Safe Haskell	None
Language	GHC2024

Proarrow.Core

Contents

Type Infrastructure
- Basic Type Definitions
- Universal Constraint
Category Infrastructure
- CategoryOf Class
- Category Class
Profunctors
Promonads
- Promonad Class
- Promonad Utilities
Object Identities
Type Family Utilities
- Kind Unwrapping

Description

Synopsis

type (+->) j k = k -> j -> Type
type CAT k = k +-> k
type OB k = k -> Constraint
type Kind = Type
class Any (a :: k)
class Promonad ((~>) :: CAT k) => CategoryOf k where
- type (~>) :: CAT k
- type Ob (a :: k)
class (Promonad cat, CategoryOf k, cat ~ ((~>) :: CAT k)) => Category (cat :: CAT k)
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
type (:~>) (p :: k -> k1 -> Type) (q :: k -> k1 -> Type) = forall (a :: k) (b :: k1). p a b -> q a b
(//) :: forall {k1} {k2} p (a :: k2) (b :: k1) r. Profunctor p => p a b -> ((Ob a, Ob b) => r) -> 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
dimapDefault :: forall {k} p (c :: k) (a :: k) (b :: k) (d :: k). Promonad p => p c a -> p b d -> p a b -> p c d
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
arr :: forall {k} p (a :: k) (b :: k). Promonad p => (a ~> b) -> p a b
type Obj (a :: k) = a ~> a
obj :: forall {k} (a :: k). (CategoryOf k, Ob a) => Obj a
src :: forall {j} {k} (a :: k) (b :: j) p. Profunctor p => p a b -> Obj a
tgt :: forall {k1} {k2} (a :: k2) (b :: k1) p. Profunctor p => p a b -> Obj b
type family UN (w :: j -> k) (wa :: k) :: j
type Is (w :: j -> k) (a :: k) = a ~ w (UN w a)

Type Infrastructure

Basic Type Definitions

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.

type CAT k = k +-> k Source Comments #

The kind of categories on kind k.

type OB k = k -> Constraint Source Comments #

Object constraints for kind k.

type Kind = Type Source Comments #

Alias for Type for clarity in kind signatures.

Universal Constraint

class Any (a :: k) Source Comments #

A constraint that's always satisfied, used as a default when no specific object constraints are needed.

Instances

Instances details

Any (a :: k) Source Comments #
Instance details Defined in Proarrow.Core

Category Infrastructure

CategoryOf Class

class Promonad ((~>) :: CAT k) => CategoryOf k Source Comments #

Establishes that k is a category by specifying the morphism type and object constraints.

Associated Types

type (~>) :: CAT k infixr 0 Source Comments #

The type of morphisms in the category.

type Ob (a :: k) Source Comments #

What constraints objects must satisfy.

type Ob (a :: k) = Any a

Instances

Instances details

CategoryOf Nat Source Comments #

The category of qubits, to implement ZX calculus from quantum computing.

Instance details

Defined in Proarrow.Category.Instance.ZX

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.ZX type (~>) = ZX
type Ob (a :: Nat)
Instance details Defined in Proarrow.Category.Instance.ZX type Ob (a :: Nat) = KnownNat a

CategoryOf BOOL Source Comments #

The category of 2 objects and one arrow between them, a.k.a. the walking arrow.

Instance details

Defined in Proarrow.Category.Instance.Bool

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Bool type (~>) = Booleans
type Ob (b :: BOOL)
Instance details Defined in Proarrow.Category.Instance.Bool type Ob (b :: BOOL) = IsBool b

CategoryOf KIND Source Comments #

The category of categories and profunctors between them.

Instance details

Defined in Proarrow.Category.Instance.Cat

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Cat type (~>) = Cat
type Ob (c :: KIND)
Instance details Defined in Proarrow.Category.Instance.Cat type Ob (c :: KIND) = (Is 'K c, CategoryOf (UN 'K c))

CategoryOf CONSTRAINT Source Comments #

The category of type class constraints. An arrow from constraint a to constraint b | means that a implies b, i.e. if a holds then b holds.

Instance details

Defined in Proarrow.Category.Instance.Constraint

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Constraint type (~>) = (:-)
type Ob (a :: CONSTRAINT)
Instance details Defined in Proarrow.Category.Instance.Constraint type Ob (a :: CONSTRAINT) = Is 'CNSTRNT a

CategoryOf COST Source Comments #

Cost category. Categories enriched in the cost category are lawvere metric spaces.

Instance details

Defined in Proarrow.Category.Instance.Cost

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Cost type (~>) = GTE
type Ob (a :: COST)
Instance details Defined in Proarrow.Category.Instance.Cost type Ob (a :: COST) = IsCost a

CategoryOf LINEAR Source Comments #

Category of linear functions.

Instance details

Defined in Proarrow.Category.Instance.Linear

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Linear type (~>) = Linear
type Ob (a :: LINEAR)
Instance details Defined in Proarrow.Category.Instance.Linear type Ob (a :: LINEAR) = Is 'L a

CategoryOf POINTED Source Comments #

The category of types with an added point and point-preserving morphisms.

