Safe Haskell	None
Language	GHC2024

Proarrow.Promonad

Synopsis

class Profunctor p => Promonad (p :: k +-> k) where
- id :: forall (a :: k). Ob a => p a a
- (.) :: forall (b :: k) (c :: k) (a :: k). p b c -> p a b -> p a c
class Profunctor p => Procomonad (p :: i +-> i) where
- extract :: p :~> ((~>) :: CAT i)
- duplicate :: p :~> (p :.: p)

Documentation

class Profunctor p => Promonad (p :: k +-> k) where Source Comments #

A promonad is a category-like profunctor with identity morphisms and composition.

Laws:

Left identity: id . f = f
Right identity: f . id = f
Associativity: (h . g) . f = h . (g . f)

Methods

id :: forall (a :: k). Ob a => p a a Source Comments #

Identity morphisms.

(.) :: forall (b :: k) (c :: k) (a :: k). p b c -> p a b -> p a c infixr 9 Source Comments #

Composition (note the parameter order matches function composition).

Instances

Instances details

Promonad ZX Source Comments #
Instance details Defined in Proarrow.Category.Instance.ZX Methods id :: forall (a :: Nat). Ob a => ZX a a Source Comments # (.) :: forall (b :: Nat) (c :: Nat) (a :: Nat). ZX b c -> ZX a b -> ZX a c Source Comments #
Promonad Booleans Source Comments #
Instance details Defined in Proarrow.Category.Instance.Bool Methods id :: forall (a :: BOOL). Ob a => Booleans a a Source Comments # (.) :: forall (b :: BOOL) (c :: BOOL) (a :: BOOL). Booleans b c -> Booleans a b -> Booleans a c Source Comments #
Promonad Cat Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods id :: forall (a :: KIND). Ob a => Cat a a Source Comments # (.) :: forall (b :: KIND) (c :: KIND) (a :: KIND). Cat b c -> Cat a b -> Cat a c Source Comments #
Promonad (:-) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Constraint Methods id :: forall (a :: CONSTRAINT). Ob a => a :- a Source Comments # (.) :: forall (b :: CONSTRAINT) (c :: CONSTRAINT) (a :: CONSTRAINT). (b :- c) -> (a :- b) -> a :- c Source Comments #
Promonad GTE Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cost Methods id :: forall (a :: COST). Ob a => GTE a a Source Comments # (.) :: forall (b :: COST) (c :: COST) (a :: COST). GTE b c -> GTE a b -> GTE a c Source Comments #
Promonad Linear Source Comments #
Instance details Defined in Proarrow.Category.Instance.Linear Methods id :: forall (a :: LINEAR). Ob a => Linear a a Source Comments # (.) :: forall (b :: LINEAR) (c :: LINEAR) (a :: LINEAR). Linear b c -> Linear a b -> Linear a c Source Comments #
Promonad Pointed Source Comments #
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods id :: forall (a :: POINTED). Ob a => Pointed a a Source Comments # (.) :: forall (b :: POINTED) (c :: POINTED) (a :: POINTED). Pointed b c -> Pointed a b -> Pointed a c Source Comments #
Promonad Simplex Source Comments #
Instance details Defined in Proarrow.Category.Instance.Simplex Methods id :: forall (a :: Nat). Ob a => Simplex a a Source Comments # (.) :: forall (b :: Nat) (c :: Nat) (a :: Nat). Simplex b c -> Simplex a b -> Simplex a c Source Comments #
Promonad Zero Source Comments #
Instance details Defined in Proarrow.Category.Instance.Zero Methods id :: forall (a :: VOID). Ob a => Zero a a Source Comments # (.) :: forall (b :: VOID) (c :: VOID) (a :: VOID). Zero b c -> Zero a b -> Zero a c Source Comments #
Promonad Unit Source Comments #
Instance details Defined in Proarrow.Category.Instance.Unit Methods id :: forall (a :: ()). Ob a => Unit a a Source Comments # (.) :: forall (b :: ()) (c :: ()) (a :: ()). Unit b c -> Unit a b -> Unit a c Source Comments #
Promonad Sym Source Comments #
Instance details Defined in Proarrow.Tools.Laws Methods id :: forall (a :: Symbol). Ob a => Sym a a Source Comments # (.) :: forall (b :: Symbol) (c :: Symbol) (a :: Symbol). Sym b c -> Sym a b -> Sym a c Source Comments #
Comonoid w => Promonad (ComonoidAsCat w :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: Ob a => ComonoidAsCat w a a Source Comments # (.) :: ComonoidAsCat w b c -> ComonoidAsCat w a b -> ComonoidAsCat w a c Source Comments #
CategoryOf k => Promonad (Id :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Identity Methods id :: forall (a :: k). Ob a => Id a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). Id b c -> Id a b -> Id a c Source Comments #
