Safe Haskell	None
Language	Haskell2010

Proarrow.Profunctor

Documentation

type PRO j k = j -> k -> Type Source Comments #

class (CategoryOf j, CategoryOf k) => Profunctor (p :: PRO j k) where Source Comments #

Minimal complete definition

dimap

Methods

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

(\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> p a b -> r infixl 1 Source Comments #

default (\\) :: forall (a :: j) (b :: k) r. (Ob a, Ob b) => ((Ob a, Ob b) => r) -> p a b -> r Source Comments #

Instances

Instances details

Profunctor Booleans Source Comments #
Instance details Defined in Proarrow.Category.Instance.Bool Methods dimap :: forall (c :: BOOL) (a :: BOOL) (b :: BOOL) (d :: BOOL). (c ~> a) -> (b ~> d) -> Booleans a b -> Booleans c d Source Comments # (\\) :: forall (a :: BOOL) (b :: BOOL) r. ((Ob a, Ob b) => r) -> Booleans a b -> r Source Comments #
Profunctor Cat Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: KIND) (a :: KIND) (b :: KIND) (d :: KIND). (c ~> a) -> (b ~> d) -> Cat a b -> Cat c d Source Comments # (\\) :: forall (a :: KIND) (b :: KIND) r. ((Ob a, Ob b) => r) -> Cat a b -> r Source Comments #
Profunctor (:-) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Constraint Methods dimap :: forall (c :: CONSTRAINT) (a :: CONSTRAINT) (b :: CONSTRAINT) (d :: CONSTRAINT). (c ~> a) -> (b ~> d) -> (a :- b) -> c :- d Source Comments # (\\) :: forall (a :: CONSTRAINT) (b :: CONSTRAINT) r. ((Ob a, Ob b) => r) -> (a :- b) -> r 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 Forget Source Comments #
Instance details Defined in Proarrow.Category.Instance.Linear Methods dimap :: forall (c :: LINEAR) (a :: LINEAR) b d. (c ~> a) -> (b ~> d) -> Forget a b -> Forget c d Source Comments # (\\) :: forall (a :: LINEAR) b r. ((Ob a, Ob b) => r) -> Forget a b -> r Source Comments #
Profunctor Simplex Source Comments #
Instance details Defined in Proarrow.Category.Instance.Simplex Methods dimap :: forall (c :: Nat) (a :: Nat) (b :: Nat) (d :: Nat). (c ~> a) -> (b ~> d) -> Simplex a b -> Simplex c d Source Comments # (\\) :: forall (a :: Nat) (b :: Nat) r. ((Ob a, Ob b) => r) -> Simplex a b -> r Source Comments #
Profunctor Unit Source Comments #
Instance details Defined in Proarrow.Category.Instance.Unit Methods dimap :: forall (c :: UNIT) (a :: UNIT) (b :: UNIT) (d :: UNIT). (c ~> a) -> (b ~> d) -> Unit a b -> Unit c d Source Comments # (\\) :: forall (a :: UNIT) (b :: UNIT) r. ((Ob a, Ob b) => r) -> Unit a b -> r Source Comments #
Profunctor Zero Source Comments #
Instance details Defined in Proarrow.Category.Instance.Zero Methods dimap :: forall (c :: VOID) (a :: VOID) (b :: VOID) (d :: VOID). (c ~> a) -> (b ~> d) -> Zero a b -> Zero c d Source Comments # (\\) :: forall (a :: VOID) (b :: VOID) r. ((Ob a, Ob b) => r) -> Zero a b -> r Source Comments #
Profunctor Free Source Comments #
Instance details Defined in Proarrow.Category.Instance.Linear Methods dimap :: forall c a (b :: LINEAR) (d :: LINEAR). (c ~> a) -> (b ~> d) -> Free a b -> Free c d Source Comments # (\\) :: forall a (b :: LINEAR) r. ((Ob a, Ob b) => r) -> Free a b -> r Source Comments #
Profunctor Forget Source Comments #
Instance details Defined in Proarrow.Category.Instance.Simplex Methods dimap :: forall c a (b :: Nat) (d :: Nat). (c ~> a) -> (b ~> d) -> Forget a b -> Forget c d Source Comments # (\\) :: forall a (b :: Nat) r. ((Ob a, Ob b) => r) -> Forget a b -> r Source Comments #
CategoryOf k => Profunctor (Terminate :: UNIT -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: UNIT) (a :: UNIT) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Terminate a b -> Terminate c d Source Comments # (\\) :: forall (a :: UNIT) (b :: k) r. ((Ob a, Ob b) => r) -> Terminate a b -> r Source Comments #
Profunctor (Reader r :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Reader Methods dimap :: (c ~> a) -> (b ~> d) -> Reader r a b -> Reader r c d Source Comments # (\\) :: ((Ob a, Ob b) => r0) -> Reader r a b -> r0 Source Comments #
