Safe Haskell	None
Language	GHC2024

Proarrow.Category.Instance.CatFun

Contents

Orphan instances

Documentation

data family CurryH :: ((i, j) +-> k) -> i -> j +-> k Source Github #

Instances

Instances details

(Representable f, Ob a, CategoryOf i, CategoryOf j) => FunctorForRep (CurryH f a :: j +-> k) Source Github #
Instance details Defined in Proarrow.Category.Instance.CatFun Methods fmap :: forall (a0 :: j) (b :: j). (a0 ~> b) -> (CurryH f a @ a0) ~> (CurryH f a @ b) Source Github #
type (CurryH f a :: j +-> k) @ (b :: j) Source Github #
Instance details Defined in Proarrow.Category.Instance.CatFun type (CurryH f a :: j +-> k) @ (b :: j) = f % '(a, b)

data family Curry :: ((i, j) +-> k) -> i +-> FUN j k Source Github #

Instances

Instances details

(Representable f, CategoryOf i, CategoryOf j) => FunctorForRep (Curry f :: i +-> FUN j k) Source Github #
Instance details Defined in Proarrow.Category.Instance.CatFun Methods fmap :: forall (a :: i) (b :: i). (a ~> b) -> (Curry f @ a) ~> (Curry f @ b) Source Github #
type (Curry f :: i +-> FUN j k) @ (a :: i) Source Github #
Instance details Defined in Proarrow.Category.Instance.CatFun type (Curry f :: i +-> FUN j k) @ (a :: i) = 'SUB (Rep (CurryH f a)) :: SUBCAT (Representable :: (j +-> k) -> Constraint)

data family Apply :: (FUN j k, j) +-> k Source Github #

Instances

Instances details

(CategoryOf j, CategoryOf k) => FunctorForRep (Apply :: (FUN j k, j) +-> k) Source Github #
Instance details Defined in Proarrow.Category.Instance.CatFun Methods fmap :: forall (a :: (FUN j k, j)) (b :: (FUN j k, j)). (a ~> b) -> ((Apply :: (FUN j k, j) +-> k) @ a) ~> ((Apply :: (FUN j k, j) +-> k) @ b) Source Github #
type (Apply :: (FUN j k, j) +-> k) @ ('(f, x) :: (FUN j k, j)) Source Github #
Instance details Defined in Proarrow.Category.Instance.CatFun type (Apply :: (FUN j k, j) +-> k) @ ('(f, x) :: (FUN j k, j)) = UN ('SUB :: (j +-> k) -> SUBCAT (Representable :: (j +-> k) -> Constraint)) f % x

Orphan instances

Monoidal (BI FUNK) Source Github #

Instance details

Associated Types

type Unit
Instance details Defined in Proarrow.Category.Instance.CatFun type Unit = 'B () :: BI FUNK
type (j :: BI FUNK) ** (k :: BI FUNK)
Instance details Defined in Proarrow.Category.Instance.CatFun type (j :: BI FUNK) ** (k :: BI FUNK) = 'B (UN ('B :: Type -> BI FUNK) j, UN ('B :: Type -> BI FUNK) k) :: BI FUNK

Methods

withOb2 :: forall (a :: BI FUNK) (b :: BI FUNK) r. (Ob a, Ob b) => (Ob (a ** b) => r) -> r Source Github #

leftUnitor :: forall (a :: BI FUNK). Ob a => ((Unit :: BI FUNK) ** a) ~> a Source Github #

leftUnitorInv :: forall (a :: BI FUNK). Ob a => a ~> ((Unit :: BI FUNK) ** a) Source Github #

rightUnitor :: forall (a :: BI FUNK). Ob a => (a ** (Unit :: BI FUNK)) ~> a Source Github #

rightUnitorInv :: forall (a :: BI FUNK). Ob a => a ~> (a ** (Unit :: BI FUNK)) Source Github #

associator :: forall (a :: BI FUNK) (b :: BI FUNK) (c :: BI FUNK). (Ob a, Ob b, Ob c) => ((a ** b) ** c) ~> (a ** (b ** c)) Source Github #

associatorInv :: forall (a :: BI FUNK) (b :: BI FUNK) (c :: BI FUNK). (Ob a, Ob b, Ob c) => (a ** (b ** c)) ~> ((a ** b) ** c) Source Github #

SymMonoidal (BI FUNK) Source Github #

Instance details

Methods

swap :: forall (a :: BI FUNK) (b :: BI FUNK). (Ob a, Ob b) => (a ** b) ~> (b ** a) Source Github #

Closed (BI FUNK) Source Github #

Instance details

Associated Types

type ('B j :: BI FUNK) ~~> ('B k :: BI FUNK)
Instance details Defined in Proarrow.Category.Instance.CatFun type ('B j :: BI FUNK) ~~> ('B k :: BI FUNK) = 'B (FUN j k) :: BI FUNK

Methods

withObExp :: forall (a :: BI FUNK) (b :: BI FUNK) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: BI FUNK) (b :: BI FUNK) (c :: BI FUNK). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: BI FUNK) (b :: BI FUNK). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: BI FUNK) (b :: BI FUNK) (x :: BI FUNK) (y :: BI FUNK). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

Distributive (BI FUNK) Source Github #

Instance details

Methods

distL :: forall (a :: BI FUNK) (b :: BI FUNK) (c :: BI FUNK). (Ob a, Ob b, Ob c) => (a ** (b || c)) ~> ((a ** b) || (a ** c)) Source Github #

distR :: forall (a :: BI FUNK) (b :: BI FUNK) (c :: BI FUNK). (Ob a, Ob b, Ob c) => ((a || b) ** c) ~> ((a ** c) || (b ** c)) Source Github #

absorbL :: forall (a :: BI FUNK). Ob a => (a ** (InitialObject :: BI FUNK)) ~> (InitialObject :: BI FUNK) Source Github #

absorbR :: forall (a :: BI FUNK). Ob a => ((InitialObject :: BI FUNK) ** a) ~> (InitialObject :: BI FUNK) Source Github #