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.PointedHask type (~>) = Pointed
type Ob (a :: POINTED)
Instance details Defined in Proarrow.Category.Instance.PointedHask type Ob (a :: POINTED) = a ~ 'P (UN 'P a)

CategoryOf Nat Source Comments #

The (augmented) simplex category is the category of finite ordinals and order preserving maps.

Instance details

Defined in Proarrow.Category.Instance.Simplex

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Simplex type (~>) = Simplex
type Ob (a :: Nat)
Instance details Defined in Proarrow.Category.Instance.Simplex type Ob (a :: Nat) = IsNat a

CategoryOf VOID Source Comments #

The category with no objects, the initial category.

Instance details

Defined in Proarrow.Category.Instance.Zero

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Zero type (~>) = Zero
type Ob (a :: VOID)
Instance details Defined in Proarrow.Category.Instance.Zero type Ob (a :: VOID) = Bottom

CategoryOf () Source Comments #

The category with one object, the terminal category.

Instance details

Defined in Proarrow.Category.Instance.Unit

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Unit type (~>) = Unit
type Ob (a :: ())
Instance details Defined in Proarrow.Category.Instance.Unit type Ob (a :: ()) = a ~ '()

CategoryOf Symbol Source Comments #

Instance details

Defined in Proarrow.Tools.Laws

Associated Types

type (~>)
Instance details Defined in Proarrow.Tools.Laws type (~>) = Sym
type Ob (a :: Symbol)
Instance details Defined in Proarrow.Tools.Laws type Ob (a :: Symbol) = KnownSymbol a

CategoryOf Type Source Comments #

The category of Haskell types (a.k.a Hask), where the arrows are functions.

Instance details

Defined in Proarrow.Core

Associated Types

type (~>)
Instance details Defined in Proarrow.Core type (~>) = (->)
type Ob (a :: Type)
Instance details Defined in Proarrow.Core type Ob (a :: Type) = Any a

CategoryOf (CODISCRETE k) Source Comments #

The codiscrete category has exactly one arrow between every object, every type of kind k is an object.

Instance details

Defined in Proarrow.Category.Instance.Discrete

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Discrete type (~>) = Codiscrete :: CODISCRETE k -> CODISCRETE k -> Type

CategoryOf (DISCRETE k) Source Comments #

The discrete category with only identity arrows, every type of kind k is an object.

Instance details

Defined in Proarrow.Category.Instance.Discrete

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Discrete type (~>) = Discrete :: DISCRETE k -> DISCRETE k -> Type

CategoryOf (FIN n) Source Comments #

The (thin) category of finite ordinals. An arrow from a to b means that a is less than or equal to b.

Instance details

Defined in Proarrow.Category.Instance.Fin

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Fin type (~>) = LTE :: FIN n -> FIN n -> Type

TracedMonoidal k => CategoryOf (INT k) Source Comments #

The Int construction, a.k.a. the geometry of interaction, the free compact closed category on a traced monoidal category.

Instance details

Defined in Proarrow.Category.Instance.IntConstruction

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.IntConstruction type (~>) = IntConstruction :: INT k -> INT k -> Type

Num a => CategoryOf (MatK a) Source Comments #

The category of matrices with entries in a type a, where the objects are natural numbers and the arrows n ~> m are matrices of dimension n by m.

Instance details

Defined in Proarrow.Category.Instance.Mat

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Mat type (~>) = Mat :: MatK a -> MatK a -> Type

CategoryOf k => CategoryOf (REV k) Source Comments #

The reverse of the category of k, i.e. with the tensor flipped.

Instance details

Defined in Proarrow.Category.Monoidal.Rev

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Monoidal.Rev type (~>) = Rev ((~>) :: CAT k)

CategoryOf k => CategoryOf (OPPOSITE k) Source Comments #

The opposite category of the category of k.

Instance details

Defined in Proarrow.Category.Opposite

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Opposite type (~>) = Op ((~>) :: CAT k)

CategoryOf k => CategoryOf (COPROD k) Source Comments #

The same category as the category of k, but with coproducts as the tensor.

Instance details

Defined in Proarrow.Object.BinaryCoproduct

Associated Types

type (~>)
Instance details Defined in Proarrow.Object.BinaryCoproduct type (~>) = Coprod (Id :: k -> k -> Type)

CategoryOf k => CategoryOf (PROD k) Source Comments #

The same category as the category of k, but with products as the tensor.

Instance details

Defined in Proarrow.Object.BinaryProduct

Associated Types

type (~>)
Instance details Defined in Proarrow.Object.BinaryProduct type (~>) = Prod ((~>) :: CAT k)

CategoryOf k => CategoryOf (LIST k) Source Comments #

The category of lists of arrows.

Instance details

Defined in Proarrow.Profunctor.List

Associated Types

type (~>)
Instance details Defined in Proarrow.Profunctor.List type (~>) = List ((~>) :: CAT k)

Monoidal k => CategoryOf [k] Source Comments #

The strictified monoidal category, making the unitors and associators identities.