Profunctor (Writer m :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Writer Methods dimap :: (c ~> a) -> (b ~> d) -> Writer m a b -> Writer m c d Source Comments # (\\) :: ((Ob a, Ob b) => r) -> Writer m a b -> r Source Comments #
CategoryOf k => Profunctor (Hom :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal Methods dimap :: forall (c :: k) (a :: k) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Hom a b -> Hom c d Source Comments # (\\) :: forall (a :: k) (b :: k) r. ((Ob a, Ob b) => r) -> Hom a b -> r Source Comments #
CategoryOf k => Profunctor (Id :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Identity Methods dimap :: forall (c :: k) (a :: k) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Id a b -> Id c d Source Comments # (\\) :: forall (a :: k) (b :: k) r. ((Ob a, Ob b) => r) -> Id a b -> r Source Comments #
CategoryOf k => Profunctor (CoproductColimit d :: UNIT -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Colimit Methods dimap :: forall (c :: UNIT) (a :: UNIT) (b :: k) (d0 :: k). (c ~> a) -> (b ~> d0) -> CoproductColimit d a b -> CoproductColimit d c d0 Source Comments # (\\) :: forall (a :: UNIT) (b :: k) r. ((Ob a, Ob b) => r) -> CoproductColimit d a b -> r Source Comments #
HasInitialObject k => Profunctor (InitialLimit d :: UNIT -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Colimit Methods dimap :: forall (c :: UNIT) (a :: UNIT) (b :: k) (d0 :: k). (c ~> a) -> (b ~> d0) -> InitialLimit d a b -> InitialLimit d c d0 Source Comments # (\\) :: forall (a :: UNIT) (b :: k) r. ((Ob a, Ob b) => r) -> InitialLimit d a b -> r Source Comments #
Representable d => Profunctor (EndLimit d :: Type -> UNIT -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Limit Methods dimap :: forall c a (b :: UNIT) (d0 :: UNIT). (c ~> a) -> (b ~> d0) -> EndLimit d a b -> EndLimit d c d0 Source Comments # (\\) :: forall a (b :: UNIT) r. ((Ob a, Ob b) => r) -> EndLimit d a b -> r Source Comments #
Profunctor (Replacing a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: (c ~> a0) -> (b0 ~> d) -> Replacing a b a0 b0 -> Replacing a b c d Source Comments # (\\) :: ((Ob a0, Ob b0) => r) -> Replacing a b a0 b0 -> r Source Comments #
Profunctor (Setting a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: (c ~> a0) -> (b0 ~> d) -> Setting a b a0 b0 -> Setting a b c d Source Comments # (\\) :: ((Ob a0, Ob b0) => r) -> Setting a b a0 b0 -> r Source Comments #
Profunctor (Viewing a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: (c ~> a0) -> (b0 ~> d) -> Viewing a b a0 b0 -> Viewing a b c d Source Comments # (\\) :: ((Ob a0, Ob b0) => r) -> Viewing a b a0 b0 -> r Source Comments #
Profunctor (->) Source Comments #
Instance details Defined in Proarrow.Core Methods dimap :: (c ~> a) -> (b ~> d) -> (a -> b) -> c -> d Source Comments # (\\) :: ((Ob a, Ob b) => r) -> (a -> b) -> r Source Comments #
Monoid m => Profunctor (Replicate m :: j -> Nat -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Simplex Methods dimap :: forall (c :: j) (a :: j) (b :: Nat) (d :: Nat). (c ~> a) -> (b ~> d) -> Replicate m a b -> Replicate m c d Source Comments # (\\) :: forall (a :: j) (b :: Nat) r. ((Ob a, Ob b) => r) -> Replicate m a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (DayUnit :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Day Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> DayUnit a b -> DayUnit c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> DayUnit a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (InitialProfunctor :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Initial Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> InitialProfunctor a b -> InitialProfunctor c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> InitialProfunctor a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (TerminalProfunctor :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Terminal Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> TerminalProfunctor a b -> TerminalProfunctor c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> TerminalProfunctor a b -> r Source Comments #
