Safe Haskell	Safe-Inferred
Language	Haskell2010

ZkFold.Base.Algebra.Basic.Number

Synopsis

data Natural
class KnownNat (n :: Nat)
class KnownNat p => Prime p
type family KnownPrime p where ...
type family IsPrime p where ...
type family Log2 (a :: Natural) :: Natural where ...
type family Mod (a :: Natural) (b :: Natural) :: Natural where ...
type family Div (a :: Natural) (b :: Natural) :: Natural where ...
value :: forall n. KnownNat n => Natural
type (<=) (x :: t) (y :: t) = Assert (x <=? y) (LeErrMsg x y :: Constraint)
type family (a :: Natural) * (b :: Natural) :: Natural where ...
type family (a :: Natural) + (b :: Natural) :: Natural where ...
type family (a :: Natural) - (b :: Natural) :: Natural where ...
type family (a :: Natural) ^ (b :: Natural) :: Natural where ...

Documentation

data Natural #

Natural number

Invariant: numbers <= 0xffffffffffffffff use the NS constructor

Instances

Instances details

FromJSON Natural
Instance details Defined in Data.Aeson.Types.FromJSON Methods parseJSON :: Value -> Parser Natural # parseJSONList :: Value -> Parser [Natural] #
FromJSONKey Natural
Instance details Defined in Data.Aeson.Types.FromJSON Methods fromJSONKey :: FromJSONKeyFunction Natural # fromJSONKeyList :: FromJSONKeyFunction [Natural] #
ToJSON Natural
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSON :: Natural -> Value # toEncoding :: Natural -> Encoding # toJSONList :: [Natural] -> Value # toEncodingList :: [Natural] -> Encoding #
ToJSONKey Natural
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSONKey :: ToJSONKeyFunction Natural # toJSONKeyList :: ToJSONKeyFunction [Natural] #
Bits Natural	Since: base-4.8.0
Instance details Defined in GHC.Bits Methods (.&.) :: Natural -> Natural -> Natural # (.\|.) :: Natural -> Natural -> Natural # xor :: Natural -> Natural -> Natural # complement :: Natural -> Natural # shift :: Natural -> Int -> Natural # rotate :: Natural -> Int -> Natural # zeroBits :: Natural # bit :: Int -> Natural # setBit :: Natural -> Int -> Natural # clearBit :: Natural -> Int -> Natural # complementBit :: Natural -> Int -> Natural # testBit :: Natural -> Int -> Bool # bitSizeMaybe :: Natural -> Maybe Int # bitSize :: Natural -> Int # isSigned :: Natural -> Bool # shiftL :: Natural -> Int -> Natural # unsafeShiftL :: Natural -> Int -> Natural # shiftR :: Natural -> Int -> Natural # unsafeShiftR :: Natural -> Int -> Natural # rotateL :: Natural -> Int -> Natural # rotateR :: Natural -> Int -> Natural # popCount :: Natural -> Int #
Enum Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Enum Methods succ :: Natural -> Natural # pred :: Natural -> Natural # toEnum :: Int -> Natural # fromEnum :: Natural -> Int # enumFrom :: Natural -> [Natural] # enumFromThen :: Natural -> Natural -> [Natural] # enumFromTo :: Natural -> Natural -> [Natural] # enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] #
Num Natural	Note that `Natural`'s `Num` instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though. Since: base-4.8.0.0
Instance details Defined in GHC.Num Methods (+) :: Natural -> Natural -> Natural # (-) :: Natural -> Natural -> Natural # (*) :: Natural -> Natural -> Natural # negate :: Natural -> Natural # abs :: Natural -> Natural # signum :: Natural -> Natural # fromInteger :: Integer -> Natural #
Read Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Natural # readList :: ReadS [Natural] # readPrec :: ReadPrec Natural # readListPrec :: ReadPrec [Natural] #
Integral Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Real Methods quot :: Natural -> Natural -> Natural # rem :: Natural -> Natural -> Natural # div :: Natural -> Natural -> Natural # mod :: Natural -> Natural -> Natural # quotRem :: Natural -> Natural -> (Natural, Natural) # divMod :: Natural -> Natural -> (Natural, Natural) # toInteger :: Natural -> Integer #