Instance details

Defined in Proarrow.Category.Monoidal.Strictified

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Monoidal.Strictified type (~>) = Strictified :: [k] -> [k] -> Type

CategoryOf (PROFK j k) Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory.Prof

Associated Types

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

(Applicative f, CategoryOf k) => CategoryOf (AP f k) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Ap

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Ap type (~>) = Ap ((~>) :: CAT k) :: AP f k -> AP f k -> Type

(CategoryOf j, CategoryOf k) => CategoryOf (COPRODUCT j k) Source Comments #

The coproduct of two categories.

Instance details

Defined in Proarrow.Category.Instance.Coproduct

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Coproduct type (~>) = ((~>) :: CAT j) :++: ((~>) :: CAT k)

Promonad p => CategoryOf (KLEISLI p) Source Comments #

Every promonad makes a category.

Instance details

Defined in Proarrow.Category.Instance.Kleisli

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Kleisli type (~>) = Kleisli :: KLEISLI p -> KLEISLI p -> Type

CategoryOf (NatK j k) Source Comments #

The category of functors and natural transformations.

Instance details

Defined in Proarrow.Category.Instance.Nat

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Nat type (~>) = Nat' :: NatK j k -> NatK j k -> Type

CategoryOf k => CategoryOf (SUBCAT ob) Source Comments #

The subcategory with objects with instances of the given constraint ob.

Instance details

Defined in Proarrow.Category.Instance.Sub

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Sub type (~>) = Sub ((~>) :: CAT k) :: SUBCAT ob -> SUBCAT ob -> Type

(j ~ '(), k ~ '()) => CategoryOf (Unit j k) Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory.Terminal

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Bicategory.Terminal type (~>) = Terminal :: Unit j k -> Unit j k -> Type

CategoryOf (j +-> k) Source Comments #

The category of profunctors and natural transformations between them.

Instance details

Defined in Proarrow.Category.Instance.Prof

Associated Types

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

Monoid m => CategoryOf (MONOIDK m) Source Comments #

A monoid as a one object category.

Instance details

Defined in Proarrow.Monoid

Associated Types

type (~>)
Instance details Defined in Proarrow.Monoid type (~>) = Mon :: MONOIDK m -> MONOIDK m -> Type

(CategoryOf k1, CategoryOf k2) => CategoryOf (k1, k2) Source Comments #

The product of two categories.

Instance details

Defined in Proarrow.Category.Instance.Product

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Product type (~>) = ((~>) :: CAT k1) :**: ((~>) :: CAT k2)

CategoryOf (k1 -> k2 -> k3 -> k4 -> Type) Source Comments #

The category of functors with target category k2 -> k3 -> k4 -> Type.

Instance details

Defined in Proarrow.Category.Instance.Nat

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Nat type (~>) = Nat :: (k1 -> k2 -> k3 -> k4 -> Type) -> (k1 -> k2 -> k3 -> k4 -> Type) -> Type

CategoryOf (k1 -> k2 -> k3 -> Type) Source Comments #

The category of functors with target category k2 -> k3 -> Type. Note that CategoryOf (k1 -> k2 -> Type) is reserved for profunctors.

Instance details

Defined in Proarrow.Category.Instance.Nat

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Nat type (~>) = Nat :: (k1 -> k2 -> k3 -> Type) -> (k1 -> k2 -> k3 -> Type) -> Type

CategoryOf (k1 -> Type) Source Comments #

The category of functors with target category Hask.

Instance details

Defined in Proarrow.Category.Instance.Nat

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Nat type (~>) = Nat :: (k1 -> Type) -> (k1 -> Type) -> Type

(CategoryOf k, Ob i, Ob j) => CategoryOf (PLAINK k i j) Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory.CategoryAsBi

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Bicategory.CategoryAsBi type (~>) = Category :: PLAINK k i j -> PLAINK k i j -> Type

CategoryOf k => CategoryOf (MonK k i j) Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory.MonoidalAsBi

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Bicategory.MonoidalAsBi type (~>) = Mon2 :: MonK k i j -> MonK k i j -> Type

Profunctor p => CategoryOf (COLLAGE p) Source Comments #

The collage of a profunctor.

Instance details

Defined in Proarrow.Category.Instance.Collage

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Collage type (~>) = Collage :: COLLAGE p -> COLLAGE p -> Type

Ok cs p => CategoryOf (FREE cs p) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Free

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Free type (~>) = Free :: FREE cs p -> FREE cs p -> Type

(Bicategory kk, Ob0 kk k) => CategoryOf (ENDO kk k) Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal.Endo

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Monoidal.Endo type (~>) = Endo :: ENDO kk k -> ENDO kk k -> Type

CategoryOf (DiscreteK ob j k) Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory.Bidiscrete

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Bicategory.Bidiscrete type (~>) = Bidiscrete :: DiscreteK ob j k -> DiscreteK ob j k -> Type

CategoryOf (kk j k2) => CategoryOf (COK kk j k2) Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory.Co

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Bicategory.Co type (~>) = Co :: COK kk j k2 -> COK kk j k2 -> Type

CategoryOf (kk k2 j) => CategoryOf (OPK kk j k2) Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory.Op

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Bicategory.Op type (~>) = Op :: OPK kk j k2 -> OPK kk j k2 -> Type

(CategoryOf (kk j k2), Bicategory kk) => CategoryOf (Path kk j k2) Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory.Strictified

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Bicategory.Strictified type (~>) = Strictified :: Path kk j k2 -> Path kk j k2 -> Type

MonoidalAction m k => CategoryOf (STT m k i j) Source Comments #

Instance details

Defined in Proarrow.Category.Equipment.Stateful

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Equipment.Stateful type (~>) = StT :: STT m k i j -> STT m k i j -> Type

IsChart m c d => CategoryOf (CHART m c d) Source Comments #

The category of charts.

