proarrow
Safe HaskellNone
LanguageGHC2024

Proarrow.Category.Instance.Cat

Documentation

newtype KIND Source Comments #

Constructors

K Kind 

Instances

Instances details
Monoidal KIND Source Comments #

Products as monoidal structure.

Instance details

Defined in Proarrow.Category.Instance.Cat

Associated Types

type Unit 
Instance details

Defined in Proarrow.Category.Instance.Cat

type Unit = 'K ()
type (l :: KIND) ** (r :: KIND) 
Instance details

Defined in Proarrow.Category.Instance.Cat

type (l :: KIND) ** (r :: KIND) = 'K (UN 'K l, UN 'K r)

Methods

withOb2 :: forall (a :: KIND) (b :: KIND) r. (Ob a, Ob b) => (Ob (a ** b) => r) -> r Source Comments #

leftUnitor :: forall (a :: KIND). Ob a => ((Unit :: KIND) ** a) ~> a Source Comments #

leftUnitorInv :: forall (a :: KIND). Ob a => a ~> ((Unit :: KIND) ** a) Source Comments #

rightUnitor :: forall (a :: KIND). Ob a => (a ** (Unit :: KIND)) ~> a Source Comments #

rightUnitorInv :: forall (a :: KIND). Ob a => a ~> (a ** (Unit :: KIND)) Source Comments #

associator :: forall (a :: KIND) (b :: KIND) (c :: KIND). (Ob a, Ob b, Ob c) => ((a ** b) ** c) ~> (a ** (b ** c)) Source Comments #

associatorInv :: forall (a :: KIND) (b :: KIND) (c :: KIND). (Ob a, Ob b, Ob c) => (a ** (b ** c)) ~> ((a ** b) ** c) Source Comments #

SymMonoidal KIND Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

swap :: forall (a :: KIND) (b :: KIND). (Ob a, Ob b) => (a ** b) ~> (b ** a) Source Comments #

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))
CopyDiscard KIND Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

copy :: forall (a :: KIND). Ob a => a ~> (a ** a) Source Comments #

discard :: forall (a :: KIND). Ob a => a ~> (Unit :: KIND) Source Comments #

HasBinaryCoproducts KIND Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Associated Types

type ('K l :: KIND) || ('K r :: KIND) 
Instance details

Defined in Proarrow.Category.Instance.Cat

type ('K l :: KIND) || ('K r :: KIND) = 'K (COPRODUCT l r)

Methods

withObCoprod :: forall (a :: KIND) (b :: KIND) r. (Ob a, Ob b) => (Ob (a || b) => r) -> r Source Comments #

lft :: forall (a :: KIND) (b :: KIND). (Ob a, Ob b) => a ~> (a || b) Source Comments #

rgt :: forall (a :: KIND) (b :: KIND). (Ob a, Ob b) => b ~> (a || b) Source Comments #

(|||) :: forall (x :: KIND) (a :: KIND) (y :: KIND). (x ~> a) -> (y ~> a) -> (x || y) ~> a Source Comments #

(+++) :: forall (a :: KIND) (b :: KIND) (x :: KIND) (y :: KIND). (a ~> x) -> (b ~> y) -> (a || b) ~> (x || y) Source Comments #

HasBinaryProducts KIND Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Associated Types

type (l :: KIND) && (r :: KIND) 
Instance details

Defined in Proarrow.Category.Instance.Cat

type (l :: KIND) && (r :: KIND) = 'K (UN 'K l, UN 'K r)

Methods

withObProd :: forall (a :: KIND) (b :: KIND) r. (Ob a, Ob b) => (Ob (a && b) => r) -> r Source Comments #

fst :: forall (a :: KIND) (b :: KIND). (Ob a, Ob b) => (a && b) ~> a Source Comments #

snd :: forall (a :: KIND) (b :: KIND). (Ob a, Ob b) => (a && b) ~> b Source Comments #

(&&&) :: forall (a :: KIND) (x :: KIND) (y :: KIND). (a ~> x) -> (a ~> y) -> a ~> (x && y) Source Comments #

(***) :: forall (a :: KIND) (b :: KIND) (x :: KIND) (y :: KIND). (a ~> x) -> (b ~> y) -> (a && b) ~> (x && y) Source Comments #

CompactClosed KIND Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

distribDual :: forall (a :: KIND) (b :: KIND). (Ob a, Ob b) => Dual (a ** b) ~> (Dual a ** Dual b) Source Comments #

dualUnit :: Dual (Unit :: KIND) ~> (Unit :: KIND) Source Comments #

StarAutonomous KIND Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Associated Types

type Dual ('K a :: KIND) 
Instance details

Defined in Proarrow.Category.Instance.Cat

type Dual ('K a :: KIND) = 'K (OPPOSITE a)