Promonad (->) Source Comments #
Instance details Defined in Proarrow.Core Methods id :: Ob a => a -> a Source Comments # (.) :: (b -> c) -> (a -> b) -> a -> c Source Comments #
Promonad p => Promonad (Fix p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Fix Methods id :: forall (a :: k). Ob a => Fix p a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). Fix p b c -> Fix p a b -> Fix p a c Source Comments #
Profunctor p => Promonad (FreePromonad p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Free Methods id :: forall (a :: k). Ob a => FreePromonad p a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). FreePromonad p b c -> FreePromonad p a b -> FreePromonad p a c Source Comments #
CategoryOf k => Promonad (TerminalProfunctor :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Terminal Methods id :: forall (a :: k). Ob a => TerminalProfunctor a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). TerminalProfunctor b c -> TerminalProfunctor a b -> TerminalProfunctor a c Source Comments #
CategoryOf k => Promonad (Cont r :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Cont Methods id :: forall (a :: k). Ob a => Cont r a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). Cont r b c -> Cont r a b -> Cont r a c Source Comments #
(Monoidal k, Ob s) => Promonad (State s :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.State Methods id :: forall (a :: k). Ob a => State s a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). State s b c -> State s a b -> State s a c 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 #
(Monoid c, CategoryOf k) => Promonad (HaskValue c :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.HaskValue Methods id :: forall (a :: k). Ob a => HaskValue c a a Source Comments # (.) :: forall (b :: k) (c0 :: k) (a :: k). HaskValue c b c0 -> HaskValue c a b -> HaskValue c a c0 Source Comments #
Promonad p => Promonad (Wrapped p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Wrapped Methods id :: forall (a :: k). Ob a => Wrapped p a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). Wrapped p b c -> Wrapped p a b -> Wrapped p a c Source Comments #
(Comonoid r, MonoidalAction m k) => Promonad (Reader ('OP r) :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Reader Methods id :: forall (a :: k). Ob a => Reader ('OP r) a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). Reader ('OP r) b c -> Reader ('OP r) a b -> Reader ('OP r) a c Source Comments #
(Monoid w, MonoidalAction m k) => Promonad (Writer w :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Writer Methods id :: forall (a :: k). Ob a => Writer w a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). Writer w b c -> Writer w a b -> Writer w a c Source Comments #
Adjunction p q => Promonad (q :.: p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Adjunction Methods id :: forall (a :: k). Ob a => (q :.: p) a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). (q :.: p) b c -> (q :.: p) a b -> (q :.: p) a c Source Comments #
(p ~ j, Profunctor p) => Promonad (Ran ('OP j) p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Ran Methods id :: forall (a :: k). Ob a => Ran ('OP j) p a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). Ran ('OP j) p b c -> Ran ('OP j) p a b -> Ran ('OP j) p a c Source Comments #
(p ~ j, Profunctor p) => Promonad (Rift ('OP j) p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Rift Methods id :: forall (a :: k). Ob a => Rift ('OP j) p a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). Rift ('OP j) p b c -> Rift ('OP j) p a b -> Rift ('OP j) p a c Source Comments #
Promonad (Codiscrete :: CODISCRETE k -> CODISCRETE k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Discrete Methods id :: forall (a :: CODISCRETE k). Ob a => Codiscrete a a Source Comments # (.) :: forall (b :: CODISCRETE k) (c :: CODISCRETE k) (a :: CODISCRETE k). Codiscrete b c -> Codiscrete a b -> Codiscrete a c Source Comments #
Promonad (Discrete :: DISCRETE k -> DISCRETE k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Discrete Methods id :: forall (a :: DISCRETE k). Ob a => Discrete a a Source Comments # (.) :: forall (b :: DISCRETE k) (c :: DISCRETE k) (a :: DISCRETE k). Discrete b c -> Discrete a b -> Discrete a c Source Comments #