Instance details

Defined in Proarrow.Category.Monoidal.Optic

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Monoidal.Optic type (~>) = ChartCat :: CHART m c d -> CHART m c d -> Type

IsOptic m c d => CategoryOf (OPTIC m c d) Source Comments #

The category of optics.

Instance details

Defined in Proarrow.Category.Monoidal.Optic

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Monoidal.Optic type (~>) = OpticCat :: OPTIC m c d -> OPTIC m c d -> Type

CategoryOf (kk i j) => CategoryOf (HK kk i j) Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory.Hom

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Bicategory.Hom type (~>) = HomW :: HK kk i j -> HK kk i j -> Type

CategoryOf (kk i j) => CategoryOf (SUBCAT tag kk i j) Source Comments #

The subcategory with objects with instances of the given constraint `IsOb tag`.

Instance details

Defined in Proarrow.Category.Bicategory.Sub

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Bicategory.Sub type (~>) = Sub :: SUBCAT tag kk i j -> SUBCAT tag kk i j -> Type

CategoryOf (kk i j) => CategoryOf (WKK kk i j) Source Comments #

Instance details

Defined in Proarrow.Category.Equipment.BiAsEquipment

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Equipment.BiAsEquipment type (~>) = W :: WKK kk i j -> WKK kk i j -> Type

CategoryOf (kk i j) => CategoryOf (QKK kk i j) Source Comments #

Instance details

Defined in Proarrow.Category.Equipment.Quintet

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Equipment.Quintet type (~>) = Q2 :: QKK kk i j -> QKK kk i j -> Type

(CategoryOf (jj (Fst ik) (Fst jl)), CategoryOf (kk (Snd ik) (Snd jl))) => CategoryOf (PRODK jj kk ik jl) Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory.Product

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Bicategory.Product type (~>) = Prod :: PRODK jj kk ik jl -> PRODK jj kk ik jl -> Type

Category Class

class (Promonad cat, CategoryOf k, cat ~ ((~>) :: CAT k)) => Category (cat :: CAT k) Source Comments #

A convenience class that bundles together the requirements for a well-formed category. The automatic instance means you get Category for free once you have CategoryOf and Promonad.

Instances

Instances details

(Promonad cat, CategoryOf k, cat ~ ((~>) :: CAT k)) => Category (cat :: k +-> k) Source Comments #
Instance details Defined in Proarrow.Core