(HasBinaryProducts k, Representable d) => Profunctor (ProductLimit d :: k -> UNIT -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Limit Methods dimap :: forall (c :: k) (a :: k) (b :: UNIT) (d0 :: UNIT). (c ~> a) -> (b ~> d0) -> ProductLimit d a b -> ProductLimit d c d0 Source Comments # (\\) :: forall (a :: k) (b :: UNIT) r. ((Ob a, Ob b) => r) -> ProductLimit d a b -> r Source Comments #
HasTerminalObject k => Profunctor (TerminalLimit d :: k -> UNIT -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Limit Methods dimap :: forall (c :: k) (a :: k) (b :: UNIT) (d0 :: UNIT). (c ~> a) -> (b ~> d0) -> TerminalLimit d a b -> TerminalLimit d c d0 Source Comments # (\\) :: forall (a :: k) (b :: UNIT) r. ((Ob a, Ob b) => r) -> TerminalLimit d a b -> r Source Comments #
Profunctor p => Profunctor (Fix p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Fix Methods dimap :: forall (c :: k) (a :: k) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Fix p a b -> Fix p c d Source Comments # (\\) :: forall (a :: k) (b :: k) r. ((Ob a, Ob b) => r) -> Fix p a b -> r Source Comments #
(Monoidal k, Ob s) => Profunctor (State s :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.State Methods dimap :: forall (c :: k) (a :: k) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> State s a b -> State s c d Source Comments # (\\) :: forall (a :: k) (b :: k) r. ((Ob a, Ob b) => r) -> State s a b -> r Source Comments #
Functor f => Profunctor (Costar f :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Costar Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Costar f a b -> Costar f c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> Costar f a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (Coyoneda p :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Coyoneda Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Coyoneda p a b -> Coyoneda p c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> Coyoneda p a b -> r Source Comments #
Functor f => Profunctor (Star f :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Star f a b -> Star f c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> Star f a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (Yoneda p :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Yoneda Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Yoneda p a b -> Yoneda p c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> Yoneda p a b -> r Source Comments #
(Monoidal k, Ob a, Ob b) => Profunctor (Bipara a b :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Enriched.Bipara Methods dimap :: forall (c :: k) (a0 :: k) (b0 :: k) (d :: k). (c ~> a0) -> (b0 ~> d) -> Bipara a b a0 b0 -> Bipara a b c d Source Comments # (\\) :: forall (a0 :: k) (b0 :: k) r. ((Ob a0, Ob b0) => r) -> Bipara a b a0 b0 -> r Source Comments #
Monad m => Profunctor (Classifying m a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: (c ~> a0) -> (b0 ~> d) -> Classifying m a b a0 b0 -> Classifying m a b c d Source Comments # (\\) :: ((Ob a0, Ob b0) => r) -> Classifying m a b a0 b0 -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :+: q :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Coproduct Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> (p :+: q) a b -> (p :+: q) c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> (p :+: q) a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (Day p q :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Day Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Day p q a b -> Day p q c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> Day p q a b -> r Source Comments #
