Safe Haskell	None
Language	GHC2024

Proarrow.Category.Instance.FinRel

Synopsis

newtype Bitstring (n :: Nat) = BS Natural
shiftN :: forall (n :: Nat). SNatI n => Natural -> Natural
split :: forall (n :: Nat) (m :: Nat). SNatI n => Bitstring (Plus n m) -> (Bitstring n, Bitstring m)
splits :: forall (n :: Nat) (m :: Nat). (SNatI n, SNatI m) => Bitstring (Mult n m) -> Vec n (Bitstring m)
combine :: forall (n :: Nat) (m :: Nat). SNatI n => Bitstring n -> Bitstring m -> Bitstring (Plus n m)
combines :: forall (m :: Nat) (n :: Nat). SNatI m => Vec n (Bitstring m) -> Bitstring (Mult n m)
pop :: forall (n :: Nat). Bitstring ('S n) -> (Bitstring n, Bool)
push :: forall (n :: Nat). Bool -> Bitstring n -> Bitstring ('S n)
mult :: forall (n :: Nat) (m :: Nat). (SNatI n, SNatI m) => Bitstring n -> Bitstring m -> Bitstring (Mult n m)
bit :: forall (n :: Nat). SNatI n => Fin n -> Bitstring n
zero :: forall (n :: Nat) (m :: Nat). (SNatI n, SNatI m) => Vec n (Bitstring m)
pick :: forall (n :: Nat) a. Vec n a -> Bitstring n -> [a]
fromBools :: forall (n :: Nat). Vec n Bool -> Bitstring n
toBools :: forall (n :: Nat). SNatI n => Bitstring n -> Vec n Bool
arr :: forall (n :: Nat) (m :: Nat). FinSet ('FS m) ('FS n) -> FinRel ('FR m) ('FR n)
data FINREL = FR Nat
data FinRel (a :: FINREL) (b :: FINREL) where
- FinRel :: forall (n :: Nat) (m :: Nat). (SNatI n, SNatI m) => {..} -> FinRel ('FR n) ('FR m)
data family Fun :: FINSET +-> FINREL

Documentation

newtype Bitstring (n :: Nat) Source Github #

Constructors

BS Natural

Instances

Instances details

Bits (Bitstring n) Source Github #
Instance details Defined in Proarrow.Category.Instance.FinRel Methods (.&.) :: Bitstring n -> Bitstring n -> Bitstring n Github # (.\|.) :: Bitstring n -> Bitstring n -> Bitstring n Github # xor :: Bitstring n -> Bitstring n -> Bitstring n Github # complement :: Bitstring n -> Bitstring n Github # shift :: Bitstring n -> Int -> Bitstring n Github # rotate :: Bitstring n -> Int -> Bitstring n Github # zeroBits :: Bitstring n Github # bit :: Int -> Bitstring n Github # setBit :: Bitstring n -> Int -> Bitstring n Github # clearBit :: Bitstring n -> Int -> Bitstring n Github # complementBit :: Bitstring n -> Int -> Bitstring n Github # testBit :: Bitstring n -> Int -> Bool Github # bitSizeMaybe :: Bitstring n -> Maybe Int Github # bitSize :: Bitstring n -> Int Github # isSigned :: Bitstring n -> Bool Github # shiftL :: Bitstring n -> Int -> Bitstring n Github # unsafeShiftL :: Bitstring n -> Int -> Bitstring n Github # shiftR :: Bitstring n -> Int -> Bitstring n Github # unsafeShiftR :: Bitstring n -> Int -> Bitstring n Github # rotateL :: Bitstring n -> Int -> Bitstring n Github # rotateR :: Bitstring n -> Int -> Bitstring n Github # popCount :: Bitstring n -> Int Github #
SNatI n => Bounded (Bitstring n) Source Github #
Instance details Defined in Proarrow.Category.Instance.FinRel Methods minBound :: Bitstring n Github # maxBound :: Bitstring n Github #
Enum (Bitstring n) Source Github #
Instance details Defined in Proarrow.Category.Instance.FinRel Methods succ :: Bitstring n -> Bitstring n Github # pred :: Bitstring n -> Bitstring n Github # toEnum :: Int -> Bitstring n Github # fromEnum :: Bitstring n -> Int Github # enumFrom :: Bitstring n -> [Bitstring n] Github # enumFromThen :: Bitstring n -> Bitstring n -> [Bitstring n] Github # enumFromTo :: Bitstring n -> Bitstring n -> [Bitstring n] Github # enumFromThenTo :: Bitstring n -> Bitstring n -> Bitstring n -> [Bitstring n] Github #
Num (Bitstring n) Source Github #
Instance details Defined in Proarrow.Category.Instance.FinRel Methods (+) :: Bitstring n -> Bitstring n -> Bitstring n Github # (-) :: Bitstring n -> Bitstring n -> Bitstring n Github # (*) :: Bitstring n -> Bitstring n -> Bitstring n Github # negate :: Bitstring n -> Bitstring n Github # abs :: Bitstring n -> Bitstring n Github # signum :: Bitstring n -> Bitstring n Github # fromInteger :: Integer -> Bitstring n Github #
SNatI n => Show (Bitstring n) Source Github #
Instance details Defined in Proarrow.Category.Instance.FinRel Methods showsPrec :: Int -> Bitstring n -> ShowS Github # show :: Bitstring n -> String Github # showList :: [Bitstring n] -> ShowS Github #
Eq (Bitstring n) Source Github #
Instance details Defined in Proarrow.Category.Instance.FinRel Methods (==) :: Bitstring n -> Bitstring n -> Bool Github # (/=) :: Bitstring n -> Bitstring n -> Bool Github #
Ord (Bitstring n) Source Github #
Instance details Defined in Proarrow.Category.Instance.FinRel Methods compare :: Bitstring n -> Bitstring n -> Ordering Github # (<) :: Bitstring n -> Bitstring n -> Bool Github # (<=) :: Bitstring n -> Bitstring n -> Bool Github # (>) :: Bitstring n -> Bitstring n -> Bool Github # (>=) :: Bitstring n -> Bitstring n -> Bool Github # max :: Bitstring n -> Bitstring n -> Bitstring n Github # min :: Bitstring n -> Bitstring n -> Bitstring n Github #

