Safe Haskell	None
Language	GHC2024

Proarrow

Synopsis

module Proarrow.Category
module Proarrow.Functor
module Proarrow.Monoid
module Proarrow.Object
module Proarrow.Profunctor
module Proarrow.Universal
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

Documentation

module Proarrow.Category

module Proarrow.Functor

module Proarrow.Monoid

module Proarrow.Object

module Proarrow.Profunctor

module Proarrow.Universal

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

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

This is also known as a category structure, or an identity-on-objects functor.

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 Github #

Identity morphisms.

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

Composition (note the parameter order matches function composition).

Instances

Instances details

Promonad Simplex Source Github #
Instance details Defined in Proarrow.Category.Instance.Simplex Methods id :: forall (a :: Nat). Ob a => Simplex a a Source Github # (.) :: forall (b :: Nat) (c :: Nat) (a :: Nat). Simplex b c -> Simplex a b -> Simplex a c Source Github #
Promonad ZX Source Github #
Instance details Defined in Proarrow.Category.Instance.ZX Methods id :: forall (a :: Nat). Ob a => ZX a a Source Github # (.) :: forall (b :: Nat) (c :: Nat) (a :: Nat). ZX b c -> ZX a b -> ZX a c Source Github #
Promonad Booleans Source Github #
Instance details Defined in Proarrow.Category.Instance.Bool Methods id :: forall (a :: BOOL). Ob a => Booleans a a Source Github # (.) :: forall (b :: BOOL) (c :: BOOL) (a :: BOOL). Booleans b c -> Booleans a b -> Booleans a c Source Github #
Promonad Cat Source Github #
Instance details Defined in Proarrow.Category.Instance.Cat Methods id :: forall (a :: KIND). Ob a => Cat a a Source Github # (.) :: forall (b :: KIND) (c :: KIND) (a :: KIND). Cat b c -> Cat a b -> Cat a c Source Github #
Promonad (:-) Source Github #
Instance details Defined in Proarrow.Category.Instance.Constraint Methods id :: forall (a :: CONSTRAINT). Ob a => a :- a Source Github # (.) :: forall (b :: CONSTRAINT) (c :: CONSTRAINT) (a :: CONSTRAINT). (b :- c) -> (a :- b) -> a :- c Source Github #
Promonad GTE Source Github #
Instance details Defined in Proarrow.Category.Instance.Cost Methods id :: forall (a :: COST). Ob a => GTE a a Source Github # (.) :: forall (b :: COST) (c :: COST) (a :: COST). GTE b c -> GTE a b -> GTE a c Source Github #
Promonad FinRel Source Github #
Instance details Defined in Proarrow.Category.Instance.FinRel Methods id :: forall (a :: FINREL). Ob a => FinRel a a Source Github # (.) :: forall (b :: FINREL) (c :: FINREL) (a :: FINREL). FinRel b c -> FinRel a b -> FinRel a c Source Github #
Promonad FinSet Source Github #
Instance details Defined in Proarrow.Category.Instance.FinSet Methods id :: forall (a :: FINSET). Ob a => FinSet a a Source Github # (.) :: forall (b :: FINSET) (c :: FINSET) (a :: FINSET). FinSet b c -> FinSet a b -> FinSet a c Source Github #
Promonad Linear Source Github #
Instance details Defined in Proarrow.Category.Instance.Linear Methods id :: forall (a :: LINEAR). Ob a => Linear a a Source Github # (.) :: forall (b :: LINEAR) (c :: LINEAR) (a :: LINEAR). Linear b c -> Linear a b -> Linear a c Source Github #
Promonad Pointed Source Github #
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods id :: forall (a :: POINTED). Ob a => Pointed a a Source Github # (.) :: forall (b :: POINTED) (c :: POINTED) (a :: POINTED). Pointed b c -> Pointed a b -> Pointed a c Source Github #
Promonad Zero Source Github #
Instance details Defined in Proarrow.Category.Instance.Zero Methods id :: forall (a :: VOID). Ob a => Zero a a Source Github # (.) :: forall (b :: VOID) (c :: VOID) (a :: VOID). Zero b c -> Zero a b -> Zero a c Source Github #
Promonad Dot Source Github #
