Safe Haskell	None
Language	GHC2024

Proarrow.Category.Monoidal.Rev

Documentation

data REV k Source Github #

Constructors

R k

Instances

Instances details

Monoidal k => Monoidal (REV k) Source Github #

The flipped tensor.

Instance details

Defined in Proarrow.Category.Monoidal.Rev

Associated Types

type Unit
Instance details Defined in Proarrow.Category.Monoidal.Rev type Unit = 'R (Unit :: k)

Methods

withOb2 :: forall (a :: REV k) (b :: REV k) r. (Ob a, Ob b) => (Ob (a ** b) => r) -> r Source Github #

leftUnitor :: forall (a :: REV k). Ob a => ((Unit :: REV k) ** a) ~> a Source Github #

leftUnitorInv :: forall (a :: REV k). Ob a => a ~> ((Unit :: REV k) ** a) Source Github #

rightUnitor :: forall (a :: REV k). Ob a => (a ** (Unit :: REV k)) ~> a Source Github #

rightUnitorInv :: forall (a :: REV k). Ob a => a ~> (a ** (Unit :: REV k)) Source Github #

associator :: forall (a :: REV k) (b :: REV k) (c :: REV k). (Ob a, Ob b, Ob c) => ((a ** b) ** c) ~> (a ** (b ** c)) Source Github #

associatorInv :: forall (a :: REV k) (b :: REV k) (c :: REV k). (Ob a, Ob b, Ob c) => (a ** (b ** c)) ~> ((a ** b) ** c) Source Github #

SymMonoidal k => SymMonoidal (REV k) Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Rev

Methods

swap :: forall (a :: REV k) (b :: REV k). (Ob a, Ob b) => (a ** b) ~> (b ** a) Source Github #

CopyDiscard k => CopyDiscard (REV k) Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Rev

Methods

copy :: forall (a :: REV k). Ob a => a ~> (a ** a) Source Github #

discard :: forall (a :: REV k). Ob a => a ~> (Unit :: REV k) Source Github #

CategoryOf k => CategoryOf (REV k) Source Github #

The reverse of the category of k, i.e. with the tensor flipped.

Instance details

Defined in Proarrow.Category.Monoidal.Rev

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Monoidal.Rev type (~>) = Rev ((~>) :: CAT k)

MonoidalProfunctor p => MonoidalProfunctor (Rev p :: REV k -> REV j -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Rev

Methods

par0 :: Rev p (Unit :: REV k) (Unit :: REV j) Source Github #

par :: forall (x1 :: REV k) (x2 :: REV j) (y1 :: REV k) (y2 :: REV j). Rev p x1 x2 -> Rev p y1 y2 -> Rev p (x1 ** y1) (x2 ** y2) Source Github #

Profunctor p => Profunctor (Rev p :: REV k -> REV j -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Rev

Methods

dimap :: forall (c :: REV k) (a :: REV k) (b :: REV j) (d :: REV j). (c ~> a) -> (b ~> d) -> Rev p a b -> Rev p c d Source Github #

lmap :: forall (c :: REV k) (a :: REV k) (b :: REV j). (c ~> a) -> Rev p a b -> Rev p c b Source Github #

rmap :: forall (b :: REV j) (d :: REV j) (a :: REV k). (b ~> d) -> Rev p a b -> Rev p a d Source Github #

(\\) :: forall (a :: REV k) (b :: REV j) r. ((Ob a, Ob b) => r) -> Rev p a b -> r Source Github #

Comonoid a => Comonoid ('R a :: REV k) Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Rev

Methods

counit :: 'R a ~> (Unit :: REV k) Source Github #

comult :: 'R a ~> ('R a ** 'R a) Source Github #

Monoid a => Monoid ('R a :: REV k) Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Rev

Methods

mempty :: (Unit :: REV k) ~> 'R a Source Github #

mappend :: ('R a ** 'R a) ~> 'R a Source Github #

Promonad p => Promonad (Rev p :: REV j -> REV j -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Rev

Methods

id :: forall (a :: REV j). Ob a => Rev p a a Source Github #

(.) :: forall (b :: REV j) (c :: REV j) (a :: REV j). Rev p b c -> Rev p a b -> Rev p a c Source Github #

type UN ('R :: j -> REV j) ('R a :: REV j) Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Rev

type UN ('R :: j -> REV j) ('R a :: REV j) = a

type Unit Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Rev

type Unit = 'R (Unit :: k)

type (~>) Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Rev

type (~>) = Rev ((~>) :: CAT k)

type Ob (a :: REV k) Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Rev

type Ob (a :: REV k) = (Is ('R :: k -> REV k) a, Ob (UN ('R :: k -> REV k) a))

type ('R a :: REV k) ** ('R b :: REV k) Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Rev

type ('R a :: REV k) ** ('R b :: REV k) = 'R (b ** a)

data Rev (p :: j +-> k) (a :: REV k) (b :: REV j) where Source Github #

Constructors

Rev :: forall {j} {k} (p :: j +-> k) (a1 :: k) (b1 :: j). p a1 b1 -> Rev p ('R a1) ('R b1)

Instances

Instances details

MonoidalProfunctor p => MonoidalProfunctor (Rev p :: REV k -> REV j -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Rev Methods par0 :: Rev p (Unit :: REV k) (Unit :: REV j) Source Github # par :: forall (x1 :: REV k) (x2 :: REV j) (y1 :: REV k) (y2 :: REV j). Rev p x1 x2 -> Rev p y1 y2 -> Rev p (x1 y1) (x2 y2) Source Github #
Profunctor p => Profunctor (Rev p :: REV k -> REV j -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Rev Methods dimap :: forall (c :: REV k) (a :: REV k) (b :: REV j) (d :: REV j). (c ~> a) -> (b ~> d) -> Rev p a b -> Rev p c d Source Github # lmap :: forall (c :: REV k) (a :: REV k) (b :: REV j). (c ~> a) -> Rev p a b -> Rev p c b Source Github # rmap :: forall (b :: REV j) (d :: REV j) (a :: REV k). (b ~> d) -> Rev p a b -> Rev p a d Source Github # (\\) :: forall (a :: REV k) (b :: REV j) r. ((Ob a, Ob b) => r) -> Rev p a b -> r Source Github #
Promonad p => Promonad (Rev p :: REV j -> REV j -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Rev Methods id :: forall (a :: REV j). Ob a => Rev p a a Source Github # (.) :: forall (b :: REV j) (c :: REV j) (a :: REV j). Rev p b c -> Rev p a b -> Rev p a c Source Github #