Profunctors

Profunctor Class

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 Forget Source Comments #
Instance details Defined in Proarrow.Category.Instance.Linear Methods dimap :: forall c a (b :: LINEAR) (d :: LINEAR). (c ~> a) -> (b ~> d) -> Forget a b -> Forget c d Source Comments # (\\) :: forall a (b :: LINEAR) r. ((Ob a, Ob b) => r) -> Forget 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 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 Sym Source Comments #
Instance details Defined in Proarrow.Tools.Laws Methods dimap :: forall (c :: Symbol) (a :: Symbol) (b :: Symbol) (d :: Symbol). (c ~> a) -> (b ~> d) -> Sym a b -> Sym c d Source Comments # (\\) :: forall (a :: Symbol) (b :: Symbol) r. ((Ob a, Ob b) => r) -> Sym a b -> r Source Comments #
Profunctor Free Source Comments #
Instance details Defined in Proarrow.Category.Instance.Linear Methods dimap :: forall (c :: LINEAR) (a :: LINEAR) b d. (c ~> a) -> (b ~> d) -> Free a b -> Free c d Source Comments # (\\) :: forall (a :: LINEAR) b r. ((Ob a, Ob b) => r) -> Free 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 #
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 #
Monoid m => Profunctor (Replicate m :: k -> Nat -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Simplex Methods dimap :: forall (c :: k) (a :: k) (b :: Nat) (d :: Nat). (c ~> a) -> (b ~> d) -> Replicate m a b -> Replicate m c d Source Comments # (\\) :: forall (a :: k) (b :: Nat) r. ((Ob a, Ob b) => r) -> Replicate m a b -> r Source Comments #
Corepresentable d => Profunctor (CoendLimit d :: () -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Colimit Methods dimap :: forall (c :: ()) (a :: ()) b d0. (c ~> a) -> (b ~> d0) -> CoendLimit d a b -> CoendLimit d c d0 Source Comments # (\\) :: forall (a :: ()) b r. ((Ob a, Ob b) => r) -> CoendLimit d a b -> r Source Comments #
Profunctor (Replacing a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: (c ~> a0) -> (b0 ~> d) -> Replacing a b a0 b0 -> Replacing a b c d Source Comments # (\\) :: ((Ob a0, Ob b0) => r) -> Replacing a b a0 b0 -> r Source Comments #
Profunctor (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 (CoproductColimit d :: () -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Colimit Methods dimap :: forall (c :: ()) (a :: ()) (b :: k) (d0 :: k). (c ~> a) -> (b ~> d0) -> CoproductColimit d a b -> CoproductColimit d c d0 Source Comments # (\\) :: forall (a :: ()) (b :: k) r. ((Ob a, Ob b) => r) -> CoproductColimit d a b -> r Source Comments #
HasInitialObject k => Profunctor (InitialLimit d :: () -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Colimit Methods dimap :: forall (c :: ()) (a :: ()) (b :: k) (d0 :: k). (c ~> a) -> (b ~> d0) -> InitialLimit d a b -> InitialLimit d c d0 Source Comments # (\\) :: forall (a :: ()) (b :: k) r. ((Ob a, Ob b) => r) -> InitialLimit d 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 #
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 #
(CategoryOf j, CategoryOf k, Ob c) => Profunctor (ConstIn c :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Constant Methods dimap :: forall (c0 :: k) (a :: k) (b :: j) (d :: j). (c0 ~> a) -> (b ~> d) -> ConstIn c a b -> ConstIn c c0 d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> ConstIn c a b -> r Source Comments #
(CategoryOf j, CategoryOf k, Ob c) => Profunctor (Constant c :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Constant Methods dimap :: forall (c0 :: k) (a :: k) (b :: j) (d :: j). (c0 ~> a) -> (b ~> d) -> Constant c a b -> Constant c c0 d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> Constant c a b -> r Source Comments #
Corepresentable p => Profunctor (Corep p :: 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 p a b -> Corep p c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> Corep p 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 #
(Corepresentable d, Copowered Type k) => Profunctor (CopowerLimit n d :: () -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Colimit Methods dimap :: forall (c :: ()) (a :: ()) (b :: k) (d0 :: k). (c ~> a) -> (b ~> d0) -> CopowerLimit n d a b -> CopowerLimit n d c d0 Source Comments # (\\) :: forall (a :: ()) (b :: k) r. ((Ob a, Ob b) => r) -> CopowerLimit n d 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 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 j3, Profunctor p) => Profunctor (Precompose j3 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) -> Precompose j3 p a b -> Precompose j3 p c d Source Comments # (\\) :: forall (a :: k) (b :: j1) r. ((Ob a, Ob b) => r) -> Precompose j3 p 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 #
(CategoryOf j, CategoryOf k) => Profunctor (LftCat :: COPRODUCT j k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: COPRODUCT j k) (a :: COPRODUCT j k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> LftCat a b -> LftCat c d Source Comments # (\\) :: forall (a :: COPRODUCT j k) (b :: j) r. ((Ob a, Ob b) => r) -> LftCat 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 #
HasFree ob => Profunctor (FreeSub ob :: SUBCAT ob -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Free Methods dimap :: forall (c :: SUBCAT ob) (a :: SUBCAT ob) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> FreeSub ob a b -> FreeSub ob c d Source Comments # (\\) :: forall (a :: SUBCAT ob) (b :: j) r. ((Ob a, Ob b) => r) -> FreeSub ob a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (RgtCat :: COPRODUCT j k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: COPRODUCT j k) (a :: COPRODUCT j k) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> RgtCat a b -> RgtCat c d Source Comments # (\\) :: forall (a :: COPRODUCT j k) (b :: k) r. ((Ob a, Ob b) => r) -> RgtCat a b -> r Source Comments #
CategoryOf k => Profunctor (CofreeSub ob :: SUBCAT ob -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Cofree Methods dimap :: forall (c :: SUBCAT ob) (a :: SUBCAT ob) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> CofreeSub ob a b -> CofreeSub ob c d Source Comments # (\\) :: forall (a :: SUBCAT ob) (b :: k) r. ((Ob a, Ob b) => r) -> CofreeSub ob 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 #
Profunctor p => Profunctor (InjL p :: COLLAGE p -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Collage Methods dimap :: forall (c :: COLLAGE p) (a :: COLLAGE p) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> InjL p a b -> InjL p c d Source Comments # (\\) :: forall (a :: COLLAGE p) (b :: j) r. ((Ob a, Ob b) => r) -> InjL p a b -> r Source Comments #
Profunctor p => Profunctor (InjR p :: COLLAGE p -> j1 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Collage Methods dimap :: forall (c :: COLLAGE p) (a :: COLLAGE p) (b :: j1) (d :: j1). (c ~> a) -> (b ~> d) -> InjR p a b -> InjR p c d Source Comments # (\\) :: forall (a :: COLLAGE p) (b :: j1) r. ((Ob a, Ob b) => r) -> InjR p a b -> r Source Comments #