Real Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Real Methods toRational :: Natural -> Rational #
Show Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Natural -> ShowS # show :: Natural -> String # showList :: [Natural] -> ShowS #
Binary Natural	Since: binary-0.7.3.0
Instance details Defined in Data.Binary.Class Methods put :: Natural -> Put # get :: Get Natural # putList :: [Natural] -> Put #
NFData Natural	Since: deepseq-1.4.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: Natural -> () #
Eq Natural
Instance details Defined in GHC.Num.Natural Methods (==) :: Natural -> Natural -> Bool # (/=) :: Natural -> Natural -> Bool #
Ord Natural
Instance details Defined in GHC.Num.Natural Methods compare :: Natural -> Natural -> Ordering # (<) :: Natural -> Natural -> Bool # (<=) :: Natural -> Natural -> Bool # (>) :: Natural -> Natural -> Bool # (>=) :: Natural -> Natural -> Bool # max :: Natural -> Natural -> Natural # min :: Natural -> Natural -> Natural #
Hashable Natural
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Natural -> Int # hash :: Natural -> Int #
Pretty Natural
Instance details Defined in Prettyprinter.Internal Methods pretty :: Natural -> Doc ann # prettyList :: [Natural] -> Doc ann #
UniformRange Natural
Instance details Defined in System.Random.Internal Methods uniformRM :: StatefulGen g m => (Natural, Natural) -> g -> m Natural #
ToParamSchema Natural
Instance details Defined in Data.Swagger.Internal.ParamSchema Methods toParamSchema :: forall (t :: SwaggerKind Type). Proxy Natural -> ParamSchema t #
ToSchema Natural
Instance details Defined in Data.Swagger.Internal.Schema Methods declareNamedSchema :: Proxy Natural -> Declare (Definitions Schema) NamedSchema #
AdditiveMonoid Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Methods zero :: Natural Source #
AdditiveSemigroup Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Methods (+) :: Natural -> Natural -> Natural Source #
BinaryExpansion Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Associated Types type Bits Natural Source # Methods binaryExpansion :: Natural -> Bits Natural Source # fromBinary :: Bits Natural -> Natural Source #
MultiplicativeMonoid Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Methods one :: Natural Source #
MultiplicativeSemigroup Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Methods (*) :: Natural -> Natural -> Natural Source #
SemiEuclidean Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Methods divMod :: Natural -> Natural -> (Natural, Natural) Source # div :: Natural -> Natural -> Natural Source # mod :: Natural -> Natural -> Natural Source #
Semiring Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class
Eq Natural Source #
Instance details Defined in ZkFold.Symbolic.Data.Eq Associated Types type BooleanOf Natural Source # Methods (==) :: Natural -> Natural -> BooleanOf Natural Source # (/=) :: Natural -> Natural -> BooleanOf Natural Source #
Ord Natural Source #
Instance details Defined in ZkFold.Symbolic.Data.Ord Associated Types type OrderingOf Natural Source # Methods ordering :: Natural -> Natural -> Natural -> OrderingOf Natural -> Natural Source # compare :: Natural -> Natural -> OrderingOf Natural Source # (<) :: Natural -> Natural -> BooleanOf Natural Source # (<=) :: Natural -> Natural -> BooleanOf Natural Source # (>) :: Natural -> Natural -> BooleanOf Natural Source # (>=) :: Natural -> Natural -> BooleanOf Natural Source # max :: Natural -> Natural -> Natural Source # min :: Natural -> Natural -> Natural Source #
TestCoercion SNat	Since: base-4.18.0.0
Instance details Defined in GHC.TypeNats Methods testCoercion :: forall (a :: k) (b :: k). SNat a -> SNat b -> Maybe (Coercion a b) #
TestEquality SNat	Since: base-4.18.0.0