Instance details Defined in Proarrow.Tools.Diagrams.Dot Methods id :: forall (a :: DOT). Ob a => Dot a a Source Github # (.) :: forall (b :: DOT) (c :: DOT) (a :: DOT). Dot b c -> Dot a b -> Dot a c Source Github #
Promonad Unit Source Github #
Instance details Defined in Proarrow.Category.Instance.Unit Methods id :: forall (a :: ()). Ob a => Unit a a Source Github # (.) :: forall (b :: ()) (c :: ()) (a :: ()). Unit b c -> Unit a b -> Unit a c Source Github #
Promonad SymRefl Source Github #
Instance details Defined in Proarrow.Tools.Diagrams.Dot Methods id :: forall (a :: Symbol). Ob a => SymRefl a a Source Github # (.) :: forall (b :: Symbol) (c :: Symbol) (a :: Symbol). SymRefl b c -> SymRefl a b -> SymRefl a c Source Github #
Monad m => Promonad (Kleisli m :: Type -> Type -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Arrow Methods id :: Ob a => Kleisli m a a Source Github # (.) :: Kleisli m b c -> Kleisli m a b -> Kleisli m a c Source Github #
Comonoid w => Promonad (ComonoidAsCat w :: Type -> Type -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: Ob a => ComonoidAsCat w a a Source Github # (.) :: ComonoidAsCat w b c -> ComonoidAsCat w a b -> ComonoidAsCat w a c Source Github #
Arrow arr => Promonad (Arr arr :: Type -> Type -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Arrow Methods id :: Ob a => Arr arr a a Source Github # (.) :: Arr arr b c -> Arr arr a b -> Arr arr a c Source Github #
CategoryOf k => Promonad (Id :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Identity Methods id :: forall (a :: k). Ob a => Id a a Source Github # (.) :: forall (b :: k) (c :: k) (a :: k). Id b c -> Id a b -> Id a c Source Github #
Promonad (->) Source Github #
Instance details Defined in Proarrow.Core Methods id :: Ob a => a -> a Source Github # (.) :: (b -> c) -> (a -> b) -> a -> c Source Github #
Promonad p => Promonad (Fix p :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Fix Methods id :: forall (a :: k). Ob a => Fix p a a Source Github # (.) :: forall (b :: k) (c :: k) (a :: k). Fix p b c -> Fix p a b -> Fix p a c Source Github #
Profunctor p => Promonad (FreePromonad p :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Free Methods id :: forall (a :: k). Ob a => FreePromonad p a a Source Github # (.) :: forall (b :: k) (c :: k) (a :: k). FreePromonad p b c -> FreePromonad p a b -> FreePromonad p a c Source Github #
CategoryOf k => Promonad (TerminalProfunctor :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Terminal Methods id :: forall (a :: k). Ob a => TerminalProfunctor a a Source Github # (.) :: forall (b :: k) (c :: k) (a :: k). TerminalProfunctor b c -> TerminalProfunctor a b -> TerminalProfunctor a c Source Github #
CategoryOf k => Promonad (Cont r :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Promonad.Cont Methods id :: forall (a :: k). Ob a => Cont r a a Source Github # (.) :: forall (b :: k) (c :: k) (a :: k). Cont r b c -> Cont r a b -> Cont r a c Source Github #
(Comonoid r, Monoidal k) => Promonad (Reader ('OP r) :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Promonad.Reader Methods id :: forall (a :: k). Ob a => Reader ('OP r) a a Source Github # (.) :: forall (b :: k) (c :: k) (a :: k). Reader ('OP r) b c -> Reader ('OP r) a b -> Reader ('OP r) a c Source Github #
(Monoidal k, Ob s) => Promonad (State s :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Promonad.State Methods id :: forall (a :: k). Ob a => State s a a Source Github # (.) :: forall (b :: k) (c :: k) (a :: k). State s b c -> State s a b -> State s a c Source Github #
(Monoid w, Monoidal k) => Promonad (Writer w :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Promonad.Writer Methods id :: forall (a :: k). Ob a => Writer w a a Source Github # (.) :: forall (b :: k) (c :: k) (a :: k). Writer w b c -> Writer w a b -> Writer w a c Source Github #
