Safe Haskell	None
Language	Haskell2010

Proarrow.Core

Synopsis

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

Documentation

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

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

type CAT k = PRO k k Source Comments #

type BI k = (k, k) -> k Source Comments #

type OB k = k -> Constraint Source Comments #

type Kind = Type Source Comments #

class Any (a :: k) Source Comments #

Instances

Instances details

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

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

Associated Types

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

type Ob (a :: k) Source Comments #

type Ob (a :: k) = Any a

Instances

Instances details

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 #

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 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 #

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 #

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 Type Source Comments #

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 (FIN n) Source Comments #

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 #

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

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

Instance details

Defined in Proarrow.Category.Instance.List

Associated Types

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

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

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

PreorderOf k => CategoryOf (POCATK k) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PreorderAsCategory

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.PreorderAsCategory type (~>) = PoAsCat :: POCATK k -> POCATK k -> Type

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

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)

BiCCC k => CategoryOf (FK k) Source Comments #

Instance details

Defined in Proarrow.Helper.CCC

Associated Types

type (~>)
Instance details Defined in Proarrow.Helper.CCC type (~>) = FreeCCC :: FK k -> FK k -> Type

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

Instance details

Defined in Proarrow.Object.BinaryCoproduct

Associated Types

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

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

Instance details

Defined in Proarrow.Object.BinaryProduct

Associated Types

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

Monoidal k => CategoryOf [k] Source Comments #

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

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

Instance details

Defined in Proarrow.Category.Instance.Coproduct

Associated Types

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

Rewrite g => CategoryOf (FREE g) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Free

Associated Types

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

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 #

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 (Simplex j k) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Simplex

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Simplex type (~>) = BiSimplex :: Simplex j k -> Simplex 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

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

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 #

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 #

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 #

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 #

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

(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

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

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 w c d => CategoryOf (OPTIC w c d) Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal.Optic