Instance details Defined in GHC.TypeNats Methods testEquality :: forall (a :: k) (b :: k). SNat a -> SNat b -> Maybe (a :~: b) #
Exponent Rational Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Methods (^) :: Rational -> Natural -> Rational Source #
Exponent BLS12_381_GT Natural Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Methods (^) :: BLS12_381_GT -> Natural -> BLS12_381_GT Source #
Exponent BN254_GT Natural Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254 Methods (^) :: BN254_GT -> Natural -> BN254_GT Source #
Exponent Integer Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Methods (^) :: Integer -> Natural -> Integer Source #
Exponent Natural Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Methods (^) :: Natural -> Natural -> Natural Source #
FromConstant Natural Rational Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Methods fromConstant :: Natural -> Rational Source #
FromConstant Natural Integer Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Methods fromConstant :: Natural -> Integer Source #
FromConstant Natural Bool Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Methods fromConstant :: Natural -> Bool Source #
Scale Natural Rational Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Methods scale :: Natural -> Rational -> Rational Source #
Scale Natural Integer Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Methods scale :: Natural -> Integer -> Integer Source #
Scale Natural Bool Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Methods scale :: Natural -> Bool -> Bool Source #
Conditional Bool Natural Source #
Instance details Defined in ZkFold.Symbolic.Data.Conditional Methods bool :: Natural -> Natural -> Bool -> Natural Source #
Lift Natural
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Quote m => Natural -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Natural -> Code m Natural #
(BaseCaseSearch a z y a, BaseCaseSearching_ a z y) => BaseCaseSearching a (z :: Nat)
Instance details Defined in Generic.Random.Internal.BaseCase Methods baseCaseSearching :: proxy '(z, a) -> Gen a #
KnownNat n => Reifies (n :: Nat) Integer
Instance details Defined in Data.Reflection Methods reflect :: proxy n -> Integer #
(Generic a, GBCS (Rep a) z y e, IsMaybe y) => GBaseCaseSearch a (z :: Nat) (y :: Maybe Nat) (e :: Type)
Instance details Defined in Generic.Random.Internal.BaseCase Methods gBaseCaseSearch :: prox y -> proxy '(z, e) -> IfM y Gen Proxy a #
GBCSSum (f :: k1 -> Type) (g :: k1 -> Type) (z :: k2) (e :: k3) ('Nothing :: Maybe Nat) ('Nothing :: Maybe Nat)
Instance details Defined in Generic.Random.Internal.BaseCase Methods gbcsSum :: forall prox proxy (p :: k). prox '('Nothing, 'Nothing) -> proxy '(z, e) -> IfM 'Nothing Weighted Proxy (f p) -> IfM 'Nothing Weighted Proxy (g p) -> IfM ('Nothing \|\|? 'Nothing) Weighted Proxy ((f :+: g) p) #
GBCSSum (f :: k1 -> Type) (g :: k1 -> Type) (z :: k2) (e :: k3) ('Nothing :: Maybe Nat) ('Just n)
Instance details Defined in Generic.Random.Internal.BaseCase Methods gbcsSum :: forall prox proxy (p :: k). prox '('Nothing, 'Just n) -> proxy '(z, e) -> IfM 'Nothing Weighted Proxy (f p) -> IfM ('Just n) Weighted Proxy (g p) -> IfM ('Nothing \|\|? 'Just n) Weighted Proxy ((f :+: g) p) #
GBCSSum (f :: k1 -> Type) (g :: k1 -> Type) (z :: k2) (e :: k3) ('Just m) ('Nothing :: Maybe Nat)
Instance details Defined in Generic.Random.Internal.BaseCase Methods gbcsSum :: forall prox proxy (p :: k). prox '('Just m, 'Nothing) -> proxy '(z, e) -> IfM ('Just m) Weighted Proxy (f p) -> IfM 'Nothing Weighted Proxy (g p) -> IfM ('Just m \|\|? 'Nothing) Weighted Proxy ((f :+: g) p) #
GBCSProduct (f :: k1 -> Type) (g :: k1 -> Type) (z :: k2) (e :: k3) ('Just m) ('Just n)
