Safe Haskell	None
Language	GHC2024

Proarrow.Profunctor

Synopsis

type (+->) j k = k -> j -> Type
class (CategoryOf j, CategoryOf k) => Profunctor (p :: j +-> k) where
- dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> p a b -> p c d
- (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> p a b -> r
lmap :: forall {j} {k} p (c :: k) (a :: k) (b :: j). Profunctor p => (c ~> a) -> p a b -> p c b
rmap :: forall {j} {k} p (b :: j) (d :: j) (a :: k). Profunctor p => (b ~> d) -> p a b -> p a d
(//) :: forall {k1} {k2} p (a :: k2) (b :: k1) r. Profunctor p => p a b -> ((Ob a, Ob b) => r) -> r

Documentation

type (+->) j k = k -> j -> Type infixr 0 Source Comments #

The kind j +-> k of profunctors from category j to category k. Note that this follows mathematical convention, swapping the order compared to Haskell's contravariant-first ordering.

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

The core profunctor abstraction. A profunctor is contravariant in its first argument and covariant in its second argument.

Laws:

```
dimap id id = id
```

dimap (f . g) (h . i) = dimap g h . dimap f i

Minimal complete definition

dimap

Methods

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

Map contravariantly over the first argument and covariantly over the second.

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

Constraint elimination, extracts object constraints from a profunctor heteromorphism.

