Stage 1 "public callback"

[qwang98]

In #1756, a mapping of public reference to values are calculated in witgen, similar to how a witness column is solved. However, this is only for stage 0 publics and I think there's a need for "public callback" similar to witness callback for stage 1 publics. This is needed for #2502, which tries to decouple publics from a trace in witness.

For example, the following test fails for plonky3/stark.rs when I uncomment the rows below in #2502. The backend can only fetch stage 1 publics from stage 1 witness, which negates our purpose to decouple publics from witness trace:

#[test]
    fn stage_1_public() {
        let content = r#"
        let N: int = 8;

        namespace Global(N);
            let alpha: expr = std::prelude::challenge(0, 41);
            let beta: expr = std::prelude::challenge(0, 42);
            col witness stage(0) x;
            col witness stage(1) y;
            x = y + beta * alpha;

            // public out = y(N - 1);
            
            // Currently, public references are now required along with public declaration in #2502
            // col fixed ISLAST(i) { if i == N - 1 { 1 } else { 0 } };
            // ISLAST * (:out - y) = 0;
        "#;
        run_test(content);
    }

[Schaeff]

Would it make sense to extend the notion of witness to "witness + publics"?