Monad m => Promonad (Star (Prelude m) :: Type -> Type -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Star Methods id :: Ob a => Star (Prelude m) a a Source Github # (.) :: Star (Prelude m) b c -> Star (Prelude m) a b -> Star (Prelude m) a c Source Github #
(Monoid c, CategoryOf k) => Promonad (HaskValue c :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.HaskValue Methods id :: forall (a :: k). Ob a => HaskValue c a a Source Github # (.) :: forall (b :: k) (c0 :: k) (a :: k). HaskValue c b c0 -> HaskValue c a b -> HaskValue c a c0 Source Github #
Promonad p => Promonad (Wrapped p :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Wrapped Methods id :: forall (a :: k). Ob a => Wrapped p a a Source Github # (.) :: forall (b :: k) (c :: k) (a :: k). Wrapped p b c -> Wrapped p a b -> Wrapped p a c Source Github #
Proadjunction p q => Promonad (q :.: p :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Adjunction Methods id :: forall (a :: k). Ob a => (q :.: p) a a Source Github # (.) :: forall (b :: k) (c :: k) (a :: k). (q :.: p) b c -> (q :.: p) a b -> (q :.: p) a c Source Github #
(p ~ j, Profunctor p) => Promonad (Ran ('OP j) p :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Ran Methods id :: forall (a :: k). Ob a => Ran ('OP j) p a a Source Github # (.) :: 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 Github #
(p ~ j, Profunctor p) => Promonad (Rift ('OP j) p :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Rift Methods id :: forall (a :: k). Ob a => Rift ('OP j) p a a Source Github # (.) :: 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 Github #
HasPushouts k => Promonad (Cospan :: COSPAN k -> COSPAN k -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Cospan Methods id :: forall (a :: COSPAN k). Ob a => Cospan a a Source Github # (.) :: forall (b :: COSPAN k) (c :: COSPAN k) (a :: COSPAN k). Cospan b c -> Cospan a b -> Cospan a c Source Github #
Promonad (Codiscrete :: CODISCRETE k -> CODISCRETE k -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Discrete Methods id :: forall (a :: CODISCRETE k). Ob a => Codiscrete a a Source Github # (.) :: forall (b :: CODISCRETE k) (c :: CODISCRETE k) (a :: CODISCRETE k). Codiscrete b c -> Codiscrete a b -> Codiscrete a c Source Github #
Promonad (Discrete :: DISCRETE k -> DISCRETE k -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Discrete Methods id :: forall (a :: DISCRETE k). Ob a => Discrete a a Source Github # (.) :: forall (b :: DISCRETE k) (c :: DISCRETE k) (a :: DISCRETE k). Discrete b c -> Discrete a b -> Discrete a c Source Github #
CategoryOf k => Promonad (Fam :: FAM k -> FAM k -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Fam Methods id :: forall (a :: FAM k). Ob a => Fam a a Source Github # (.) :: forall (b :: FAM k) (c :: FAM k) (a :: FAM k). Fam b c -> Fam a b -> Fam a c Source Github #
Promonad (LTE :: FIN n -> FIN n -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Fin Methods id :: forall (a :: FIN n). Ob a => LTE a a Source Github # (.) :: forall (b :: FIN n) (c :: FIN n) (a :: FIN n). LTE b c -> LTE a b -> LTE a c Source Github #
TracedMonoidal k => Promonad (IntConstruction :: INT k -> INT k -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.IntConstruction Methods id :: forall (a :: INT k). Ob a => IntConstruction a a Source Github # (.) :: forall (b :: INT k) (c :: INT k) (a :: INT k). IntConstruction b c -> IntConstruction a b -> IntConstruction a c Source Github #
Num a => Promonad (Mat :: MatK a -> MatK a -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Mat Methods id :: forall (a0 :: MatK a). Ob a0 => Mat a0 a0 Source Github # (.) :: forall (b :: MatK a) (c :: MatK a) (a0 :: MatK a). Mat b c -> Mat a0 b -> Mat a0 c Source Github #