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

Instances

Instances details

Profunctor ZX Source Comments #
Instance details Defined in Proarrow.Category.Instance.ZX Methods dimap :: forall (c :: Nat) (a :: Nat) (b :: Nat) (d :: Nat). (c ~> a) -> (b ~> d) -> ZX a b -> ZX c d Source Comments # (\\) :: forall (a :: Nat) (b :: Nat) r. ((Ob a, Ob b) => r) -> ZX a b -> r Source Comments #
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 GTE Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cost Methods dimap :: forall (c :: COST) (a :: COST) (b :: COST) (d :: COST). (c ~> a) -> (b ~> d) -> GTE a b -> GTE c d Source Comments # (\\) :: forall (a :: COST) (b :: COST) r. ((Ob a, Ob b) => r) -> GTE 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 Pointed Source Comments #
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods dimap :: forall (c :: POINTED) (a :: POINTED) (b :: POINTED) (d :: POINTED). (c ~> a) -> (b ~> d) -> Pointed a b -> Pointed c d Source Comments # (\\) :: forall (a :: POINTED) (b :: POINTED) r. ((Ob a, Ob b) => r) -> Pointed 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 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 Dot Source Comments #
Instance details Defined in Proarrow.Tools.Diagrams.Dot Methods dimap :: forall (c :: DOT) (a :: DOT) (b :: DOT) (d :: DOT). (c ~> a) -> (b ~> d) -> Dot a b -> Dot c d Source Comments # (\\) :: forall (a :: DOT) (b :: DOT) r. ((Ob a, Ob b) => r) -> Dot a b -> r Source Comments #
Profunctor Unit Source Comments #
Instance details Defined in Proarrow.Category.Instance.Unit Methods dimap :: forall (c :: ()) (a :: ()) (b :: ()) (d :: ()). (c ~> a) -> (b ~> d) -> Unit a b -> Unit c d Source Comments # (\\) :: forall (a :: ()) (b :: ()) r. ((Ob a, Ob b) => r) -> Unit a b -> r Source Comments #
Profunctor SymRefl Source Comments #
Instance details Defined in Proarrow.Tools.Diagrams.Dot Methods dimap :: forall (c :: Symbol) (a :: Symbol) (b :: Symbol) (d :: Symbol). (c ~> a) -> (b ~> d) -> SymRefl a b -> SymRefl c d Source Comments # (\\) :: forall (a :: Symbol) (b :: Symbol) r. ((Ob a, Ob b) => r) -> SymRefl a b -> r Source Comments #
CategoryOf k => Profunctor (Term :: k -> () -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Fam Methods dimap :: forall (c :: k) (a :: k) (b :: ()) (d :: ()). (c ~> a) -> (b ~> d) -> Term a b -> Term c d Source Comments # (\\) :: forall (a :: k) (b :: ()) r. ((Ob a, Ob b) => r) -> Term a b -> r Source Comments #
Functor m => Profunctor (Kleisli m :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Arrow Methods dimap :: (c ~> a) -> (b ~> d) -> Kleisli m a b -> Kleisli m c d Source Comments # (\\) :: ((Ob a, Ob b) => r) -> Kleisli m a b -> r Source Comments #
Functor w => Profunctor (ComonoidAsCat w :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods dimap :: (c ~> a) -> (b ~> d) -> ComonoidAsCat w a b -> ComonoidAsCat w c d Source Comments # (\\) :: ((Ob a, Ob b) => r) -> ComonoidAsCat w a b -> r Source Comments #
Arrow arr => Profunctor (Arr arr :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Arrow Methods dimap :: (c ~> a) -> (b ~> d) -> Arr arr a b -> Arr arr c d Source Comments # (\\) :: ((Ob a, Ob b) => r) -> Arr arr a b -> r Source Comments #
CategoryOf k => Profunctor (Fold :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Fold Methods dimap :: forall (c :: k) (a :: k) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Fold a b -> Fold c d Source Comments # (\\) :: forall (a :: k) (b :: k) r. ((Ob a, Ob b) => r) -> Fold 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 #
Profunctor (Previewing a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: (c ~> a0) -> (b0 ~> d) -> Previewing a b a0 b0 -> Previewing a b c d Source Comments # (\\) :: ((Ob a0, Ob b0) => r) -> Previewing a b a0 b0 -> 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 (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 #
Profunctor p => Profunctor (Fix p :: j -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Fix Methods dimap :: forall (c :: j) (a :: j) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> Fix p a b -> Fix p c d Source Comments # (\\) :: forall (a :: j) (b :: j) r. ((Ob a, Ob b) => r) -> Fix p a b -> r Source Comments #
