Safe Haskell	None
Language	Haskell2010

Proarrow.Core

Synopsis

type PRO j k = j -> k -> Type
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)
type IsCategoryOf k (cat :: CAT k) = (CategoryOf k, cat ~ ((~>) :: CAT k), Promonad cat)
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 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 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 UNIT 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 :: UNIT)
Instance details Defined in Proarrow.Category.Instance.Unit type Ob (a :: UNIT) = a ~ 'U

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) = IsVoid 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 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

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 :: REV k -> REV k -> Type

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

The opposite category of the category of k.

Instance details

Defined in Proarrow.Category.Opposite

Associated Types

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

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

Instance details

Defined in Proarrow.Object.BinaryCoproduct

Associated Types

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

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 :: PROD k -> PROD k -> Type

Monoidal k => CategoryOf [k] Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal

Associated Types

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

CategoryOf (DiscreteK 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 j k -> DiscreteK j k -> Type

(j ~ 'T0, k ~ 'T0) => CategoryOf (TERMK 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 :: TERMK j k -> TERMK 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 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 :: SUBCAT ob -> SUBCAT ob -> Type

CategoryOf (PRO 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 :: PRO j k -> PRO 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

CategoryOf (ProfK cl 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 cl j k -> ProfK cl j k -> 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 (kk j k2), Ob0 kk j, Ob0 kk k2, Bicategory kk) => CategoryOf (Path kk j k2) Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Bicategory type (~>) = Strictified :: Path kk j k2 -> Path kk j k2 -> 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 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 (QKK kk i j) Source Comments #

Instance details

Defined in Proarrow.Category.Double.Quintet

Associated Types

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

(MonoidalProfunctor w, MonoidalAction m c, MonoidalAction m' 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 (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

type IsCategoryOf k (cat :: CAT k) = (CategoryOf k, cat ~ ((~>) :: CAT k), Promonad cat) Source Comments #

