Safe Haskell	None
Language	GHC2024

Proarrow.Category.Instance.Prof

Contents

Orphan instances

Documentation

data Prof (p :: j +-> k) (q :: j +-> k) where Source Github #

Constructors

Prof
Fields :: forall {j} {k} (p :: j +-> k) (q :: j +-> k). (Profunctor p, Profunctor q) => { unProf :: p :~> q } -> Prof p q

Instances

Instances details

Promonad (Prof :: (j +-> k) -> (j +-> k) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Prof Methods id :: forall (a :: j +-> k). Ob a => Prof a a Source Github # (.) :: forall (b :: j +-> k) (c :: j +-> k) (a :: j +-> k). Prof b c -> Prof a b -> Prof a c Source Github #
(CategoryOf j, CategoryOf k) => Strong (PROD (j +-> k)) (Prof :: (j +-> k) -> (j +-> k) -> Type) Source Github #
Instance details Defined in Proarrow.Object.BinaryProduct Methods act :: forall (a :: PROD (j +-> k)) (b :: PROD (j +-> k)) (x :: j +-> k) (y :: j +-> k). (a ~> b) -> Prof x y -> Prof (Act a x) (Act b y) Source Github #
(Monoidal j, Monoidal k) => MonoidalProfunctor (Prof :: (j +-> k) -> (j +-> k) -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Day Methods par0 :: Prof (Unit :: j +-> k) (Unit :: j +-> k) Source Github # par :: forall (x1 :: j +-> k) (x2 :: j +-> k) (y1 :: j +-> k) (y2 :: j +-> k). Prof x1 x2 -> Prof y1 y2 -> Prof (x1 y1) (x2 y2) Source Github #
Profunctor (Prof :: (j +-> k) -> (j +-> k) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Prof Methods dimap :: forall (c :: j +-> k) (a :: j +-> k) (b :: j +-> k) (d :: j +-> k). (c ~> a) -> (b ~> d) -> Prof a b -> Prof c d Source Github # lmap :: forall (c :: j +-> k) (a :: j +-> k) (b :: j +-> k). (c ~> a) -> Prof a b -> Prof c b Source Github # rmap :: forall (b :: j +-> k) (d :: j +-> k) (a :: j +-> k). (b ~> d) -> Prof a b -> Prof a d Source Github # (\\) :: forall (a :: j +-> k) (b :: j +-> k) r. ((Ob a, Ob b) => r) -> Prof a b -> r Source Github #
(Monoidal j, Monoidal k) => Strong (j +-> k) (Prof :: (j +-> k) -> (j +-> k) -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Day Methods act :: forall (a :: j +-> k) (b :: j +-> k) (x :: j +-> k) (y :: j +-> k). (a ~> b) -> Prof x y -> Prof (Act a x) (Act b y) Source Github #
Thin k => ThinProfunctor (Sub (Prof :: (j +-> k) -> (j +-> k) -> Type) :: SUBCAT (Representable :: (j +-> k) -> Constraint) -> SUBCAT (Representable :: (j +-> k) -> Constraint) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Rep Methods arr :: forall (a :: REPK j k) (b :: REPK j k). (Ob a, Ob b, HasArrow (Sub (Prof :: (j +-> k) -> (j +-> k) -> Type) :: SUBCAT (Representable :: (j +-> k) -> Constraint) -> SUBCAT (Representable :: (j +-> k) -> Constraint) -> Type) a b) => Sub (Prof :: (j +-> k) -> (j +-> k) -> Type) a b Source Github # withArr :: forall (a :: REPK j k) (b :: REPK j k) r. Sub (Prof :: (j +-> k) -> (j +-> k) -> Type) a b -> (HasArrow (Sub (Prof :: (j +-> k) -> (j +-> k) -> Type) :: SUBCAT (Representable :: (j +-> k) -> Constraint) -> SUBCAT (Representable :: (j +-> k) -> Constraint) -> Type) a b => r) -> r Source Github #
type HasArrow (Sub (Prof :: (j +-> k) -> (j +-> k) -> Type) :: SUBCAT (Representable :: (j +-> k) -> Constraint) -> SUBCAT (Representable :: (j +-> k) -> Constraint) -> Type) (REP p :: REPK j k) (REP q :: REPK j k) Source Github #
Instance details Defined in Proarrow.Category.Instance.Rep type HasArrow (Sub (Prof :: (j +-> k) -> (j +-> k) -> Type) :: SUBCAT (Representable :: (j +-> k) -> Constraint) -> SUBCAT (Representable :: (j +-> k) -> Constraint) -> Type) (REP p :: REPK j k) (REP q :: REPK j k) = HasAllArrows p q

Orphan instances

CategoryOf (j +-> k) Source Github #

The category of profunctors and natural transformations between them.

Instance details

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Prof type (~>) = Prof :: (j +-> k) -> (j +-> k) -> Type