Profunctor p => Profunctor (FreePromonad p :: j -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Free Methods dimap :: forall (c :: j) (a :: j) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> FreePromonad p a b -> FreePromonad p c d Source Comments # (\\) :: forall (a :: j) (b :: j) r. ((Ob a, Ob b) => r) -> FreePromonad p a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (DayUnit :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Day Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> DayUnit a b -> DayUnit c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> DayUnit a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (InitialProfunctor :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Initial Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> InitialProfunctor a b -> InitialProfunctor c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> InitialProfunctor a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (TerminalProfunctor :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Terminal Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> TerminalProfunctor a b -> TerminalProfunctor c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> TerminalProfunctor a b -> r Source Comments #
CategoryOf k => Profunctor (Cont r :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Cont Methods dimap :: forall (c :: k) (a :: k) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Cont r a b -> Cont r c d Source Comments # (\\) :: forall (a :: k) (b :: k) r0. ((Ob a, Ob b) => r0) -> Cont r a b -> r0 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 #
(CategoryOf k, Profunctor dx) => Profunctor (AsPresheaf dx :: k -> () -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Fam Methods dimap :: forall (c :: k) (a :: k) (b :: ()) (d :: ()). (c ~> a) -> (b ~> d) -> AsPresheaf dx a b -> AsPresheaf dx c d Source Comments # (\\) :: forall (a :: k) (b :: ()) r. ((Ob a, Ob b) => r) -> AsPresheaf dx a b -> r Source Comments #
Relation p => Profunctor (Converse p :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Rel Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> Converse p a b -> Converse p c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> Converse p a b -> r Source Comments #
(CategoryOf j, CategoryOf k, Profunctor p) => Profunctor (UnOp p :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Opposite Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> UnOp p a b -> UnOp p c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> UnOp p a b -> r Source Comments #
FunctorForRep f => Profunctor (Corep f :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Corepresentable Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> Corep f a b -> Corep f c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> Corep f a b -> r Source Comments #
Functor f => Profunctor (Costar f :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Costar Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> Costar f a b -> Costar f c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> Costar f a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (Coyoneda p :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Coyoneda Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> Coyoneda p a b -> Coyoneda p c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> Coyoneda p a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (HaskValue c :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.HaskValue Methods dimap :: forall (c0 :: k) (a :: k) (b :: j) (d :: j). (c0 ~> a) -> (b ~> d) -> HaskValue c a b -> HaskValue c c0 d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> HaskValue c a b -> r Source Comments #
Corepresentable p => Profunctor (CorepStar p :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Representable Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> CorepStar p a b -> CorepStar p c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> CorepStar p a b -> r Source Comments #
FunctorForRep f => Profunctor (Rep f :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Representable Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> Rep f a b -> Rep f c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> Rep f a b -> r Source Comments #
Representable p => Profunctor (RepCostar p :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Representable Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> RepCostar p a b -> RepCostar p c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> RepCostar p a b -> r 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 #
Profunctor p => Profunctor (Wrapped p :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Wrapped Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> Wrapped p a b -> Wrapped p c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> Wrapped p a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (Yoneda p :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Yoneda Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> Yoneda p a b -> Yoneda p c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> Yoneda p a b -> r Source Comments #
