Safe Haskell	Safe-Inferred
Language	Haskell2010

ZkFold.Symbolic.Data.FieldElement

Documentation

newtype FieldElement c Source #

Constructors

FieldElement
Fields fromFieldElement :: c Par1

Instances

Instances details

(Symbolic c, FromConstant k (BaseField c)) => FromConstant k (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods fromConstant :: k -> FieldElement c Source #
(Symbolic c, Scale k (BaseField c)) => Scale k (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods scale :: k -> FieldElement c -> FieldElement c Source #
Generic (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Associated Types type Rep (FieldElement c) :: Type -> Type # Methods from :: FieldElement c -> Rep (FieldElement c) x # to :: Rep (FieldElement c) x -> FieldElement c #
Show (c Par1) => Show (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods showsPrec :: Int -> FieldElement c -> ShowS # show :: FieldElement c -> String # showList :: [FieldElement c] -> ShowS #
NFData (c Par1) => NFData (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods rnf :: FieldElement c -> () #
Eq (c Par1) => Eq (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods (==) :: FieldElement c -> FieldElement c -> Bool # (/=) :: FieldElement c -> FieldElement c -> Bool #
Ord (c Par1) => Ord (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods compare :: FieldElement c -> FieldElement c -> Ordering # (<) :: FieldElement c -> FieldElement c -> Bool # (<=) :: FieldElement c -> FieldElement c -> Bool # (>) :: FieldElement c -> FieldElement c -> Bool # (>=) :: FieldElement c -> FieldElement c -> Bool # max :: FieldElement c -> FieldElement c -> FieldElement c # min :: FieldElement c -> FieldElement c -> FieldElement c #
Symbolic c => AdditiveGroup (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods (-) :: FieldElement c -> FieldElement c -> FieldElement c Source # negate :: FieldElement c -> FieldElement c Source #
Symbolic c => AdditiveMonoid (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods zero :: FieldElement c Source #
Symbolic c => AdditiveSemigroup (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods (+) :: FieldElement c -> FieldElement c -> FieldElement c Source #
Symbolic c => BinaryExpansion (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Associated Types type Bits (FieldElement c) Source # Methods binaryExpansion :: FieldElement c -> Bits (FieldElement c) Source # fromBinary :: Bits (FieldElement c) -> FieldElement c Source #
Symbolic c => Field (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods (//) :: FieldElement c -> FieldElement c -> FieldElement c Source # finv :: FieldElement c -> FieldElement c Source # rootOfUnity :: Natural -> Maybe (FieldElement c) Source #
(KnownNat (Order (FieldElement c)), KnownNat (NumberOfBits (FieldElement c))) => Finite (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Associated Types type Order (FieldElement c) :: Natural Source #
Symbolic c => MultiplicativeMonoid (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods one :: FieldElement c Source #
Symbolic c => MultiplicativeSemigroup (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods (*) :: FieldElement c -> FieldElement c -> FieldElement c Source #
Symbolic c => Ring (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement
Symbolic c => Semiring (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement
ToConstant (FieldElement (Interpreter a)) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Associated Types type Const (FieldElement (Interpreter a)) Source # Methods toConstant :: FieldElement (Interpreter a) -> Const (FieldElement (Interpreter a)) Source #
Symbolic c => SymbolicData (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Associated Types type Context (FieldElement c) :: (Type -> Type) -> Type Source # type Support (FieldElement c) Source # type Layout (FieldElement c) :: Type -> Type Source # type Payload (FieldElement c) :: Type -> Type Source # Methods arithmetize :: FieldElement c -> Support (FieldElement c) -> Context (FieldElement c) (Layout (FieldElement c)) Source # payload :: FieldElement c -> Support (FieldElement c) -> Payload (FieldElement c) (WitnessField (Context (FieldElement c))) Source # restore :: Context (FieldElement c) ~ c0 => (Support (FieldElement c) -> (c0 (Layout (FieldElement c)), Payload (FieldElement c) (WitnessField c0))) -> FieldElement c Source #