(Monoidal j, Monoidal k, Profunctor p, Profunctor q) => Profunctor (DayExp p q :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Day Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> DayExp p q a b -> DayExp p q c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> DayExp p q a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :~>: q :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Exponential Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> (p :~>: q) a b -> (p :~>: q) c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> (p :~>: q) a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :*: q :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Product Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> (p :: q) a b -> (p :: q) c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> (p :*: q) a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (Yo a b :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Yoneda Methods dimap :: forall (c :: j) (a0 :: j) (b0 :: k) (d :: k). (c ~> a0) -> (b0 ~> d) -> Yo a b a0 b0 -> Yo a b c d Source Comments # (\\) :: forall (a0 :: j) (b0 :: k) r. ((Ob a0, Ob b0) => r) -> Yo a b a0 b0 -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :.: q :: j1 -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Composition Methods dimap :: forall (c :: j1) (a :: j1) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> (p :.: q) a b -> (p :.: q) c d Source Comments # (\\) :: forall (a :: j1) (b :: k) r. ((Ob a, Ob b) => r) -> (p :.: q) a b -> r Source Comments #
(Profunctor p, Profunctor j2) => Profunctor (Ran ('OP j2) p :: j1 -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Ran Methods dimap :: forall (c :: j1) (a :: j1) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Ran ('OP j2) p a b -> Ran ('OP j2) p c d Source Comments # (\\) :: forall (a :: j1) (b :: k) r. ((Ob a, Ob b) => r) -> Ran ('OP j2) p a b -> r Source Comments #
(Profunctor p, Profunctor j2) => Profunctor (Rift ('OP j2) p :: j1 -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Rift Methods dimap :: forall (c :: j1) (a :: j1) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Rift ('OP j2) p a b -> Rift ('OP j2) p c d Source Comments # (\\) :: forall (a :: j1) (b :: k) r. ((Ob a, Ob b) => r) -> Rift ('OP j2) p a b -> r Source Comments #
(Profunctor j3, Profunctor p) => Profunctor (Precompose j3 p :: j2 -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Rift Methods dimap :: forall (c :: j2) (a :: j2) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Precompose j3 p a b -> Precompose j3 p c d Source Comments # (\\) :: forall (a :: j2) (b :: k) r. ((Ob a, Ob b) => r) -> Precompose j3 p a b -> r Source Comments #
(Profunctor w, Profunctor p) => Profunctor (DayAct w p :: c -> d -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: forall (c0 :: c) (a :: c) (b :: d) (d0 :: d). (c0 ~> a) -> (b ~> d0) -> DayAct w p a b -> DayAct w p c0 d0 Source Comments # (\\) :: forall (a :: c) (b :: d) r. ((Ob a, Ob b) => r) -> DayAct w p a b -> r Source Comments #
(CategoryOf c, CategoryOf d) => Profunctor (Optic w a b :: c -> d -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: forall (c0 :: c) (a0 :: c) (b0 :: d) (d0 :: d). (c0 ~> a0) -> (b0 ~> d0) -> Optic w a b a0 b0 -> Optic w a b c0 d0 Source Comments # (\\) :: forall (a0 :: c) (b0 :: d) r. ((Ob a0, Ob b0) => r) -> Optic w a b a0 b0 -> r 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 #
CategoryOf k => Profunctor (Hom :: UNIT -> (OPPOSITE k, k) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Limit Methods dimap :: forall (c :: UNIT) (a :: UNIT) (b :: (OPPOSITE k, k)) (d :: (OPPOSITE k, k)). (c ~> a) -> (b ~> d) -> Hom a b -> Hom c d Source Comments # (\\) :: forall (a :: UNIT) (b :: (OPPOSITE k, k)) r. ((Ob a, Ob b) => r) -> Hom a b -> r Source Comments #
Closed k => Profunctor (ExponentialFunctor :: k -> (OPPOSITE k, k) -> Type) Source Comments #
Instance details Defined in Proarrow.Object.Exponential Methods dimap :: forall (c :: k) (a :: k) (b :: (OPPOSITE k, k)) (d :: (OPPOSITE k, k)). (c ~> a) -> (b ~> d) -> ExponentialFunctor a b -> ExponentialFunctor c d Source Comments # (\\) :: forall (a :: k) (b :: (OPPOSITE k, k)) r. ((Ob a, Ob b) => r) -> ExponentialFunctor a b -> r Source Comments #
