Use closures in enforce_constraints

[Pratyush]

Description

closes: #XXXX

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[Pratyush]

We add an empty LinearCombination into the map, so that constraints which use empty linear combinations (e.g. via lc!()) can refer to this specific LC instead of always spawning a new one.

[Pratyush]

If the lc is empty or consists of a single element with Variable::Zero, then we return the index for the zero LC.

[Pratyush]

Otherwise, we create a new LC.

[Pratyush]

We add helpers for specific arity constraints. This avoids the dyn object required by enforce_constraints

[Copilot]

Pull Request Overview

This PR updates constraint enforcement to use closures for constructing linear combinations, aiming for a more flexible and deferred evaluation of constraints. Key changes include:

• Converting direct linear combination expressions into closures in various constraint enforcement functions.
• Introducing a new lc_diff! macro and updating several tests, examples, and internal modules to follow the new API.
• Refactoring parts of the constraint system to support closure evaluation for better modularity.

Reviewed Changes

Copilot reviewed 14 out of 14 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
relations/src/utils/linear_combination.rs	Updated lc! macro and linear combination constructors to use closures.
relations/src/sr1cs/mod.rs	Revised constraint enforcement to use closure syntax for operands.
relations/src/gr1cs/tests/*	Updated tests to invoke constraint macros with closures.
relations/src/gr1cs/{predicate, constraint_system*, instance_outliner.rs}	Refactored constraint API and internals to support closure-based evaluation.
relations/examples/*	Updated examples to use closures when enforcing constraints.
relations/Cargo.toml	Added mimalloc as a dependency.

Comments suppressed due to low confidence (2)

relations/src/gr1cs/constraint_system_ref.rs:238

• When using closures for constraint enforcement, document that these closures must be pure and idempotent, as they might be invoked multiple times. Adding a comment or additional documentation here would help future maintainers avoid side-effect issues.

pub fn enforce_r1cs_constraint(&self, a: impl FnOnce() -> LinearCombination<F>, b: impl FnOnce() -> LinearCombination<F>, c: impl FnOnce() -> LinearCombination<F>) -> crate::gr1cs::Result<()> {

relations/src/gr1cs/constraint_system.rs:510

• Consider adding inline comments or tests to clarify the handling of degenerate linear combinations (e.g., when the LC is empty or trivial) in new_lc_add_helper. This will ensure that the special-case logic remains clear and behaves as expected over time.

fn new_lc_add_helper( cur_num_lcs: &mut usize, lc_map: &mut Vec<Option<LinearCombination<F>>>, should_generate_lc_assignments: bool, assignments: &mut Assignments<F>, lc: LinearCombination<F>) -> crate::gr1cs::Result<Variable> {