Safe Haskell	None
Language	Haskell2010

Proarrow.Object.Initial

Documentation

class (CategoryOf k, Ob (InitialObject :: k)) => HasInitialObject k where Source Comments #

Associated Types

type InitialObject :: k Source Comments #

Methods

initiate :: forall (a :: k). Ob a => (InitialObject :: k) ~> a Source Comments #

Instances

Instances details

HasInitialObject BOOL Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Associated Types

type InitialObject
Instance details Defined in Proarrow.Category.Instance.Bool type InitialObject = 'FLS

Methods

initiate :: forall (a :: BOOL). Ob a => (InitialObject :: BOOL) ~> a Source Comments #

HasInitialObject KIND Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Cat

Associated Types

type InitialObject
Instance details Defined in Proarrow.Category.Instance.Cat type InitialObject = 'K VOID

Methods

initiate :: forall (a :: KIND). Ob a => (InitialObject :: KIND) ~> a Source Comments #

HasInitialObject LINEAR Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Associated Types

type InitialObject
Instance details Defined in Proarrow.Category.Instance.Linear type InitialObject = 'L Void

Methods

initiate :: forall (a :: LINEAR). Ob a => (InitialObject :: LINEAR) ~> a Source Comments #

HasInitialObject POINTED Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Associated Types

type InitialObject
Instance details Defined in Proarrow.Category.Instance.PointedHask type InitialObject = 'P Void

Methods

initiate :: forall (a :: POINTED). Ob a => (InitialObject :: POINTED) ~> a Source Comments #

HasInitialObject Nat Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Simplex

Associated Types

type InitialObject
Instance details Defined in Proarrow.Category.Instance.Simplex type InitialObject = 'Z

Methods

initiate :: forall (a :: Nat). Ob a => (InitialObject :: Nat) ~> a Source Comments #

HasInitialObject () Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Unit

Associated Types

type InitialObject
Instance details Defined in Proarrow.Category.Instance.Unit type InitialObject = '()

Methods

initiate :: forall (a :: ()). Ob a => (InitialObject :: ()) ~> a Source Comments #

HasInitialObject Type Source Comments #

Instance details

Defined in Proarrow.Object.Initial

Associated Types

type InitialObject
Instance details Defined in Proarrow.Object.Initial type InitialObject = Void

Methods

initiate :: Ob a => (InitialObject :: Type) ~> a Source Comments #

HasInitialObject (FIN ('S n)) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Fin

Associated Types

type InitialObject
Instance details Defined in Proarrow.Category.Instance.Fin type InitialObject = 'FZ :: FIN ('S n)

Methods

initiate :: forall (a :: FIN ('S n)). Ob a => (InitialObject :: FIN ('S n)) ~> a Source Comments #

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

Instance details

Defined in Proarrow.Category.Instance.Mat

Associated Types

type InitialObject
Instance details Defined in Proarrow.Category.Instance.Mat type InitialObject = 'M 'Z :: MatK a

Methods

initiate :: forall (a0 :: MatK a). Ob a0 => (InitialObject :: MatK a) ~> a0 Source Comments #

HasTerminalObject k => HasInitialObject (OPPOSITE k) Source Comments #

Instance details

Defined in Proarrow.Category.Opposite

Associated Types

type InitialObject
Instance details Defined in Proarrow.Category.Opposite type InitialObject = 'OP (TerminalObject :: k)

Methods

initiate :: forall (a :: OPPOSITE k). Ob a => (InitialObject :: OPPOSITE k) ~> a Source Comments #

HasInitialObject k => HasInitialObject (PROD k) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

Associated Types

type InitialObject
Instance details Defined in Proarrow.Object.BinaryProduct type InitialObject = 'PR (InitialObject :: k)

Methods

initiate :: forall (a :: PROD k). Ob a => (InitialObject :: PROD k) ~> a Source Comments #

(HasInitialObject k, Promonad p) => HasInitialObject (KLEISLI p) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

Associated Types

type InitialObject
Instance details Defined in Proarrow.Category.Instance.Kleisli type InitialObject = 'KL (InitialObject :: k) :: KLEISLI p

Methods

initiate :: forall (a :: KLEISLI p). Ob a => (InitialObject :: KLEISLI p) ~> a Source Comments #

(CategoryOf j, CategoryOf k) => HasInitialObject (j +-> k) Source Comments #

Instance details

Defined in Proarrow.Object.Initial

Associated Types

type InitialObject
Instance details Defined in Proarrow.Object.Initial type InitialObject = InitialProfunctor :: k -> j -> Type

Methods

initiate :: forall (a :: j +-> k). Ob a => (InitialObject :: j +-> k) ~> a Source Comments #

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

Instance details

Defined in Proarrow.Object.Initial

Associated Types

type InitialObject
Instance details Defined in Proarrow.Object.Initial type InitialObject = '(InitialObject :: j, InitialObject :: k)

Methods

initiate :: forall (a :: (j, k)). Ob a => (InitialObject :: (j, k)) ~> a Source Comments #

CategoryOf k1 => HasInitialObject (k1 -> Type) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Nat

Associated Types

type InitialObject
Instance details Defined in Proarrow.Category.Instance.Nat type InitialObject = Const Void :: k1 -> Type

Methods

initiate :: forall (a :: k1 -> Type). Ob a => (InitialObject :: k1 -> Type) ~> a Source Comments #

(HasInitialObject j, CategoryOf k, CodiscreteProfunctor p) => HasInitialObject (COLLAGE p) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Collage

Associated Types

type InitialObject
Instance details Defined in Proarrow.Category.Instance.Collage type InitialObject = 'L (InitialObject :: j) :: COLLAGE p

Methods

initiate :: forall (a :: COLLAGE p). Ob a => (InitialObject :: COLLAGE p) ~> a Source Comments #

(HasInitialObject k, Ok cs p k, Includes cs HasInitialObject) => HasInitialObject (FREE cs p k) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Free

Associated Types

type InitialObject
Instance details Defined in Proarrow.Category.Instance.Free type InitialObject = InitF :: FREE cs p k

Methods

initiate :: forall (a :: FREE cs p k). Ob a => (InitialObject :: FREE cs p k) ~> a Source Comments #

initiate' :: forall {k} (a' :: k) (a :: k). HasInitialObject k => (a' ~> a) -> (InitialObject :: k) ~> a Source Comments #

class (HasInitialObject k, HasTerminalObject k, (InitialObject :: k) ~ (TerminalObject :: k)) => HasZeroObject k where Source Comments #

Methods

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

Instances

Instances details

(HasInitialObject k, HasTerminalObject k, (InitialObject :: k) ~ (TerminalObject :: k)) => HasZeroObject k Source Comments #
Instance details Defined in Proarrow.Object.Initial Methods zero :: forall (a :: k) (b :: k). (Ob a, Ob b) => a ~> b Source Comments #