Promonad p => Profunctor (KleisliForget p :: j -> KLEISLI p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods dimap :: forall (c :: j) (a :: j) (b :: KLEISLI p) (d :: KLEISLI p). (c ~> a) -> (b ~> d) -> KleisliForget p a b -> KleisliForget p c d Source Comments # (\\) :: forall (a :: j) (b :: KLEISLI p) r. ((Ob a, Ob b) => r) -> KleisliForget p a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (FstCat :: j -> (j, k) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: j) (a :: j) (b :: (j, k)) (d :: (j, k)). (c ~> a) -> (b ~> d) -> FstCat a b -> FstCat c d Source Comments # (\\) :: forall (a :: j) (b :: (j, k)) r. ((Ob a, Ob b) => r) -> FstCat a b -> r Source Comments #
CategoryOf k => Profunctor (Forget ob :: k -> SUBCAT ob -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Forget Methods dimap :: forall (c :: k) (a :: k) (b :: SUBCAT ob) (d :: SUBCAT ob). (c ~> a) -> (b ~> d) -> Forget ob a b -> Forget ob c d Source Comments # (\\) :: forall (a :: k) (b :: SUBCAT ob) r. ((Ob a, Ob b) => r) -> Forget ob a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (SndCat :: k -> (j, k) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: k) (a :: k) (b :: (j, k)) (d :: (j, k)). (c ~> a) -> (b ~> d) -> SndCat a b -> SndCat c d Source Comments # (\\) :: forall (a :: k) (b :: (j, k)) r. ((Ob a, Ob b) => r) -> SndCat a b -> r Source Comments #
CategoryOf k => Profunctor (List :: LIST k -> LIST k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.List Methods dimap :: forall (c :: LIST k) (a :: LIST k) (b :: LIST k) (d :: LIST k). (c ~> a) -> (b ~> d) -> List a b -> List c d Source Comments # (\\) :: forall (a :: LIST k) (b :: LIST k) r. ((Ob a, Ob b) => r) -> List a b -> r Source Comments #
CategoryOf k => Profunctor (Rev :: REV k -> REV k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Rev Methods dimap :: forall (c :: REV k) (a :: REV k) (b :: REV k) (d :: REV k). (c ~> a) -> (b ~> d) -> Rev a b -> Rev c d Source Comments # (\\) :: forall (a :: REV k) (b :: REV k) r. ((Ob a, Ob b) => r) -> Rev a b -> r Source Comments #
CategoryOf k => Profunctor (Coprod :: COPROD k -> COPROD k -> Type) Source Comments #
Instance details Defined in Proarrow.Object.BinaryCoproduct Methods dimap :: forall (c :: COPROD k) (a :: COPROD k) (b :: COPROD k) (d :: COPROD k). (c ~> a) -> (b ~> d) -> Coprod a b -> Coprod c d Source Comments # (\\) :: forall (a :: COPROD k) (b :: COPROD k) r. ((Ob a, Ob b) => r) -> Coprod a b -> r Source Comments #
CategoryOf k => Profunctor (Prod :: PROD k -> PROD k -> Type) Source Comments #
Instance details Defined in Proarrow.Object.BinaryProduct Methods dimap :: forall (c :: PROD k) (a :: PROD k) (b :: PROD k) (d :: PROD k). (c ~> a) -> (b ~> d) -> Prod a b -> Prod c d Source Comments # (\\) :: forall (a :: PROD k) (b :: PROD k) r. ((Ob a, Ob b) => r) -> Prod a b -> r Source Comments #
Monoidal k => Profunctor (Strictified :: [k] -> [k] -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal Methods dimap :: forall (c :: [k]) (a :: [k]) (b :: [k]) (d :: [k]). (c ~> a) -> (b ~> d) -> Strictified a b -> Strictified c d Source Comments # (\\) :: forall (a :: [k]) (b :: [k]) r. ((Ob a, Ob b) => r) -> Strictified a b -> r Source Comments #
Profunctor (Previewing a b :: COPROD Type -> COPROD Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: forall (c :: COPROD Type) (a0 :: COPROD Type) (b0 :: COPROD Type) (d :: COPROD Type). (c ~> a0) -> (b0 ~> d) -> Previewing a b a0 b0 -> Previewing a b c d Source Comments # (\\) :: forall (a0 :: COPROD Type) (b0 :: COPROD Type) r. ((Ob a0, Ob b0) => r) -> Previewing a b a0 b0 -> r Source Comments #
Profunctor p => Profunctor (Op p :: OPPOSITE k -> OPPOSITE j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Opposite Methods dimap :: forall (c :: OPPOSITE k) (a :: OPPOSITE k) (b :: OPPOSITE j) (d :: OPPOSITE j). (c ~> a) -> (b ~> d) -> Op p a b -> Op p c d Source Comments # (\\) :: forall (a :: OPPOSITE k) (b :: OPPOSITE j) r. ((Ob a, Ob b) => r) -> Op p a b -> r Source Comments #