Methods

dual :: forall (a :: KIND) (b :: KIND). (a ~> b) -> Dual b ~> Dual a Source Comments #

dualInv :: forall (a :: KIND) (b :: KIND). (Ob a, Ob b) => (Dual a ~> Dual b) -> b ~> a Source Comments #

linDist :: forall (a :: KIND) (b :: KIND) (c :: KIND). (Ob a, Ob b, Ob c) => ((a ** b) ~> Dual c) -> a ~> Dual (b ** c) Source Comments #

linDistInv :: forall (a :: KIND) (b :: KIND) (c :: KIND). (Ob a, Ob b, Ob c) => (a ~> Dual (b ** c)) -> (a ** b) ~> Dual c Source Comments #

Closed KIND Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Associated Types

type ('K a :: KIND) ~~> ('K b :: KIND) 
Instance details

Defined in Proarrow.Category.Instance.Cat

type ('K a :: KIND) ~~> ('K b :: KIND) = 'K (OPPOSITE a, b)

Methods

withObExp :: forall (a :: KIND) (b :: KIND) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Comments #

curry :: forall (a :: KIND) (b :: KIND) (c :: KIND). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Comments #

apply :: forall (a :: KIND) (b :: KIND). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Comments #

(^^^) :: forall (a :: KIND) (b :: KIND) (x :: KIND) (y :: KIND). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Comments #

HasInitialObject KIND Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Associated Types

type InitialObject 
Instance details

Defined in Proarrow.Category.Instance.Cat

type InitialObject = 'K VOID

Methods

initiate :: forall (a :: KIND). Ob a => (InitialObject :: KIND) ~> a Source Comments #

HasTerminalObject KIND Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Associated Types

type TerminalObject 
Instance details

Defined in Proarrow.Category.Instance.Cat

type TerminalObject = 'K ()

Methods

terminate :: forall (a :: KIND). Ob a => a ~> (TerminalObject :: KIND) Source Comments #

MonoidalAction KIND KIND Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Associated Types

type Act (a :: KIND) (x :: KIND) 
Instance details

Defined in Proarrow.Category.Instance.Cat

type Act (a :: KIND) (x :: KIND) = a ** x

Methods

withObAct :: forall (a :: KIND) (x :: KIND) r. (Ob a, Ob x) => (Ob (Act a x) => r) -> r Source Comments #

unitor :: forall (x :: KIND). Ob x => Act (Unit :: KIND) x ~> x Source Comments #

unitorInv :: forall (x :: KIND). Ob x => x ~> Act (Unit :: KIND) x Source Comments #

multiplicator :: forall (a :: KIND) (b :: KIND) (x :: KIND). (Ob a, Ob b, Ob x) => Act a (Act b x) ~> Act (a ** b) x Source Comments #

multiplicatorInv :: forall (a :: KIND) (b :: KIND) (x :: KIND). (Ob a, Ob b, Ob x) => Act (a ** b) x ~> Act a (Act b x) 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 #

Ob a => Comonoid (a :: KIND) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

counit :: a ~> (Unit :: KIND) Source Comments #

comult :: a ~> (a ** a) Source Comments #

MonoidalProfunctor Cat Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

par0 :: Cat (Unit :: KIND) (Unit :: KIND) Source Comments #

par :: forall (x1 :: KIND) (x2 :: KIND) (y1 :: KIND) (y2 :: KIND). Cat x1 x2 -> Cat y1 y2 -> Cat (x1 ** y1) (x2 ** y2) 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 #

Costrong KIND Cat Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

coact :: forall (a :: KIND) (x :: KIND) (y :: KIND). (Ob a, Ob x, Ob y) => Cat (Act a x) (Act a y) -> Cat x y Source Comments #