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 Forget Source Comments #
Instance details Defined in Proarrow.Category.Instance.Linear Methods dimap :: forall (c :: LINEAR) (a :: LINEAR) b d. (c ~> a) -> (b ~> d) -> Forget a b -> Forget c d Source Comments # (\\) :: forall (a :: LINEAR) b r. ((Ob a, Ob b) => r) -> Forget 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 Unit Source Comments #
Instance details Defined in Proarrow.Category.Instance.Unit Methods dimap :: forall (c :: UNIT) (a :: UNIT) (b :: UNIT) (d :: UNIT). (c ~> a) -> (b ~> d) -> Unit a b -> Unit c d Source Comments # (\\) :: forall (a :: UNIT) (b :: UNIT) r. ((Ob a, Ob b) => r) -> Unit 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 Free Source Comments #
Instance details Defined in Proarrow.Category.Instance.Linear Methods dimap :: forall c a (b :: LINEAR) (d :: LINEAR). (c ~> a) -> (b ~> d) -> Free a b -> Free c d Source Comments # (\\) :: forall a (b :: LINEAR) r. ((Ob a, Ob b) => r) -> Free 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 :: UNIT -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods dimap :: forall (c :: UNIT) (a :: UNIT) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Terminate a b -> Terminate c d Source Comments # (\\) :: forall (a :: UNIT) (b :: k) r. ((Ob a, Ob b) => r) -> Terminate a b -> r Source Comments #
Profunctor (Reader r :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Reader Methods dimap :: (c ~> a) -> (b ~> d) -> Reader r a b -> Reader r c d Source Comments # (\\) :: ((Ob a, Ob b) => r0) -> Reader r a b -> r0 Source Comments #
Profunctor (Writer m :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Writer Methods dimap :: (c ~> a) -> (b ~> d) -> Writer m a b -> Writer m c d Source Comments # (\\) :: ((Ob a, Ob b) => r) -> Writer m a b -> r Source Comments #
CategoryOf k => Profunctor (Hom :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal Methods dimap :: forall (c :: k) (a :: k) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Hom a b -> Hom c d Source Comments # (\\) :: forall (a :: k) (b :: k) r. ((Ob a, Ob b) => r) -> Hom 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 #
CategoryOf k => Profunctor (CoproductColimit d :: UNIT -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Colimit Methods dimap :: forall (c :: UNIT) (a :: UNIT) (b :: k) (d0 :: k). (c ~> a) -> (b ~> d0) -> CoproductColimit d a b -> CoproductColimit d c d0 Source Comments # (\\) :: forall (a :: UNIT) (b :: k) r. ((Ob a, Ob b) => r) -> CoproductColimit d a b -> r Source Comments #
HasInitialObject k => Profunctor (InitialLimit d :: UNIT -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Colimit Methods dimap :: forall (c :: UNIT) (a :: UNIT) (b :: k) (d0 :: k). (c ~> a) -> (b ~> d0) -> InitialLimit d a b -> InitialLimit d c d0 Source Comments # (\\) :: forall (a :: UNIT) (b :: k) r. ((Ob a, Ob b) => r) -> InitialLimit d a b -> r Source Comments #
Representable d => Profunctor (EndLimit d :: Type -> UNIT -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Limit Methods dimap :: forall c a (b :: UNIT) (d0 :: UNIT). (c ~> a) -> (b ~> d0) -> EndLimit d a b -> EndLimit d c d0 Source Comments # (\\) :: forall a (b :: UNIT) 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 #
(CategoryOf j, CategoryOf k) => Profunctor (InitialProfunctor :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Initial Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> InitialProfunctor a b -> InitialProfunctor c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> InitialProfunctor a b -> r Source Comments #
(CategoryOf j, CategoryOf k) => Profunctor (TerminalProfunctor :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Terminal Methods dimap :: forall (c :: j) (a :: j) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> TerminalProfunctor a b -> TerminalProfunctor c d Source Comments # (\\) :: forall (a :: j) (b :: k) r. ((Ob a, Ob b) => r) -> TerminalProfunctor a b -> r Source Comments #
(HasBinaryProducts k, Representable d) => Profunctor (ProductLimit d :: k -> UNIT -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Limit Methods dimap :: forall (c :: k) (a :: k) (b :: UNIT) (d0 :: UNIT). (c ~> a) -> (b ~> d0) -> ProductLimit d a b -> ProductLimit d c d0 Source Comments # (\\) :: forall (a :: k) (b :: UNIT) r. ((Ob a, Ob b) => r) -> ProductLimit d a b -> r Source Comments #
HasTerminalObject k => Profunctor (TerminalLimit d :: k -> UNIT -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Limit Methods dimap :: forall (c :: k) (a :: k) (b :: UNIT) (d0 :: UNIT). (c ~> a) -> (b ~> d0) -> TerminalLimit d a b -> TerminalLimit d c d0 Source Comments # (\\) :: forall (a :: k) (b :: UNIT) r. ((Ob a, Ob b) => r) -> TerminalLimit d 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 #
(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 #
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 #
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 #
(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 #