Associated Types

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

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

Instances

Instances details

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

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

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

Minimal complete definition

dimap

Methods

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

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

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

Instances

Instances details

Profunctor Booleans Source Comments #
Instance details Defined in Proarrow.Category.Instance.Bool Methods dimap :: forall (c :: BOOL) (a :: BOOL) (b :: BOOL) (d :: BOOL). (c ~> a) -> (b ~> d) -> Booleans a b -> Booleans c d Source Comments # (\\) :: forall (a :: BOOL) (b :: BOOL) r. ((Ob a, Ob b) => r) -> Booleans a b -> r Source Comments #
Profunctor Cat Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: KIND) (a :: KIND) (b :: KIND) (d :: KIND). (c ~> a) -> (b ~> d) -> Cat a b -> Cat c d Source Comments # (\\) :: forall (a :: KIND) (b :: KIND) r. ((Ob a, Ob b) => r) -> Cat a b -> r Source Comments #
Profunctor (:-) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Constraint Methods dimap :: forall (c :: CONSTRAINT) (a :: CONSTRAINT) (b :: CONSTRAINT) (d :: CONSTRAINT). (c ~> a) -> (b ~> d) -> (a :- b) -> c :- d Source Comments # (\\) :: forall (a :: CONSTRAINT) (b :: CONSTRAINT) r. ((Ob a, Ob b) => r) -> (a :- b) -> r Source Comments #
Profunctor Linear Source Comments #
Instance details Defined in Proarrow.Category.Instance.Linear Methods dimap :: forall (c :: LINEAR) (a :: LINEAR) (b :: LINEAR) (d :: LINEAR). (c ~> a) -> (b ~> d) -> Linear a b -> Linear c d Source Comments # (\\) :: forall (a :: LINEAR) (b :: LINEAR) r. ((Ob a, Ob b) => r) -> Linear a b -> r Source Comments #
Profunctor 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 #
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 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 Forget Source Comments #
Instance details Defined in Proarrow.Category.Instance.Simplex Methods dimap :: forall c a (b :: Nat) (d :: Nat). (c ~> a) -> (b ~> d) -> Forget a b -> Forget c d Source Comments # (\\) :: forall a (b :: Nat) r. ((Ob a, Ob b) => r) -> Forget a b -> r Source Comments #
CategoryOf k => Profunctor (Terminate :: () -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: ()) (a :: ()) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Terminate a b -> Terminate c d Source Comments # (\\) :: forall (a :: ()) (b :: k) r. ((Ob a, Ob b) => r) -> Terminate 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 #
Profunctor (Cont r :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Cont Methods dimap :: (c ~> a) -> (b ~> d) -> Cont r a b -> Cont r c d Source Comments # (\\) :: ((Ob a, Ob b) => r0) -> Cont r a b -> r0 Source Comments #
CategoryOf k => Profunctor (Initiate :: k -> VOID -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: k) (a :: k) (b :: VOID) (d :: VOID). (c ~> a) -> (b ~> d) -> Initiate a b -> Initiate c d Source Comments # (\\) :: forall (a :: k) (b :: VOID) r. ((Ob a, Ob b) => r) -> Initiate 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 #
Representable d => Profunctor (EndLimit d :: Type -> () -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Limit Methods dimap :: forall c a (b :: ()) (d0 :: ()). (c ~> a) -> (b ~> d0) -> EndLimit d a b -> EndLimit d c d0 Source Comments # (\\) :: forall a (b :: ()) r. ((Ob a, Ob b) => r) -> EndLimit d a b -> r Source Comments #
Profunctor (Replacing a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: (c ~> a0) -> (b0 ~> d) -> Replacing a b a0 b0 -> Replacing a b c d Source Comments # (\\) :: ((Ob a0, Ob b0) => r) -> Replacing a b a0 b0 -> r Source Comments #
Profunctor (Setting a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: (c ~> a0) -> (b0 ~> d) -> Setting a b a0 b0 -> Setting a b c d Source Comments # (\\) :: ((Ob a0, Ob b0) => r) -> Setting a b a0 b0 -> r Source Comments #
Profunctor (Viewing a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: (c ~> a0) -> (b0 ~> d) -> Viewing a b a0 b0 -> Viewing a b c d Source Comments # (\\) :: ((Ob a0, Ob b0) => r) -> Viewing a b a0 b0 -> r Source Comments #
Profunctor (->) Source Comments #