Profunctor l => Profunctor (AsLeftAdjoint l :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Universal Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> AsLeftAdjoint l a b -> AsLeftAdjoint l c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> AsLeftAdjoint l a b -> r Source Comments #
Profunctor r => Profunctor (AsRightAdjoint r :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Universal Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> AsRightAdjoint r a b -> AsRightAdjoint r c d Source Comments # (\\) :: forall (a :: k) (b :: j) r0. ((Ob a, Ob b) => r0) -> AsRightAdjoint r a b -> r0 Source Comments #
Profunctor p => Profunctor (FromAdjunction p :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Universal Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> FromAdjunction p a b -> FromAdjunction p c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> FromAdjunction p a b -> r Source Comments #
(Ob r, MonoidalAction m k) => Profunctor (Reader ('OP r) :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Reader Methods dimap :: forall (c :: k) (a :: k) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Reader ('OP r) a b -> Reader ('OP r) c d Source Comments # (\\) :: forall (a :: k) (b :: k) r0. ((Ob a, Ob b) => r0) -> Reader ('OP r) a b -> r0 Source Comments #
(Ob w, MonoidalAction m k) => Profunctor (Writer w :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Writer Methods dimap :: forall (c :: k) (a :: k) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Writer w a b -> Writer w c d Source Comments # (\\) :: forall (a :: k) (b :: k) r. ((Ob a, Ob b) => r) -> Writer w a b -> 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 (n :*.: p :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Object.Copower Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> (n :.: p) a b -> (n :.: p) c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> (n :*.: p) a b -> r Source Comments #
Profunctor p => Profunctor (p :^: n :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Object.Power Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> (p :^: n) a b -> (p :^: n) c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> (p :^: n) a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :+: q :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Coproduct Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> (p :+: q) a b -> (p :+: q) c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> (p :+: q) a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (Day p q :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Day Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> Day p q a b -> Day p q c d Source Comments # (\\) :: forall (a :: k) (b :: j) 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 :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Day Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> DayExp p q a b -> DayExp p q c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> DayExp p q a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :~>: q :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Exponential Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> (p :~>: q) a b -> (p :~>: q) c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> (p :~>: q) a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :*: q :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Product Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> (p :: q) a b -> (p :: q) c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> (p :*: q) a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (Yo a ('OP b) :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Yoneda Methods dimap :: forall (c :: k) (a0 :: k) (b0 :: j) (d :: j). (c ~> a0) -> (b0 ~> d) -> Yo a ('OP b) a0 b0 -> Yo a ('OP b) c d Source Comments # (\\) :: forall (a0 :: k) (b0 :: j) r. ((Ob a0, Ob b0) => r) -> Yo a ('OP b) a0 b0 -> r Source Comments #
CategoryOf k => Profunctor (Exchange a b :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Core Methods dimap :: forall (c :: k) (a0 :: k) (b0 :: k) (d :: k). (c ~> a0) -> (b0 ~> d) -> Exchange a b a0 b0 -> Exchange a b c d Source Comments # (\\) :: forall (a0 :: k) (b0 :: k) r. ((Ob a0, Ob b0) => r) -> Exchange a b a0 b0 -> r Source Comments #
(CategoryOf c, CategoryOf d) => Profunctor (Optic m a b :: d -> c -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: forall (c0 :: d) (a0 :: d) (b0 :: c) (d0 :: c). (c0 ~> a0) -> (b0 ~> d0) -> Optic m a b a0 b0 -> Optic m a b c0 d0 Source Comments # (\\) :: forall (a0 :: d) (b0 :: c) r. ((Ob a0, Ob b0) => r) -> Optic m a b a0 b0 -> r Source Comments #