Profunctor p => Profunctor (Alt p :: PROD j -> COPROD k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Applicative Methods dimap :: forall (c :: PROD j) (a :: PROD j) (b :: COPROD k) (d :: COPROD k). (c ~> a) -> (b ~> d) -> Alt p a b -> Alt p c d Source Comments # (\\) :: forall (a :: PROD j) (b :: COPROD k) r. ((Ob a, Ob b) => r) -> Alt p a b -> r Source Comments #
Profunctor p => Profunctor (App p :: PROD j -> PROD k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Applicative Methods dimap :: forall (c :: PROD j) (a :: PROD j) (b :: PROD k) (d :: PROD k). (c ~> a) -> (b ~> d) -> App p a b -> App p c d Source Comments # (\\) :: forall (a :: PROD j) (b :: PROD k) r. ((Ob a, Ob b) => r) -> App p a b -> r Source Comments #
Profunctor List Source Comments #
Instance details Defined in Proarrow.Profunctor.Forget Methods dimap :: forall (c :: SUBCAT Monoid) (a :: SUBCAT Monoid) b d. (c ~> a) -> (b ~> d) -> List a b -> List c d Source Comments # (\\) :: forall (a :: SUBCAT Monoid) b r. ((Ob a, Ob b) => r) -> List a b -> r Source Comments #
Promonad p => Profunctor (KleisliFree p :: KLEISLI p -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods dimap :: forall (c :: KLEISLI p) (a :: KLEISLI p) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> KleisliFree p a b -> KleisliFree p c d Source Comments # (\\) :: forall (a :: KLEISLI p) (b :: k) r. ((Ob a, Ob b) => r) -> KleisliFree p a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :&&&: q :: (i, j) -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: (i, j)) (a :: (i, j)) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> (p :&&&: q) a b -> (p :&&&: q) c d Source Comments # (\\) :: forall (a :: (i, j)) (b :: k) r. ((Ob a, Ob b) => r) -> (p :&&&: q) a b -> r Source Comments #
Profunctor (Bidiscrete :: DiscreteK j k -> DiscreteK j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Bidiscrete Methods dimap :: forall (c :: DiscreteK j k) (a :: DiscreteK j k) (b :: DiscreteK j k) (d :: DiscreteK j k). (c ~> a) -> (b ~> d) -> Bidiscrete a b -> Bidiscrete c d Source Comments # (\\) :: forall (a :: DiscreteK j k) (b :: DiscreteK j k) r. ((Ob a, Ob b) => r) -> Bidiscrete a b -> r Source Comments #
Profunctor (Terminal :: TERMK 'T0 'T0 -> TERMK 'T0 'T0 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Terminal Methods dimap :: forall (c :: TERMK 'T0 'T0) (a :: TERMK 'T0 'T0) (b :: TERMK 'T0 'T0) (d :: TERMK 'T0 'T0). (c ~> a) -> (b ~> d) -> Terminal a b -> Terminal c d Source Comments # (\\) :: forall (a :: TERMK 'T0 'T0) (b :: TERMK 'T0 'T0) r. ((Ob a, Ob b) => r) -> Terminal a b -> r Source Comments #
Rewrite g => Profunctor (Free :: FREE g -> FREE g -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Free Methods dimap :: forall (c :: FREE g) (a :: FREE g) (b :: FREE g) (d :: FREE g). (c ~> a) -> (b ~> d) -> Free a b -> Free c d Source Comments # (\\) :: forall (a :: FREE g) (b :: FREE g) r. ((Ob a, Ob b) => r) -> Free a b -> r Source Comments #
Promonad p => Profunctor (Kleisli :: KLEISLI p -> KLEISLI p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods dimap :: forall (c :: KLEISLI p) (a :: KLEISLI p) (b :: KLEISLI p) (d :: KLEISLI p). (c ~> a) -> (b ~> d) -> Kleisli a b -> Kleisli c d Source Comments # (\\) :: forall (a :: KLEISLI p) (b :: KLEISLI p) r. ((Ob a, Ob b) => r) -> Kleisli a b -> r Source Comments #
Profunctor (Nat' :: NatK j k -> NatK j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods dimap :: forall (c :: NatK j k) (a :: NatK j k) (b :: NatK j k) (d :: NatK j k). (c ~> a) -> (b ~> d) -> Nat' a b -> Nat' c d Source Comments # (\\) :: forall (a :: NatK j k) (b :: NatK j k) r. ((Ob a, Ob b) => r) -> Nat' a b -> r Source Comments #
Profunctor ((~>) :: CAT k) => Profunctor (Sub :: SUBCAT ob -> SUBCAT ob -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Sub Methods dimap :: forall (c :: SUBCAT ob) (a :: SUBCAT ob) (b :: SUBCAT ob) (d :: SUBCAT ob). (c ~> a) -> (b ~> d) -> Sub a b -> Sub c d Source Comments # (\\) :: forall (a :: SUBCAT ob) (b :: SUBCAT ob) r. ((Ob a, Ob b) => r) -> Sub a b -> r Source Comments #