Promonad (LTE :: FIN n -> FIN n -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Fin Methods id :: forall (a :: FIN n). Ob a => LTE a a Source Comments # (.) :: forall (b :: FIN n) (c :: FIN n) (a :: FIN n). LTE b c -> LTE a b -> LTE a c Source Comments #
TracedMonoidal k => Promonad (IntConstruction :: INT k -> INT k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.IntConstruction Methods id :: forall (a :: INT k). Ob a => IntConstruction a a Source Comments # (.) :: forall (b :: INT k) (c :: INT k) (a :: INT k). IntConstruction b c -> IntConstruction a b -> IntConstruction a c Source Comments #
Num a => Promonad (Mat :: MatK a -> MatK a -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Mat Methods id :: forall (a0 :: MatK a). Ob a0 => Mat a0 a0 Source Comments # (.) :: forall (b :: MatK a) (c :: MatK a) (a0 :: MatK a). Mat b c -> Mat a0 b -> Mat a0 c Source Comments #
Monoidal k => Promonad (Strictified :: [k] -> [k] -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Strictified Methods id :: forall (a :: [k]). Ob a => Strictified a a Source Comments # (.) :: forall (b :: [k]) (c :: [k]) (a :: [k]). Strictified b c -> Strictified a b -> Strictified a c Source Comments #
Promonad p => Promonad (Rev p :: REV j -> REV j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Rev Methods id :: forall (a :: REV j). Ob a => Rev p a a Source Comments # (.) :: forall (b :: REV j) (c :: REV j) (a :: REV j). Rev p b c -> Rev p a b -> Rev p a c Source Comments #
Promonad c => Promonad (Op c :: OPPOSITE j -> OPPOSITE j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Opposite Methods id :: forall (a :: OPPOSITE j). Ob a => Op c a a Source Comments # (.) :: forall (b :: OPPOSITE j) (c0 :: OPPOSITE j) (a :: OPPOSITE j). Op c b c0 -> Op c a b -> Op c a c0 Source Comments #
Promonad p => Promonad (Coprod p :: COPROD j -> COPROD j -> Type) Source Comments #
Instance details Defined in Proarrow.Object.BinaryCoproduct Methods id :: forall (a :: COPROD j). Ob a => Coprod p a a Source Comments # (.) :: forall (b :: COPROD j) (c :: COPROD j) (a :: COPROD j). Coprod p b c -> Coprod p a b -> Coprod p a c Source Comments #
Promonad p => Promonad (Prod p :: PROD j -> PROD j -> Type) Source Comments #
Instance details Defined in Proarrow.Object.BinaryProduct Methods id :: forall (a :: PROD j). Ob a => Prod p a a Source Comments # (.) :: forall (b :: PROD j) (c :: PROD j) (a :: PROD j). Prod p b c -> Prod p a b -> Prod p a c Source Comments #
Promonad p => Promonad (List p :: LIST j -> LIST j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.List Methods id :: forall (a :: LIST j). Ob a => List p a a Source Comments # (.) :: forall (b :: LIST j) (c :: LIST j) (a :: LIST j). List p b c -> List p a b -> List p a c Source Comments #
Promonad (Prof :: PROFK j k -> PROFK j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Prof Methods id :: forall (a :: PROFK j k). Ob a => Prof a a Source Comments # (.) :: forall (b :: PROFK j k) (c :: PROFK j k) (a :: PROFK j k). Prof b c -> Prof a b -> Prof a c Source Comments #
Promonad p => Promonad (Kleisli :: KLEISLI p -> KLEISLI p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods id :: forall (a :: KLEISLI p). Ob a => Kleisli a a Source Comments # (.) :: forall (b :: KLEISLI p) (c :: KLEISLI p) (a :: KLEISLI p). Kleisli b c -> Kleisli a b -> Kleisli a c Source Comments #
Promonad (Nat' :: NatK j k -> NatK j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: forall (a :: NatK j k). Ob a => Nat' a a Source Comments # (.) :: forall (b :: NatK j k) (c :: NatK j k) (a :: NatK j k). Nat' b c -> Nat' a b -> Nat' a c Source Comments #
Promonad (Terminal :: Unit '() '() -> Unit '() '() -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Terminal Methods id :: forall (a :: Unit '() '()). Ob a => Terminal a a Source Comments # (.) :: forall (b :: Unit '() '()) (c :: Unit '() '()) (a :: Unit '() '()). Terminal b c -> Terminal a b -> Terminal a c Source Comments #
Promonad (Prof :: (j +-> k) -> (j +-> k) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Prof Methods id :: forall (a :: j +-> k). Ob a => Prof a a Source Comments # (.) :: forall (b :: j +-> k) (c :: j +-> k) (a :: j +-> k). Prof b c -> Prof a b -> Prof a c Source Comments #
