Type Alias E

pub type E<F> = Expr<ConstantExpr<F, BerkeleyChallengeTerm>, Column<usize>>;

An expression over /generic/ (not circuit-specific) columns defined in the msm project. To represent constraints as multi variate polynomials. The variables are over the columns.

For instance, if there are 3 columns X1, X2, X3, then to constraint X3 to be equals to sum of the X1 and X2 on a row, we would use the multivariate polynomial X3 - X1 - X2 = 0. Using the expression framework, this constraint would be

use kimchi::circuits::expr::{ConstantExprInner, ExprInner, Operations, Variable};
use kimchi::circuits::gate::CurrOrNext;
use kimchi::circuits::berkeley_columns::BerkeleyChallengeTerm;
use kimchi_msm::columns::{Column as GenericColumn};
use kimchi_msm::expr::E;
pub type Fp = ark_bn254::Fr;
pub type Column = GenericColumn<usize>;
let x1 = E::<Fp>::Atom(
    ExprInner::<Operations<ConstantExprInner<Fp, BerkeleyChallengeTerm>>, Column>::Cell(Variable {
        col: Column::Relation(1),
        row: CurrOrNext::Curr,
    }),
);
let x2 = E::<Fp>::Atom(
    ExprInner::<Operations<ConstantExprInner<Fp, BerkeleyChallengeTerm>>, Column>::Cell(Variable {
        col: Column::Relation(1),
        row: CurrOrNext::Curr,
    }),
);
let x3 = E::<Fp>::Atom(
    ExprInner::<Operations<ConstantExprInner<Fp, BerkeleyChallengeTerm>>, Column>::Cell(Variable {
        col: Column::Relation(1),
        row: CurrOrNext::Curr,
    }),
);
let constraint = x3 - x1 - x2;

A list of such constraints is used to represent the entire circuit and will be used to build the quotient polynomial.

Aliased Type

pub enum E<F> {
    Atom(ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>),
    Pow(Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>, u64),
    Add(Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>, Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>),
    Mul(Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>, Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>),
    Sub(Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>, Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>),
    Double(Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>),
    Square(Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>),
    Cache(CacheId, Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>),
    IfFeature(FeatureFlag, Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>, Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>),
}

Variants

Atom(ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>)

Pow(Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>, u64)

Add(Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>, Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>)

Mul(Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>, Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>)

Sub(Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>, Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>)

Double(Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>)

Square(Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>)

Cache(CacheId, Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>)

IfFeature(FeatureFlag, Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>, Box<Operations<ExprInner<Operations<ConstantExprInner<F, BerkeleyChallengeTerm>>, Column<usize>>>>)