HasBinaryCoproducts (BI FUNK) Source Github #

Instance details

Associated Types

type ('B l :: BI FUNK) \|\| ('B r :: BI FUNK)
Instance details Defined in Proarrow.Category.Instance.CatFun type ('B l :: BI FUNK) \|\| ('B r :: BI FUNK) = 'B (COPRODUCT l r) :: BI FUNK

Methods

withObCoprod :: forall (a :: BI FUNK) (b :: BI FUNK) r. (Ob a, Ob b) => (Ob (a || b) => r) -> r Source Github #

lft :: forall (a :: BI FUNK) (b :: BI FUNK). (Ob a, Ob b) => a ~> (a || b) Source Github #

rgt :: forall (a :: BI FUNK) (b :: BI FUNK). (Ob a, Ob b) => b ~> (a || b) Source Github #

(|||) :: forall (x :: BI FUNK) (a :: BI FUNK) (y :: BI FUNK). (x ~> a) -> (y ~> a) -> (x || y) ~> a Source Github #

(+++) :: forall (a :: BI FUNK) (b :: BI FUNK) (x :: BI FUNK) (y :: BI FUNK). (a ~> x) -> (b ~> y) -> (a || b) ~> (x || y) Source Github #

HasInitialObject (BI FUNK) Source Github #

Instance details

Associated Types

type InitialObject
Instance details Defined in Proarrow.Category.Instance.CatFun type InitialObject = 'B VOID :: BI FUNK

Methods

initiate :: forall (a :: BI FUNK). Ob a => (InitialObject :: BI FUNK) ~> a Source Github #

HasBinaryProducts (BI FUNK) Source Github #

Instance details

Associated Types

type (l :: BI FUNK) && (r :: BI FUNK)
Instance details Defined in Proarrow.Category.Instance.CatFun type (l :: BI FUNK) && (r :: BI FUNK) = 'B (UN ('B :: Type -> BI FUNK) l, UN ('B :: Type -> BI FUNK) r) :: BI FUNK

Methods

withObProd :: forall (a :: BI FUNK) (b :: BI FUNK) r. (Ob a, Ob b) => (Ob (a && b) => r) -> r Source Github #

fst :: forall (a :: BI FUNK) (b :: BI FUNK). (Ob a, Ob b) => (a && b) ~> a Source Github #

snd :: forall (a :: BI FUNK) (b :: BI FUNK). (Ob a, Ob b) => (a && b) ~> b Source Github #

(&&&) :: forall (a :: BI FUNK) (x :: BI FUNK) (y :: BI FUNK). (a ~> x) -> (a ~> y) -> a ~> (x && y) Source Github #

(***) :: forall (a :: BI FUNK) (b :: BI FUNK) (x :: BI FUNK) (y :: BI FUNK). (a ~> x) -> (b ~> y) -> (a && b) ~> (x && y) Source Github #

HasTerminalObject (BI FUNK) Source Github #

Instance details

Associated Types

type TerminalObject
Instance details Defined in Proarrow.Category.Instance.CatFun type TerminalObject = 'B () :: BI FUNK

Methods

terminate :: forall (a :: BI FUNK). Ob a => a ~> (TerminalObject :: BI FUNK) Source Github #

MonoidalProfunctor (Bi :: BI FUNK -> BI FUNK -> Type) Source Github #

Instance details

Methods

one :: Bi (Unit :: BI FUNK) (Unit :: BI FUNK) Source Github #

(**) :: forall (x1 :: BI FUNK) (x2 :: BI FUNK) (y1 :: BI FUNK) (y2 :: BI FUNK). Bi x1 x2 -> Bi y1 y2 -> Bi (x1 ** y1) (x2 ** y2) Source Github #

Bicategory kk => EnrichedProfunctor (BI FUNK) (Bi :: BI kk -> BI kk -> Type) Source Github #

Instance details

Methods

withProObj :: forall (a :: BI kk) (b :: BI kk) r. (Ob a, Ob b) => (Ob (ProObj (BI FUNK) (Bi :: BI kk -> BI kk -> Type) a b) => r) -> r Source Github #

underlying :: forall (a :: BI kk) (b :: BI kk). Bi a b -> (Unit :: BI FUNK) ~> ProObj (BI FUNK) (Bi :: BI kk -> BI kk -> Type) a b Source Github #

enriched :: forall (a :: BI kk) (b :: BI kk). (Ob a, Ob b) => ((Unit :: BI FUNK) ~> ProObj (BI FUNK) (Bi :: BI kk -> BI kk -> Type) a b) -> Bi a b Source Github #

rmap :: forall (a :: BI kk) (b :: BI kk) (c :: BI kk). (Ob a, Ob b, Ob c) => (HomObj (BI FUNK) b c ** ProObj (BI FUNK) (Bi :: BI kk -> BI kk -> Type) a b) ~> ProObj (BI FUNK) (Bi :: BI kk -> BI kk -> Type) a c Source Github #

lmap :: forall (a :: BI kk) (b :: BI kk) (c :: BI kk). (Ob a, Ob b, Ob c) => (HomObj (BI FUNK) c a ** ProObj (BI FUNK) (Bi :: BI kk -> BI kk -> Type) a b) ~> ProObj (BI FUNK) (Bi :: BI kk -> BI kk -> Type) c b Source Github #