(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 #
(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.Rift 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 w, Profunctor p) => Profunctor (DayAct w p :: c -> d -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: forall (c0 :: c) (a :: c) (b :: d) (d0 :: d). (c0 ~> a) -> (b ~> d0) -> DayAct w p a b -> DayAct w p c0 d0 Source Comments # (\\) :: forall (a :: c) (b :: d) r. ((Ob a, Ob b) => r) -> DayAct w p a b -> 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 #
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 :: UNIT -> (OPPOSITE k, k) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Limit Methods dimap :: forall (c :: UNIT) (a :: UNIT) (b :: (OPPOSITE k, k)) (d :: (OPPOSITE k, k)). (c ~> a) -> (b ~> d) -> Hom a b -> Hom c d Source Comments # (\\) :: forall (a :: UNIT) (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 #
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 #
CategoryOf k => Profunctor (Rev :: REV k -> REV k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Rev Methods dimap :: forall (c :: REV k) (a :: REV k) (b :: REV k) (d :: REV k). (c ~> a) -> (b ~> d) -> Rev a b -> Rev c d Source Comments # (\\) :: forall (a :: REV k) (b :: REV k) r. ((Ob a, Ob b) => r) -> Rev a b -> r Source Comments #
CategoryOf k => Profunctor (Coprod :: COPROD k -> COPROD k -> Type) Source Comments #
Instance details Defined in Proarrow.Object.BinaryCoproduct Methods dimap :: forall (c :: COPROD k) (a :: COPROD k) (b :: COPROD k) (d :: COPROD k). (c ~> a) -> (b ~> d) -> Coprod a b -> Coprod c d Source Comments # (\\) :: forall (a :: COPROD k) (b :: COPROD k) r. ((Ob a, Ob b) => r) -> Coprod a b -> r Source Comments #
CategoryOf k => Profunctor (Prod :: PROD k -> PROD k -> Type) Source Comments #
Instance details Defined in Proarrow.Object.BinaryProduct Methods dimap :: forall (c :: PROD k) (a :: PROD k) (b :: PROD k) (d :: PROD k). (c ~> a) -> (b ~> d) -> Prod a b -> Prod c d Source Comments # (\\) :: forall (a :: PROD k) (b :: PROD k) r. ((Ob a, Ob b) => r) -> Prod a b -> r Source Comments #
Monoidal k => Profunctor (Strictified :: [k] -> [k] -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal 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 (Op p :: OPPOSITE k -> OPPOSITE j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Opposite Methods dimap :: forall (c :: OPPOSITE k) (a :: OPPOSITE k) (b :: OPPOSITE j) (d :: OPPOSITE j). (c ~> a) -> (b ~> d) -> Op p a b -> Op p c d Source Comments # (\\) :: forall (a :: OPPOSITE k) (b :: OPPOSITE j) r. ((Ob a, Ob b) => r) -> Op p a b -> r Source Comments #
Profunctor p => Profunctor (Alt p :: PROD j -> COPROD k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Applicative Methods dimap :: forall (c :: PROD j) (a :: PROD j) (b :: COPROD k) (d :: COPROD k). (c ~> a) -> (b ~> d) -> Alt p a b -> Alt p c d Source Comments # (\\) :: forall (a :: PROD j) (b :: COPROD k) r. ((Ob a, Ob b) => r) -> Alt p a b -> r Source Comments #
Profunctor p => Profunctor (App p :: PROD j -> PROD k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Applicative Methods dimap :: forall (c :: PROD j) (a :: PROD j) (b :: PROD k) (d :: PROD k). (c ~> a) -> (b ~> d) -> App p a b -> App p c d Source Comments # (\\) :: forall (a :: PROD j) (b :: PROD k) r. ((Ob a, Ob b) => r) -> App p a b -> r Source Comments #
Profunctor List Source Comments #
Instance details Defined in Proarrow.Profunctor.Forget Methods dimap :: forall (c :: SUBCAT Monoid) (a :: SUBCAT Monoid) b d. (c ~> a) -> (b ~> d) -> List a b -> List c d Source Comments # (\\) :: forall (a :: SUBCAT Monoid) b r. ((Ob a, Ob b) => r) -> List 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 #
(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 #
Profunctor (Bidiscrete :: DiscreteK j k -> DiscreteK j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Bidiscrete Methods dimap :: forall (c :: DiscreteK j k) (a :: DiscreteK j k) (b :: DiscreteK j k) (d :: DiscreteK j k). (c ~> a) -> (b ~> d) -> Bidiscrete a b -> Bidiscrete c d Source Comments # (\\) :: forall (a :: DiscreteK j k) (b :: DiscreteK j k) r. ((Ob a, Ob b) => r) -> Bidiscrete a b -> r Source Comments #
Profunctor (Terminal :: TERMK 'T0 'T0 -> TERMK 'T0 'T0 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Terminal Methods dimap :: forall (c :: TERMK 'T0 'T0) (a :: TERMK 'T0 'T0) (b :: TERMK 'T0 'T0) (d :: TERMK 'T0 'T0). (c ~> a) -> (b ~> d) -> Terminal a b -> Terminal c d Source Comments # (\\) :: forall (a :: TERMK 'T0 'T0) (b :: TERMK 'T0 'T0) r. ((Ob a, Ob b) => r) -> Terminal 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 ((~>) :: CAT k) => Profunctor (Sub :: 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 a b -> Sub c d Source Comments # (\\) :: forall (a :: SUBCAT ob) (b :: SUBCAT ob) r. ((Ob a, Ob b) => r) -> Sub a b -> r Source Comments #