Instance details Defined in Generic.Random.Internal.BaseCase Methods gbcsProduct :: forall prox proxy (p :: k). prox '('Just m, 'Just n) -> proxy '(z, e) -> IfM ('Just m) Weighted Proxy (f p) -> IfM ('Just n) Weighted Proxy (g p) -> IfM ('Just m &&? 'Just n) Weighted Proxy ((f :*: g) p) #
GBCSSumCompare f g z e (CmpNat m n) => GBCSSum (f :: k1 -> Type) (g :: k1 -> Type) (z :: k2) (e :: k3) ('Just m) ('Just n)
Instance details Defined in Generic.Random.Internal.BaseCase Methods gbcsSum :: forall prox proxy (p :: k). prox '('Just m, 'Just n) -> proxy '(z, e) -> IfM ('Just m) Weighted Proxy (f p) -> IfM ('Just n) Weighted Proxy (g p) -> IfM ('Just m \|\|? 'Just n) Weighted Proxy ((f :+: g) p) #
BaseCaseSearching a (z + 1) => BaseCaseSearching_ a (z :: Natural) ('Nothing :: Maybe t)
Instance details Defined in Generic.Random.Internal.BaseCase Methods baseCaseSearching_ :: proxy 'Nothing -> proxy2 '(z, a) -> IfM 'Nothing Gen Proxy a -> Gen a #
() :=> (Bits Natural)
Instance details Defined in Data.Constraint Methods ins :: () :- Bits Natural #
() :=> (Enum Natural)
Instance details Defined in Data.Constraint Methods ins :: () :- Enum Natural #
() :=> (Num Natural)
Instance details Defined in Data.Constraint Methods ins :: () :- Num Natural #
() :=> (Read Natural)
Instance details Defined in Data.Constraint Methods ins :: () :- Read Natural #
() :=> (Integral Natural)
Instance details Defined in Data.Constraint Methods ins :: () :- Integral Natural #
() :=> (Real Natural)
Instance details Defined in Data.Constraint Methods ins :: () :- Real Natural #
() :=> (Show Natural)
Instance details Defined in Data.Constraint Methods ins :: () :- Show Natural #
() :=> (Eq Natural)
Instance details Defined in Data.Constraint Methods ins :: () :- Eq Natural #
() :=> (Ord Natural)
Instance details Defined in Data.Constraint Methods ins :: () :- Ord Natural #
KnownNat p => FromConstant Natural (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods fromConstant :: Natural -> Zp p Source #
FromConstant Natural (UInt 11 'Auto c) => FromConstant Natural (UTCTime c) Source #
Instance details Defined in ZkFold.Symbolic.Data.UTCTime Methods fromConstant :: Natural -> UTCTime c Source #
FromConstant Natural a => FromConstant Natural (Maybe a) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Methods fromConstant :: Natural -> Maybe a Source #
KnownNat p => Scale Natural (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods scale :: Natural -> Zp p -> Zp p Source #
Scale Natural a => Scale Natural (Maybe a) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Methods scale :: Natural -> Maybe a -> Maybe a Source #
(FromConstant Natural c, AdditiveMonoid c, KnownNat size) => FromConstant Natural (PolyVec c size) Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Univariate Methods fromConstant :: Natural -> PolyVec c size Source #
FromConstant Natural (EuclideanF a v) Source #
Instance details Defined in ZkFold.Symbolic.Compiler.ArithmeticCircuit.Witness Methods fromConstant :: Natural -> EuclideanF a v Source #
FromConstant Natural (WitnessF a v) Source #
Instance details Defined in ZkFold.Symbolic.Compiler.ArithmeticCircuit.Witness Methods fromConstant :: Natural -> WitnessF a v Source #
FromConstant Natural a => FromConstant Natural (UVar a i) Source #
Instance details Defined in ZkFold.Symbolic.Compiler.ArithmeticCircuit.WitnessEstimation Methods fromConstant :: Natural -> UVar a i Source #
(Symbolic c, KnownNat n) => FromConstant Natural (ByteString n c) Source #	Pack a ByteString using one field element per bit. `fromConstant` discards bits after `n`. If the constant is greater than `2^n`, only the part modulo `2^n` will be converted into a ByteString.
Instance details Defined in ZkFold.Symbolic.Data.ByteString Methods fromConstant :: Natural -> ByteString n c Source #
(Symbolic ctx, KnownNat n) => FromConstant Natural (VarByteString n ctx) Source #
