Type Definition kimchi_msm::expr::E

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

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;
use kimchi_msm::expr::E;
pub type Fp = ark_bn254::Fr;
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.