Strong KIND Cat Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

act :: forall (a :: KIND) (b :: KIND) (x :: KIND) (y :: KIND). (a ~> b) -> Cat x y -> Cat (Act a x) (Act b y) Source Comments #

type Unit Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type Unit = 'K ()
type (~>) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type (~>) = Cat
type InitialObject Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type InitialObject = 'K VOID
type TerminalObject Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type TerminalObject = 'K ()
type Ob (c :: KIND) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type Ob (c :: KIND) = (Is 'K c, CategoryOf (UN 'K c))
type (l :: KIND) ** (r :: KIND) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type (l :: KIND) ** (r :: KIND) = 'K (UN 'K l, UN 'K r)
type (l :: KIND) && (r :: KIND) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type (l :: KIND) && (r :: KIND) = 'K (UN 'K l, UN 'K r)
type Act (a :: KIND) (x :: KIND) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type Act (a :: KIND) (x :: KIND) = a ** x
type UN 'K ('K k :: KIND) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type UN 'K ('K k :: KIND) = k
type Dual ('K a :: KIND) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type Dual ('K a :: KIND) = 'K (OPPOSITE a)
type ('K l :: KIND) || ('K r :: KIND) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type ('K l :: KIND) || ('K r :: KIND) = 'K (COPRODUCT l r)
type ('K a :: KIND) ~~> ('K b :: KIND) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type ('K a :: KIND) ~~> ('K b :: KIND) = 'K (OPPOSITE a, b)

data Cat (a :: KIND) (b :: KIND) where Source Comments #

Constructors

Cat :: forall {j} {k} (p :: j +-> k). Profunctor p => Cat ('K j) ('K k) 

Instances

Instances details
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 #

MonoidalProfunctor Cat Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

par0 :: Cat (Unit :: KIND) (Unit :: KIND) Source Comments #

par :: forall (x1 :: KIND) (x2 :: KIND) (y1 :: KIND) (y2 :: KIND). Cat x1 x2 -> Cat y1 y2 -> Cat (x1 ** y1) (x2 ** y2) 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 #

Costrong KIND Cat Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

coact :: forall (a :: KIND) (x :: KIND) (y :: KIND). (Ob a, Ob x, Ob y) => Cat (Act a x) (Act a y) -> Cat x y Source Comments #

Strong KIND Cat Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

act :: forall (a :: KIND) (b :: KIND) (x :: KIND) (y :: KIND). (a ~> b) -> Cat x y -> Cat (Act a x) (Act b y) Source Comments #

data family Terminate :: k +-> () Source Comments #

Instances

Instances details
CategoryOf k => FunctorForRep (Terminate :: k +-> ()) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

fmap :: forall (a :: k) (b :: k). (a ~> b) -> ((Terminate :: k +-> ()) @ a) ~> ((Terminate :: k +-> ()) @ b) Source Comments #

type (Terminate :: k +-> ()) @ (a :: k) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type (Terminate :: k +-> ()) @ (a :: k) = '()

data family Initiate :: VOID +-> k Source Comments #

Instances

Instances details
CategoryOf k => FunctorForRep (Initiate :: VOID +-> k) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

fmap :: forall (a :: VOID) (b :: VOID). (a ~> b) -> ((Initiate :: VOID +-> k) @ a) ~> ((Initiate :: VOID +-> k) @ b) Source Comments #

type (Initiate :: VOID +-> k) @ (a :: VOID) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type (Initiate :: VOID +-> k) @ (a :: VOID) = Any :: k

data family FstCat :: (j, k) +-> j Source Comments #

Instances

Instances details
(CategoryOf j, CategoryOf k) => FunctorForRep (FstCat :: (j, k) +-> j) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

fmap :: forall (a :: (j, k)) (b :: (j, k)). (a ~> b) -> ((FstCat :: (j, k) +-> j) @ a) ~> ((FstCat :: (j, k) +-> j) @ b) Source Comments #

type (FstCat :: (j, k) +-> j) @ ('(a, b) :: (j, k)) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type (FstCat :: (j, k) +-> j) @ ('(a, b) :: (j, k)) = a

data family SndCat :: (j, k) +-> k Source Comments #

Instances

Instances details
(CategoryOf j, CategoryOf k) => FunctorForRep (SndCat :: (j, k) +-> k) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

fmap :: forall (a :: (j, k)) (b :: (j, k)). (a ~> b) -> ((SndCat :: (j, k) +-> k) @ a) ~> ((SndCat :: (j, k) +-> k) @ b) Source Comments #

type (SndCat :: (j, k) +-> k) @ ('(a, b) :: (j, k)) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type (SndCat :: (j, k) +-> k) @ ('(a, b) :: (j, k)) = b

data ((p :: k +-> i) :&&&: (q :: k +-> j)) (a :: (i, j)) (b :: k) where Source Comments #

Constructors

(:&&&:) :: forall {k} {i} {j} (p :: k +-> i) (a1 :: i) (b :: k) (q :: k +-> j) (b1 :: j). p a1 b -> q b1 b -> (p :&&&: q) '(a1, b1) b 

