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Language	Haskell2010

Proarrow.Category.Instance.Linear

Documentation

data LINEAR Source Comments #

Constructors

L Type

Instances

Instances details

Monoidal LINEAR Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Associated Types

type Unit
Instance details Defined in Proarrow.Category.Instance.Linear type Unit = 'L ()
type ('L a :: LINEAR) ** ('L b :: LINEAR)
Instance details Defined in Proarrow.Category.Instance.Linear type ('L a :: LINEAR) ** ('L b :: LINEAR) = 'L (a, b)

Methods

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

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

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

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

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

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

SymMonoidal LINEAR Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Methods

swap' :: forall (a :: LINEAR) (a' :: LINEAR) (b :: LINEAR) (b' :: LINEAR). (a ~> a') -> (b ~> b') -> (a ** b) ~> (b' ** a') Source Comments #

CategoryOf LINEAR Source Comments #

Category of linear functions.

Instance details

Defined in Proarrow.Category.Instance.Linear

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Linear type (~>) = Linear
type Ob (a :: LINEAR)
Instance details Defined in Proarrow.Category.Instance.Linear type Ob (a :: LINEAR) = Is 'L a

HasBinaryCoproducts LINEAR Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Associated Types

type ('L a :: LINEAR) \|\| ('L b :: LINEAR)
Instance details Defined in Proarrow.Category.Instance.Linear type ('L a :: LINEAR) \|\| ('L b :: LINEAR) = 'L (Either a b)

Methods

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

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

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

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

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

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

HasBinaryProducts LINEAR Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Associated Types

type ('L a :: LINEAR) && ('L b :: LINEAR)
Instance details Defined in Proarrow.Category.Instance.Linear type ('L a :: LINEAR) && ('L b :: LINEAR) = 'L (With a b)

Methods

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

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

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

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

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

(***) :: forall (a :: LINEAR) (b :: LINEAR) (x :: LINEAR) (y :: LINEAR). (a ~> x) -> (b ~> y) -> (a && b) ~> (x && y) Source Comments #

Closed LINEAR Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Associated Types

type (a :: LINEAR) ~~> (b :: LINEAR)
Instance details Defined in Proarrow.Category.Instance.Linear type (a :: LINEAR) ~~> (b :: LINEAR) = 'L (UN 'L a %1 -> UN 'L b)

Methods

curry' :: forall (a :: LINEAR) (b :: LINEAR) (c :: LINEAR). Obj a -> Obj b -> ((a ** b) ~> c) -> a ~> (b ~~> c) Source Comments #

uncurry' :: forall (b :: LINEAR) (c :: LINEAR) (a :: LINEAR). Obj b -> Obj c -> (a ~> (b ~~> c)) -> (a ** b) ~> c Source Comments #

(^^^) :: forall (b :: LINEAR) (y :: LINEAR) (x :: LINEAR) (a :: LINEAR). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) 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 #

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

HasTerminalObject LINEAR Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Associated Types

type TerminalObject
Instance details Defined in Proarrow.Category.Instance.Linear type TerminalObject = 'L Top

Methods

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

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

Promonad Linear Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Methods

id :: forall (a :: LINEAR). Ob a => Linear a a Source Comments #

(.) :: forall (b :: LINEAR) (c :: LINEAR) (a :: LINEAR). Linear b c -> Linear a b -> Linear a c Source Comments #

MonoidalProfunctor Linear Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Methods

par0 :: Linear (Unit :: LINEAR) (Unit :: LINEAR) Source Comments #

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

MonoidalProfunctor Forget Source Comments #

Forget is a lax monoidal functor

Instance details

Defined in Proarrow.Category.Instance.Linear

Methods

par0 :: Forget (Unit :: Type) (Unit :: LINEAR) Source Comments #

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

MonoidalProfunctor Free Source Comments #

Free is a lax monoidal functor

Instance details

Defined in Proarrow.Category.Instance.Linear

Methods

par0 :: Free (Unit :: LINEAR) (Unit :: Type) Source Comments #

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

Profunctor Linear Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Methods

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

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

Profunctor Free Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Methods

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

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

Profunctor Forget Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Methods

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

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

Representable Forget Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Associated Types

type Forget % (a :: LINEAR)
Instance details Defined in Proarrow.Category.Instance.Linear type Forget % (a :: LINEAR) = UN 'L a

Methods

index :: forall a (b :: LINEAR). Forget a b -> a ~> (Forget % b) Source Comments #

tabulate :: forall (b :: LINEAR) a. Ob b => (a ~> (Forget % b)) -> Forget a b Source Comments #

repMap :: forall (a :: LINEAR) (b :: LINEAR). (a ~> b) -> (Forget % a) ~> (Forget % b) Source Comments #

Representable Free Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Associated Types

type Free % (a :: Type)
Instance details Defined in Proarrow.Category.Instance.Linear type Free % (a :: Type) = 'L (Ur a)