Instance details Defined in Proarrow.Core Methods dimap :: (c ~> a) -> (b ~> d) -> (a -> b) -> c -> d Source Comments # (\\) :: ((Ob a, Ob b) => r) -> (a -> b) -> r Source Comments #
Monoid m => Profunctor (Replicate m :: j -> Nat -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Simplex Methods dimap :: forall (c :: j) (a :: j) (b :: Nat) (d :: Nat). (c ~> a) -> (b ~> d) -> Replicate m a b -> Replicate m c d Source Comments # (\\) :: forall (a :: j) (b :: Nat) r. ((Ob a, Ob b) => r) -> Replicate m a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (DayUnit :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Day Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> DayUnit a b -> DayUnit c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> DayUnit a b -> r Source Comments #
(HasBinaryCoproducts k, Representable d) => Profunctor (CoproductColimit d :: k -> () -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Colimit Methods dimap :: forall (c :: k) (a :: k) (b :: ()) (d0 :: ()). (c ~> a) -> (b ~> d0) -> CoproductColimit d a b -> CoproductColimit d c d0 Source Comments # (\\) :: forall (a :: k) (b :: ()) 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 :: k) (a :: k) (b :: ()) (d0 :: ()). (c ~> a) -> (b ~> d0) -> InitialLimit d a b -> InitialLimit d c d0 Source Comments # (\\) :: forall (a :: k) (b :: ()) r. ((Ob a, Ob b) => r) -> InitialLimit d a b -> r Source Comments #
(HasBinaryProducts k, Representable d) => Profunctor (ProductLimit d :: k -> () -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Limit Methods dimap :: forall (c :: k) (a :: k) (b :: ()) (d0 :: ()). (c ~> a) -> (b ~> d0) -> ProductLimit d a b -> ProductLimit d c d0 Source Comments # (\\) :: forall (a :: k) (b :: ()) r. ((Ob a, Ob b) => r) -> ProductLimit d a b -> r Source Comments #
HasTerminalObject k => Profunctor (TerminalLimit d :: k -> () -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Limit Methods dimap :: forall (c :: k) (a :: k) (b :: ()) (d0 :: ()). (c ~> a) -> (b ~> d0) -> TerminalLimit d a b -> TerminalLimit d c d0 Source Comments # (\\) :: forall (a :: k) (b :: ()) r. ((Ob a, Ob b) => r) -> TerminalLimit d 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 #
Profunctor p => Profunctor (Fix p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Fix Methods dimap :: forall (c :: k) (a :: k) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Fix p a b -> Fix p c d Source Comments # (\\) :: forall (a :: k) (b :: k) r. ((Ob a, Ob b) => r) -> Fix p a b -> r Source Comments #
Profunctor p => Profunctor (FreeMonoid p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Free Methods dimap :: forall (c :: k) (a :: k) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> FreeMonoid p a b -> FreeMonoid p c d Source Comments # (\\) :: forall (a :: k) (b :: k) r. ((Ob a, Ob b) => r) -> FreeMonoid p a b -> r Source Comments #
Profunctor p => Profunctor (FreePromonad p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Free Methods dimap :: forall (c :: k) (a :: k) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> FreePromonad p a b -> FreePromonad p c d Source Comments # (\\) :: forall (a :: k) (b :: k) r. ((Ob a, Ob b) => r) -> FreePromonad p a b -> r Source Comments #
(BiCCC k, Ob r) => Profunctor (Reader 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 r a b -> Reader r c d Source Comments # (\\) :: forall (a :: k) (b :: k) r0. ((Ob a, Ob b) => r0) -> Reader 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 #
(BiCCC k, Ob m) => Profunctor (Writer m :: 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 m a b -> Writer m c d Source Comments # (\\) :: forall (a :: k) (b :: k) r. ((Ob a, Ob b) => r) -> Writer m a b -> r Source Comments #
Corepresentable p => Profunctor (Corep p :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Corepresentable Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Corep p a b -> Corep p c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> Corep p a b -> r Source Comments #
Functor f => Profunctor (Costar f :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Costar Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Costar f a b -> Costar f c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> Costar f a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (Coyoneda p :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Coyoneda Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Coyoneda p a b -> Coyoneda p c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> Coyoneda p a b -> r Source Comments #