Instance details Defined in ZkFold.Symbolic.Data.VarByteString Methods fromConstant :: Natural -> VarByteString n ctx Source #
Scale Natural (EuclideanF a v) Source #
Instance details Defined in ZkFold.Symbolic.Compiler.ArithmeticCircuit.Witness Methods scale :: Natural -> EuclideanF a v -> EuclideanF a v Source #
Scale Natural (WitnessF a v) Source #
Instance details Defined in ZkFold.Symbolic.Compiler.ArithmeticCircuit.Witness Methods scale :: Natural -> WitnessF a v -> WitnessF a v Source #
(Semiring a, Eq a) => Scale Natural (UVar a i) Source #
Instance details Defined in ZkFold.Symbolic.Compiler.ArithmeticCircuit.WitnessEstimation Methods scale :: Natural -> UVar a i -> UVar a i Source #
(Symbolic c, KnownNat n, KnownRegisterSize r) => FromConstant Natural (UInt n r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods fromConstant :: Natural -> UInt n r c Source #
(TwistedEdwardsCurve curve field, Field field) => Scale Natural (TwistedEdwards curve (AffinePoint field)) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods scale :: Natural -> TwistedEdwards curve (AffinePoint field) -> TwistedEdwards curve (AffinePoint field) Source #
(WeierstrassCurve curve field, Conditional (BooleanOf field) (BooleanOf field), Conditional (BooleanOf field) field, Eq field, Field field) => Scale Natural (Weierstrass curve (Point field)) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods scale :: Natural -> Weierstrass curve (Point field) -> Weierstrass curve (Point field) Source #
(Symbolic c, KnownNat n, KnownRegisterSize r) => Scale Natural (UInt n r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods scale :: Natural -> UInt n r c -> UInt n r c Source #
(Symbolic c, KnownNat n, KnownRegisterSize rs) => StrictConv Natural (UInt n rs c) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods strictConv :: Natural -> UInt n rs c Source #
Euclidean (MerkleHash ('Nothing :: Maybe Natural)) Source #
Instance details Defined in ZkFold.Symbolic.Compiler.ArithmeticCircuit.MerkleHash Methods eea :: MerkleHash 'Nothing -> MerkleHash 'Nothing -> (MerkleHash 'Nothing, MerkleHash 'Nothing, MerkleHash 'Nothing) Source # gcd :: MerkleHash 'Nothing -> MerkleHash 'Nothing -> MerkleHash 'Nothing Source # bezoutL :: MerkleHash 'Nothing -> MerkleHash 'Nothing -> MerkleHash 'Nothing Source # bezoutR :: MerkleHash 'Nothing -> MerkleHash 'Nothing -> MerkleHash 'Nothing Source #
Field (MerkleHash ('Just n)) Source #
Instance details Defined in ZkFold.Symbolic.Compiler.ArithmeticCircuit.MerkleHash Methods (//) :: MerkleHash ('Just n) -> MerkleHash ('Just n) -> MerkleHash ('Just n) Source # finv :: MerkleHash ('Just n) -> MerkleHash ('Just n) Source # rootOfUnity :: Natural -> Maybe (MerkleHash ('Just n)) Source #
Finite (Zp n) => Finite (MerkleHash ('Just n)) Source #
Instance details Defined in ZkFold.Symbolic.Compiler.ArithmeticCircuit.MerkleHash Associated Types type Order (MerkleHash ('Just n)) :: Natural Source #
SemiEuclidean (MerkleHash ('Nothing :: Maybe Natural)) Source #
Instance details Defined in ZkFold.Symbolic.Compiler.ArithmeticCircuit.MerkleHash Methods divMod :: MerkleHash 'Nothing -> MerkleHash 'Nothing -> (MerkleHash 'Nothing, MerkleHash 'Nothing) Source # div :: MerkleHash 'Nothing -> MerkleHash 'Nothing -> MerkleHash 'Nothing Source # mod :: MerkleHash 'Nothing -> MerkleHash 'Nothing -> MerkleHash 'Nothing Source #
Finite (Zp n) => ResidueField (MerkleHash ('Just n)) Source #
Instance details Defined in ZkFold.Symbolic.Compiler.ArithmeticCircuit.MerkleHash Associated Types type IntegralOf (MerkleHash ('Just n)) Source # Methods fromIntegral :: IntegralOf (MerkleHash ('Just n)) -> MerkleHash ('Just n) Source # toIntegral :: MerkleHash ('Just n) -> IntegralOf (MerkleHash ('Just n)) Source #
KnownNat p => Exponent (Zp p) Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (^) :: Zp p -> Natural -> Zp p Source #