Profunctor DualUnit Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: ()) (a :: ()) (b :: OPPOSITE ()) (d :: OPPOSITE ()). (c ~> a) -> (b ~> d) -> DualUnit a b -> DualUnit c d Source Comments # (\\) :: forall (a :: ()) (b :: OPPOSITE ()) r. ((Ob a, Ob b) => r) -> DualUnit 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 #
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 (Previewing a b :: COPROD Type -> COPROD Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: forall (c :: COPROD Type) (a0 :: COPROD Type) (b0 :: COPROD Type) (d :: COPROD Type). (c ~> a0) -> (b0 ~> d) -> Previewing a b a0 b0 -> Previewing a b c d Source Comments # (\\) :: forall (a0 :: COPROD Type) (b0 :: COPROD Type) r. ((Ob a0, Ob b0) => r) -> Previewing a b a0 b0 -> r Source Comments #
Profunctor p => Profunctor (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 j, CategoryOf k) => Profunctor (DistribDual :: (OPPOSITE j, OPPOSITE k) -> OPPOSITE (j, k) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: (OPPOSITE j, OPPOSITE k)) (a :: (OPPOSITE j, OPPOSITE k)) (b :: OPPOSITE (j, k)) (d :: OPPOSITE (j, k)). (c ~> a) -> (b ~> d) -> DistribDual a b -> DistribDual c d Source Comments # (\\) :: forall (a :: (OPPOSITE j, OPPOSITE k)) (b :: OPPOSITE (j, k)) r. ((Ob a, Ob b) => r) -> DistribDual 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 #
Closed k => Profunctor (ExponentialFunctor :: k -> (OPPOSITE k, k) -> Type) Source Comments #
Instance details Defined in Proarrow.Object.Exponential Methods dimap :: forall (c :: k) (a :: k) (b :: (OPPOSITE k, k)) (d :: (OPPOSITE k, k)). (c ~> a) -> (b ~> d) -> ExponentialFunctor a b -> ExponentialFunctor c d Source Comments # (\\) :: forall (a :: k) (b :: (OPPOSITE k, k)) r. ((Ob a, Ob b) => r) -> ExponentialFunctor a b -> r Source Comments #
Promonad p => Profunctor (KleisliForget p :: 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 #
CategoryOf k => Profunctor (Forget ob :: k -> SUBCAT ob -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Forget Methods dimap :: forall (c :: k) (a :: k) (b :: SUBCAT ob) (d :: SUBCAT ob). (c ~> a) -> (b ~> d) -> Forget ob a b -> Forget ob c d Source Comments # (\\) :: forall (a :: k) (b :: SUBCAT ob) r. ((Ob a, Ob b) => r) -> Forget ob a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (FstCat :: j -> (j, k) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: j) (a :: j) (b :: (j, k)) (d :: (j, k)). (c ~> a) -> (b ~> d) -> FstCat a b -> FstCat c d Source Comments # (\\) :: forall (a :: j) (b :: (j, k)) r. ((Ob a, Ob b) => r) -> FstCat a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (SndCat :: k -> (j, k) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: k) (a :: k) (b :: (j, k)) (d :: (j, k)). (c ~> a) -> (b ~> d) -> SndCat a b -> SndCat c d Source Comments # (\\) :: forall (a :: k) (b :: (j, k)) r. ((Ob a, Ob b) => r) -> SndCat a b -> r Source Comments #
(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.Cat 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 #
(CategoryOf j, CategoryOf k) => Profunctor (CombineDual :: OPPOSITE (j, k) -> (OPPOSITE j, OPPOSITE k) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: OPPOSITE (j, k)) (a :: OPPOSITE (j, k)) (b :: (OPPOSITE j, OPPOSITE k)) (d :: (OPPOSITE j, OPPOSITE k)). (c ~> a) -> (b ~> d) -> CombineDual a b -> CombineDual c d Source Comments # (\\) :: forall (a :: OPPOSITE (j, k)) (b :: (OPPOSITE j, OPPOSITE k)) r. ((Ob a, Ob b) => r) -> CombineDual a b -> 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' :: NatK j k -> NatK j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods dimap :: forall (c :: NatK j k) (a :: NatK j k) (b :: NatK j k) (d :: NatK j k). (c ~> a) -> (b ~> d) -> Nat' a b -> Nat' c d Source Comments # (\\) :: forall (a :: NatK j k) (b :: NatK j k) r. ((Ob a, Ob b) => r) -> Nat' a b -> r Source Comments #
Profunctor (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 #
(CategoryOf j, CategoryOf k) => Profunctor (Swap :: (k, j) -> (j, k) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: (k, j)) (a :: (k, j)) (b :: (j, k)) (d :: (j, k)). (c ~> a) -> (b ~> d) -> Swap a b -> Swap c d Source Comments # (\\) :: forall (a :: (k, j)) (b :: (j, k)) r. ((Ob a, Ob b) => r) -> Swap 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 #
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 #
(HasCompanions hk vk, Ob0 vk h, Ob0 vk i, Ob0 vk j, Ob0 vk k) => Profunctor (RetroSq :: (hk k i, vk j k) -> (hk j h, vk h i) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Equipment Methods dimap :: forall (c0 :: (hk k i, vk j k)) (a :: (hk k i, vk j k)) (b :: (hk j h, vk h i)) (d :: (hk j h, vk h i)). (c0 ~> a) -> (b ~> d) -> RetroSq a b -> RetroSq c0 d Source Comments # (\\) :: forall (a :: (hk k i, vk j k)) (b :: (hk j h, vk h i)) r. ((Ob a, Ob b) => r) -> RetroSq a b -> r Source Comments #
(HasCompanions hk vk, Ob0 vk h, Ob0 vk i, Ob0 vk j, Ob0 vk k) => Profunctor (Sq :: (hk j h, vk h i) -> (hk k i, vk j k) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Equipment Methods dimap :: forall (c0 :: (hk j h, vk h i)) (a :: (hk j h, vk h i)) (b :: (hk k i, vk j k)) (d :: (hk k i, vk j k)). (c0 ~> a) -> (b ~> d) -> Sq a b -> Sq c0 d Source Comments # (\\) :: forall (a :: (hk j h, vk h i)) (b :: (hk k i, vk j k)) r. ((Ob a, Ob b) => r) -> Sq a b -> r Source Comments #
(Profunctor p, Representable f, Representable g, Reifies s (ProfSq p (Id :: k2 -> k2 -> Type) f g)) => Profunctor (CotabulatorFactorizer s p f g :: k2 -> COLLAGE p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Prof Methods dimap :: forall (c :: k2) (a :: k2) (b :: COLLAGE p) (d :: COLLAGE p). (c ~> a) -> (b ~> d) -> CotabulatorFactorizer s p f g a b -> CotabulatorFactorizer s p f g c d Source Comments # (\\) :: forall (a :: k2) (b :: COLLAGE p) r. ((Ob a, Ob b) => r) -> CotabulatorFactorizer s p f g 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 #
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 #
CategoryOf (kk i j) => Profunctor (W :: WKK kk i j -> WKK kk i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Equipment.BiAsEquipment Methods dimap :: forall (c :: WKK kk i j) (a :: WKK kk i j) (b :: WKK kk i j) (d :: WKK kk i j). (c ~> a) -> (b ~> d) -> W a b -> W c d Source Comments # (\\) :: forall (a :: WKK kk i j) (b :: WKK kk i j) r. ((Ob a, Ob b) => r) -> W a b -> r Source Comments #
CategoryOf (kk i j) => Profunctor (Q2 :: QKK kk i j -> QKK kk i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Equipment.Quintet Methods dimap :: forall (c :: QKK kk i j) (a :: QKK kk i j) (b :: QKK kk i j) (d :: QKK kk i j). (c ~> a) -> (b ~> d) -> Q2 a b -> Q2 c d Source Comments # (\\) :: forall (a :: QKK kk i j) (b :: QKK kk i j) r. ((Ob a, Ob b) => r) -> Q2 a b -> r Source Comments #
(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 #