Promonad (Nat :: (j -> Type) -> (j -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: forall (a :: j -> Type). Ob a => Nat a a Source Comments # (.) :: forall (b :: j -> Type) (c :: j -> Type) (a :: j -> Type). Nat b c -> Nat a b -> Nat a c Source Comments #
Promonad (Nat :: (k1 -> k2 -> k3 -> k4 -> Type) -> (k1 -> k2 -> k3 -> k4 -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: forall (a :: k1 -> k2 -> k3 -> k4 -> Type). Ob a => Nat a a Source Comments # (.) :: forall (b :: k1 -> k2 -> k3 -> k4 -> Type) (c :: k1 -> k2 -> k3 -> k4 -> Type) (a :: k1 -> k2 -> k3 -> k4 -> Type). Nat b c -> Nat a b -> Nat a c Source Comments #
Promonad (Nat :: (k1 -> k2 -> k3 -> Type) -> (k1 -> k2 -> k3 -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: forall (a :: k1 -> k2 -> k3 -> Type). Ob a => Nat a a Source Comments # (.) :: forall (b :: k1 -> k2 -> k3 -> Type) (c :: k1 -> k2 -> k3 -> Type) (a :: k1 -> k2 -> k3 -> Type). Nat b c -> Nat a b -> Nat a c Source Comments #
Promonad p => Promonad (Sub p :: SUBCAT ob -> SUBCAT ob -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Sub Methods id :: forall (a :: SUBCAT ob). Ob a => Sub p a a Source Comments # (.) :: forall (b :: SUBCAT ob) (c :: SUBCAT ob) (a :: SUBCAT ob). Sub p b c -> Sub p a b -> Sub p a c Source Comments #
(Applicative f, Promonad p) => Promonad (Ap p :: AP f k -> AP f k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Ap Methods id :: forall (a :: AP f k). Ob a => Ap p a a Source Comments # (.) :: forall (b :: AP f k) (c :: AP f k) (a :: AP f k). Ap p b c -> Ap p a b -> Ap p a c Source Comments #
Monoid m => Promonad (Mon :: MONOIDK m -> MONOIDK m -> Type) Source Comments #
Instance details Defined in Proarrow.Monoid Methods id :: forall (a :: MONOIDK m). Ob a => Mon a a Source Comments # (.) :: forall (b :: MONOIDK m) (c :: MONOIDK m) (a :: MONOIDK m). Mon b c -> Mon a b -> Mon a c Source Comments #
(Promonad p, Promonad q) => Promonad (p :++: q :: COPRODUCT j1 j2 -> COPRODUCT j1 j2 -> Type) Source Comments #	The coproduct of two promonads.
Instance details Defined in Proarrow.Category.Instance.Coproduct Methods id :: forall (a :: COPRODUCT j1 j2). Ob a => (p :++: q) a a Source Comments # (.) :: forall (b :: COPRODUCT j1 j2) (c :: COPRODUCT j1 j2) (a :: COPRODUCT j1 j2). (p :++: q) b c -> (p :++: q) a b -> (p :++: q) a c Source Comments #
(Promonad p, Promonad q) => Promonad (p :**: q :: (j1, j2) -> (j1, j2) -> Type) Source Comments #	The product promonad of promonads `p` and `q`.
Instance details Defined in Proarrow.Category.Instance.Product Methods id :: forall (a :: (j1, j2)). Ob a => (p :: q) a a Source Comments # (.) :: forall (b :: (j1, j2)) (c :: (j1, j2)) (a :: (j1, j2)). (p :: q) b c -> (p :: q) a b -> (p :: q) a c Source Comments #
(CategoryOf k, Ob i, Ob j) => Promonad (Category :: PLAINK k i j -> PLAINK k i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.CategoryAsBi Methods id :: forall (a :: PLAINK k i j). Ob a => Category a a Source Comments # (.) :: forall (b :: PLAINK k i j) (c :: PLAINK k i j) (a :: PLAINK k i j). Category b c -> Category a b -> Category a c Source Comments #
CategoryOf k => Promonad (Mon2 :: MonK k i j -> MonK k i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.MonoidalAsBi Methods id :: forall (a :: MonK k i j). Ob a => Mon2 a a Source Comments # (.) :: forall (b :: MonK k i j) (c :: MonK k i j) (a :: MonK k i j). Mon2 b c -> Mon2 a b -> Mon2 a c Source Comments #
Profunctor p => Promonad (Collage :: COLLAGE p -> COLLAGE p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Collage Methods id :: forall (a :: COLLAGE p). Ob a => Collage a a Source Comments # (.) :: forall (b :: COLLAGE p) (c :: COLLAGE p) (a :: COLLAGE p). Collage b c -> Collage a b -> Collage a c Source Comments #
Ok cs p => Promonad (Free :: FREE cs p -> FREE cs p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Free Methods id :: forall (a :: FREE cs p). Ob a => Free a a Source Comments # (.) :: forall (b :: FREE cs p) (c :: FREE cs p) (a :: FREE cs p). Free b c -> Free a b -> Free a c Source Comments #
(Bicategory kk, Ob0 kk k) => Promonad (Endo :: ENDO kk k -> ENDO kk k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Endo Methods id :: forall (a :: ENDO kk k). Ob a => Endo a a Source Comments # (.) :: forall (b :: ENDO kk k) (c :: ENDO kk k) (a :: ENDO kk k). Endo b c -> Endo a b -> Endo a c Source Comments #
