Take public logup sum into account in check_relation_uses

[az-starkware]

No description provided.

[cursor]

PR Summary

Medium Risk
Changes the core verifier’s relation-usage accounting by incorporating statement-level (public logup) relation uses and requires all Statement implementations to return per-relation use counts, which could cause verification failures if counts are wrong or incomplete.

Overview
Updates the Statement::public_logup_sum API to return both the public logup sum and a per-relation use-count map, and threads this through the verifier.

Extends check_relation_uses to include these extra statement-level uses when bounding relation usage, and updates Cairo/Circuit/example statements to track and report relation names/counts (including new Cairo relation-name constants and a LogupSum helper).

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[reviewable-StarkWare]

This change is 

[cursor]

Cursor Bugbot has reviewed your changes and found 1 potential issue.

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[cursor]

add_yield_term wrong sign when var is None

Medium Severity

add_yield_term uses .or(Some(term)) as the fallback when self.var is None, which sets the sum to +term instead of -term. A yield term represents a subtraction, so an empty LogupSum getting a yield term first would produce the wrong sign. Currently the only call site (line 607) always calls add_use_term first, so the None path isn't hit — but the method's contract is broken for that case, making it a latent correctness issue.

 

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[ilyalesokhin-starkware]

crates/cairo_air/src/statement.rs line 76 at r1 (raw file):

    pub fn add_yield_term(&mut self, context: &mut Context<impl IValue>, term: Var) {
        self.var = self.var.map(|var| eval!(context, (var) - (term))).or(Some(term));
    }

Don't we count yields?

Code quote:

    pub fn add_yield_term(&mut self, context: &mut Context<impl IValue>, term: Var) {
        self.var = self.var.map(|var| eval!(context, (var) - (term))).or(Some(term));
    }

[ilyalesokhin-starkware]

crates/cairo_air/src/statement.rs line 76 at r1 (raw file):

Previously, ilyalesokhin-starkware wrote…

Don't we count yields?

I guess the use count is also a bound on the yield_count for opcodes.

[ilyalesokhin-starkware]

crates/cairo_air/src/statement.rs line 58 at r2 (raw file):

#[derive(Default)]
struct LogupSum {

Document.

Code quote:

LogupSum

[ilyalesokhin-starkware]

crates/cairo_air/src/statement.rs line 58 at r2 (raw file):

#[derive(Default)]
struct LogupSum {

consider renaming to TrackedLogupSum or PublicLogupSum

Code quote:

LogupSum