(Field c, Eq c) => Exponent (Poly c) Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Univariate Methods (^) :: Poly c -> Natural -> Poly c Source #
Exponent (MerkleHash n) Natural Source #
Instance details Defined in ZkFold.Symbolic.Compiler.ArithmeticCircuit.MerkleHash Methods (^) :: MerkleHash n -> Natural -> MerkleHash n Source #
Symbolic c => Exponent (FieldElement c) Natural Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods (^) :: FieldElement c -> Natural -> FieldElement c Source #
Exponent a Natural => Exponent (Maybe a) Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Methods (^) :: Maybe a -> Natural -> Maybe a Source #
FromConstant Natural a => FromConstant (Maybe Natural) (Maybe a) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class Methods fromConstant :: Maybe Natural -> Maybe a Source #
KnownNat weight => TypeLevelWeights ('[weight] :: [Nat]) (L x)
Instance details Defined in Generic.Random.DerivingVia Methods typeLevelWeightsBuilder :: (L x, Int)
(KnownNat weight, TypeLevelWeights weights a) => TypeLevelWeights (weight ': weights :: [Nat]) (L x :\| a)
Instance details Defined in Generic.Random.DerivingVia Methods typeLevelWeightsBuilder :: (L x :\| a, Int)
a ~ a' => FindGen ('Match 'INCOHERENT) ('S _fg _coh '(con, i, 'Just s)) (FieldGen s a) gs a'	Matching custom generator for field `s`.
Instance details Defined in Generic.Random.Internal.Generic Methods findGen :: (Proxy ('Match 'INCOHERENT), Proxy ('S _fg _coh '(con, i, 'Just s)), FullGenListOf ('S _fg _coh '(con, i, 'Just s))) -> FieldGen s a -> gs -> Gen a' #
a ~ a' => FindGen ('Match 'INCOHERENT) ('S _fg _coh '('Just c, i, s)) (ConstrGen c i a) gs a'	Matching custom generator for `i`-th field of constructor `c`.
Instance details Defined in Generic.Random.Internal.Generic Methods findGen :: (Proxy ('Match 'INCOHERENT), Proxy ('S _fg _coh '('Just c, i, s)), FullGenListOf ('S _fg _coh '('Just c, i, s))) -> ConstrGen c i a -> gs -> Gen a' #
MultiplicativeMonoid (Ext2 f e) => Exponent (Ext2 f e) Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (^) :: Ext2 f e -> Natural -> Ext2 f e Source #
MultiplicativeMonoid (Ext3 f e) => Exponent (Ext3 f e) Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (^) :: Ext3 f e -> Natural -> Ext3 f e Source #
Monomial i j => Exponent (Mono i j) Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial Methods (^) :: Mono i j -> Natural -> Mono i j Source #
(Field c, KnownNat size) => Exponent (PolyVec c size) Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Univariate Methods (^) :: PolyVec c size -> Natural -> PolyVec c size Source #
Exponent (EuclideanF a v) Natural Source #
Instance details Defined in ZkFold.Symbolic.Compiler.ArithmeticCircuit.Witness Methods (^) :: EuclideanF a v -> Natural -> EuclideanF a v Source #
Exponent (WitnessF a v) Natural Source #
Instance details Defined in ZkFold.Symbolic.Compiler.ArithmeticCircuit.Witness Methods (^) :: WitnessF a v -> Natural -> WitnessF a v Source #
MultiplicativeMonoid a => Exponent (UVar a i) Natural Source #
Instance details Defined in ZkFold.Symbolic.Compiler.ArithmeticCircuit.WitnessEstimation Methods (^) :: UVar a i -> Natural -> UVar a i Source #
(path ~ GPositionPath con epath, When (IsLeft epath) (HideReps g h), GFieldProd path g h a b) => GPositionSum ('PathLeaf epath) (M1 C ('MetaCons con fix hs) g) (M1 C ('MetaCons con fix hs) h) a b
Instance details Defined in Optics.Internal.Generic Methods gpositionSum :: LensVL (M1 C ('MetaCons con fix hs) g x) (M1 C ('MetaCons con fix hs) h x) a b #
Polynomial c i j => Exponent (Poly c i j) Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Polynomial Methods (^) :: Poly c i j -> Natural -> Poly c i j Source #
