Safe Haskell	None
Language	Haskell2010

Proarrow.Category.Instance.PointedHask

Documentation

data POINTED Source Comments #

Constructors

P Type

Instances

Instances details

Monoidal POINTED Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Associated Types

type Unit
Instance details Defined in Proarrow.Category.Instance.PointedHask type Unit = 'P ()
type ('P a :: POINTED) ** ('P b :: POINTED)
Instance details Defined in Proarrow.Category.Instance.PointedHask type ('P a :: POINTED) ** ('P b :: POINTED) = 'P (a, b)

Methods

leftUnitor :: forall (a :: POINTED). Ob a => ((Unit :: POINTED) ** a) ~> a Source Comments #

leftUnitorInv :: forall (a :: POINTED). Ob a => a ~> ((Unit :: POINTED) ** a) Source Comments #

rightUnitor :: forall (a :: POINTED). Ob a => (a ** (Unit :: POINTED)) ~> a Source Comments #

rightUnitorInv :: forall (a :: POINTED). Ob a => a ~> (a ** (Unit :: POINTED)) Source Comments #

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

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

CategoryOf POINTED Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.PointedHask type (~>) = Pointed
type Ob (a :: POINTED)
Instance details Defined in Proarrow.Category.Instance.PointedHask type Ob (a :: POINTED) = a ~ 'P (UN 'P a)

HasBinaryCoproducts POINTED Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Associated Types

type ('P a :: POINTED) \|\| ('P b :: POINTED)
Instance details Defined in Proarrow.Category.Instance.PointedHask type ('P a :: POINTED) \|\| ('P b :: POINTED) = 'P (a \|\| b)

Methods

lft :: forall (a :: POINTED) (b :: POINTED). (Ob a, Ob b) => a ~> (a || b) Source Comments #

lft' :: forall (a :: POINTED) (a' :: POINTED) (b :: POINTED). (a ~> a') -> Obj b -> a ~> (a' || b) Source Comments #

rgt :: forall (a :: POINTED) (b :: POINTED). (Ob a, Ob b) => b ~> (a || b) Source Comments #

rgt' :: forall (a :: POINTED) (b :: POINTED) (b' :: POINTED). Obj a -> (b ~> b') -> b ~> (a || b') Source Comments #

(|||) :: forall (x :: POINTED) (a :: POINTED) (y :: POINTED). (x ~> a) -> (y ~> a) -> (x || y) ~> a Source Comments #

(+++) :: forall (a :: POINTED) (b :: POINTED) (x :: POINTED) (y :: POINTED). (a ~> x) -> (b ~> y) -> (a || b) ~> (x || y) Source Comments #

HasBinaryProducts POINTED Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Associated Types

type ('P a :: POINTED) && ('P b :: POINTED)
Instance details Defined in Proarrow.Category.Instance.PointedHask type ('P a :: POINTED) && ('P b :: POINTED) = 'P (These a b)

Methods

fst :: forall (a :: POINTED) (b :: POINTED). (Ob a, Ob b) => (a && b) ~> a Source Comments #

fst' :: forall (a :: POINTED) (a' :: POINTED) (b :: POINTED). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

snd :: forall (a :: POINTED) (b :: POINTED). (Ob a, Ob b) => (a && b) ~> b Source Comments #

snd' :: forall (a :: POINTED) (b :: POINTED) (b' :: POINTED). Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

(&&&) :: forall (a :: POINTED) (x :: POINTED) (y :: POINTED). (a ~> x) -> (a ~> y) -> a ~> (x && y) Source Comments #

(***) :: forall (a :: POINTED) (b :: POINTED) (x :: POINTED) (y :: POINTED). (a ~> x) -> (b ~> y) -> (a && b) ~> (x && y) 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 #

initiate' :: forall (a' :: POINTED) (a :: POINTED). (a' ~> a) -> (InitialObject :: POINTED) ~> a Source Comments #

HasTerminalObject POINTED Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Associated Types

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

Methods

terminate :: forall (a :: POINTED). Ob a => a ~> (TerminalObject :: POINTED) Source Comments #

terminate' :: forall (a :: POINTED) (a' :: POINTED). (a ~> a') -> a ~> (TerminalObject :: POINTED) Source Comments #

Promonad Pointed Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Methods

id :: forall (a :: POINTED). Ob a => Pointed a a Source Comments #

(.) :: forall (b :: POINTED) (c :: POINTED) (a :: POINTED). Pointed b c -> Pointed a b -> Pointed a c Source Comments #

MonoidalProfunctor Pointed Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Methods

par0 :: Pointed (Unit :: POINTED) (Unit :: POINTED) Source Comments #

par :: forall (x1 :: POINTED) (x2 :: POINTED) (y1 :: POINTED) (y2 :: POINTED). Pointed x1 x2 -> Pointed y1 y2 -> Pointed (x1 ** y1) (x2 ** y2) Source Comments #

Profunctor Pointed Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Methods

dimap :: forall (c :: POINTED) (a :: POINTED) (b :: POINTED) (d :: POINTED). (c ~> a) -> (b ~> d) -> Pointed a b -> Pointed c d Source Comments #

(\\) :: forall (a :: POINTED) (b :: POINTED) r. ((Ob a, Ob b) => r) -> Pointed a b -> r Source Comments #

type Unit Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type Unit = 'P ()

type (~>) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type (~>) = Pointed

type InitialObject Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type InitialObject = 'P Void

type TerminalObject Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type TerminalObject = 'P Void

type Ob (a :: POINTED) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type Ob (a :: POINTED) = a ~ 'P (UN 'P a)

type UN 'P ('P a :: POINTED) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type UN 'P ('P a :: POINTED) = a

type ('P a :: POINTED) ** ('P b :: POINTED) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type ('P a :: POINTED) ** ('P b :: POINTED) = 'P (a, b)

type ('P a :: POINTED) || ('P b :: POINTED) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type ('P a :: POINTED) || ('P b :: POINTED) = 'P (a || b)

type ('P a :: POINTED) && ('P b :: POINTED) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type ('P a :: POINTED) && ('P b :: POINTED) = 'P (These a b)

data Pointed (a :: POINTED) (b :: POINTED) where Source Comments #

Constructors

P :: forall a1 b1. (Maybe a1 -> Maybe b1) -> Pointed ('P a1) ('P b1)

Instances

Instances details

Promonad Pointed Source Comments #
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods id :: forall (a :: POINTED). Ob a => Pointed a a Source Comments # (.) :: forall (b :: POINTED) (c :: POINTED) (a :: POINTED). Pointed b c -> Pointed a b -> Pointed a c Source Comments #
MonoidalProfunctor Pointed Source Comments #
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods par0 :: Pointed (Unit :: POINTED) (Unit :: POINTED) Source Comments # par :: forall (x1 :: POINTED) (x2 :: POINTED) (y1 :: POINTED) (y2 :: POINTED). Pointed x1 x2 -> Pointed y1 y2 -> Pointed (x1 y1) (x2 y2) Source Comments #
Profunctor Pointed Source Comments #
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods dimap :: forall (c :: POINTED) (a :: POINTED) (b :: POINTED) (d :: POINTED). (c ~> a) -> (b ~> d) -> Pointed a b -> Pointed c d Source Comments # (\\) :: forall (a :: POINTED) (b :: POINTED) r. ((Ob a, Ob b) => r) -> Pointed a b -> r Source Comments #

data These a b Source Comments #

Constructors

This a
That b
These a b