HasPullbacks k => Promonad (Span :: SPAN k -> SPAN k -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Span Methods id :: forall (a :: SPAN k). Ob a => Span a a Source Github # (.) :: forall (b :: SPAN k) (c :: SPAN k) (a :: SPAN k). Span b c -> Span a b -> Span a c Source Github #
Monoidal k => Promonad (Strictified :: [k] -> [k] -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Strictified Methods id :: forall (a :: [k]). Ob a => Strictified a a Source Github # (.) :: forall (b :: [k]) (c :: [k]) (a :: [k]). Strictified b c -> Strictified a b -> Strictified a c Source Github #
Promonad p => Promonad (Rev p :: REV j -> REV j -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Rev Methods id :: forall (a :: REV j). Ob a => Rev p a a Source Github # (.) :: forall (b :: REV j) (c :: REV j) (a :: REV j). Rev p b c -> Rev p a b -> Rev p a c Source Github #
Promonad c => Promonad (Op c :: OPPOSITE j -> OPPOSITE j -> Type) Source Github #
Instance details Defined in Proarrow.Category.Opposite Methods id :: forall (a :: OPPOSITE j). Ob a => Op c a a Source Github # (.) :: forall (b :: OPPOSITE j) (c0 :: OPPOSITE j) (a :: OPPOSITE j). Op c b c0 -> Op c a b -> Op c a c0 Source Github #
Promonad p => Promonad (Coprod p :: COPROD j -> COPROD j -> Type) Source Github #
Instance details Defined in Proarrow.Object.BinaryCoproduct Methods id :: forall (a :: COPROD j). Ob a => Coprod p a a Source Github # (.) :: forall (b :: COPROD j) (c :: COPROD j) (a :: COPROD j). Coprod p b c -> Coprod p a b -> Coprod p a c Source Github #
Promonad p => Promonad (Prod p :: PROD j -> PROD j -> Type) Source Github #
Instance details Defined in Proarrow.Object.BinaryProduct Methods id :: forall (a :: PROD j). Ob a => Prod p a a Source Github # (.) :: forall (b :: PROD j) (c :: PROD j) (a :: PROD j). Prod p b c -> Prod p a b -> Prod p a c Source Github #
Promonad p => Promonad (List p :: LIST j -> LIST j -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.List Methods id :: forall (a :: LIST j). Ob a => List p a a Source Github # (.) :: forall (b :: LIST j) (c :: LIST j) (a :: LIST j). List p b c -> List p a b -> List p a c Source Github #
Promonad (Adj :: ADJK a b -> ADJK a b -> Type) Source Github #
Instance details Defined in Proarrow.Category.Bicategory.Adj Methods id :: forall (a0 :: ADJK a b). Ob a0 => Adj a0 a0 Source Github # (.) :: forall (b0 :: ADJK a b) (c :: ADJK a b) (a0 :: ADJK a b). Adj b0 c -> Adj a0 b0 -> Adj a0 c Source Github #
Promonad (Prof :: PROFK j k -> PROFK j k -> Type) Source Github #
Instance details Defined in Proarrow.Category.Bicategory.Prof Methods id :: forall (a :: PROFK j k). Ob a => Prof a a Source Github # (.) :: forall (b :: PROFK j k) (c :: PROFK j k) (a :: PROFK j k). Prof b c -> Prof a b -> Prof a c Source Github #
Promonad p => Promonad (Kleisli :: KLEISLI p -> KLEISLI p -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods id :: forall (a :: KLEISLI p). Ob a => Kleisli a a Source Github # (.) :: forall (b :: KLEISLI p) (c :: KLEISLI p) (a :: KLEISLI p). Kleisli b c -> Kleisli a b -> Kleisli a c Source Github #
Promonad (Nat' :: (j .-> k) -> (j .-> k) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: forall (a :: j .-> k). Ob a => Nat' a a Source Github # (.) :: forall (b :: j .-> k) (c :: j .-> k) (a :: j .-> k). Nat' b c -> Nat' a b -> Nat' a c Source Github #
Promonad (Terminal :: Unit '() '() -> Unit '() '() -> Type) Source Github #
Instance details Defined in Proarrow.Category.Bicategory.Terminal Methods id :: forall (a :: Unit '() '()). Ob a => Terminal a a Source Github # (.) :: forall (b :: Unit '() '()) (c :: Unit '() '()) (a :: Unit '() '()). Terminal b c -> Terminal a b -> Terminal a c Source Github #