(Symbolic c, KnownFFA p r c) => Exponent (FFA p r c) Natural Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Methods (^) :: FFA p r c -> Natural -> FFA p r c Source #
MultiplicativeMonoid (UInt n r c) => Exponent (UInt n r c) Natural Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods (^) :: UInt n r c -> Natural -> UInt n r c Source #
(GPositionSum path1 g1 h1 a b, GPositionSum path2 g2 h2 a b) => GPositionSum ('PathTree path1 path2) (g1 :+: g2) (h1 :+: h2) a b
Instance details Defined in Optics.Internal.Generic Methods gpositionSum :: LensVL ((g1 :+: g2) x) ((h1 :+: h2) x) a b #
type Bits Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Class type Bits Natural = [Natural]
type BooleanOf Natural Source #
Instance details Defined in ZkFold.Symbolic.Data.Eq type BooleanOf Natural = Bool
type OrderingOf Natural Source #
Instance details Defined in ZkFold.Symbolic.Data.Ord type OrderingOf Natural = Ordering
type Compare (a :: Natural) (b :: Natural)
Instance details Defined in Data.Type.Ord type Compare (a :: Natural) (b :: Natural) = CmpNat a b
type m &&? ('Nothing :: Maybe Nat)
Instance details Defined in Generic.Random.Internal.BaseCase type m &&? ('Nothing :: Maybe Nat) = 'Nothing :: Maybe Nat
type m \|\|? ('Nothing :: Maybe Nat)
Instance details Defined in Generic.Random.Internal.BaseCase type m \|\|? ('Nothing :: Maybe Nat) = m
type Eval (Sum ns :: Nat -> Type)
Instance details Defined in Fcf.Class.Foldable type Eval (Sum ns :: Nat -> Type) = Eval (Foldr (+) 0 ns)
type Eval (Length ('[] :: [a]) :: Nat -> Type)
Instance details Defined in Fcf.Data.List type Eval (Length ('[] :: [a]) :: Nat -> Type) = 0
type Eval (Length (a2 ': as) :: Nat -> Type)
Instance details Defined in Fcf.Data.List type Eval (Length (a2 ': as) :: Nat -> Type) = 1 + Eval (Length as)
type Eval (a * b :: Nat -> Type)
Instance details Defined in Fcf.Data.Nat type Eval (a * b :: Nat -> Type) = a * b
type Eval (a + b :: Nat -> Type)
Instance details Defined in Fcf.Data.Nat type Eval (a + b :: Nat -> Type) = a + b
type Eval (a - b :: Nat -> Type)
Instance details Defined in Fcf.Data.Nat type Eval (a - b :: Nat -> Type) = a - b
type Eval (a ^ b :: Nat -> Type)
Instance details Defined in Fcf.Data.Nat type Eval (a ^ b :: Nat -> Type) = a ^ b
type Order (MerkleHash ('Just n)) Source #
Instance details Defined in ZkFold.Symbolic.Compiler.ArithmeticCircuit.MerkleHash type Order (MerkleHash ('Just n)) = n
type IntegralOf (MerkleHash ('Just n)) Source #
Instance details Defined in ZkFold.Symbolic.Compiler.ArithmeticCircuit.MerkleHash type IntegralOf (MerkleHash ('Just n)) = MerkleHash ('Nothing :: Maybe Natural)
type ('Nothing :: Maybe Nat) &&? n
Instance details Defined in Generic.Random.Internal.BaseCase type ('Nothing :: Maybe Nat) &&? n = 'Nothing :: Maybe Nat
type ('Nothing :: Maybe Nat) \|\|? n
Instance details Defined in Generic.Random.Internal.BaseCase type ('Nothing :: Maybe Nat) \|\|? n = n
type Eval (FindIndex _p ('[] :: [a]) :: Maybe Nat -> Type)
Instance details Defined in Fcf.Data.List type Eval (FindIndex _p ('[] :: [a]) :: Maybe Nat -> Type) = 'Nothing :: Maybe Nat
type Eval (FindIndex p (a2 ': as) :: Maybe Nat -> Type)
Instance details Defined in Fcf.Data.List type Eval (FindIndex p (a2 ': as) :: Maybe Nat -> Type) = Eval (If (Eval (p a2)) (Pure ('Just 0)) ((Map ((+) 1) :: Maybe Nat -> Maybe Nat -> Type) =<< FindIndex p as))
type Eval (NumIter a s :: Maybe (k, Nat) -> Type)
Instance details Defined in Fcf.Data.List type Eval (NumIter a s :: Maybe (k, Nat) -> Type) = If (Eval (s > 0)) ('Just '(a, s - 1)) ('Nothing :: Maybe (k, Natural))
type ('Just m) &&? ('Just n)
Instance details Defined in Generic.Random.Internal.BaseCase type ('Just m) &&? ('Just n) = 'Just (Max m n)
type ('Just m) \|\|? ('Just n)
Instance details Defined in Generic.Random.Internal.BaseCase type ('Just m) \|\|? ('Just n) = 'Just (Min m n)