Corepresentable p => Profunctor (CorepStar p :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Representable Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> CorepStar p a b -> CorepStar p c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> CorepStar p a b -> r Source Comments #
Representable p => Profunctor (RepCostar p :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Representable Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> RepCostar p a b -> RepCostar p c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> RepCostar p a b -> r Source Comments #
Representable p => Profunctor (RepStar p :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Representable Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> RepStar p a b -> RepStar p c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> RepStar p a b -> r Source Comments #
Functor f => Profunctor (Star f :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Star f a b -> Star f c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> Star f a b -> r Source Comments #
Profunctor p => Profunctor (Wrapped p :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Wrapped Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Wrapped p a b -> Wrapped p c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> Wrapped p a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (Yoneda p :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Yoneda Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Yoneda p a b -> Yoneda p c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> Yoneda p a b -> r Source Comments #
(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 #
(Monoidal k, Ob a, Ob b) => Profunctor (Bipara a b :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Enriched.Bipara Methods dimap :: forall (c :: k) (a0 :: k) (b0 :: k) (d :: k). (c ~> a0) -> (b0 ~> d) -> Bipara a b a0 b0 -> Bipara a b c d Source Comments # (\\) :: forall (a0 :: k) (b0 :: k) r. ((Ob a0, Ob b0) => r) -> Bipara a b a0 b0 -> r Source Comments #
Monad m => Profunctor (Classifying m a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: (c ~> a0) -> (b0 ~> d) -> Classifying m a b a0 b0 -> Classifying m a b c d Source Comments # (\\) :: ((Ob a0, Ob b0) => r) -> Classifying m a b a0 b0 -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :+: q :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Coproduct Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> (p :+: q) a b -> (p :+: q) c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> (p :+: q) a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (Day p q :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Day Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Day p q a b -> Day p q c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> Day p q a b -> r Source Comments #
(Monoidal j, Monoidal k, Profunctor p, Profunctor q) => Profunctor (DayExp p q :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Day Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> DayExp p q a b -> DayExp p q c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> DayExp p q a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :~>: q :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Exponential Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> (p :~>: q) a b -> (p :~>: q) c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> (p :~>: q) a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :*: q :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Product Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> (p :: q) a b -> (p :: q) c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> (p :*: q) a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (Yo a b :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Yoneda Methods dimap :: forall (c :: j) (a0 :: j) (b0 :: k) (d :: k). (c ~> a0) -> (b0 ~> d) -> Yo a b a0 b0 -> Yo a b c d Source Comments # (\\) :: forall (a0 :: j) (b0 :: k) r. ((Ob a0, Ob b0) => r) -> Yo a b a0 b0 -> r Source Comments #
