Safe Haskell	Safe-Inferred
Language	Haskell2010

ZkFold.Symbolic.Data.FFA

Documentation

data FFA p r c Source #

Constructors

FFA
Fields nativeResidue :: FieldElement c uintResidue :: UIntFFA p r c

Instances

Instances details

(Symbolic c, KnownFFA p r c, FromConstant a (Zp p)) => FromConstant a (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Methods fromConstant :: a -> FFA p r c Source #
(Symbolic c, KnownFFA p r c, Scale a (Zp p)) => Scale a (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Methods scale :: a -> FFA p r c -> FFA p r c Source #
(Symbolic c, KnownFFA p r c, b ~ Bool c) => Conditional b (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Methods bool :: FFA p r c -> FFA p r c -> b -> FFA p r c Source #
(Symbolic ctx, KnownFFA BLS12_381_Base 'Auto ctx) => CyclicGroup (BLS12_381_G1_Point ctx) Source #
Instance details Defined in ZkFold.Symbolic.Data.BLS12_381 Associated Types type ScalarFieldOf (BLS12_381_G1_Point ctx) Source # Methods pointGen :: BLS12_381_G1_Point ctx Source #
(Symbolic ctx, KnownFFA Ed25519_Base 'Auto ctx) => CyclicGroup (Ed25519_Point ctx) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 Associated Types type ScalarFieldOf (Ed25519_Point ctx) Source # Methods pointGen :: Ed25519_Point ctx Source #
(Symbolic ctx, KnownFFA Secp256k1_Base 'Auto ctx) => CyclicGroup (Secp256k1_Point ctx) Source #
Instance details Defined in ZkFold.Symbolic.Data.Secp256k1 Associated Types type ScalarFieldOf (Secp256k1_Point ctx) Source # Methods pointGen :: Secp256k1_Point ctx Source #
(Symbolic ctx, a ~ BaseField ctx, bits ~ NumberOfBits a, KnownFFA BLS12_381_Base 'Auto ctx) => Scale (FieldElement ctx) (BLS12_381_G1_Point ctx) Source #
Instance details Defined in ZkFold.Symbolic.Data.BLS12_381 Methods scale :: FieldElement ctx -> BLS12_381_G1_Point ctx -> BLS12_381_G1_Point ctx Source #
(Symbolic ctx, a ~ BaseField ctx, bits ~ NumberOfBits a, KnownFFA Ed25519_Base 'Auto ctx) => Scale (FieldElement ctx) (Ed25519_Point ctx) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 Methods scale :: FieldElement ctx -> Ed25519_Point ctx -> Ed25519_Point ctx Source #
(Symbolic ctx, a ~ BaseField ctx, bits ~ NumberOfBits a, KnownFFA Secp256k1_Base 'Auto ctx) => Scale (FieldElement ctx) (Secp256k1_Point ctx) Source #
Instance details Defined in ZkFold.Symbolic.Data.Secp256k1 Methods scale :: FieldElement ctx -> Secp256k1_Point ctx -> Secp256k1_Point ctx Source #
Generic (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Associated Types type Rep (FFA p r c) :: Type -> Type # Methods from :: FFA p r c -> Rep (FFA p r c) x # to :: Rep (FFA p r c) x -> FFA p r c #
(Show (FieldElement c), Show (UIntFFA p r c)) => Show (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Methods showsPrec :: Int -> FFA p r c -> ShowS # show :: FFA p r c -> String # showList :: [FFA p r c] -> ShowS #
(NFData (FieldElement c), NFData (UIntFFA p r c)) => NFData (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Methods rnf :: FFA p r c -> () #
(Symbolic c, KnownFFA p r c) => AdditiveGroup (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Methods (-) :: FFA p r c -> FFA p r c -> FFA p r c Source # negate :: FFA p r c -> FFA p r c Source #
(Symbolic c, KnownFFA p r c) => AdditiveMonoid (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Methods zero :: FFA p r c Source #
(Symbolic c, KnownFFA p r c) => AdditiveSemigroup (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Methods (+) :: FFA p r c -> FFA p r c -> FFA p r c Source #
(Symbolic c, KnownFFA p r c) => BinaryExpansion (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Associated Types type Bits (FFA p r c) Source # Methods binaryExpansion :: FFA p r c -> Bits (FFA p r c) Source # fromBinary :: Bits (FFA p r c) -> FFA p r c Source #
(Symbolic c, KnownFFA p r c, Prime p) => Field (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Methods (//) :: FFA p r c -> FFA p r c -> FFA p r c Source # finv :: FFA p r c -> FFA p r c Source # rootOfUnity :: Natural -> Maybe (FFA p r c) Source #
Finite (Zp p) => Finite (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Associated Types type Order (FFA p r c) :: Natural Source #
(Symbolic c, KnownFFA p r c) => MultiplicativeMonoid (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Methods one :: FFA p r c Source #