shiftN :: forall (n :: Nat). SNatI n => Natural -> Natural Source Github #

split :: forall (n :: Nat) (m :: Nat). SNatI n => Bitstring (Plus n m) -> (Bitstring n, Bitstring m) Source Github #

Split n + m bits into two parts: the lower n bits and the higher m bits.

splits :: forall (n :: Nat) (m :: Nat). (SNatI n, SNatI m) => Bitstring (Mult n m) -> Vec n (Bitstring m) Source Github #

combine :: forall (n :: Nat) (m :: Nat). SNatI n => Bitstring n -> Bitstring m -> Bitstring (Plus n m) Source Github #

Combine two bitstrings of lengths n and m into one bitstring with the n lower bits or m higher bits.

combines :: forall (m :: Nat) (n :: Nat). SNatI m => Vec n (Bitstring m) -> Bitstring (Mult n m) Source Github #

pop :: forall (n :: Nat). Bitstring ('S n) -> (Bitstring n, Bool) Source Github #

push :: forall (n :: Nat). Bool -> Bitstring n -> Bitstring ('S n) Source Github #

mult :: forall (n :: Nat) (m :: Nat). (SNatI n, SNatI m) => Bitstring n -> Bitstring m -> Bitstring (Mult n m) Source Github #

bit :: forall (n :: Nat). SNatI n => Fin n -> Bitstring n Source Github #

zero :: forall (n :: Nat) (m :: Nat). (SNatI n, SNatI m) => Vec n (Bitstring m) Source Github #

pick :: forall (n :: Nat) a. Vec n a -> Bitstring n -> [a] Source Github #

fromBools :: forall (n :: Nat). Vec n Bool -> Bitstring n Source Github #

toBools :: forall (n :: Nat). SNatI n => Bitstring n -> Vec n Bool Source Github #

arr :: forall (n :: Nat) (m :: Nat). FinSet ('FS m) ('FS n) -> FinRel ('FR m) ('FR n) Source Github #

data FINREL Source Github #

Constructors

FR Nat

Instances

Instances details

Monoidal FINREL Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Associated Types

type Unit
Instance details Defined in Proarrow.Category.Instance.FinRel type Unit = 'FR Nat1
type ('FR a :: FINREL) ** ('FR b :: FINREL)
Instance details Defined in Proarrow.Category.Instance.FinRel type ('FR a :: FINREL) ** ('FR b :: FINREL) = 'FR (Mult a b)