(CategoryOf c, CategoryOf d) => Profunctor (Optic w a b :: c -> d -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: forall (c0 :: c) (a0 :: c) (b0 :: d) (d0 :: d). (c0 ~> a0) -> (b0 ~> d0) -> Optic w a b a0 b0 -> Optic w a b c0 d0 Source Comments # (\\) :: forall (a0 :: c) (b0 :: d) r. ((Ob a0, Ob b0) => r) -> Optic w a b a0 b0 -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :.: q :: j1 -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Composition Methods dimap :: forall (c :: j1) (a :: j1) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> (p :.: q) a b -> (p :.: q) c d Source Comments # (\\) :: forall (a :: j1) (b :: k) r. ((Ob a, Ob b) => r) -> (p :.: q) a b -> r Source Comments #
(Profunctor p, Profunctor j2) => Profunctor (Ran ('OP j2) p :: j1 -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Ran Methods dimap :: forall (c :: j1) (a :: j1) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Ran ('OP j2) p a b -> Ran ('OP j2) p c d Source Comments # (\\) :: forall (a :: j1) (b :: k) r. ((Ob a, Ob b) => r) -> Ran ('OP j2) p a b -> r Source Comments #
(Profunctor p, Profunctor j2) => Profunctor (Rift ('OP j2) p :: j1 -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Rift Methods dimap :: forall (c :: j1) (a :: j1) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Rift ('OP j2) p a b -> Rift ('OP j2) p c d Source Comments # (\\) :: forall (a :: j1) (b :: k) r. ((Ob a, Ob b) => r) -> Rift ('OP j2) p a b -> r Source Comments #
(Profunctor j3, Profunctor p) => Profunctor (Precompose j3 p :: j2 -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Ran Methods dimap :: forall (c :: j2) (a :: j2) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Precompose j3 p a b -> Precompose j3 p c d Source Comments # (\\) :: forall (a :: j2) (b :: k) r. ((Ob a, Ob b) => r) -> Precompose j3 p a b -> r Source Comments #
Profunctor 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 #
Profunctor p => Profunctor (CoprodDom p :: j1 -> COPROD j2 -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods dimap :: forall (c :: j1) (a :: j1) (b :: COPROD j2) (d :: COPROD j2). (c ~> a) -> (b ~> d) -> CoprodDom p a b -> CoprodDom p c d Source Comments # (\\) :: forall (a :: j1) (b :: COPROD j2) 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 #
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 :: j -> KLEISLI p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods dimap :: forall (c :: j) (a :: j) (b :: KLEISLI p) (d :: KLEISLI p). (c ~> a) -> (b ~> d) -> KleisliForget p a b -> KleisliForget p c d Source Comments # (\\) :: forall (a :: j) (b :: KLEISLI p) r. ((Ob a, Ob b) => r) -> KleisliForget p a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (FstCat :: j -> (j, k) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: j) (a :: j) (b :: (j, k)) (d :: (j, k)). (c ~> a) -> (b ~> d) -> FstCat a b -> FstCat c d Source Comments # (\\) :: forall (a :: j) (b :: (j, k)) r. ((Ob a, Ob b) => r) -> FstCat a b -> r Source Comments #
CategoryOf k => Profunctor (Forget ob :: k -> SUBCAT ob -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Forget Methods dimap :: forall (c :: k) (a :: k) (b :: SUBCAT ob) (d :: SUBCAT ob). (c ~> a) -> (b ~> d) -> Forget ob a b -> Forget ob c d Source Comments # (\\) :: forall (a :: k) (b :: SUBCAT ob) r. ((Ob a, Ob b) => r) -> Forget ob a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (SndCat :: k -> (j, k) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: k) (a :: k) (b :: (j, k)) (d :: (j, k)). (c ~> a) -> (b ~> d) -> SndCat a b -> SndCat c d Source Comments # (\\) :: forall (a :: k) (b :: (j, k)) r. ((Ob a, Ob b) => r) -> SndCat a b -> r Source Comments #
(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 :: j1 -> COPRODUCT i j2 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: j1) (a :: j1) (b :: COPRODUCT i j2) (d :: COPRODUCT i j2). (c ~> a) -> (b ~> d) -> (p :\|\|\|: q) a b -> (p :\|\|\|: q) c d Source Comments # (\\) :: forall (a :: j1) (b :: COPRODUCT i j2) r. ((Ob a, Ob b) => r) -> (p :\|\|\|: q) a b -> r Source Comments #
(Profunctor p, Representable f, Representable g, Reifies s (ProfSq p (Id :: j2 -> j2 -> Type) f g)) => Profunctor (CotabulatorFactorizer s p f g :: j2 -> COLLAGE p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Prof Methods dimap :: forall (c :: j2) (a :: j2) (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 :: j2) (b :: COLLAGE p) r. ((Ob a, Ob b) => r) -> CotabulatorFactorizer s p f g 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 #