(Symbolic c, KnownFFA p r c) => MultiplicativeSemigroup (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Methods (*) :: FFA p r c -> FFA p r c -> FFA p r c Source #
(Symbolic c, KnownFFA p r c) => Ring (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA
(Symbolic c, KnownFFA p r c) => Semiring (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA
(Arithmetic a, KnownFFA p r (Interpreter a)) => ToConstant (FFA p r (Interpreter a)) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Associated Types type Const (FFA p r (Interpreter a)) Source # Methods toConstant :: FFA p r (Interpreter a) -> Const (FFA p r (Interpreter a)) Source #
(Symbolic c, KnownFFA p r c) => SymbolicData (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Associated Types type Context (FFA p r c) :: (Type -> Type) -> Type Source # type Support (FFA p r c) Source # type Layout (FFA p r c) :: Type -> Type Source # type Payload (FFA p r c) :: Type -> Type Source # Methods arithmetize :: FFA p r c -> Support (FFA p r c) -> Context (FFA p r c) (Layout (FFA p r c)) Source # payload :: FFA p r c -> Support (FFA p r c) -> Payload (FFA p r c) (WitnessField (Context (FFA p r c))) Source # restore :: Context (FFA p r c) ~ c0 => (Support (FFA p r c) -> (c0 (Layout (FFA p r c)), Payload (FFA p r c) (WitnessField c0))) -> FFA p r c Source #
(Symbolic c, KnownFFA p r c) => Eq (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Associated Types type BooleanOf (FFA p r c) Source # Methods (==) :: FFA p r c -> FFA p r c -> BooleanOf (FFA p r c) Source # (/=) :: FFA p r c -> FFA p r c -> BooleanOf (FFA p r c) Source #
(Symbolic c, KnownFFA p r c) => SymbolicInput (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Methods isValid :: FFA p r c -> Bool (Context (FFA p r c)) Source #
(Symbolic c, KnownFFA p r c, Prime p) => Exponent (FFA p r c) Integer Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Methods (^) :: FFA p r c -> Integer -> FFA p r c 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 #
FromConstant (FFA p r c) (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Methods fromConstant :: FFA p r c -> FFA p r c Source #
(Symbolic c, KnownFFA p r c) => Scale (FFA p r c) (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA Methods scale :: FFA p r c -> FFA p r c -> FFA p r c Source #
type ScalarFieldOf (BLS12_381_G1_Point ctx) Source #
Instance details Defined in ZkFold.Symbolic.Data.BLS12_381 type ScalarFieldOf (BLS12_381_G1_Point ctx) = FieldElement ctx
type ScalarFieldOf (Ed25519_Point ctx) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 type ScalarFieldOf (Ed25519_Point ctx) = FieldElement ctx
type ScalarFieldOf (Secp256k1_Point ctx) Source #
Instance details Defined in ZkFold.Symbolic.Data.Secp256k1 type ScalarFieldOf (Secp256k1_Point ctx) = FieldElement ctx
type Rep (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA type Rep (FFA p r c)
type Bits (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA type Bits (FFA p r c) = ByteString (NumberOfBits (Zp p)) c
type Const (FFA p r (Interpreter a)) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA type Const (FFA p r (Interpreter a)) = Zp p
type Order (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA type Order (FFA p r c) = p
type Context (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA type Context (FFA p r c) = GContext (Rep (FFA p r c))
type Layout (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA type Layout (FFA p r c) = GLayout (Rep (FFA p r c))
type Payload (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA type Payload (FFA p r c) = GPayload (Rep (FFA p r c))
type Support (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA type Support (FFA p r c) = GSupport (Rep (FFA p r c))
type BooleanOf (FFA p r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FFA type BooleanOf (FFA p r c) = GBooleanOf (Rep (FFA p r c))

type KnownFFA p r c = (KnownNat (FFAUIntSize p (Order (BaseField c))), KnownNat p, KnownRegisterSize r, KnownRegisters c (FFAUIntSize p (Order (BaseField c))) r, KnownNat (FFAMaxBits p c), KnownNat (GetRegisterSize (BaseField c) (FFAMaxBits p c) r), KnownRegisters c (FFAMaxBits p c) r, KnownNat (Ceil (GetRegisterSize (BaseField c) (FFAMaxBits p c) r) OrdWord), KnownRegisters c (NumberOfBits (Zp p)) r, KnownNat (GetRegisterSize (BaseField c) (NumberOfBits (Zp p)) r), KnownNat (NumberOfBits (Zp p))) Source #