Thin

type HasArrow Zero (a :: VOID) (b :: VOID) = Holds Zero a b ~ 'TRU

type Holds Zero (a :: VOID) (b :: VOID) Source Github #

Instance details

Defined in Proarrow.Category.Enriched.Thin

type Holds Zero (a :: VOID) (b :: VOID) = 'FLS

type (Initiate :: VOID +-> k) @ (a :: VOID) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Fam

type (Initiate :: VOID +-> k) @ (a :: VOID) = Any :: k

data Zero (a :: VOID) (b :: VOID) Source Github #

Instances

Instances details

DaggerProfunctor Zero Source Github #

Instance details

Defined in Proarrow.Category.Instance.Zero

Methods

dagger :: forall (a :: VOID) (b :: VOID). Zero a b -> Zero b a Source Github #

Promonad Zero Source Github #

Instance details

Defined in Proarrow.Category.Instance.Zero

Methods

id :: forall (a :: VOID). Ob a => Zero a a Source Github #

(.) :: forall (b :: VOID) (c :: VOID) (a :: VOID). Zero b c -> Zero a b -> Zero a c Source Github #

DecidableProfunctor Zero Source Github #

Instance details

Defined in Proarrow.Category.Enriched.Thin

Associated Types

type Holds Zero (a :: VOID) (b :: VOID)
Instance details Defined in Proarrow.Category.Enriched.Thin type Holds Zero (a :: VOID) (b :: VOID) = 'FLS

Methods

decide :: forall (a :: VOID) (b :: VOID). (Ob a, Ob b) => Decision Zero a b (Holds Zero a b) Source Github #

toHolds :: forall (a :: VOID) (b :: VOID) r. Zero a b -> ((Holds Zero a b ~ 'TRU, Ob a, Ob b) => r) -> r Source Github #

ThinProfunctor Zero Source Github #

Instance details

Defined in Proarrow.Category.Enriched.Thin

Associated Types

type HasArrow Zero (a :: VOID) (b :: VOID)
Instance details Defined in Proarrow.Category.Enriched.Thin type HasArrow Zero (a :: VOID) (b :: VOID) = Holds Zero a b ~ 'TRU

Methods

arr :: forall (a :: VOID) (b :: VOID). (Ob a, Ob b, HasArrow Zero a b) => Zero a b Source Github #

withArr :: forall (a :: VOID) (b :: VOID) r. Zero a b -> ((HasArrow Zero a b, Ob a, Ob b) => r) -> r Source Github #

Profunctor Zero Source Github #

Instance details

Defined in Proarrow.Category.Instance.Zero

Methods

dimap :: forall (c :: VOID) (a :: VOID) (b :: VOID) (d :: VOID). (c ~> a) -> (b ~> d) -> Zero a b -> Zero c d Source Github #

lmap :: forall (c :: VOID) (a :: VOID) (b :: VOID). (c ~> a) -> Zero a b -> Zero c b Source Github #

rmap :: forall (b :: VOID) (d :: VOID) (a :: VOID). (b ~> d) -> Zero a b -> Zero a d Source Github #

(\\) :: forall (a :: VOID) (b :: VOID) r. ((Ob a, Ob b) => r) -> Zero a b -> r Source Github #

type HasArrow Zero (a :: VOID) (b :: VOID) Source Github #

Instance details

Defined in Proarrow.Category.Enriched.Thin

type HasArrow Zero (a :: VOID) (b :: VOID) = Holds Zero a b ~ 'TRU

type Holds Zero (a :: VOID) (b :: VOID) Source Github #

Instance details

Defined in Proarrow.Category.Enriched.Thin

type Holds Zero (a :: VOID) (b :: VOID) = 'FLS

class Bottom where Source Github #

Methods

no :: a Source Github #

data family Absurd :: VOID +-> k Source Github #

Instances

Instances details

CategoryOf k => FunctorForRep (Absurd :: VOID +-> k) Source Github #
Instance details Defined in Proarrow.Category.Instance.Zero Methods fmap :: forall (a :: VOID) (b :: VOID). (a ~> b) -> ((Absurd :: VOID +-> k) @ a) ~> ((Absurd :: VOID +-> k) @ b) Source Github #