(Profunctor tk, Profunctor tj) => Profunctor (Day tk tj ps :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Promonoidal Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> Day tk tj ps a b -> Day tk tj ps c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> Day tk tj ps a b -> r Source Comments #
(Profunctor p, Profunctor j2) => Profunctor (Ran ('OP j2) p :: k -> j1 -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Ran Methods dimap :: forall (c :: k) (a :: k) (b :: j1) (d :: j1). (c ~> a) -> (b ~> d) -> Ran ('OP j2) p a b -> Ran ('OP j2) p c d Source Comments # (\\) :: forall (a :: k) (b :: j1) r. ((Ob a, Ob b) => r) -> Ran ('OP j2) p a b -> r Source Comments #
(Profunctor p, Profunctor j2) => Profunctor (Rift ('OP j2) p :: k -> j1 -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Rift Methods dimap :: forall (c :: k) (a :: k) (b :: j1) (d :: j1). (c ~> a) -> (b ~> d) -> Rift ('OP j2) p a b -> Rift ('OP j2) p c d Source Comments # (\\) :: forall (a :: k) (b :: j1) r. ((Ob a, Ob b) => r) -> Rift ('OP j2) p a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :.: q :: k -> j2 -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Composition Methods dimap :: forall (c :: k) (a :: k) (b :: j2) (d :: j2). (c ~> a) -> (b ~> d) -> (p :.: q) a b -> (p :.: q) c d Source Comments # (\\) :: forall (a :: k) (b :: j2) r. ((Ob a, Ob b) => r) -> (p :.: q) a b -> r Source Comments #
CategoryOf k => Profunctor (Hom :: (OPPOSITE k, k) -> () -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Colimit Methods dimap :: forall (c :: (OPPOSITE k, k)) (a :: (OPPOSITE k, k)) (b :: ()) (d :: ()). (c ~> a) -> (b ~> d) -> Hom a b -> Hom c d Source Comments # (\\) :: forall (a :: (OPPOSITE k, k)) (b :: ()) r. ((Ob a, Ob b) => r) -> Hom a b -> r Source Comments #
Promonad p => Profunctor (KleisliFree p :: KLEISLI p -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods dimap :: forall (c :: KLEISLI p) (a :: KLEISLI p) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> KleisliFree p a b -> KleisliFree p c d Source Comments # (\\) :: forall (a :: KLEISLI p) (b :: j) r. ((Ob a, Ob b) => r) -> KleisliFree p a b -> r Source Comments #
(Profunctor p, CategoryOf i, CategoryOf j) => Profunctor (Curry p :: (OPPOSITE j, k) -> i -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: (OPPOSITE j, k)) (a :: (OPPOSITE j, k)) (b :: i) (d :: i). (c ~> a) -> (b ~> d) -> Curry p a b -> Curry p c d Source Comments # (\\) :: forall (a :: (OPPOSITE j, k)) (b :: i) r. ((Ob a, Ob b) => r) -> Curry p a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :&&&: q :: (i, j2) -> j1 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: (i, j2)) (a :: (i, j2)) (b :: j1) (d :: j1). (c ~> a) -> (b ~> d) -> (p :&&&: q) a b -> (p :&&&: q) c d Source Comments # (\\) :: forall (a :: (i, j2)) (b :: j1) r. ((Ob a, Ob b) => r) -> (p :&&&: q) a b -> r Source Comments #
Monoidal k => Profunctor (Tensor :: k -> LIST k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Promonoidal Methods dimap :: forall (c :: k) (a :: k) (b :: LIST k) (d :: LIST k). (c ~> a) -> (b ~> d) -> Tensor a b -> Tensor c d Source Comments # (\\) :: forall (a :: k) (b :: LIST k) r. ((Ob a, Ob b) => r) -> Tensor a b -> r 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 #
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 #
Profunctor (Codiscrete :: CODISCRETE k -> CODISCRETE k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Discrete Methods dimap :: forall (c :: CODISCRETE k) (a :: CODISCRETE k) (b :: CODISCRETE k) (d :: CODISCRETE k). (c ~> a) -> (b ~> d) -> Codiscrete a b -> Codiscrete c d Source Comments # (\\) :: forall (a :: CODISCRETE k) (b :: CODISCRETE k) r. ((Ob a, Ob b) => r) -> Codiscrete a b -> r Source Comments #
Profunctor (Discrete :: DISCRETE k -> DISCRETE k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Discrete Methods dimap :: forall (c :: DISCRETE k) (a :: DISCRETE k) (b :: DISCRETE k) (d :: DISCRETE k). (c ~> a) -> (b ~> d) -> Discrete a b -> Discrete c d Source Comments # (\\) :: forall (a :: DISCRETE k) (b :: DISCRETE k) r. ((Ob a, Ob b) => r) -> Discrete a b -> r Source Comments #
CategoryOf k => Profunctor (Fam :: FAM k -> FAM k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Fam Methods dimap :: forall (c :: FAM k) (a :: FAM k) (b :: FAM k) (d :: FAM k). (c ~> a) -> (b ~> d) -> Fam a b -> Fam c d Source Comments # (\\) :: forall (a :: FAM k) (b :: FAM k) r. ((Ob a, Ob b) => r) -> Fam a b -> r Source Comments #
Profunctor (LTE :: FIN n -> FIN n -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Fin Methods dimap :: forall (c :: FIN n) (a :: FIN n) (b :: FIN n) (d :: FIN n). (c ~> a) -> (b ~> d) -> LTE a b -> LTE c d Source Comments # (\\) :: forall (a :: FIN n) (b :: FIN n) r. ((Ob a, Ob b) => r) -> LTE a b -> r Source Comments #