Profunctor (Prof :: PRO j k -> PRO j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Prof Methods dimap :: forall (c :: PRO j k) (a :: PRO j k) (b :: PRO j k) (d :: PRO j k). (c ~> a) -> (b ~> d) -> Prof a b -> Prof c d Source Comments # (\\) :: forall (a :: PRO j k) (b :: PRO 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 (Collage p :: COPRODUCT j k -> COPRODUCT j k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Collage Methods dimap :: forall (c :: COPRODUCT j k) (a :: COPRODUCT j k) (b :: COPRODUCT j k) (d :: COPRODUCT j k). (c ~> a) -> (b ~> d) -> Collage p a b -> Collage p c d Source Comments # (\\) :: forall (a :: COPRODUCT j k) (b :: COPRODUCT j k) r. ((Ob a, Ob b) => r) -> Collage p a b -> r Source Comments #
(Profunctor c, Profunctor d) => Profunctor (c :++: d :: COPRODUCT j k -> COPRODUCT j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Coproduct Methods dimap :: forall (c0 :: COPRODUCT j k) (a :: COPRODUCT j k) (b :: COPRODUCT j k) (d0 :: COPRODUCT j k). (c0 ~> a) -> (b ~> d0) -> (c :++: d) a b -> (c :++: d) c0 d0 Source Comments # (\\) :: forall (a :: COPRODUCT j k) (b :: COPRODUCT j k) r. ((Ob a, Ob b) => r) -> (c :++: d) a b -> r Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :**: q :: (k1, k2) -> (k1, k2) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Product Methods dimap :: forall (c :: (k1, k2)) (a :: (k1, k2)) (b :: (k1, k2)) (d :: (k1, k2)). (c ~> a) -> (b ~> d) -> (p :: q) a b -> (p :: q) c d Source Comments # (\\) :: forall (a :: (k1, k2)) (b :: (k1, k2)) r. ((Ob a, Ob b) => r) -> (p :**: q) 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 (Prof :: ProfK cl j k -> ProfK cl j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Prof Methods dimap :: forall (c :: ProfK cl j k) (a :: ProfK cl j k) (b :: ProfK cl j k) (d :: ProfK cl j k). (c ~> a) -> (b ~> d) -> Prof a b -> Prof c d Source Comments # (\\) :: forall (a :: ProfK cl j k) (b :: ProfK cl j k) r. ((Ob a, Ob b) => r) -> Prof 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 #
(CategoryOf (kk j k2), Ob0 kk j, Ob0 kk k2, Bicategory kk) => Profunctor (Strictified :: Path kk j k2 -> Path kk j k2 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory 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 #
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 #
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 (Q2 :: QKK kk i j -> QKK kk i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Double.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 #
(MonoidalProfunctor w, MonoidalAction m c, MonoidalAction m' 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 #
(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 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 Unit Source Comments #
Instance details Defined in Proarrow.Category.Instance.Unit Methods id :: forall (a :: UNIT). Ob a => Unit a a Source Comments # (.) :: forall (b :: UNIT) (c :: UNIT) (a :: UNIT). Unit b c -> Unit a b -> Unit 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 (Reader r :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Reader Methods id :: Ob a => Reader r a a Source Comments # (.) :: Reader r b c -> Reader r a b -> Reader r a c Source Comments #
Monoid m => Promonad (Writer m :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Writer Methods id :: Ob a => Writer m a a Source Comments # (.) :: Writer m b c -> Writer m a b -> Writer m 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 #
(Monoidal k, Ob s) => Promonad (State s :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.State Methods id :: forall (a :: k). Ob a => State s a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). State s b c -> State s a b -> State s a c Source Comments #
Monad m => Promonad (Star (Prelude m) :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods id :: Ob a => Star (Prelude m) a a Source Comments # (.) :: Star (Prelude m) b c -> Star (Prelude m) a b -> Star (Prelude m) a c Source Comments #
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 #
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 #
CategoryOf k => Promonad (Rev :: REV k -> REV k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Rev Methods id :: forall (a :: REV k). Ob a => Rev a a Source Comments # (.) :: forall (b :: REV k) (c :: REV k) (a :: REV k). Rev b c -> Rev a b -> Rev a c Source Comments #
CategoryOf k => Promonad (Coprod :: COPROD k -> COPROD k -> Type) Source Comments #
Instance details Defined in Proarrow.Object.BinaryCoproduct Methods id :: forall (a :: COPROD k). Ob a => Coprod a a Source Comments # (.) :: forall (b :: COPROD k) (c :: COPROD k) (a :: COPROD k). Coprod b c -> Coprod a b -> Coprod a c Source Comments #
CategoryOf k => Promonad (Prod :: PROD k -> PROD k -> Type) Source Comments #
Instance details Defined in Proarrow.Object.BinaryProduct Methods id :: forall (a :: PROD k). Ob a => Prod a a Source Comments # (.) :: forall (b :: PROD k) (c :: PROD k) (a :: PROD k). Prod b c -> Prod a b -> Prod a c Source Comments #