Promonad (Bidiscrete :: DiscreteK ob j k -> DiscreteK ob j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Bidiscrete Methods id :: forall (a :: DiscreteK ob j k). Ob a => Bidiscrete a a Source Comments # (.) :: forall (b :: DiscreteK ob j k) (c0 :: DiscreteK ob j k) (a :: DiscreteK ob j k). Bidiscrete b c0 -> Bidiscrete a b -> Bidiscrete a c0 Source Comments #
CategoryOf (kk j k2) => Promonad (Co :: COK kk j k2 -> COK kk j k2 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Co Methods id :: forall (a :: COK kk j k2). Ob a => Co a a Source Comments # (.) :: forall (b :: COK kk j k2) (c :: COK kk j k2) (a :: COK kk j k2). Co b c -> Co a b -> Co a c Source Comments #
CategoryOf (kk k2 j) => Promonad (Op :: OPK kk j k2 -> OPK kk j k2 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Op Methods id :: forall (a :: OPK kk j k2). Ob a => Op a a Source Comments # (.) :: forall (b :: OPK kk j k2) (c :: OPK kk j k2) (a :: OPK kk j k2). Op b c -> Op a b -> Op a c Source Comments #
(CategoryOf (kk j k2), Bicategory kk) => Promonad (Strictified :: Path kk j k2 -> Path kk j k2 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Strictified Methods id :: forall (a :: Path kk j k2). Ob a => Strictified a a Source Comments # (.) :: forall (b :: Path kk j k2) (c :: Path kk j k2) (a :: Path kk j k2). Strictified b c -> Strictified a b -> Strictified a c Source Comments #
MonoidalAction m k => Promonad (StT :: STT m k i j -> STT m k i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Equipment.Stateful Methods id :: forall (a :: STT m k i j). Ob a => StT a a Source Comments # (.) :: forall (b :: STT m k i j) (c :: STT m k i j) (a :: STT m k i j). StT b c -> StT a b -> StT a c Source Comments #
IsChart m c d => Promonad (ChartCat :: CHART m c d -> CHART m c d -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods id :: forall (a :: CHART m c d). Ob a => ChartCat a a Source Comments # (.) :: forall (b :: CHART m c d) (c0 :: CHART m c d) (a :: CHART m c d). ChartCat b c0 -> ChartCat a b -> ChartCat a c0 Source Comments #
IsOptic m c d => Promonad (OpticCat :: OPTIC m c d -> OPTIC m c d -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods id :: forall (a :: OPTIC m c d). Ob a => OpticCat a a Source Comments # (.) :: forall (b :: OPTIC m c d) (c0 :: OPTIC m c d) (a :: OPTIC m c d). OpticCat b c0 -> OpticCat a b -> OpticCat a c0 Source Comments #
Promonad ((~>) :: CAT (kk i j)) => Promonad (HomW :: HK kk i j -> HK kk i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Hom Methods id :: forall (a :: HK kk i j). Ob a => HomW a a Source Comments # (.) :: forall (b :: HK kk i j) (c :: HK kk i j) (a :: HK kk i j). HomW b c -> HomW a b -> HomW a c Source Comments #
Promonad ((~>) :: CAT (kk i j)) => Promonad (Sub :: SUBCAT tag kk i j -> SUBCAT tag kk i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Sub Methods id :: forall (a :: SUBCAT tag kk i j). Ob a => Sub a a Source Comments # (.) :: forall (b :: SUBCAT tag kk i j) (c :: SUBCAT tag kk i j) (a :: SUBCAT tag kk i j). Sub b c -> Sub a b -> Sub a c Source Comments #
CategoryOf (kk i j) => Promonad (W :: WKK kk i j -> WKK kk i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Equipment.BiAsEquipment Methods id :: forall (a :: WKK kk i j). Ob a => W a a Source Comments # (.) :: forall (b :: WKK kk i j) (c :: WKK kk i j) (a :: WKK kk i j). W b c -> W a b -> W a c Source Comments #
CategoryOf (kk i j) => Promonad (Q2 :: QKK kk i j -> QKK kk i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Equipment.Quintet Methods id :: forall (a :: QKK kk i j). Ob a => Q2 a a Source Comments # (.) :: forall (b :: QKK kk i j) (c :: QKK kk i j) (a :: QKK kk i j). Q2 b c -> Q2 a b -> Q2 a c Source Comments #
(CategoryOf (jj (Fst ik) (Fst jl)), CategoryOf (kk (Snd ik) (Snd jl))) => Promonad (Prod :: PRODK jj kk ik jl -> PRODK jj kk ik jl -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Product Methods id :: forall (a :: PRODK jj kk ik jl). Ob a => Prod a a Source Comments # (.) :: forall (b :: PRODK jj kk ik jl) (c :: PRODK jj kk ik jl) (a :: PRODK jj kk ik jl). Prod b c -> Prod a b -> Prod a c Source Comments #

