Safe Haskell	None
Language	GHC2024

Proarrow.Profunctor.Star

Documentation

data Star' (f :: j .-> k) (a :: k) (b :: j) where Source Comments #

Constructors

Star' :: forall {j} {k} (b :: j) (a :: k) (f1 :: j -> k). Ob b => (a ~> f1 b) -> Star' ('NT f1) a b

Instances

Instances details

Functor f => Strong Type (Star f :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods act :: (a ~> b) -> Star f x y -> Star f (Act a x) (Act b y) Source Comments #
(Functor f, Applicative f) => Strong (SUBCAT Traversable) (Star (Prelude f) :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods act :: forall (a :: SUBCAT Traversable) (b :: SUBCAT Traversable) x y. (a ~> b) -> Star (Prelude f) x y -> Star (Prelude f) (Act a x) (Act b y) Source Comments #
(Functor f, Thin j, Discrete k) => ThinProfunctor (Star f :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods arr :: forall (a :: k) (b :: j). (Ob a, Ob b, HasArrow (Star f) a b) => Star f a b Source Comments # withArr :: forall (a :: k) (b :: j) r. Star f a b -> (HasArrow (Star f) a b => r) -> r Source Comments #
(Applicative f, Monoidal j, Monoidal k) => MonoidalProfunctor (Star f :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods par0 :: Star f (Unit :: k) (Unit :: j) Source Comments # par :: forall (x1 :: k) (x2 :: j) (y1 :: k) (y2 :: j). Star f x1 x2 -> Star f y1 y2 -> Star f (x1 y1) (x2 y2) Source Comments #
Functor f => Profunctor (Star f :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> Star f a b -> Star f c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> Star f a b -> r Source Comments #
Corepresentable (Star ((->) a) :: Type -> Type -> Type) Source Comments #	The left adjoint of `((->) a)` is `(,) a`.
Instance details Defined in Proarrow.Adjunction Methods coindex :: Star ((->) a) a0 b -> (Star ((->) a) %% a0) ~> b Source Comments # cotabulate :: Ob a0 => ((Star ((->) a) %% a0) ~> b) -> Star ((->) a) a0 b Source Comments # corepMap :: (a0 ~> b) -> (Star ((->) a) %% a0) ~> (Star ((->) a) %% b) Source Comments #
Functor f => Representable (Star f :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods index :: forall (a :: k) (b :: j). Star f a b -> a ~> (Star f % b) Source Comments # tabulate :: forall (b :: j) (a :: k). Ob b => (a ~> (Star f % b)) -> Star f a b Source Comments # repMap :: forall (a :: j) (b :: j). (a ~> b) -> (Star f % a) ~> (Star f % b) Source Comments #
Functor f => Proadjunction (Star f :: k -> j -> Type) (Costar f :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Adjunction Methods unit :: forall (a :: j). Ob a => (Costar f :.: Star f) a a Source Comments # counit :: (Star f :.: Costar f) :~> ((~>) :: CAT k) Source Comments #
Traversable (Star Maybe) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods traverse :: forall (p :: Type +-> Type). (DistributiveProfunctor p, Strong Type p, SelfAction Type) => (Star Maybe :.: p) :~> (p :.: Star Maybe) Source Comments #
Traversable (Star []) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods traverse :: forall (p :: Type +-> Type). (DistributiveProfunctor p, Strong Type p, SelfAction Type) => (Star [] :.: p) :~> (p :.: Star []) Source Comments #
Monad m => Promonad (Star (Prelude m) :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods id :: Ob a => Star (Prelude m) a a Source Comments # (.) :: Star (Prelude m) b c -> Star (Prelude m) a b -> Star (Prelude m) a c Source Comments #
Monad m => Strong Type (Updating a b :: Type -> KlCat m -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods act :: forall a0 b0 x (y :: KlCat m). (a0 ~> b0) -> Updating a b x y -> Updating a b (Act a0 x) (Act b0 y) Source Comments #
(Alternative f, Monoidal k, Distributive j) => MonoidalProfunctor (CoprodDom (Star f) :: k -> COPROD j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods par0 :: CoprodDom (Star f) (Unit :: k) (Unit :: COPROD j) Source Comments # par :: forall (x1 :: k) (x2 :: COPROD j) (y1 :: k) (y2 :: COPROD j). CoprodDom (Star f) x1 x2 -> CoprodDom (Star f) y1 y2 -> CoprodDom (Star f) (x1 y1) (x2 y2) Source Comments #
Monad m => Profunctor (Updating a b :: Type -> KlCat m -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: forall c a0 (b0 :: KlCat m) (d :: KlCat m). (c ~> a0) -> (b0 ~> d) -> Updating a b a0 b0 -> Updating a b c d Source Comments # (\\) :: forall a0 (b0 :: KlCat m) r. ((Ob a0, Ob b0) => r) -> Updating a b a0 b0 -> r Source Comments #
(Functor f, HasCoproducts j, HasCoproducts k) => MonoidalProfunctor (Coprod (Star f) :: COPROD k -> COPROD j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods par0 :: Coprod (Star f) (Unit :: COPROD k) (Unit :: COPROD j) Source Comments # par :: forall (x1 :: COPROD k) (x2 :: COPROD j) (y1 :: COPROD k) (y2 :: COPROD j). Coprod (Star f) x1 x2 -> Coprod (Star f) y1 y2 -> Coprod (Star f) (x1 y1) (x2 y2) Source Comments #
(CategoryOf j, CategoryOf k) => Functor (Star' :: (j .-> k) -> k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods map :: forall (a :: j .-> k) (b :: j .-> k). (a ~> b) -> Star' a ~> Star' b Source Comments #
Profunctor j2 => Corepresentable (Star (Ran ('OP j2) :: (i +-> k) -> k -> j1 -> Type) :: (k -> j1 -> Type) -> (i +-> k) -> Type) Source Comments #	The right Kan extension is the right adjoint of the precomposition functor.