Promonad (Prof :: (j +-> k) -> (j +-> k) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Prof Methods id :: forall (a :: j +-> k). Ob a => Prof a a Source Github # (.) :: forall (b :: j +-> k) (c :: j +-> k) (a :: j +-> k). Prof b c -> Prof a b -> Prof a c Source Github #
Promonad (Nat :: (j -> Type) -> (j -> Type) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: forall (a :: j -> Type). Ob a => Nat a a Source Github # (.) :: forall (b :: j -> Type) (c :: j -> Type) (a :: j -> Type). Nat b c -> Nat a b -> Nat a c Source Github #
Promonad (Nat :: (k1 -> k2 -> k3 -> k4 -> Type) -> (k1 -> k2 -> k3 -> k4 -> Type) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: forall (a :: k1 -> k2 -> k3 -> k4 -> Type). Ob a => Nat a a Source Github # (.) :: 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 Github #
Promonad (Nat :: (k1 -> k2 -> k3 -> Type) -> (k1 -> k2 -> k3 -> Type) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: forall (a :: k1 -> k2 -> k3 -> Type). Ob a => Nat a a Source Github # (.) :: 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 Github #
Promonad p => Promonad (Sub p :: SUBCAT ob -> SUBCAT ob -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Sub Methods id :: forall (a :: SUBCAT ob). Ob a => Sub p a a Source Github # (.) :: forall (b :: SUBCAT ob) (c :: SUBCAT ob) (a :: SUBCAT ob). Sub p b c -> Sub p a b -> Sub p a c Source Github #
Promonad (Costar (Coyoneda :: (j +-> k) -> k -> j -> Type) :: (j +-> k) -> (k -> j -> Type) -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Coyoneda Methods id :: forall (a :: j +-> k). Ob a => Costar (Coyoneda :: (j +-> k) -> k -> j -> Type) a a Source Github # (.) :: forall (b :: j +-> k) (c :: j +-> k) (a :: j +-> k). Costar (Coyoneda :: (j +-> k) -> k -> j -> Type) b c -> Costar (Coyoneda :: (j +-> k) -> k -> j -> Type) a b -> Costar (Coyoneda :: (j +-> k) -> k -> j -> Type) a c Source Github #
Profunctor p => Promonad (Costar ((:*:) p) :: (j +-> k) -> (k -> j -> Type) -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Costar Methods id :: forall (a :: j +-> k). Ob a => Costar ((::) p) a a Source Github # (.) :: forall (b :: j +-> k) (c :: j +-> k) (a :: j +-> k). Costar ((::) p) b c -> Costar ((::) p) a b -> Costar ((::) p) a c Source Github #
Promonad (Costar (Yoneda :: (j +-> k) -> k -> j -> Type) :: (j +-> k) -> (k -> j -> Type) -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Yoneda Methods id :: forall (a :: j +-> k). Ob a => Costar (Yoneda :: (j +-> k) -> k -> j -> Type) a a Source Github # (.) :: forall (b :: j +-> k) (c :: j +-> k) (a :: j +-> k). Costar (Yoneda :: (j +-> k) -> k -> j -> Type) b c -> Costar (Yoneda :: (j +-> k) -> k -> j -> Type) a b -> Costar (Yoneda :: (j +-> k) -> k -> j -> Type) a c Source Github #
Procomonad j => Promonad (Star (Ran ('OP j) :: (i +-> k) -> k -> i -> Type) :: (k -> i -> Type) -> (i +-> k) -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Ran Methods id :: forall (a :: k -> i -> Type). Ob a => Star (Ran ('OP j) :: (i +-> k) -> k -> i -> Type) a a Source Github # (.) :: forall (b :: k -> i -> Type) (c :: k -> i -> Type) (a :: k -> i -> Type). Star (Ran ('OP j) :: (i +-> k) -> k -> i -> Type) b c -> Star (Ran ('OP j) :: (i +-> k) -> k -> i -> Type) a b -> Star (Ran ('OP j) :: (i +-> k) -> k -> i -> Type) a c Source Github #
Profunctor p => Promonad (Star ((:+:) p) :: (k -> j -> Type) -> (j +-> k) -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Star Methods id :: forall (a :: k -> j -> Type). Ob a => Star ((:+:) p) a a Source Github # (.) :: forall (b :: k -> j -> Type) (c :: k -> j -> Type) (a :: k -> j -> Type). Star ((:+:) p) b c -> Star ((:+:) p) a b -> Star ((:+:) p) a c Source Github #