class KnownNat (n :: Nat) #

This class gives the integer associated with a type-level natural. There are instances of the class for every concrete literal: 0, 1, 2, etc.

Since: base-4.7.0.0

Minimal complete definition

natSing

class KnownNat p => Prime p Source #

Instances

Instances details

Prime BLS12_381_Base Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381
Prime BLS12_381_Scalar Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381
Prime BN254_Base Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254
Prime BN254_Scalar Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254
Prime Ed25519_Base Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Ed25519
Prime Ed25519_Scalar Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Ed25519
Prime FpModulus Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta
Prime FqModulus Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta
Prime PlutoEris_p Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.PlutoEris
Prime PlutoEris_q Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.PlutoEris
Prime Secp256k1_Base Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Secp256k1
Prime Secp256k1_Scalar Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Secp256k1
(KnownNat p, KnownPrime p) => Prime p Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Number

type family KnownPrime p where ... Source #

Equations

KnownPrime p = If (IsPrime p) (() :: Constraint) (TypeError (NotPrimeError p))

type family IsPrime p where ... Source #

Equations

IsPrime 0 = 'False
IsPrime 1 = 'False
IsPrime 2 = 'True
IsPrime 3 = 'True
IsPrime n = NotDividesFromTo n 2 (AtLeastSqrt n)

type family Log2 (a :: Natural) :: Natural where ... #

Log base 2 (round down) of natural numbers. Log 0 is undefined (i.e., it cannot be reduced).

Since: base-4.11.0.0

type family Mod (a :: Natural) (b :: Natural) :: Natural where ... infixl 7 #

Modulus of natural numbers. Mod x 0 is undefined (i.e., it cannot be reduced).

Since: base-4.11.0.0

type family Div (a :: Natural) (b :: Natural) :: Natural where ... infixl 7 #

Division (round down) of natural numbers. Div x 0 is undefined (i.e., it cannot be reduced).

Since: base-4.11.0.0

value :: forall n. KnownNat n => Natural Source #

type (<=) (x :: t) (y :: t) = Assert (x <=? y) (LeErrMsg x y :: Constraint) infix 4 #

Comparison (<=) of comparable types, as a constraint.

Since: base-4.16.0.0

type family (a :: Natural) * (b :: Natural) :: Natural where ... infixl 7 #

Multiplication of type-level naturals.

Since: base-4.7.0.0

type family (a :: Natural) + (b :: Natural) :: Natural where ... infixl 6 #

Addition of type-level naturals.

Since: base-4.7.0.0

type family (a :: Natural) - (b :: Natural) :: Natural where ... infixl 6 #

Subtraction of type-level naturals.

Since: base-4.7.0.0

type family (a :: Natural) ^ (b :: Natural) :: Natural where ... infixr 8 #

Exponentiation of type-level naturals.

Since: base-4.7.0.0