Instances

Instances details
(Profunctor p, Profunctor q) => Profunctor (p :&&&: q :: (i, j2) -> j1 -> Type) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

dimap :: forall (c :: (i, j2)) (a :: (i, j2)) (b :: j1) (d :: j1). (c ~> a) -> (b ~> d) -> (p :&&&: q) a b -> (p :&&&: q) c d Source Comments #

(\\) :: forall (a :: (i, j2)) (b :: j1) r. ((Ob a, Ob b) => r) -> (p :&&&: q) a b -> r Source Comments #

(Representable p, Representable q) => Representable (p :&&&: q :: (i, j2) -> j1 -> Type) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

index :: forall (a :: (i, j2)) (b :: j1). (p :&&&: q) a b -> a ~> ((p :&&&: q) % b) Source Comments #

tabulate :: forall (b :: j1) (a :: (i, j2)). Ob b => (a ~> ((p :&&&: q) % b)) -> (p :&&&: q) a b Source Comments #

repMap :: forall (a :: j1) (b :: j1). (a ~> b) -> ((p :&&&: q) % a) ~> ((p :&&&: q) % b) Source Comments #

type (p :&&&: q :: (i, j2) -> j1 -> Type) % (a :: j1) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type (p :&&&: q :: (i, j2) -> j1 -> Type) % (a :: j1) = '(p % a, q % a)

data family LftCat :: j +-> COPRODUCT j k Source Comments #

Instances

Instances details
(CategoryOf j, CategoryOf k) => FunctorForRep (LftCat :: j +-> COPRODUCT j k) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

fmap :: forall (a :: j) (b :: j). (a ~> b) -> ((LftCat :: j +-> COPRODUCT j k) @ a) ~> ((LftCat :: j +-> COPRODUCT j k) @ b) Source Comments #

type (LftCat :: j +-> COPRODUCT j k) @ (a :: j) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type (LftCat :: j +-> COPRODUCT j k) @ (a :: j) = 'L a :: COPRODUCT j k

data family RgtCat :: k +-> COPRODUCT j k Source Comments #

Instances

Instances details
(CategoryOf j, CategoryOf k) => FunctorForRep (RgtCat :: k +-> COPRODUCT j k) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

fmap :: forall (a :: k) (b :: k). (a ~> b) -> ((RgtCat :: k +-> COPRODUCT j k) @ a) ~> ((RgtCat :: k +-> COPRODUCT j k) @ b) Source Comments #

type (RgtCat :: k +-> COPRODUCT j k) @ (a :: k) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type (RgtCat :: k +-> COPRODUCT j k) @ (a :: k) = 'R a :: COPRODUCT j k

data ((p :: i +-> k) :|||: (q :: j +-> k)) (a :: k) (b :: COPRODUCT i j) where Source Comments #

Constructors

InjLP :: forall {i} {k} {j} (p :: i +-> k) (a :: k) (b1 :: i) (q :: j +-> k). p a b1 -> (p :|||: q) a ('L b1 :: COPRODUCT i j) 
InjRP :: forall {j} {k} {i} (q :: j +-> k) (a :: k) (b1 :: j) (p :: i +-> k). q a b1 -> (p :|||: q) a ('R b1 :: COPRODUCT i j) 

Instances

Instances details
(Profunctor p, Profunctor q) => Profunctor (p :|||: q :: k -> COPRODUCT i j -> Type) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

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

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

(Representable p, Representable q) => Representable (p :|||: q :: k -> COPRODUCT i j -> Type) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

index :: forall (a :: k) (b :: COPRODUCT i j). (p :|||: q) a b -> a ~> ((p :|||: q) % b) Source Comments #

tabulate :: forall (b :: COPRODUCT i j) (a :: k). Ob b => (a ~> ((p :|||: q) % b)) -> (p :|||: q) a b Source Comments #

repMap :: forall (a :: COPRODUCT i j) (b :: COPRODUCT i j). (a ~> b) -> ((p :|||: q) % a) ~> ((p :|||: q) % b) Source Comments #

type (p :|||: q :: k -> COPRODUCT i j -> Type) % ('L a :: COPRODUCT i j) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type (p :|||: q :: k -> COPRODUCT i j -> Type) % ('L a :: COPRODUCT i j) = p % a
type (p :|||: q :: k -> COPRODUCT i j -> Type) % ('R a :: COPRODUCT i j) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type (p :|||: q :: k -> COPRODUCT i j -> Type) % ('R a :: COPRODUCT i j) = q % a