Promonad (Star (Coyoneda :: (j +-> k) -> k -> j -> Type) :: (k -> j -> Type) -> (j +-> k) -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Coyoneda Methods id :: forall (a :: k -> j -> Type). Ob a => Star (Coyoneda :: (j +-> k) -> k -> j -> Type) a a Source Github # (.) :: forall (b :: k -> j -> Type) (c :: k -> j -> Type) (a :: k -> j -> Type). Star (Coyoneda :: (j +-> k) -> k -> j -> Type) b c -> Star (Coyoneda :: (j +-> k) -> k -> j -> Type) a b -> Star (Coyoneda :: (j +-> k) -> k -> j -> Type) a c Source Github #
Promonad (Star (Yoneda :: (j +-> k) -> k -> j -> Type) :: (k -> j -> Type) -> (j +-> k) -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Yoneda Methods id :: forall (a :: k -> j -> Type). Ob a => Star (Yoneda :: (j +-> k) -> k -> j -> Type) a a Source Github # (.) :: forall (b :: k -> j -> Type) (c :: k -> j -> Type) (a :: k -> j -> Type). Star (Yoneda :: (j +-> k) -> k -> j -> Type) b c -> Star (Yoneda :: (j +-> k) -> k -> j -> Type) a b -> Star (Yoneda :: (j +-> k) -> k -> j -> Type) a c Source Github #
Procomonad j2 => Promonad (Star (Rift ('OP j2) :: (j1 +-> k) -> k -> j1 -> Type) :: (k -> j1 -> Type) -> (j1 +-> k) -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Rift Methods id :: forall (a :: k -> j1 -> Type). Ob a => Star (Rift ('OP j2) :: (j1 +-> k) -> k -> j1 -> Type) a a Source Github # (.) :: forall (b :: k -> j1 -> Type) (c :: k -> j1 -> Type) (a :: k -> j1 -> Type). Star (Rift ('OP j2) :: (j1 +-> k) -> k -> j1 -> Type) b c -> Star (Rift ('OP j2) :: (j1 +-> k) -> k -> j1 -> Type) a b -> Star (Rift ('OP j2) :: (j1 +-> k) -> k -> j1 -> Type) a c Source Github #
(Applicative f, Promonad p) => Promonad (Ap p :: AP f k -> AP f k -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Ap Methods id :: forall (a :: AP f k). Ob a => Ap p a a Source Github # (.) :: 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 Github #
Monoid m => Promonad (Mon :: MONOIDK m -> MONOIDK m -> Type) Source Github #
Instance details Defined in Proarrow.Monoid Methods id :: forall (a :: MONOIDK m). Ob a => Mon a a Source Github # (.) :: forall (b :: MONOIDK m) (c :: MONOIDK m) (a :: MONOIDK m). Mon b c -> Mon a b -> Mon a c Source Github #
(Promonad p, Promonad q) => Promonad (p :++: q :: COPRODUCT j1 j2 -> COPRODUCT j1 j2 -> Type) Source Github #	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 Github # (.) :: 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 Github #
(Promonad p, Promonad q) => Promonad (p :**: q :: (j1, j2) -> (j1, j2) -> Type) Source Github #	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 Github # (.) :: forall (b :: (j1, j2)) (c :: (j1, j2)) (a :: (j1, j2)). (p :: q) b c -> (p :: q) a b -> (p :: q) a c Source Github #
(CategoryOf k, Ob i, Ob j) => Promonad (Category :: PLAINK k i j -> PLAINK k i j -> Type) Source Github #
Instance details Defined in Proarrow.Category.Bicategory.CategoryAsBi Methods id :: forall (a :: PLAINK k i j). Ob a => Category a a Source Github # (.) :: 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 Github #
CategoryOf k => Promonad (Mon2 :: MonK k i j -> MonK k i j -> Type) Source Github #
Instance details Defined in Proarrow.Category.Bicategory.MonoidalAsBi Methods id :: forall (a :: MonK k i j). Ob a => Mon2 a a Source Github # (.) :: 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 Github #
SelfAction k => Promonad (StT :: STT' k i j -> STT' k i j -> Type) Source Github #
Instance details Defined in Proarrow.Category.Equipment.Stateful Methods id :: forall (a :: STT' k i j). Ob a => StT a a Source Github # (.) :: forall (b :: STT' k i j) (c :: STT' k i j) (a :: STT' k i j). StT b c -> StT a b -> StT a c Source Github #
Profunctor p => Promonad (Collage :: COLLAGE p -> COLLAGE p -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Collage Methods id :: forall (a :: COLLAGE p). Ob a => Collage a a Source Github # (.) :: forall (b :: COLLAGE p) (c :: COLLAGE p) (a :: COLLAGE p). Collage b c -> Collage a b -> Collage a c Source Github #