Natural Transformations

type (:~>) (p :: k -> k1 -> Type) (q :: k -> k1 -> Type) = forall (a :: k) (b :: k1). p a b -> q a b infixr 0 Source Comments #

Natural transformation between profunctors.

Profunctor Utilities

(//) :: 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 (\\).

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).

Default Implementation

dimapDefault :: forall {k} p (c :: k) (a :: k) (b :: k) (d :: k). Promonad p => p c a -> p b d -> p a b -> p c d Source Comments #

Default implementation of dimap for promonads using composition.

Promonads

Promonad Class

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 #

Promonad Utilities

arr :: forall {k} p (a :: k) (b :: k). Promonad p => (a ~> b) -> p a b Source Comments #

Lifts morphisms from the base category into the promonad.

Object Identities

type Obj (a :: k) = a ~> a Source Comments #

Type of identity morphism for object a.

obj :: forall {k} (a :: k). (CategoryOf k, Ob a) => Obj a Source Comments #

The identity morphism for a given object. Compared to id this makes the kind argument implicit, allowing to write obj @a instead of id @k @a.

src :: forall {j} {k} (a :: k) (b :: j) p. Profunctor p => p a b -> Obj a Source Comments #

Extract source identity morphism from a profunctor heteromorphism.

tgt :: forall {k1} {k2} (a :: k2) (b :: k1) p. Profunctor p => p a b -> Obj b Source Comments #

Extract target identity morphism from a profunctor heteromorphism.

Type Family Utilities

Kind Unwrapping

type family UN (w :: j -> k) (wa :: k) :: j Source Comments #

A helper type family to unwrap a wrapped kind. This is needed because the field selector functions of newtypes have to be lower case and therefore cannot be used at the type level.