Profunctor (Prof :: PRO j k -> PRO j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Prof Methods dimap :: forall (c :: PRO j k) (a :: PRO j k) (b :: PRO j k) (d :: PRO j k). (c ~> a) -> (b ~> d) -> Prof a b -> Prof c d Source Comments # (\\) :: forall (a :: PRO j k) (b :: PRO j k) r. ((Ob a, Ob b) => r) -> Prof a b -> r Source Comments #
Profunctor (Nat :: (k1 -> k2 -> k3 -> k4 -> Type) -> (k1 -> k2 -> k3 -> k4 -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods dimap :: forall (c :: k1 -> k2 -> k3 -> k4 -> Type) (a :: k1 -> k2 -> k3 -> k4 -> Type) (b :: k1 -> k2 -> k3 -> k4 -> Type) (d :: k1 -> k2 -> k3 -> k4 -> Type). (c ~> a) -> (b ~> d) -> Nat a b -> Nat c d Source Comments # (\\) :: forall (a :: k1 -> k2 -> k3 -> k4 -> Type) (b :: k1 -> k2 -> k3 -> k4 -> Type) r. ((Ob a, Ob b) => r) -> Nat a b -> r Source Comments #
Profunctor (Nat :: (k1 -> k2 -> k3 -> Type) -> (k1 -> k2 -> k3 -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods dimap :: forall (c :: k1 -> k2 -> k3 -> Type) (a :: k1 -> k2 -> k3 -> Type) (b :: k1 -> k2 -> k3 -> Type) (d :: k1 -> k2 -> k3 -> Type). (c ~> a) -> (b ~> d) -> Nat a b -> Nat c d Source Comments # (\\) :: forall (a :: k1 -> k2 -> k3 -> Type) (b :: k1 -> k2 -> k3 -> Type) r. ((Ob a, Ob b) => r) -> Nat a b -> r Source Comments #
Profunctor (Nat :: (k1 -> Type) -> (k1 -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods dimap :: forall (c :: k1 -> Type) (a :: k1 -> Type) (b :: k1 -> Type) (d :: k1 -> Type). (c ~> a) -> (b ~> d) -> Nat a b -> Nat c d Source Comments # (\\) :: forall (a :: k1 -> Type) (b :: k1 -> Type) r. ((Ob a, Ob b) => r) -> Nat a b -> r Source Comments #
Profunctor p => Profunctor (Collage p :: COPRODUCT j k -> COPRODUCT j k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Collage Methods dimap :: forall (c :: COPRODUCT j k) (a :: COPRODUCT j k) (b :: COPRODUCT j k) (d :: COPRODUCT j k). (c ~> a) -> (b ~> d) -> Collage p a b -> Collage p c d Source Comments # (\\) :: forall (a :: COPRODUCT j k) (b :: COPRODUCT j k) r. ((Ob a, Ob b) => r) -> Collage p a b -> r Source Comments #
(Profunctor c, Profunctor d) => Profunctor (c :++: d :: COPRODUCT j k -> COPRODUCT j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Coproduct Methods dimap :: forall (c0 :: COPRODUCT j k) (a :: COPRODUCT j k) (b :: COPRODUCT j k) (d0 :: COPRODUCT j k). (c0 ~> a) -> (b ~> d0) -> (c :++: d) a b -> (c :++: d) c0 d0 Source Comments # (\\) :: forall (a :: COPRODUCT j k) (b :: COPRODUCT j k) r. ((Ob a, Ob b) => r) -> (c :++: d) a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :**: q :: (k1, k2) -> (k1, k2) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Product Methods dimap :: forall (c :: (k1, k2)) (a :: (k1, k2)) (b :: (k1, k2)) (d :: (k1, k2)). (c ~> a) -> (b ~> d) -> (p :: q) a b -> (p :: q) c d Source Comments # (\\) :: forall (a :: (k1, k2)) (b :: (k1, k2)) r. ((Ob a, Ob b) => r) -> (p :**: q) a b -> r Source Comments #
(CategoryOf k, Ob i, Ob j) => Profunctor (Category :: PLAINK k i j -> PLAINK k i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.CategoryAsBi Methods dimap :: forall (c :: PLAINK k i j) (a :: PLAINK k i j) (b :: PLAINK k i j) (d :: PLAINK k i j). (c ~> a) -> (b ~> d) -> Category a b -> Category c d Source Comments # (\\) :: forall (a :: PLAINK k i j) (b :: PLAINK k i j) r. ((Ob a, Ob b) => r) -> Category a b -> r Source Comments #
CategoryOf k => Profunctor (Mon2 :: MonK k i j -> MonK k i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.MonoidalAsBi Methods dimap :: forall (c :: MonK k i j) (a :: MonK k i j) (b :: MonK k i j) (d :: MonK k i j). (c ~> a) -> (b ~> d) -> Mon2 a b -> Mon2 c d Source Comments # (\\) :: forall (a :: MonK k i j) (b :: MonK k i j) r. ((Ob a, Ob b) => r) -> Mon2 a b -> r Source Comments #
Profunctor (Prof :: ProfK cl j k -> ProfK cl j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Prof Methods dimap :: forall (c :: ProfK cl j k) (a :: ProfK cl j k) (b :: ProfK cl j k) (d :: ProfK cl j k). (c ~> a) -> (b ~> d) -> Prof a b -> Prof c d Source Comments # (\\) :: forall (a :: ProfK cl j k) (b :: ProfK cl j k) r. ((Ob a, Ob b) => r) -> Prof a b -> r Source Comments #