Methods

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

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

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

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

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

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

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

SymMonoidal FINREL Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

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

CopyDiscard FINREL Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

copy :: forall (a :: FINREL). Ob a => a ~> (a ** a) Source Github #

discard :: forall (a :: FINREL). Ob a => a ~> (Unit :: FINREL) Source Github #

Distributive FINREL Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

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

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

distL0 :: forall (a :: FINREL). Ob a => (a ** (InitialObject :: FINREL)) ~> (InitialObject :: FINREL) Source Github #

distR0 :: forall (a :: FINREL). Ob a => ((InitialObject :: FINREL) ** a) ~> (InitialObject :: FINREL) Source Github #

Hypergraph FINREL Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

CategoryOf FINREL Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.FinRel type (~>) = FinRel
type Ob (a :: FINREL)
Instance details Defined in Proarrow.Category.Instance.FinRel type Ob (a :: FINREL) = (Is 'FR a, SNatI (UN 'FR a))

HasBinaryCoproducts FINREL Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Associated Types

type ('FR a :: FINREL) \|\| ('FR b :: FINREL)
Instance details Defined in Proarrow.Category.Instance.FinRel type ('FR a :: FINREL) \|\| ('FR b :: FINREL) = 'FR (Plus a b)

Methods

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

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

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

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

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

HasBiproducts FINREL Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

sum :: forall (a :: FINREL) (b :: FINREL). (a ~> b) -> (a ~> b) -> a ~> b Source Github #

HasBinaryProducts FINREL Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Associated Types

type (a :: FINREL) && (b :: FINREL)
Instance details Defined in Proarrow.Category.Instance.FinRel type (a :: FINREL) && (b :: FINREL) = 'FR (Plus (UN 'FR a) (UN 'FR b))

Methods

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

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

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

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

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

CompactClosed FINREL Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

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

dualUnit :: Dual (Unit :: FINREL) ~> (Unit :: FINREL) Source Github #

StarAutonomous FINREL Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Associated Types

type Dual (n :: FINREL)
Instance details Defined in Proarrow.Category.Instance.FinRel type Dual (n :: FINREL) = n

Methods

dual :: forall (a :: FINREL) (b :: FINREL). (a ~> b) -> Dual b ~> Dual a Source Github #

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

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

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

Closed FINREL Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Associated Types

type (x :: FINREL) ~~> (y :: FINREL)
Instance details Defined in Proarrow.Category.Instance.FinRel type (x :: FINREL) ~~> (y :: FINREL) = ExpSA x y

Methods

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

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

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

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

HasInitialObject FINREL Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Associated Types

type InitialObject
Instance details Defined in Proarrow.Category.Instance.FinRel type InitialObject = 'FR Nat0

Methods

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

HasTerminalObject FINREL Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Associated Types

type TerminalObject
Instance details Defined in Proarrow.Category.Instance.FinRel type TerminalObject = 'FR Nat0

Methods

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

DaggerProfunctor FinRel Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

dagger :: forall (a :: FINREL) (b :: FINREL). FinRel a b -> FinRel b a Source Github #

MonoidalAction FINREL FINREL Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Associated Types

type Act (p :: FINREL) (x :: FINREL)
Instance details Defined in Proarrow.Category.Instance.FinRel type Act (p :: FINREL) (x :: FINREL) = p ** x

Methods

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

unitor :: forall (x :: FINREL). Ob x => Act (Unit :: FINREL) x ~> x Source Github #

unitorInv :: forall (x :: FINREL). Ob x => x ~> Act (Unit :: FINREL) x Source Github #

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

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

Promonad FinRel Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

id :: forall (a :: FINREL). Ob a => FinRel a a Source Github #

(.) :: forall (b :: FINREL) (c :: FINREL) (a :: FINREL). FinRel b c -> FinRel a b -> FinRel a c Source Github #

MonoidalProfunctor FinRel Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

par0 :: FinRel (Unit :: FINREL) (Unit :: FINREL) Source Github #

par :: forall (x1 :: FINREL) (x2 :: FINREL) (y1 :: FINREL) (y2 :: FINREL). FinRel x1 x2 -> FinRel y1 y2 -> FinRel (x1 ** y1) (x2 ** y2) Source Github #

Profunctor FinRel Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

dimap :: forall (c :: FINREL) (a :: FINREL) (b :: FINREL) (d :: FINREL). (c ~> a) -> (b ~> d) -> FinRel a b -> FinRel c d Source Github #