TracedMonoidal k => Profunctor (IntConstruction :: INT k -> INT k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.IntConstruction Methods dimap :: forall (c :: INT k) (a :: INT k) (b :: INT k) (d :: INT k). (c ~> a) -> (b ~> d) -> IntConstruction a b -> IntConstruction c d Source Comments # (\\) :: forall (a :: INT k) (b :: INT k) r. ((Ob a, Ob b) => r) -> IntConstruction a b -> r Source Comments #
Num a => Profunctor (Mat :: MatK a -> MatK a -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Mat Methods dimap :: forall (c :: MatK a) (a0 :: MatK a) (b :: MatK a) (d :: MatK a). (c ~> a0) -> (b ~> d) -> Mat a0 b -> Mat c d Source Comments # (\\) :: forall (a0 :: MatK a) (b :: MatK a) r. ((Ob a0, Ob b) => r) -> Mat a0 b -> r Source Comments #
Monoidal k => Profunctor (Strictified :: [k] -> [k] -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Strictified 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 p => Profunctor (Rev p :: REV k -> REV j -> Type) Source Comments #
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 Comments # (\\) :: forall (a :: REV k) (b :: REV j) r. ((Ob a, Ob b) => r) -> Rev p a b -> r Source Comments #
Profunctor p => Profunctor (Op p :: OPPOSITE j -> OPPOSITE k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Opposite Methods dimap :: forall (c :: OPPOSITE j) (a :: OPPOSITE j) (b :: OPPOSITE k) (d :: OPPOSITE k). (c ~> a) -> (b ~> d) -> Op p a b -> Op p c d Source Comments # (\\) :: forall (a :: OPPOSITE j) (b :: OPPOSITE k) r. ((Ob a, Ob b) => r) -> Op p a b -> r Source Comments #
Profunctor p => Profunctor (Coprod p :: COPROD k -> COPROD j -> Type) Source Comments #
Instance details Defined in Proarrow.Object.BinaryCoproduct Methods dimap :: forall (c :: COPROD k) (a :: COPROD k) (b :: COPROD j) (d :: COPROD j). (c ~> a) -> (b ~> d) -> Coprod p a b -> Coprod p c d Source Comments # (\\) :: forall (a :: COPROD k) (b :: COPROD j) r. ((Ob a, Ob b) => r) -> Coprod p a b -> r Source Comments #
Profunctor p => Profunctor (Prod p :: PROD k -> PROD j -> Type) Source Comments #
Instance details Defined in Proarrow.Object.BinaryProduct Methods dimap :: forall (c :: PROD k) (a :: PROD k) (b :: PROD j) (d :: PROD j). (c ~> a) -> (b ~> d) -> Prod p a b -> Prod p c d Source Comments # (\\) :: forall (a :: PROD k) (b :: PROD j) r. ((Ob a, Ob b) => r) -> Prod p a b -> r Source Comments #
(CategoryOf j, CategoryOf k, Ob ps) => Profunctor (PList ps :: LIST k -> LIST j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Promonoidal Methods dimap :: forall (c :: LIST k) (a :: LIST k) (b :: LIST j) (d :: LIST j). (c ~> a) -> (b ~> d) -> PList ps a b -> PList ps c d Source Comments # (\\) :: forall (a :: LIST k) (b :: LIST j) r. ((Ob a, Ob b) => r) -> PList ps a b -> r Source Comments #
Profunctor p => Profunctor (List p :: LIST k -> LIST j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.List Methods dimap :: forall (c :: LIST k) (a :: LIST k) (b :: LIST j) (d :: LIST j). (c ~> a) -> (b ~> d) -> List p a b -> List p c d Source Comments # (\\) :: forall (a :: LIST k) (b :: LIST j) r. ((Ob a, Ob b) => r) -> List p a b -> r Source Comments #
CategoryOf k => Profunctor (Hom :: () -> (OPPOSITE k, k) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Limit Methods dimap :: forall (c :: ()) (a :: ()) (b :: (OPPOSITE k, k)) (d :: (OPPOSITE k, k)). (c ~> a) -> (b ~> d) -> Hom a b -> Hom c d Source Comments # (\\) :: forall (a :: ()) (b :: (OPPOSITE k, k)) r. ((Ob a, Ob b) => r) -> Hom a b -> r Source Comments #
Promonad p => Profunctor (KleisliForget p :: k -> KLEISLI p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods dimap :: forall (c :: k) (a :: k) (b :: KLEISLI p) (d :: KLEISLI p). (c ~> a) -> (b ~> d) -> KleisliForget p a b -> KleisliForget p c d Source Comments # (\\) :: forall (a :: k) (b :: KLEISLI p) r. ((Ob a, Ob b) => r) -> KleisliForget p a b -> r Source Comments #
(Profunctor p, CategoryOf j, CategoryOf k) => Profunctor (Uncurry p :: k -> (i, j) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: k) (a :: k) (b :: (i, j)) (d :: (i, j)). (c ~> a) -> (b ~> d) -> Uncurry p a b -> Uncurry p c d Source Comments # (\\) :: forall (a :: k) (b :: (i, j)) r. ((Ob a, Ob b) => r) -> Uncurry p a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :\|\|\|: q :: k -> COPRODUCT i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Fam Methods dimap :: forall (c :: k) (a :: k) (b :: COPRODUCT i j) (d :: COPRODUCT i j). (c ~> a) -> (b ~> d) -> (p :\|\|\|: q) a b -> (p :\|\|\|: q) c d Source Comments # (\\) :: forall (a :: k) (b :: COPRODUCT i j) r. ((Ob a, Ob b) => r) -> (p :\|\|\|: q) a b -> r Source Comments #