Monoidal k => Promonad (Strictified :: [k] -> [k] -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal 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 c => Promonad (Op c :: OPPOSITE k -> OPPOSITE k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Opposite Methods id :: forall (a :: OPPOSITE k). Ob a => Op c a a Source Comments # (.) :: forall (b :: OPPOSITE k) (c0 :: OPPOSITE k) (a :: OPPOSITE k). Op c b c0 -> Op c a b -> Op c a c0 Source Comments #
Promonad (Bidiscrete :: DiscreteK j k -> DiscreteK j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Bidiscrete Methods id :: forall (a :: DiscreteK j k). Ob a => Bidiscrete a a Source Comments # (.) :: forall (b :: DiscreteK j k) (c :: DiscreteK j k) (a :: DiscreteK j k). Bidiscrete b c -> Bidiscrete a b -> Bidiscrete a c Source Comments #
Promonad (Terminal :: TERMK 'T0 'T0 -> TERMK 'T0 'T0 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Terminal Methods id :: forall (a :: TERMK 'T0 'T0). Ob a => Terminal a a Source Comments # (.) :: forall (b :: TERMK 'T0 'T0) (c :: TERMK 'T0 'T0) (a :: TERMK 'T0 'T0). Terminal b c -> Terminal a b -> Terminal 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 ((~>) :: CAT k) => Promonad (Sub :: SUBCAT ob -> SUBCAT ob -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Sub Methods id :: forall (a :: SUBCAT ob). Ob a => Sub a a Source Comments # (.) :: forall (b :: SUBCAT ob) (c :: SUBCAT ob) (a :: SUBCAT ob). Sub b c -> Sub a b -> Sub a c Source Comments #
Promonad (Prof :: PRO j k -> PRO j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Prof Methods id :: forall (a :: PRO j k). Ob a => Prof a a Source Comments # (.) :: forall (b :: PRO j k) (c :: PRO j k) (a :: PRO 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 #
Profunctor p => Promonad (Collage p :: COPRODUCT j k -> COPRODUCT j k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Collage Methods id :: forall (a :: COPRODUCT j k). Ob a => Collage p a a Source Comments # (.) :: forall (b :: COPRODUCT j k) (c :: COPRODUCT j k) (a :: COPRODUCT j k). Collage p b c -> Collage p a b -> Collage p a c Source Comments #
(IsCategoryOf j c, IsCategoryOf k d) => Promonad (c :++: d :: COPRODUCT j k -> COPRODUCT j k -> Type) Source Comments #	The coproduct category of the categories `c` and `d`.
Instance details Defined in Proarrow.Category.Instance.Coproduct Methods id :: forall (a :: COPRODUCT j k). Ob a => (c :++: d) a a Source Comments # (.) :: forall (b :: COPRODUCT j k) (c0 :: COPRODUCT j k) (a :: COPRODUCT j k). (c :++: d) b c0 -> (c :++: d) a b -> (c :++: d) a c0 Source Comments #
(Promonad p, Promonad q) => Promonad (p :**: q :: (k1, k2) -> (k1, k2) -> Type) Source Comments #	The product promonad of promonads `p` and `q`.
Instance details Defined in Proarrow.Category.Instance.Product Methods id :: forall (a :: (k1, k2)). Ob a => (p :: q) a a Source Comments # (.) :: forall (b :: (k1, k2)) (c :: (k1, k2)) (a :: (k1, k2)). (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 #
Promonad (Prof :: ProfK cl j k -> ProfK cl j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Prof Methods id :: forall (a :: ProfK cl j k). Ob a => Prof a a Source Comments # (.) :: forall (b :: ProfK cl j k) (c :: ProfK cl j k) (a :: ProfK cl j k). Prof b c -> Prof a b -> Prof 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 #
(CategoryOf (kk j k2), Ob0 kk j, Ob0 kk k2, Bicategory kk) => Promonad (Strictified :: Path kk j k2 -> Path kk j k2 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory 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 #
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 #
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 (Q2 :: QKK kk i j -> QKK kk i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Double.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 #
(MonoidalProfunctor w, MonoidalAction m c, MonoidalAction m' 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 #
(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 ('R :: j -> REV j) ('R a :: REV j) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Rev type UN ('R :: j -> REV j) ('R a :: REV j) = a
type UN ('OP :: j -> OPPOSITE j) ('OP k :: OPPOSITE j) Source Comments #
Instance details Defined in Proarrow.Category.Opposite type UN ('OP :: j -> OPPOSITE j) ('OP k :: OPPOSITE j) = k
type UN ('COPR :: j -> COPROD j) ('COPR k :: COPROD j) Source Comments #
Instance details Defined in Proarrow.Object.BinaryCoproduct type UN ('COPR :: j -> COPROD j) ('COPR k :: COPROD j) = k
type UN ('PR :: j -> PROD j) ('PR k :: PROD j) Source Comments #
Instance details Defined in Proarrow.Object.BinaryProduct type UN ('PR :: j -> PROD j) ('PR k :: PROD j) = k
type UN ('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 ('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 ('PK :: PRO j k -> ProfK cl j k) ('PK p :: ProfK cl j k) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Prof type UN ('PK :: PRO j k -> ProfK cl j k) ('PK p :: ProfK cl j k) = p
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 ('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 ('QK :: kk i j -> QKK kk i j) ('QK p :: QKK kk i j) Source Comments #
Instance details Defined in Proarrow.Category.Double.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.