data family Swap :: (j, k) +-> (k, j) Source Comments #

Instances

Instances details
(CategoryOf j, CategoryOf k) => FunctorForRep (Swap :: (j, k) +-> (k, j)) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

fmap :: forall (a :: (j, k)) (b :: (j, k)). (a ~> b) -> ((Swap :: (j, k) +-> (k, j)) @ a) ~> ((Swap :: (j, k) +-> (k, j)) @ b) Source Comments #

type (Swap :: (j, k) +-> (k, j)) @ ('(a, b) :: (j, k)) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type (Swap :: (j, k) +-> (k, j)) @ ('(a, b) :: (j, k)) = '(b, a)

data Curry (p :: (i, j) +-> k) (a :: (OPPOSITE j, k)) (b :: i) where Source Comments #

Constructors

Curry :: forall {i} {j} {k} (p :: (i, j) +-> k) (c :: k) (b :: i) (b1 :: j). p c '(b, b1) -> Curry p '('OP b1, c) b 

Instances

Instances details
(Profunctor p, CategoryOf i, CategoryOf j) => Profunctor (Curry p :: (OPPOSITE j, k) -> i -> Type) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

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

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

data Uncurry (p :: i +-> (OPPOSITE j, k)) (a :: k) (b :: (i, j)) where Source Comments #

Constructors

Uncurry :: forall {i} {j} {k} (p :: i +-> (OPPOSITE j, k)) (b1 :: j) (a :: k) (a1 :: i). p '('OP b1, a) a1 -> Uncurry p a '(a1, b1) 

Instances

Instances details
(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 #

data family CombineDual :: (OPPOSITE j, OPPOSITE k) +-> OPPOSITE (j, k) Source Comments #

Instances

Instances details
(CategoryOf j, CategoryOf k) => FunctorForRep (CombineDual :: (OPPOSITE j, OPPOSITE k) +-> OPPOSITE (j, k)) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

fmap :: forall (a :: (OPPOSITE j, OPPOSITE k)) (b :: (OPPOSITE j, OPPOSITE k)). (a ~> b) -> ((CombineDual :: (OPPOSITE j, OPPOSITE k) +-> OPPOSITE (j, k)) @ a) ~> ((CombineDual :: (OPPOSITE j, OPPOSITE k) +-> OPPOSITE (j, k)) @ b) Source Comments #

type (CombineDual :: (OPPOSITE j, OPPOSITE k) +-> OPPOSITE (j, k)) @ ('('OP a, 'OP b) :: (OPPOSITE j, OPPOSITE k)) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type (CombineDual :: (OPPOSITE j, OPPOSITE k) +-> OPPOSITE (j, k)) @ ('('OP a, 'OP b) :: (OPPOSITE j, OPPOSITE k)) = 'OP '(a, b)

data family DistribDual :: OPPOSITE (j, k) +-> (OPPOSITE j, OPPOSITE k) Source Comments #

Instances

Instances details
(CategoryOf j, CategoryOf k) => FunctorForRep (DistribDual :: OPPOSITE (j, k) +-> (OPPOSITE j, OPPOSITE k)) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

fmap :: forall (a :: OPPOSITE (j, k)) (b :: OPPOSITE (j, k)). (a ~> b) -> ((DistribDual :: OPPOSITE (j, k) +-> (OPPOSITE j, OPPOSITE k)) @ a) ~> ((DistribDual :: OPPOSITE (j, k) +-> (OPPOSITE j, OPPOSITE k)) @ b) Source Comments #

type (DistribDual :: OPPOSITE (j, k) +-> (OPPOSITE j, OPPOSITE k)) @ ('OP '(a, b) :: OPPOSITE (j, k)) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type (DistribDual :: OPPOSITE (j, k) +-> (OPPOSITE j, OPPOSITE k)) @ ('OP '(a, b) :: OPPOSITE (j, k)) = '('OP a, 'OP b)

data family DualUnit :: OPPOSITE () +-> () Source Comments #

Instances

Instances details
FunctorForRep DualUnit Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

Associated Types

type DualUnit @ ('OP '()) 
Instance details

Defined in Proarrow.Category.Instance.Cat

type DualUnit @ ('OP '()) = '()

Methods

fmap :: forall (a :: OPPOSITE ()) (b :: OPPOSITE ()). (a ~> b) -> (DualUnit @ a) ~> (DualUnit @ b) Source Comments #

type DualUnit @ ('OP '()) Source Comments # 
Instance details

Defined in Proarrow.Category.Instance.Cat

type DualUnit @ ('OP '()) = '()