Instance details Defined in Proarrow.Profunctor.Ran Methods coindex :: forall (a :: k -> j1 -> Type) (b :: i +-> k). Star (Ran ('OP j2) :: (i +-> k) -> k -> j1 -> Type) a b -> (Star (Ran ('OP j2) :: (i +-> k) -> k -> j1 -> Type) %% a) ~> b Source Comments # cotabulate :: forall (a :: k -> j1 -> Type) (b :: i +-> k). Ob a => ((Star (Ran ('OP j2) :: (i +-> k) -> k -> j1 -> Type) %% a) ~> b) -> Star (Ran ('OP j2) :: (i +-> k) -> k -> j1 -> Type) a b Source Comments # corepMap :: forall (a :: k -> j1 -> Type) (b :: k -> j1 -> Type). (a ~> b) -> (Star (Ran ('OP j2) :: (i +-> k) -> k -> j1 -> Type) %% a) ~> (Star (Ran ('OP j2) :: (i +-> k) -> k -> j1 -> Type) %% b) Source Comments #
Profunctor j2 => Corepresentable (Star (Rift ('OP j2) :: (j1 +-> i) -> k -> j1 -> Type) :: (k -> j1 -> Type) -> (j1 +-> i) -> Type) Source Comments #	The right Kan lift is the right adjoint of the postcomposition functor.
Instance details Defined in Proarrow.Profunctor.Rift Methods coindex :: forall (a :: k -> j1 -> Type) (b :: j1 +-> i). Star (Rift ('OP j2) :: (j1 +-> i) -> k -> j1 -> Type) a b -> (Star (Rift ('OP j2) :: (j1 +-> i) -> k -> j1 -> Type) %% a) ~> b Source Comments # cotabulate :: forall (a :: k -> j1 -> Type) (b :: j1 +-> i). Ob a => ((Star (Rift ('OP j2) :: (j1 +-> i) -> k -> j1 -> Type) %% a) ~> b) -> Star (Rift ('OP j2) :: (j1 +-> i) -> k -> j1 -> Type) a b Source Comments # corepMap :: forall (a :: k -> j1 -> Type) (b :: k -> j1 -> Type). (a ~> b) -> (Star (Rift ('OP j2) :: (j1 +-> i) -> k -> j1 -> Type) %% a) ~> (Star (Rift ('OP j2) :: (j1 +-> i) -> k -> j1 -> Type) %% b) Source Comments #
Procomonad j => Promonad (Star (Ran ('OP j) :: (i +-> k) -> k -> i -> Type) :: (k -> i -> Type) -> (i +-> k) -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Ran Methods id :: forall (a :: k -> i -> Type). Ob a => Star (Ran ('OP j) :: (i +-> k) -> k -> i -> Type) a a Source Comments # (.) :: forall (b :: k -> i -> Type) (c :: k -> i -> Type) (a :: k -> i -> Type). Star (Ran ('OP j) :: (i +-> k) -> k -> i -> Type) b c -> Star (Ran ('OP j) :: (i +-> k) -> k -> i -> Type) a b -> Star (Ran ('OP j) :: (i +-> k) -> k -> i -> Type) a c Source Comments #
Profunctor p => Promonad (Star ((:+:) p) :: (k -> j -> Type) -> (j +-> k) -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods id :: forall (a :: k -> j -> Type). Ob a => Star ((:+:) p) a a Source Comments # (.) :: forall (b :: k -> j -> Type) (c :: k -> j -> Type) (a :: k -> j -> Type). Star ((:+:) p) b c -> Star ((:+:) p) a b -> Star ((:+:) p) a c Source Comments #
Promonad (Star (Coyoneda :: (j +-> k) -> k -> j -> Type) :: (k -> j -> Type) -> (j +-> k) -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Coyoneda Methods id :: forall (a :: k -> j -> Type). Ob a => Star (Coyoneda :: (j +-> k) -> k -> j -> Type) a a Source Comments # (.) :: forall (b :: k -> j -> Type) (c :: k -> j -> Type) (a :: k -> j -> Type). Star (Coyoneda :: (j +-> k) -> k -> j -> Type) b c -> Star (Coyoneda :: (j +-> k) -> k -> j -> Type) a b -> Star (Coyoneda :: (j +-> k) -> k -> j -> Type) a c Source Comments #
Promonad (Star (Yoneda :: (j +-> k) -> k -> j -> Type) :: (k -> j -> Type) -> (j +-> k) -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Yoneda Methods id :: forall (a :: k -> j -> Type). Ob a => Star (Yoneda :: (j +-> k) -> k -> j -> Type) a a Source Comments # (.) :: forall (b :: k -> j -> Type) (c :: k -> j -> Type) (a :: k -> j -> Type). Star (Yoneda :: (j +-> k) -> k -> j -> Type) b c -> Star (Yoneda :: (j +-> k) -> k -> j -> Type) a b -> Star (Yoneda :: (j +-> k) -> k -> j -> Type) a c Source Comments #
Procomonad j2 => Promonad (Star (Rift ('OP j2) :: (j1 +-> k) -> k -> j1 -> Type) :: (k -> j1 -> Type) -> (j1 +-> k) -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Rift Methods id :: forall (a :: k -> j1 -> Type). Ob a => Star (Rift ('OP j2) :: (j1 +-> k) -> k -> j1 -> Type) a a Source Comments # (.) :: forall (b :: k -> j1 -> Type) (c :: k -> j1 -> Type) (a :: k -> j1 -> Type). Star (Rift ('OP j2) :: (j1 +-> k) -> k -> j1 -> Type) b c -> Star (Rift ('OP j2) :: (j1 +-> k) -> k -> j1 -> Type) a b -> Star (Rift ('OP j2) :: (j1 +-> k) -> k -> j1 -> Type) a c Source Comments #
type (Star ((->) a) :: Type -> Type -> Type) %% (b :: Type) Source Comments #
Instance details Defined in Proarrow.Adjunction type (Star ((->) a) :: Type -> Type -> Type) %% (b :: Type) = (a, b)
type (Star f :: k -> j -> Type) % (a :: j) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star type (Star f :: k -> j -> Type) % (a :: j) = f a
type HasArrow (Star f :: k -> j -> Type) (a :: k) (b :: j) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star type HasArrow (Star f :: k -> j -> Type) (a :: k) (b :: j) = a ~ f b
type (Star (Ran ('OP j2) :: (i +-> k) -> k -> j1 -> Type) :: (k -> j1 -> Type) -> (i +-> k) -> Type) %% (p :: k -> j1 -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Ran type (Star (Ran ('OP j2) :: (i +-> k) -> k -> j1 -> Type) :: (k -> j1 -> Type) -> (i +-> k) -> Type) %% (p :: k -> j1 -> Type) = p :.: j2
type (Star (Rift ('OP j2) :: (j1 +-> i) -> k -> j1 -> Type) :: (k -> j1 -> Type) -> (j1 +-> i) -> Type) %% (p :: k -> j1 -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Rift type (Star (Rift ('OP j2) :: (j1 +-> i) -> k -> j1 -> Type) :: (k -> j1 -> Type) -> (j1 +-> i) -> Type) %% (p :: k -> j1 -> Type) = j2 :.: p