(\\) :: forall (a :: FINREL) (b :: FINREL) r. ((Ob a, Ob b) => r) -> FinRel a b -> r Source Github #

FunctorForRep Fun Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Associated Types

type Fun @ ('FS a :: FINSET)
Instance details Defined in Proarrow.Category.Instance.FinRel type Fun @ ('FS a :: FINSET) = 'FR a

Methods

fmap :: forall (a :: FINSET) (b :: FINSET). (a ~> b) -> (Fun @ a) ~> (Fun @ b) Source Github #

Costrong FINREL FinRel Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

coact :: forall (a :: FINREL) (x :: FINREL) (y :: FINREL). (Ob a, Ob x, Ob y) => FinRel (Act a x) (Act a y) -> FinRel x y Source Github #

Strong FINREL FinRel Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

act :: forall (a :: FINREL) (b :: FINREL) (x :: FINREL) (y :: FINREL). (a ~> b) -> FinRel x y -> FinRel (Act a x) (Act b y) Source Github #

MonoidalProfunctor (Rep Fun) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

par0 :: Rep Fun (Unit :: FINREL) (Unit :: FINSET) Source Github #

par :: forall (x1 :: FINREL) (x2 :: FINSET) (y1 :: FINREL) (y2 :: FINSET). Rep Fun x1 x2 -> Rep Fun y1 y2 -> Rep Fun (x1 ** y1) (x2 ** y2) Source Github #

SNatI a => Frobenius ('FR a :: FINREL) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

spider :: forall (n :: Nat) (m :: Nat). (SNatI n, SNatI m) => NFold n ('FR a) ~> NFold m ('FR a) Source Github #

SNatI a => Comonoid ('FR a :: FINREL) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

counit :: 'FR a ~> (Unit :: FINREL) Source Github #

comult :: 'FR a ~> ('FR a ** 'FR a) Source Github #

SNatI a => Monoid ('FR a :: FINREL) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

mempty :: (Unit :: FINREL) ~> 'FR a Source Github #

mappend :: ('FR a ** 'FR a) ~> 'FR a Source Github #

MonoidalProfunctor (Coprod (Rep Fun)) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

par0 :: Coprod (Rep Fun) (Unit :: COPROD FINREL) (Unit :: COPROD FINSET) Source Github #

par :: forall (x1 :: COPROD FINREL) (x2 :: COPROD FINSET) (y1 :: COPROD FINREL) (y2 :: COPROD FINSET). Coprod (Rep Fun) x1 x2 -> Coprod (Rep Fun) y1 y2 -> Coprod (Rep Fun) (x1 ** y1) (x2 ** y2) Source Github #

type Unit Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

type Unit = 'FR Nat1

type (~>) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

type (~>) = FinRel

type InitialObject Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

type InitialObject = 'FR Nat0

type TerminalObject Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

type TerminalObject = 'FR Nat0

type Ob (a :: FINREL) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

type Ob (a :: FINREL) = (Is 'FR a, SNatI (UN 'FR a))

type Dual (n :: FINREL) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

type Dual (n :: FINREL) = n

type (a :: FINREL) && (b :: FINREL) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

type (a :: FINREL) && (b :: FINREL) = 'FR (Plus (UN 'FR a) (UN 'FR b))

type (x :: FINREL) ~~> (y :: FINREL) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

type (x :: FINREL) ~~> (y :: FINREL) = ExpSA x y

type Act (p :: FINREL) (x :: FINREL) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

type Act (p :: FINREL) (x :: FINREL) = p ** x

type UN 'FR ('FR n :: FINREL) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

type UN 'FR ('FR n :: FINREL) = n

type Fun @ ('FS a :: FINSET) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

type Fun @ ('FS a :: FINSET) = 'FR a

type ('FR a :: FINREL) ** ('FR b :: FINREL) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

type ('FR a :: FINREL) ** ('FR b :: FINREL) = 'FR (Mult a b)

type ('FR a :: FINREL) || ('FR b :: FINREL) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

type ('FR a :: FINREL) || ('FR b :: FINREL) = 'FR (Plus a b)

data FinRel (a :: FINREL) (b :: FINREL) where Source Github #

Constructors

FinRel
Fields :: forall (n :: Nat) (m :: Nat). (SNatI n, SNatI m) => { unFinRel :: Vec n (Bitstring m) } -> FinRel ('FR n) ('FR m)