Instances

Instances details

type UN 'K ('K k :: KIND) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat type UN 'K ('K k :: KIND) = k
type UN 'CNSTRNT ('CNSTRNT a :: CONSTRAINT) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Constraint type UN 'CNSTRNT ('CNSTRNT a :: CONSTRAINT) = a
type UN 'L ('L a :: LINEAR) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Linear type UN 'L ('L a :: LINEAR) = a
type UN 'P ('P a :: POINTED) Source Comments #
Instance details Defined in Proarrow.Category.Instance.PointedHask type UN 'P ('P a :: POINTED) = a
type UN ('M :: Nat -> MatK a) ('M n :: MatK a) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Mat type UN ('M :: Nat -> MatK a) ('M n :: MatK a) = n
type UN ('CD :: j -> CODISCRETE j) ('CD a :: CODISCRETE j) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Discrete type UN ('CD :: j -> CODISCRETE j) ('CD a :: CODISCRETE j) = a
type UN ('D :: j -> DISCRETE j) ('D a :: DISCRETE j) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Discrete type UN ('D :: j -> DISCRETE j) ('D a :: DISCRETE j) = a
type UN ('R :: j -> REV j) ('R a :: REV j) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Rev type UN ('R :: j -> REV j) ('R a :: REV j) = a
type UN ('OP :: j -> OPPOSITE j) ('OP k :: OPPOSITE j) Source Comments #
Instance details Defined in Proarrow.Category.Opposite type UN ('OP :: j -> OPPOSITE j) ('OP k :: OPPOSITE j) = k
type UN ('COPR :: j -> COPROD j) ('COPR k :: COPROD j) Source Comments #
Instance details Defined in Proarrow.Object.BinaryCoproduct type UN ('COPR :: j -> COPROD j) ('COPR k :: COPROD j) = k
type UN ('PR :: j -> PROD j) ('PR k :: PROD j) Source Comments #
Instance details Defined in Proarrow.Object.BinaryProduct type UN ('PR :: j -> PROD j) ('PR k :: PROD j) = k
type UN ('F :: j -> FK j) ('F a :: FK j) Source Comments #
Instance details Defined in Proarrow.Tools.CCC type UN ('F :: j -> FK j) ('F a :: FK j) = a
type UN ('A :: j -> AP f j) ('A k :: AP f j) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Ap type UN ('A :: j -> AP f j) ('A k :: AP f j) = k
type UN ('KL :: j -> KLEISLI p) ('KL k :: KLEISLI p) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli type UN ('KL :: j -> KLEISLI p) ('KL k :: KLEISLI p) = k
type UN ('SUB :: j -> SUBCAT ob) ('SUB k :: SUBCAT ob) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Sub type UN ('SUB :: j -> SUBCAT ob) ('SUB k :: SUBCAT ob) = k
type UN ('EMB :: j -> FREE cs p) ('EMB a :: FREE cs p) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Free type UN ('EMB :: j -> FREE cs p) ('EMB a :: FREE cs p) = a
type UN ('MK :: j1 -> MonK j1 i j2) ('MK k :: MonK j1 i j2) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.MonoidalAsBi type UN ('MK :: j1 -> MonK j1 i j2) ('MK k :: MonK j1 i j2) = k
type UN ('L :: [k] -> LIST k) ('L as :: LIST k) Source Comments #
Instance details Defined in Proarrow.Profunctor.List type UN ('L :: [k] -> LIST k) ('L as :: LIST k) = as
type UN ('PK :: (j +-> k) -> PROFK j k) ('PK p :: PROFK j k) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Prof type UN ('PK :: (j +-> k) -> PROFK j k) ('PK p :: PROFK j k) = p
type UN ('NT :: (j -> k) -> NatK j k) ('NT f :: NatK j k) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat type UN ('NT :: (j -> k) -> NatK j k) ('NT f :: NatK j k) = f
type UN ('E :: kk k k -> ENDO kk k) ('E p :: ENDO kk k) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Endo type UN ('E :: kk k k -> ENDO kk k) ('E p :: ENDO kk k) = p
type UN ('ST :: (k +-> k) -> STT m k i j) ('ST p :: STT m k i j) Source Comments #
Instance details Defined in Proarrow.Category.Equipment.Stateful type UN ('ST :: (k +-> k) -> STT m k i j) ('ST p :: STT m k i j) = p
type UN ('CO :: kk j k2 -> COK kk j k2) ('CO k3 :: COK kk j k2) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Co type UN ('CO :: kk j k2 -> COK kk j k2) ('CO k3 :: COK kk j k2) = k3
type UN ('OP :: kk k2 j -> OPK kk j k2) ('OP k3 :: OPK kk j k2) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Op type UN ('OP :: kk k2 j -> OPK kk j k2) ('OP k3 :: OPK kk j k2) = k3
type UN ('HomK :: kk i j -> HK kk i j) ('HomK k3 :: HK kk i j) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Hom type UN ('HomK :: kk i j -> HK kk i j) ('HomK k3 :: HK kk i j) = k3
type UN ('SUB :: kk i j -> SUBCAT tag kk i j) ('SUB p :: SUBCAT tag kk i j) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Sub type UN ('SUB :: kk i j -> SUBCAT tag kk i j) ('SUB p :: SUBCAT tag kk i j) = p
type UN ('WK :: kk i j -> WKK kk i j) ('WK p :: WKK kk i j) Source Comments #
Instance details Defined in Proarrow.Category.Equipment.BiAsEquipment type UN ('WK :: kk i j -> WKK kk i j) ('WK p :: WKK kk i j) = p
type UN ('QK :: kk i j -> QKK kk i j) ('QK p :: QKK kk i j) Source Comments #
Instance details Defined in Proarrow.Category.Equipment.Quintet type UN ('QK :: kk i j -> QKK kk i j) ('QK p :: QKK kk i j) = p

type Is (w :: j -> k) (a :: k) = a ~ w (UN w a) Source Comments #

Is w a checks that the kind a is a kind wrapped by w.