(Profunctor l, Profunctor r, CategoryOf k) => Profunctor (l :&&: r :: k -> (x, y) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Fam Methods dimap :: forall (c :: k) (a :: k) (b :: (x, y)) (d :: (x, y)). (c ~> a) -> (b ~> d) -> (l :&&: r) a b -> (l :&&: r) c d Source Comments # (\\) :: forall (a :: k) (b :: (x, y)) r0. ((Ob a, Ob b) => r0) -> (l :&&: r) a b -> r0 Source Comments #
Profunctor (Adj :: ADJK a b -> ADJK a b -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Adj Methods dimap :: forall (c :: ADJK a b) (a0 :: ADJK a b) (b0 :: ADJK a b) (d :: ADJK a b). (c ~> a0) -> (b0 ~> d) -> Adj a0 b0 -> Adj c d Source Comments # (\\) :: forall (a0 :: ADJK a b) (b0 :: ADJK a b) r. ((Ob a0, Ob b0) => r) -> Adj a0 b0 -> r Source Comments #
Profunctor (Prof :: PROFK j k -> PROFK j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Prof Methods dimap :: forall (c :: PROFK j k) (a :: PROFK j k) (b :: PROFK j k) (d :: PROFK j k). (c ~> a) -> (b ~> d) -> Prof a b -> Prof c d Source Comments # (\\) :: forall (a :: PROFK j k) (b :: PROFK j k) r. ((Ob a, Ob b) => r) -> Prof 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' :: (j .-> k) -> (j .-> k) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods dimap :: forall (c :: j .-> k) (a :: j .-> k) (b :: j .-> k) (d :: j .-> k). (c ~> a) -> (b ~> d) -> Nat' a b -> Nat' c d Source Comments # (\\) :: forall (a :: j .-> k) (b :: j .-> k) r. ((Ob a, Ob b) => r) -> Nat' a b -> r Source Comments #
Profunctor (Terminal :: Unit '() '() -> Unit '() '() -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Terminal Methods dimap :: forall (c :: Unit '() '()) (a :: Unit '() '()) (b :: Unit '() '()) (d :: Unit '() '()). (c ~> a) -> (b ~> d) -> Terminal a b -> Terminal c d Source Comments # (\\) :: forall (a :: Unit '() '()) (b :: Unit '() '()) r. ((Ob a, Ob b) => r) -> Terminal a b -> r Source Comments #
Profunctor (Prof :: (j +-> k) -> (j +-> k) -> Type) Source Comments #
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 Comments # (\\) :: forall (a :: j +-> k) (b :: 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 (Sub p :: 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 p a b -> Sub p c d Source Comments # (\\) :: forall (a :: SUBCAT ob) (b :: SUBCAT ob) r. ((Ob a, Ob b) => r) -> Sub p a b -> r Source Comments #
(Applicative f, Profunctor p) => Profunctor (Ap p :: AP f k -> AP f j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Ap Methods dimap :: forall (c :: AP f k) (a :: AP f k) (b :: AP f j) (d :: AP f j). (c ~> a) -> (b ~> d) -> Ap p a b -> Ap p c d Source Comments # (\\) :: forall (a :: AP f k) (b :: AP f j) r. ((Ob a, Ob b) => r) -> Ap p a b -> r Source Comments #
Profunctor j => Profunctor (LimitAdj j :: COREPK b k -> REPK a k -> Type) Source Comments #
Instance details Defined in Proarrow.Adjunction Methods dimap :: forall (c :: COREPK b k) (a0 :: COREPK b k) (b0 :: REPK a k) (d :: REPK a k). (c ~> a0) -> (b0 ~> d) -> LimitAdj j a0 b0 -> LimitAdj j c d Source Comments # (\\) :: forall (a0 :: COREPK b k) (b0 :: REPK a k) r. ((Ob a0, Ob b0) => r) -> LimitAdj j a0 b0 -> r Source Comments #
Monoid m => Profunctor (Mon :: MONOIDK m -> MONOIDK m -> Type) Source Comments #
Instance details Defined in Proarrow.Monoid Methods dimap :: forall (c :: MONOIDK m) (a :: MONOIDK m) (b :: MONOIDK m) (d :: MONOIDK m). (c ~> a) -> (b ~> d) -> Mon a b -> Mon c d Source Comments # (\\) :: forall (a :: MONOIDK m) (b :: MONOIDK m) r. ((Ob a, Ob b) => r) -> Mon a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :++: q :: COPRODUCT k1 k2 -> COPRODUCT j1 j2 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Coproduct Methods dimap :: forall (c :: COPRODUCT k1 k2) (a :: COPRODUCT k1 k2) (b :: COPRODUCT j1 j2) (d :: COPRODUCT j1 j2). (c ~> a) -> (b ~> d) -> (p :++: q) a b -> (p :++: q) c d Source Comments # (\\) :: forall (a :: COPRODUCT k1 k2) (b :: COPRODUCT j1 j2) r. ((Ob a, Ob b) => r) -> (p :++: q) a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :**: q :: (k1, k2) -> (j1, j2) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Product Methods dimap :: forall (c :: (k1, k2)) (a :: (k1, k2)) (b :: (j1, j2)) (d :: (j1, j2)). (c ~> a) -> (b ~> d) -> (p :: q) a b -> (p :: q) c d Source Comments # (\\) :: forall (a :: (k1, k2)) (b :: (j1, j2)) r. ((Ob a, Ob b) => r) -> (p :**: q) a b -> r Source Comments #
(Bicategory kk, Ob0 kk h, Ob0 kk i, Ob0 kk j, Ob0 kk k) => Profunctor (Sq' :: (kk j h, SUBCAT Tight kk h i) -> (kk k i, SUBCAT Tight kk j k) -> Type) Source Comments #