Instances

Instances details

DaggerProfunctor FinRel Source Github #
Instance details Defined in Proarrow.Category.Instance.FinRel Methods dagger :: forall (a :: FINREL) (b :: FINREL). FinRel a b -> FinRel b a Source Github #
Promonad FinRel Source Github #
Instance details Defined in Proarrow.Category.Instance.FinRel Methods id :: forall (a :: FINREL). Ob a => FinRel a a Source Github # (.) :: forall (b :: FINREL) (c :: FINREL) (a :: FINREL). FinRel b c -> FinRel a b -> FinRel a c Source Github #
MonoidalProfunctor FinRel Source Github #
Instance details Defined in Proarrow.Category.Instance.FinRel Methods par0 :: FinRel (Unit :: FINREL) (Unit :: FINREL) Source Github # par :: forall (x1 :: FINREL) (x2 :: FINREL) (y1 :: FINREL) (y2 :: FINREL). FinRel x1 x2 -> FinRel y1 y2 -> FinRel (x1 y1) (x2 y2) Source Github #
Profunctor FinRel Source Github #
Instance details Defined in Proarrow.Category.Instance.FinRel Methods dimap :: forall (c :: FINREL) (a :: FINREL) (b :: FINREL) (d :: FINREL). (c ~> a) -> (b ~> d) -> FinRel a b -> FinRel c d Source Github # (\\) :: forall (a :: FINREL) (b :: FINREL) r. ((Ob a, Ob b) => r) -> FinRel a b -> r Source Github #
Costrong FINREL FinRel Source Github #
Instance details Defined in Proarrow.Category.Instance.FinRel Methods coact :: forall (a :: FINREL) (x :: FINREL) (y :: FINREL). (Ob a, Ob x, Ob y) => FinRel (Act a x) (Act a y) -> FinRel x y Source Github #
Strong FINREL FinRel Source Github #
Instance details Defined in Proarrow.Category.Instance.FinRel Methods act :: forall (a :: FINREL) (b :: FINREL) (x :: FINREL) (y :: FINREL). (a ~> b) -> FinRel x y -> FinRel (Act a x) (Act b y) Source Github #
Show (FinRel a b) Source Github #
Instance details Defined in Proarrow.Category.Instance.FinRel Methods showsPrec :: Int -> FinRel a b -> ShowS Github # show :: FinRel a b -> String Github # showList :: [FinRel a b] -> ShowS Github #
Eq (FinRel a b) Source Github #
Instance details Defined in Proarrow.Category.Instance.FinRel Methods (==) :: FinRel a b -> FinRel a b -> Bool Github # (/=) :: FinRel a b -> FinRel a b -> Bool Github #

data family Fun :: FINSET +-> FINREL Source Github #

Instances

Instances details

FunctorForRep Fun Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Associated Types

type Fun @ ('FS a :: FINSET)
Instance details Defined in Proarrow.Category.Instance.FinRel type Fun @ ('FS a :: FINSET) = 'FR a

Methods

fmap :: forall (a :: FINSET) (b :: FINSET). (a ~> b) -> (Fun @ a) ~> (Fun @ b) Source Github #

MonoidalProfunctor (Rep Fun) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

par0 :: Rep Fun (Unit :: FINREL) (Unit :: FINSET) Source Github #

par :: forall (x1 :: FINREL) (x2 :: FINSET) (y1 :: FINREL) (y2 :: FINSET). Rep Fun x1 x2 -> Rep Fun y1 y2 -> Rep Fun (x1 ** y1) (x2 ** y2) Source Github #

MonoidalProfunctor (Coprod (Rep Fun)) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

Methods

par0 :: Coprod (Rep Fun) (Unit :: COPROD FINREL) (Unit :: COPROD FINSET) Source Github #

par :: forall (x1 :: COPROD FINREL) (x2 :: COPROD FINSET) (y1 :: COPROD FINREL) (y2 :: COPROD FINSET). Coprod (Rep Fun) x1 x2 -> Coprod (Rep Fun) y1 y2 -> Coprod (Rep Fun) (x1 ** y1) (x2 ** y2) Source Github #

type Fun @ ('FS a :: FINSET) Source Github #

Instance details

Defined in Proarrow.Category.Instance.FinRel

type Fun @ ('FS a :: FINSET) = 'FR a