CategoryOf k => Profunctor (List :: LIST k -> LIST k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.List Methods dimap :: forall (c :: LIST k) (a :: LIST k) (b :: LIST k) (d :: LIST k). (c ~> a) -> (b ~> d) -> List a b -> List c d Source Comments # (\\) :: forall (a :: LIST k) (b :: LIST k) r. ((Ob a, Ob b) => r) -> List a b -> r Source Comments #
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 #
PreorderOf k => Profunctor (PoAsCat :: POCATK k -> POCATK k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.PreorderAsCategory Methods dimap :: forall (c :: POCATK k) (a :: POCATK k) (b :: POCATK k) (d :: POCATK k). (c ~> a) -> (b ~> d) -> PoAsCat a b -> PoAsCat c d Source Comments # (\\) :: forall (a :: POCATK k) (b :: POCATK k) r. ((Ob a, Ob b) => r) -> PoAsCat a b -> r Source Comments #
BiCCC k => Profunctor (FreeCCC :: FK k -> FK k -> Type) Source Comments #
Instance details Defined in Proarrow.Helper.CCC Methods dimap :: forall (c :: FK k) (a :: FK k) (b :: FK k) (d :: FK k). (c ~> a) -> (b ~> d) -> FreeCCC a b -> FreeCCC c d Source Comments # (\\) :: forall (a :: FK k) (b :: FK k) r. ((Ob a, Ob b) => r) -> FreeCCC a 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) => 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 #
(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 #
Promonad p => Profunctor (KleisliFree p :: KLEISLI p -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods dimap :: forall (c :: KLEISLI p) (a :: KLEISLI p) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> KleisliFree p a b -> KleisliFree p c d Source Comments # (\\) :: forall (a :: KLEISLI p) (b :: k) r. ((Ob a, Ob b) => r) -> KleisliFree p a b -> r Source Comments #
HasCofree ob => 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 #
HasFree ob => Profunctor (FreeSub ob :: SUBCAT ob -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Free Methods dimap :: forall (c :: SUBCAT ob) (a :: SUBCAT ob) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> FreeSub ob a b -> FreeSub ob c d Source Comments # (\\) :: forall (a :: SUBCAT ob) (b :: k) r. ((Ob a, Ob b) => r) -> FreeSub ob a b -> r Source Comments #
(Profunctor p, CategoryOf i, CategoryOf j) => Profunctor (Curry p :: (k, OPPOSITE j) -> i -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: (k, OPPOSITE j)) (a :: (k, OPPOSITE j)) (b :: i) (d :: i). (c ~> a) -> (b ~> d) -> Curry p a b -> Curry p c d Source Comments # (\\) :: forall (a :: (k, OPPOSITE j)) (b :: i) r. ((Ob a, Ob b) => r) -> Curry p a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :&&&: q :: (i, j) -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: (i, j)) (a :: (i, j)) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> (p :&&&: q) a b -> (p :&&&: q) c d Source Comments # (\\) :: forall (a :: (i, j)) (b :: k) r. ((Ob a, Ob b) => r) -> (p :&&&: q) a b -> r Source Comments #
(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 #
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 #
Rewrite g => Profunctor (Free :: FREE g -> FREE g -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Free Methods dimap :: forall (c :: FREE g) (a :: FREE g) (b :: FREE g) (d :: FREE g). (c ~> a) -> (b ~> d) -> Free a b -> Free c d Source Comments # (\\) :: forall (a :: FREE g) (b :: FREE g) r. ((Ob a, Ob b) => r) -> Free a b -> r Source Comments #
Promonad p => Profunctor (Kleisli :: KLEISLI p -> KLEISLI p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods dimap :: forall (c :: KLEISLI p) (a :: KLEISLI p) (b :: KLEISLI p) (d :: KLEISLI p). (c ~> a) -> (b ~> d) -> Kleisli a b -> Kleisli c d Source Comments # (\\) :: forall (a :: KLEISLI p) (b :: KLEISLI p) r. ((Ob a, Ob b) => r) -> Kleisli a b -> r Source Comments #
Profunctor (Nat' :: NatK j k -> NatK j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods dimap :: forall (c :: NatK j k) (a :: NatK j k) (b :: NatK j k) (d :: NatK j k). (c ~> a) -> (b ~> d) -> Nat' a b -> Nat' c d Source Comments # (\\) :: forall (a :: NatK j k) (b :: NatK j k) r. ((Ob a, Ob b) => r) -> Nat' a b -> r Source Comments #
Profunctor (BiSimplex :: Simplex j k -> Simplex j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Simplex Methods dimap :: forall (c :: Simplex j k) (a :: Simplex j k) (b :: Simplex j k) (d :: Simplex j k). (c ~> a) -> (b ~> d) -> BiSimplex a b -> BiSimplex c d Source Comments # (\\) :: forall (a :: Simplex j k) (b :: Simplex j k) r. ((Ob a, Ob b) => r) -> BiSimplex a b -> r Source Comments #