Methods

index :: forall (a :: LINEAR) b. Free a b -> a ~> (Free % b) Source Comments #

tabulate :: forall b (a :: LINEAR). Ob b => (a ~> (Free % b)) -> Free a b Source Comments #

repMap :: (a ~> b) -> (Free % a) ~> (Free % b) Source Comments #

Adjunction Free Forget Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Methods

unit :: Ob a => (Forget :.: Free) a a Source Comments #

counit :: (Free :.: Forget) :~> ((~>) :: CAT LINEAR) Source Comments #

MonoidalProfunctor (RepCostar Free) Source Comments #

Free is also a colax monoidal functor

Instance details

Defined in Proarrow.Category.Instance.Linear

Methods

par0 :: RepCostar Free (Unit :: Type) (Unit :: LINEAR) Source Comments #

par :: forall x1 (x2 :: LINEAR) y1 (y2 :: LINEAR). RepCostar Free x1 x2 -> RepCostar Free y1 y2 -> RepCostar Free (x1 ** y1) (x2 ** y2) Source Comments #

MonoidalProfunctor (RepCostar Forget) Source Comments #

Forget is also a colax monoidal functor

Instance details

Defined in Proarrow.Category.Instance.Linear

Methods

par0 :: RepCostar Forget (Unit :: LINEAR) (Unit :: Type) Source Comments #

par :: forall (x1 :: LINEAR) x2 (y1 :: LINEAR) y2. RepCostar Forget x1 x2 -> RepCostar Forget y1 y2 -> RepCostar Forget (x1 ** y1) (x2 ** y2) Source Comments #

Comonoid ('L (Ur a) :: LINEAR) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Methods

counit :: 'L (Ur a) ~> (Unit :: LINEAR) Source Comments #

comult :: 'L (Ur a) ~> ('L (Ur a) ** 'L (Ur a)) Source Comments #

type Unit Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

type Unit = 'L ()

type (~>) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

type (~>) = Linear

type InitialObject Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

type InitialObject = 'L Void

type TerminalObject Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

type TerminalObject = 'L Top

type Ob (a :: LINEAR) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

type Ob (a :: LINEAR) = Is 'L a

type (a :: LINEAR) ~~> (b :: LINEAR) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

type (a :: LINEAR) ~~> (b :: LINEAR) = 'L (UN 'L a %1 -> UN 'L b)

type Forget % (a :: LINEAR) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

type Forget % (a :: LINEAR) = UN 'L a

type Free % (a :: Type) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

type Free % (a :: Type) = 'L (Ur a)

type UN 'L ('L a :: LINEAR) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

type UN 'L ('L a :: LINEAR) = a

type ('L a :: LINEAR) ** ('L b :: LINEAR) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

type ('L a :: LINEAR) ** ('L b :: LINEAR) = 'L (a, b)

type ('L a :: LINEAR) || ('L b :: LINEAR) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

type ('L a :: LINEAR) || ('L b :: LINEAR) = 'L (Either a b)

type ('L a :: LINEAR) && ('L b :: LINEAR) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

type ('L a :: LINEAR) && ('L b :: LINEAR) = 'L (With a b)

data Linear (a :: LINEAR) (b :: LINEAR) where Source Comments #

Constructors

Linear :: forall a1 b1. (a1 %1 -> b1) -> Linear ('L a1) ('L b1)

Instances

Instances details

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

data Forget a (b :: LINEAR) where Source Comments #

Constructors

Forget :: forall a b1. (a -> b1) -> Forget a ('L b1)

Instances

Instances details

MonoidalProfunctor Forget Source Comments #

Forget is a lax monoidal functor

Instance details

Defined in Proarrow.Category.Instance.Linear

Methods

par0 :: Forget (Unit :: Type) (Unit :: LINEAR) Source Comments #

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

Profunctor Forget Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Methods

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

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

Representable Forget Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Associated Types

type Forget % (a :: LINEAR)
Instance details Defined in Proarrow.Category.Instance.Linear type Forget % (a :: LINEAR) = UN 'L a

Methods

index :: forall a (b :: LINEAR). Forget a b -> a ~> (Forget % b) Source Comments #

tabulate :: forall (b :: LINEAR) a. Ob b => (a ~> (Forget % b)) -> Forget a b Source Comments #

repMap :: forall (a :: LINEAR) (b :: LINEAR). (a ~> b) -> (Forget % a) ~> (Forget % b) Source Comments #

Adjunction Free Forget Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Methods

unit :: Ob a => (Forget :.: Free) a a Source Comments #

counit :: (Free :.: Forget) :~> ((~>) :: CAT LINEAR) Source Comments #

MonoidalProfunctor (RepCostar Forget) Source Comments #

Forget is also a colax monoidal functor

Instance details

Defined in Proarrow.Category.Instance.Linear

Methods

par0 :: RepCostar Forget (Unit :: LINEAR) (Unit :: Type) Source Comments #

par :: forall (x1 :: LINEAR) x2 (y1 :: LINEAR) y2. RepCostar Forget x1 x2 -> RepCostar Forget y1 y2 -> RepCostar Forget (x1 ** y1) (x2 ** y2) Source Comments #

type Forget % (a :: LINEAR) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

type Forget % (a :: LINEAR) = UN 'L a

data Ur a where Source Comments #

Constructors

Ur :: forall a. a -> Ur a

Instances

Instances details

Functor Ur Source Comments #
Instance details Defined in Proarrow.Category.Instance.Linear Methods map :: (a ~> b) -> Ur a ~> Ur b Source Comments #
Comonoid ('L (Ur a) :: LINEAR) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Linear Methods counit :: 'L (Ur a) ~> (Unit :: LINEAR) Source Comments # comult :: 'L (Ur a) ~> ('L (Ur a) ** 'L (Ur a)) Source Comments #