feat: GKR Add Instance

[Tabaie]

• Change the GKR API so that defining the circuit and assigning instances are separated. It removes the necessity of defining hints for the output and deferred "finalize" functions.

• Remove the Println function in favor of GetValue.

• gkrgates.Register now checks if a gate of the same name has already been registered. If so, it compares the gates and returns an error if they are not equal. If they are equal, it returns false, nil.

• Remove all logic pertaining to reordering of wires and instances.

• Unless the user explicitly provides their own initial challenge, automatically use all input and output of the circuit as initial Fiat-Shamir challenge.

• Rename GkrCompressions to GkrPermutations to correctly reflect its function. (Note: a future PR should implement compressions instead and revert the name change)

• A benchmark for gkr-poseidon2

[Copilot]

Pull Request Overview

This PR refactors the GKR API to decouple circuit definition from instance assignment, replaces the Println function with GetValue, and improves gate registration by checking for duplicate definitions and renaming GkrCompressions to GkrPermutations.

• Separation of circuit definition and instance assignment in the GKR API
• Removal of Println in favor of GetValue and updates in hint generation functions
• Enhanced gate registration logic with duplicate checks and more precise error reporting

Reviewed Changes

Copilot reviewed 51 out of 51 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
internal/gkr/bls24-315/gate_testing.go	Added EqualGateFunction helper for comparing gate functions
internal/gkr/bls12-381/solver_hints.go	Refactored SolvingData with new options and padding strategy
internal/gkr/bls12-381/gkr.go	Fixed MulAcc to correctly multiply instead of adding
internal/gkr/bls12-377/solver_hints.go & gkr.go	Similar refactoring as in bls12-381 modules
internal/generator/backend/template/*	Updated template hints and solver generation to use the new SolvingData
constraint/solver/gkrgates/registry_test.go	Modified tests to account for the updated Register API return values
constraint/solver/gkrgates/registry.go	Revised Register function to return a (bool, error) tuple and added equality check
constraint/*/solver.go (across multiple curves)	Updated solver initialization to use the new gkr.NewSolvingData helper

Comments suppressed due to low confidence (2)

constraint/solver/gkrgates/registry.go:113

• Consider adding a comment explaining the rationale behind setting curvesForTesting to [ecc.BN254] and allowedCurves to gnark.Curves() when no curves are specified, to improve maintainability.

if len(curvesForTesting) == 0 {

constraint/solver/gkrgates/registry.go:122

• The updated Register function returns (false, nil) when a gate is already registered. Consider updating the documentation to clearly define this behavior for API consumers.

if g, ok := gates[s.name]; ok {