class Profunctor p => Procomonad (p :: i +-> i) where Source Comments #

Methods

extract :: p :~> ((~>) :: CAT i) Source Comments #

duplicate :: p :~> (p :.: p) Source Comments #

Instances

Instances details

CategoryOf k => Procomonad (Fold :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Fold Methods extract :: (Fold :: k -> k -> Type) :~> ((~>) :: CAT k) Source Comments # duplicate :: (Fold :: k -> k -> Type) :~> ((Fold :: k -> k -> Type) :.: (Fold :: k -> k -> Type)) Source Comments #
CategoryOf k => Procomonad (Id :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad Methods extract :: (Id :: k -> k -> Type) :~> ((~>) :: CAT k) Source Comments # duplicate :: (Id :: k -> k -> Type) :~> ((Id :: k -> k -> Type) :.: (Id :: k -> k -> Type)) Source Comments #
Monad m => Procomonad (Costar (Prelude m) :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Costar Methods extract :: Costar (Prelude m) :~> ((~>) :: CAT Type) Source Comments # duplicate :: Costar (Prelude m) :~> (Costar (Prelude m) :.: Costar (Prelude m)) Source Comments #
(Monoid r, MonoidalAction m k) => Procomonad (Reader ('OP r) :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Reader Methods extract :: (Reader ('OP r) :: k -> k -> Type) :~> ((~>) :: CAT k) Source Comments # duplicate :: (Reader ('OP r) :: k -> k -> Type) :~> ((Reader ('OP r) :: k -> k -> Type) :.: (Reader ('OP r) :: k -> k -> Type)) Source Comments #
(Comonoid w, MonoidalAction m k) => Procomonad (Writer w :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Writer Methods extract :: (Writer w :: k -> k -> Type) :~> ((~>) :: CAT k) Source Comments # duplicate :: (Writer w :: k -> k -> Type) :~> ((Writer w :: k -> k -> Type) :.: (Writer w :: k -> k -> Type)) Source Comments #
Adjunction p q => Procomonad (p :.: q :: i -> i -> Type) Source Comments #
Instance details Defined in Proarrow.Adjunction Methods extract :: (p :.: q) :~> ((~>) :: CAT i) Source Comments # duplicate :: (p :.: q) :~> ((p :.: q) :.: (p :.: q)) Source Comments #