Profunctor (Terminal :: Unit '() '() -> Unit '() '() -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Terminal Methods dimap :: forall (c :: Unit '() '()) (a :: Unit '() '()) (b :: Unit '() '()) (d :: Unit '() '()). (c ~> a) -> (b ~> d) -> Terminal a b -> Terminal c d Source Comments # (\\) :: forall (a :: Unit '() '()) (b :: Unit '() '()) r. ((Ob a, Ob b) => r) -> Terminal a b -> r Source Comments #
Profunctor (Prof :: (j +-> k) -> (j +-> k) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Prof Methods dimap :: forall (c :: j +-> k) (a :: j +-> k) (b :: j +-> k) (d :: j +-> k). (c ~> a) -> (b ~> d) -> Prof a b -> Prof c d Source Comments # (\\) :: forall (a :: j +-> k) (b :: j +-> k) r. ((Ob a, Ob b) => r) -> Prof a b -> r Source Comments #
Profunctor (Nat :: (k1 -> k2 -> k3 -> k4 -> Type) -> (k1 -> k2 -> k3 -> k4 -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods dimap :: forall (c :: k1 -> k2 -> k3 -> k4 -> Type) (a :: k1 -> k2 -> k3 -> k4 -> Type) (b :: k1 -> k2 -> k3 -> k4 -> Type) (d :: k1 -> k2 -> k3 -> k4 -> Type). (c ~> a) -> (b ~> d) -> Nat a b -> Nat c d Source Comments # (\\) :: forall (a :: k1 -> k2 -> k3 -> k4 -> Type) (b :: k1 -> k2 -> k3 -> k4 -> Type) r. ((Ob a, Ob b) => r) -> Nat a b -> r Source Comments #
Profunctor (Nat :: (k1 -> k2 -> k3 -> Type) -> (k1 -> k2 -> k3 -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods dimap :: forall (c :: k1 -> k2 -> k3 -> Type) (a :: k1 -> k2 -> k3 -> Type) (b :: k1 -> k2 -> k3 -> Type) (d :: k1 -> k2 -> k3 -> Type). (c ~> a) -> (b ~> d) -> Nat a b -> Nat c d Source Comments # (\\) :: forall (a :: k1 -> k2 -> k3 -> Type) (b :: k1 -> k2 -> k3 -> Type) r. ((Ob a, Ob b) => r) -> Nat a b -> r Source Comments #
Profunctor (Nat :: (k1 -> Type) -> (k1 -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods dimap :: forall (c :: k1 -> Type) (a :: k1 -> Type) (b :: k1 -> Type) (d :: k1 -> Type). (c ~> a) -> (b ~> d) -> Nat a b -> Nat c d Source Comments # (\\) :: forall (a :: k1 -> Type) (b :: k1 -> Type) r. ((Ob a, Ob b) => r) -> Nat a b -> r Source Comments #
Profunctor p => Profunctor (Sub p :: SUBCAT ob -> SUBCAT ob -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Sub Methods dimap :: forall (c :: SUBCAT ob) (a :: SUBCAT ob) (b :: SUBCAT ob) (d :: SUBCAT ob). (c ~> a) -> (b ~> d) -> Sub p a b -> Sub p c d Source Comments # (\\) :: forall (a :: SUBCAT ob) (b :: SUBCAT ob) r. ((Ob a, Ob b) => r) -> Sub p a b -> r Source Comments #
(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 (Swap p q :: (k, i) -> (h, j) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: (k, i)) (a :: (k, i)) (b :: (h, j)) (d :: (h, j)). (c ~> a) -> (b ~> d) -> Swap p q a b -> Swap p q c d Source Comments # (\\) :: forall (a :: (k, i)) (b :: (h, j)) r. ((Ob a, Ob b) => r) -> Swap 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 (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 #
(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 #
Profunctor p => Profunctor (InjR p :: COLLAGE p -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Collage Methods dimap :: forall (c :: COLLAGE p) (a :: COLLAGE p) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> InjR p a b -> InjR p c d Source Comments # (\\) :: forall (a :: COLLAGE p) (b :: k) r. ((Ob a, Ob b) => r) -> InjR p a b -> r Source Comments #
Profunctor p => Profunctor (InjL p :: COLLAGE p -> k1 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Collage Methods dimap :: forall (c :: COLLAGE p) (a :: COLLAGE p) (b :: k1) (d :: k1). (c ~> a) -> (b ~> d) -> InjL p a b -> InjL p c d Source Comments # (\\) :: forall (a :: COLLAGE p) (b :: k1) r. ((Ob a, Ob b) => r) -> InjL p 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 #
(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 #
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 w c d => Profunctor (OpticCat :: OPTIC w c d -> OPTIC w c d -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: forall (c0 :: OPTIC w c d) (a :: OPTIC w c d) (b :: OPTIC w c d) (d0 :: OPTIC w c d). (c0 ~> a) -> (b ~> d0) -> OpticCat a b -> OpticCat c0 d0 Source Comments # (\\) :: forall (a :: OPTIC w c d) (b :: OPTIC w c d) r. ((Ob a, Ob b) => r) -> OpticCat a b -> r Source Comments #
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 #