Instance details Defined in Proarrow.Squares Methods dimap :: forall (c0 :: (kk j h, SUBCAT Tight kk h i)) (a :: (kk j h, SUBCAT Tight kk h i)) (b :: (kk k i, SUBCAT Tight kk j k)) (d :: (kk k i, SUBCAT Tight kk j k)). (c0 ~> a) -> (b ~> d) -> Sq' a b -> Sq' c0 d Source Comments # (\\) :: forall (a :: (kk j h, SUBCAT Tight kk h i)) (b :: (kk k i, SUBCAT Tight kk j k)) r. ((Ob a, Ob b) => r) -> Sq' 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 p => Profunctor (Collage :: COLLAGE p -> COLLAGE p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Collage Methods dimap :: forall (c :: COLLAGE p) (a :: COLLAGE p) (b :: COLLAGE p) (d :: COLLAGE p). (c ~> a) -> (b ~> d) -> Collage a b -> Collage c d Source Comments # (\\) :: forall (a :: COLLAGE p) (b :: COLLAGE p) r. ((Ob a, Ob b) => r) -> Collage a b -> r Source Comments #
Adjunction adj => Profunctor (Duploid :: DUPLOID adj -> DUPLOID adj -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Duploid Methods dimap :: forall (c :: DUPLOID adj) (a :: DUPLOID adj) (b :: DUPLOID adj) (d :: DUPLOID adj). (c ~> a) -> (b ~> d) -> Duploid a b -> Duploid c d Source Comments # (\\) :: forall (a :: DUPLOID adj) (b :: DUPLOID adj) r. ((Ob a, Ob b) => r) -> Duploid a b -> r Source Comments #
Ok cs p => Profunctor (Free :: FREE cs p -> FREE cs p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Free Methods dimap :: forall (c :: FREE cs p) (a :: FREE cs p) (b :: FREE cs p) (d :: FREE cs p). (c ~> a) -> (b ~> d) -> Free a b -> Free c d Source Comments # (\\) :: forall (a :: FREE cs p) (b :: FREE cs p) r. ((Ob a, Ob b) => r) -> Free 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 #
Profunctor (Bidiscrete :: DiscreteK ob j k -> DiscreteK ob j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Bidiscrete Methods dimap :: forall (c0 :: DiscreteK ob j k) (a :: DiscreteK ob j k) (b :: DiscreteK ob j k) (d :: DiscreteK ob j k). (c0 ~> a) -> (b ~> d) -> Bidiscrete a b -> Bidiscrete c0 d Source Comments # (\\) :: forall (a :: DiscreteK ob j k) (b :: DiscreteK ob j k) r. ((Ob a, Ob b) => r) -> Bidiscrete 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 #
(CategoryOf (kk j k2), Bicategory kk) => Profunctor (Strictified :: Path kk j k2 -> Path kk j k2 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Strictified 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 #
MonoidalAction m k => Profunctor (StT :: STT' m k i j -> STT' m k i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Equipment.Stateful Methods dimap :: forall (c :: STT' m k i j) (a :: STT' m k i j) (b :: STT' m k i j) (d :: STT' m k i j). (c ~> a) -> (b ~> d) -> StT a b -> StT c d Source Comments # (\\) :: forall (a :: STT' m k i j) (b :: STT' m k i j) r. ((Ob a, Ob b) => r) -> StT a b -> r Source Comments #
IsChart m c d => Profunctor (ChartCat :: CHART m c d -> CHART m c d -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: forall (c0 :: CHART m c d) (a :: CHART m c d) (b :: CHART m c d) (d0 :: CHART m c d). (c0 ~> a) -> (b ~> d0) -> ChartCat a b -> ChartCat c0 d0 Source Comments # (\\) :: forall (a :: CHART m c d) (b :: CHART m c d) r. ((Ob a, Ob b) => r) -> ChartCat a b -> r Source Comments #
IsOptic m c d => Profunctor (OpticCat :: OPTIC m c d -> OPTIC m c d -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: forall (c0 :: OPTIC m c d) (a :: OPTIC m c d) (b :: OPTIC m c d) (d0 :: OPTIC m c d). (c0 ~> a) -> (b ~> d0) -> OpticCat a b -> OpticCat c0 d0 Source Comments # (\\) :: forall (a :: OPTIC m c d) (b :: OPTIC m c d) r. ((Ob a, Ob b) => r) -> OpticCat a b -> r Source Comments #
Profunctor ((~>) :: CAT (kk i j)) => Profunctor (HomW :: HK kk i j -> HK kk i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Hom Methods dimap :: forall (c :: HK kk i j) (a :: HK kk i j) (b :: HK kk i j) (d :: HK kk i j). (c ~> a) -> (b ~> d) -> HomW a b -> HomW c d Source Comments # (\\) :: forall (a :: HK kk i j) (b :: HK kk i j) r. ((Ob a, Ob b) => r) -> HomW 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 #
(Bicategory kk, Ob s, Ob t, Ob0 kk h, Ob0 kk i, Ob0 kk j, Ob0 kk k2) => Profunctor (P kk kk (HK kk) s t :: HK kk h j +-> HK kk i k2) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Hom Methods dimap :: forall (c :: HK kk i k2) (a :: HK kk i k2) (b :: HK kk h j) (d :: HK kk h j). (c ~> a) -> (b ~> d) -> P kk kk (HK kk) s t a b -> P kk kk (HK kk) s t c d Source Comments # (\\) :: forall (a :: HK kk i k2) (b :: HK kk h j) r. ((Ob a, Ob b) => r) -> P kk kk (HK kk) s t 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 :: k) (a :: k) (b :: j). Profunctor p => (c ~> a) -> p a b -> p c b Source Comments #

Left mapping (contravariant mapping over first argument).

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

Right mapping (covariant mapping over second argument).

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

Flipped version of (\\).