Adjunction adj => Promonad (Duploid :: DUPLOID adj -> DUPLOID adj -> Type) Source Github #	ATTENTION: a duploid is not associative, so not really a promonad/category!
Instance details Defined in Proarrow.Category.Instance.Duploid Methods id :: forall (a :: DUPLOID adj). Ob a => Duploid a a Source Github # (.) :: forall (b :: DUPLOID adj) (c :: DUPLOID adj) (a :: DUPLOID adj). Duploid b c -> Duploid a b -> Duploid a c Source Github #
Ok cs p => Promonad (Free :: FREE cs p -> FREE cs p -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Free Methods id :: forall (a :: FREE cs p). Ob a => Free a a Source Github # (.) :: forall (b :: FREE cs p) (c :: FREE cs p) (a :: FREE cs p). Free b c -> Free a b -> Free a c Source Github #
(Bicategory kk, Ob0 kk k) => Promonad (Endo :: ENDO kk k -> ENDO kk k -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Endo Methods id :: forall (a :: ENDO kk k). Ob a => Endo a a Source Github # (.) :: forall (b :: ENDO kk k) (c :: ENDO kk k) (a :: ENDO kk k). Endo b c -> Endo a b -> Endo a c Source Github #
(CategoryOf j, CategoryOf k) => Promonad (Optic_ :: OPTIC j k c -> OPTIC j k c -> Type) Source Github #
Instance details Defined in Proarrow.Optic Methods id :: forall (a :: OPTIC j k c). Ob a => Optic_ a a Source Github # (.) :: forall (b :: OPTIC j k c) (c0 :: OPTIC j k c) (a :: OPTIC j k c). Optic_ b c0 -> Optic_ a b -> Optic_ a c0 Source Github #
ThinProfunctor p => Promonad (Graph :: GRAPH p -> GRAPH p -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.Graph Methods id :: forall (a :: GRAPH p). Ob a => Graph a a Source Github # (.) :: forall (b :: GRAPH p) (c :: GRAPH p) (a :: GRAPH p). Graph b c -> Graph a b -> Graph a c Source Github #
Promonad (Bidiscrete :: DiscreteK ob j k -> DiscreteK ob j k -> Type) Source Github #
Instance details Defined in Proarrow.Category.Bicategory.Bidiscrete Methods id :: forall (a :: DiscreteK ob j k). Ob a => Bidiscrete a a Source Github # (.) :: 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 Github #
CategoryOf (kk j k2) => Promonad (Co :: COK kk j k2 -> COK kk j k2 -> Type) Source Github #
Instance details Defined in Proarrow.Category.Bicategory.Co Methods id :: forall (a :: COK kk j k2). Ob a => Co a a Source Github # (.) :: 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 Github #
CategoryOf (kk k2 j) => Promonad (Op :: OPK kk j k2 -> OPK kk j k2 -> Type) Source Github #
Instance details Defined in Proarrow.Category.Bicategory.Op Methods id :: forall (a :: OPK kk j k2). Ob a => Op a a Source Github # (.) :: 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 Github #
(CategoryOf (kk j k2), Bicategory kk) => Promonad (Strictified :: Path kk j k2 -> Path kk j k2 -> Type) Source Github #
Instance details Defined in Proarrow.Category.Bicategory.Strictified Methods id :: forall (a :: Path kk j k2). Ob a => Strictified a a Source Github # (.) :: 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 Github #
Promonad ((~>) :: CAT (kk i j)) => Promonad (HomW :: HK kk i j -> HK kk i j -> Type) Source Github #
Instance details Defined in Proarrow.Category.Bicategory.Hom Methods id :: forall (a :: HK kk i j). Ob a => HomW a a Source Github # (.) :: 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 Github #
Promonad ((~>) :: CAT (kk i j)) => Promonad (Sub :: SUBCAT tag kk i j -> SUBCAT tag kk i j -> Type) Source Github #
Instance details Defined in Proarrow.Category.Bicategory.Sub Methods id :: forall (a :: SUBCAT tag kk i j). Ob a => Sub a a Source Github # (.) :: 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 Github #
(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 Github #
Instance details Defined in Proarrow.Category.Bicategory.Product Methods id :: forall (a :: PRODK jj kk ik jl). Ob a => Prod a a Source Github # (.) :: 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 Github #