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

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

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

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 #

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

Methods

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

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

Instances

Instances details

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 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 #
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 #
Promonad (Cont r :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Cont Methods id :: Ob a => Cont r a a Source Comments # (.) :: Cont r b c -> Cont r a b -> Cont r 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 #
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 #
(BiCCC k, Ob r) => Promonad (Reader r :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Reader Methods id :: forall (a :: k). Ob a => Reader r a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). Reader r b c -> Reader r a b -> Reader 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 #
(BiCCC k, Monoid m) => Promonad (Writer m :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Writer Methods id :: forall (a :: k). Ob a => Writer m a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). Writer m b c -> Writer m a b -> Writer m 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 #
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 #
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 p) p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Ran Methods id :: forall (a :: k). Ob a => Ran ('OP p) p a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). Ran ('OP p) p b c -> Ran ('OP p) p a b -> Ran ('OP p) p a c Source Comments #
(p ~ j, Profunctor p) => Promonad (Rift ('OP p) p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Rift Methods id :: forall (a :: k). Ob a => Rift ('OP p) p a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). Rift ('OP p) p b c -> Rift ('OP p) p a b -> Rift ('OP p) p 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 #
CategoryOf k => Promonad (List :: LIST k -> LIST k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.List Methods id :: forall (a :: LIST k). Ob a => List a a Source Comments # (.) :: forall (b :: LIST k) (c :: LIST k) (a :: LIST k). List b c -> List a b -> List 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 #
PreorderOf k => Promonad (PoAsCat :: POCATK k -> POCATK k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.PreorderAsCategory Methods id :: forall (a :: POCATK k). Ob a => PoAsCat a a Source Comments # (.) :: forall (b :: POCATK k) (c :: POCATK k) (a :: POCATK k). PoAsCat b c -> PoAsCat a b -> PoAsCat a c Source Comments #
BiCCC k => Promonad (FreeCCC :: FK k -> FK k -> Type) Source Comments #
Instance details Defined in Proarrow.Helper.CCC Methods id :: forall (a :: FK k). Ob a => FreeCCC a a Source Comments # (.) :: forall (b :: FK k) (c :: FK k) (a :: FK k). FreeCCC b c -> FreeCCC a b -> FreeCCC a 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 (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 #
Rewrite g => Promonad (Free :: FREE g -> FREE g -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Free Methods id :: forall (a :: FREE g). Ob a => Free a a Source Comments # (.) :: forall (b :: FREE g) (c :: FREE g) (a :: FREE g). Free b c -> Free a b -> Free 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 (BiSimplex :: Simplex j k -> Simplex j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Simplex Methods id :: forall (a :: Simplex j k). Ob a => BiSimplex a a Source Comments # (.) :: forall (b :: Simplex j k) (c :: Simplex j k) (a :: Simplex j k). BiSimplex b c -> BiSimplex a b -> BiSimplex 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 #
(Promonad p, Promonad q) => Promonad (p :++: q :: COPRODUCT j1 j2 -> COPRODUCT j1 j2 -> Type) Source Comments #
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 #
(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 #
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 w c d => Promonad (OpticCat :: OPTIC w c d -> OPTIC w c d -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods id :: forall (a :: OPTIC w c d). Ob a => OpticCat a a Source Comments # (.) :: forall (b :: OPTIC w c d) (c0 :: OPTIC w c d) (a :: OPTIC w 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 #

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

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

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

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

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

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 ('PC :: j -> POCATK j) ('PC k :: POCATK j) Source Comments #
Instance details Defined in Proarrow.Category.Instance.PreorderAsCategory type UN ('PC :: j -> POCATK j) ('PC k :: POCATK j) = k
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 ('F :: j -> FK j) ('F a :: FK j) Source Comments #
Instance details Defined in Proarrow.Helper.CCC type UN ('F :: j -> FK j) ('F a :: FK j) = a
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 ('T :: j -> THIN j) ('T a :: THIN j) Source Comments #
Instance details Defined in Proarrow.Preorder.ThinCategory type UN ('T :: j -> THIN j) ('T a :: THIN j) = a
type UN ('CK :: j -> CATK j i) ('CK a :: CATK j i) Source Comments #
Instance details Defined in Proarrow.Category.Enriched type UN ('CK :: j -> CATK j i) ('CK a :: CATK j i) = a
type UN ('BIPARA :: j -> BIPARAK j i) ('BIPARA a :: BIPARAK j i) Source Comments #
Instance details Defined in Proarrow.Category.Enriched.Bipara type UN ('BIPARA :: j -> BIPARAK j i) ('BIPARA a :: BIPARAK j i) = a
type UN ('F :: j -> FREE g) ('F k :: FREE g) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Free type UN ('F :: j -> FREE g) ('F k :: FREE g) = 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 ('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.Category.Instance.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 ('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.