type Star (f :: j -> k) = Star' ('NT f) Source Comments #

pattern Star :: forall {j} {k} b a (f :: j -> k). () => Ob b => (a ~> f b) -> Star f a b Source Comments #

unStar :: forall {j} {k} (f :: j -> k) (a :: k) (b :: j). Star f a b -> a ~> f b Source Comments #

composeStar :: forall {k} {j} (f :: k -> Type) (g :: j -> k). Functor f => (Star f :.: Star g) :~> Star (Compose f g) Source Comments #

data CoprodDom (p :: j +-> k) (a :: k) (b :: COPROD j) where Source Comments #

Constructors

Co
Fields :: forall {j} {k} (p :: j +-> k) (a :: k) (b1 :: j). { unCo :: p a b1 } -> CoprodDom p a ('COPR b1)

Instances

Instances details

(Alternative f, Monoidal k, Distributive j) => MonoidalProfunctor (CoprodDom (Star f) :: k -> COPROD j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods par0 :: CoprodDom (Star f) (Unit :: k) (Unit :: COPROD j) Source Comments # par :: forall (x1 :: k) (x2 :: COPROD j) (y1 :: k) (y2 :: COPROD j). CoprodDom (Star f) x1 x2 -> CoprodDom (Star f) y1 y2 -> CoprodDom (Star f) (x1 y1) (x2 y2) Source Comments #
Profunctor p => Profunctor (CoprodDom p :: k -> COPROD j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods dimap :: forall (c :: k) (a :: k) (b :: COPROD j) (d :: COPROD j). (c ~> a) -> (b ~> d) -> CoprodDom p a b -> CoprodDom p c d Source Comments # (\\) :: forall (a :: k) (b :: COPROD j) r. ((Ob a, Ob b) => r) -> CoprodDom p a b -> r Source Comments #