Symbolic c => Eq (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Associated Types type BooleanOf (FieldElement c) Source # Methods (==) :: FieldElement c -> FieldElement c -> BooleanOf (FieldElement c) Source # (/=) :: FieldElement c -> FieldElement c -> BooleanOf (FieldElement c) Source #
Symbolic c => SymbolicInput (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods isValid :: FieldElement c -> Bool (Context (FieldElement c)) Source #
Symbolic c => Ord (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Associated Types type OrderingOf (FieldElement c) Source # Methods ordering :: FieldElement c -> FieldElement c -> FieldElement c -> OrderingOf (FieldElement c) -> FieldElement c Source # compare :: FieldElement c -> FieldElement c -> OrderingOf (FieldElement c) Source # (<) :: FieldElement c -> FieldElement c -> BooleanOf (FieldElement c) Source # (<=) :: FieldElement c -> FieldElement c -> BooleanOf (FieldElement c) Source # (>) :: FieldElement c -> FieldElement c -> BooleanOf (FieldElement c) Source # (>=) :: FieldElement c -> FieldElement c -> BooleanOf (FieldElement c) Source # max :: FieldElement c -> FieldElement c -> FieldElement c Source # min :: FieldElement c -> FieldElement c -> FieldElement c Source #
Symbolic c => Exponent (FieldElement c) Integer Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods (^) :: FieldElement c -> Integer -> FieldElement c Source #
Symbolic c => Exponent (FieldElement c) Natural Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods (^) :: FieldElement c -> Natural -> FieldElement c Source #
FromConstant (FieldElement c) (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods fromConstant :: FieldElement c -> FieldElement c Source #
Symbolic c => Scale (FieldElement c) (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods scale :: FieldElement c -> FieldElement c -> FieldElement c 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 #
Symbolic c => Conditional (Bool c) (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods bool :: FieldElement c -> FieldElement c -> Bool c -> FieldElement c Source #
(Symbolic c, NumberOfBits (BaseField c) ~ n) => Iso (FieldElement c) (ByteString n c) Source #
Instance details Defined in ZkFold.Symbolic.Data.ByteString Methods from :: FieldElement c -> ByteString n c Source #
(Symbolic c, KnownRegisterSize r, NumberOfBits (BaseField c) ~ n) => Iso (FieldElement c) (UInt n r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods from :: FieldElement c -> UInt n r c Source #
(Symbolic c, NumberOfBits (BaseField c) ~ n) => Iso (ByteString n c) (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.ByteString Methods from :: ByteString n c -> FieldElement c Source #
(Symbolic c, KnownRegisterSize r, NumberOfBits (BaseField c) ~ n) => Iso (UInt n r c) (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods from :: UInt n r c -> FieldElement c Source #
type Rep (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement type Rep (FieldElement c) = D1 ('MetaData "FieldElement" "ZkFold.Symbolic.Data.FieldElement" "symbolic-base-0.1.0.0-inplace" 'True) (C1 ('MetaCons "FieldElement" 'PrefixI 'True) (S1 ('MetaSel ('Just "fromFieldElement") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (c Par1))))
type Bits (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement type Bits (FieldElement c) = c (Vector (NumberOfBits (BaseField c)))
type Const (FieldElement (Interpreter a)) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement type Const (FieldElement (Interpreter a)) = a
type Order (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement type Order (FieldElement c) = Order (BaseField c)
type Context (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement type Context (FieldElement c) = Context (c Par1)
type Layout (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement type Layout (FieldElement c) = Layout (c Par1)
type Payload (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement type Payload (FieldElement c) = Payload (c Par1)
type Support (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement type Support (FieldElement c) = Support (c Par1)
type BooleanOf (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement type BooleanOf (FieldElement c) = BooleanOf (c Par1)
type OrderingOf (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement type OrderingOf (FieldElement c) = OrderingOf (c Par1)