(Bicategory kk, Ob0 kk k) => Profunctor (Endo :: ENDO kk k -> ENDO kk k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Endo Methods dimap :: forall (c :: ENDO kk k) (a :: ENDO kk k) (b :: ENDO kk k) (d :: ENDO kk k). (c ~> a) -> (b ~> d) -> Endo a b -> Endo c d Source Comments # (\\) :: forall (a :: ENDO kk k) (b :: ENDO kk k) r. ((Ob a, Ob b) => r) -> Endo a b -> r Source Comments #
(CategoryOf (kk j k2), Ob0 kk j, Ob0 kk k2, Bicategory kk) => Profunctor (Strictified :: Path kk j k2 -> Path kk j k2 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory Methods dimap :: forall (c :: Path kk j k2) (a :: Path kk j k2) (b :: Path kk j k2) (d :: Path kk j k2). (c ~> a) -> (b ~> d) -> Strictified a b -> Strictified c d Source Comments # (\\) :: forall (a :: Path kk j k2) (b :: Path kk j k2) r. ((Ob a, Ob b) => r) -> Strictified a b -> r Source Comments #
CategoryOf (kk j k2) => Profunctor (Co :: COK kk j k2 -> COK kk j k2 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Co Methods dimap :: forall (c :: COK kk j k2) (a :: COK kk j k2) (b :: COK kk j k2) (d :: COK kk j k2). (c ~> a) -> (b ~> d) -> Co a b -> Co c d Source Comments # (\\) :: forall (a :: COK kk j k2) (b :: COK kk j k2) r. ((Ob a, Ob b) => r) -> Co a b -> r Source Comments #
CategoryOf (kk k2 j) => Profunctor (Op :: OPK kk j k2 -> OPK kk j k2 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Op Methods dimap :: forall (c :: OPK kk j k2) (a :: OPK kk j k2) (b :: OPK kk j k2) (d :: OPK kk j k2). (c ~> a) -> (b ~> d) -> Op a b -> Op c d Source Comments # (\\) :: forall (a :: OPK kk j k2) (b :: OPK kk j k2) r. ((Ob a, Ob b) => r) -> Op a b -> r Source Comments #
Profunctor ((~>) :: CAT (kk i j)) => Profunctor (Sub :: SUBCAT tag kk i j -> SUBCAT tag kk i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Sub Methods dimap :: forall (c :: SUBCAT tag kk i j) (a :: SUBCAT tag kk i j) (b :: SUBCAT tag kk i j) (d :: SUBCAT tag kk i j). (c ~> a) -> (b ~> d) -> Sub a b -> Sub c d Source Comments # (\\) :: forall (a :: SUBCAT tag kk i j) (b :: SUBCAT tag kk i j) r. ((Ob a, Ob b) => r) -> Sub a b -> r Source Comments #
CategoryOf (kk i j) => Profunctor (Q2 :: QKK kk i j -> QKK kk i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Double.Quintet Methods dimap :: forall (c :: QKK kk i j) (a :: QKK kk i j) (b :: QKK kk i j) (d :: QKK kk i j). (c ~> a) -> (b ~> d) -> Q2 a b -> Q2 c d Source Comments # (\\) :: forall (a :: QKK kk i j) (b :: QKK kk i j) r. ((Ob a, Ob b) => r) -> Q2 a b -> r Source Comments #
(MonoidalProfunctor w, MonoidalAction m c, MonoidalAction m' d) => Profunctor (OpticCat :: OPTIC w c d -> OPTIC w c d -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: forall (c0 :: OPTIC w c d) (a :: OPTIC w c d) (b :: OPTIC w c d) (d0 :: OPTIC w c d). (c0 ~> a) -> (b ~> d0) -> OpticCat a b -> OpticCat c0 d0 Source Comments # (\\) :: forall (a :: OPTIC w c d) (b :: OPTIC w c d) r. ((Ob a, Ob b) => r) -> OpticCat a b -> r Source Comments #
(CategoryOf (jj (Fst ik) (Fst jl)), CategoryOf (kk (Snd ik) (Snd jl))) => Profunctor (Prod :: PRODK jj kk ik jl -> PRODK jj kk ik jl -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Product Methods dimap :: forall (c :: PRODK jj kk ik jl) (a :: PRODK jj kk ik jl) (b :: PRODK jj kk ik jl) (d :: PRODK jj kk ik jl). (c ~> a) -> (b ~> d) -> Prod a b -> Prod c d Source Comments # (\\) :: forall (a :: PRODK jj kk ik jl) (b :: PRODK jj kk ik jl) r. ((Ob a, Ob b) => r) -> Prod a b -> r Source Comments #

lmap :: forall {j} {k} p (c :: j) (a :: j) (b :: k). Profunctor p => (c ~> a) -> p a b -> p c b Source Comments #

rmap :: forall {j} {k} p (b :: k) (d :: k) (a :: j). Profunctor p => (b ~> d) -> p a b -> p a d Source Comments #

(//) :: forall {k1} {k2} p (a :: k1) (b :: k2) r. Profunctor p => p a b -> ((Ob a, Ob b) => r) -> r infixr 0 Source Comments #