Self-Modifying Lean Proof Agents with Verifier-Grounded Benchmark Coevolution

2026-07-19

AI Summary

This work proposes a self-evolving Lean theorem-proving agent designed to autonomously optimize its proof workflow without reliance on manually engineered strategies. The approach introduces a verifier-anchored co-evolution mechanism that leverages dynamic curriculum learning and single-anchor recalibration, enabling the agent to co-evolve alongside its benchmark while preserving score comparability and ensuring progressive difficulty. The system is built upon a Lean-based verification loop, a self-modifying architecture, and a machine-readable representation of proof context. Evaluated on the miniF2F test set, the co-evolving agent achieves a success rate of 45.1%, substantially outperforming both a fixed-benchmark agent (32.0%) and the initial seed model (12.7%), thereby demonstrating the efficacy and novelty of the proposed method.

Abstract

Designing effective Lean proof agents is a central challenge in formal mathematical reasoning. Beyond building stronger provers, recent work emphasizes the workflow around Lean: how an agent decomposes proof obligations, uses tools and compiler feedback, diagnoses failures, repairs proofs, and maintains structured proof context. Motivated by code-level self-evolving agents, we study whether such workflows can be evolved rather than hand-designed. We present a self-evolving Lean proof agent in which a small fixed, trusted runtime wraps a fully mutable workspace: the proof workflow, prompts, and tools. Unlike most self-evolving systems, which optimize against a fixed external benchmark, our system coevolves the agent and its benchmark. Between generations, the highest-scoring agent (the champion) revises the active task distribution through a mastery-throttled curriculum update that introduces harder proof obligations only after the current level is mastered, and a single-anchor recalibration re-runs the champion on the updated benchmark to keep scores comparable as difficulty rises. All evolution stays inside a Lean-grounded verification loop: however the agent rewrites itself, a success counts only when its behavior yields Lean-verified proofs under a trusted snapshot, and each attempt must emit a machine-readable, Lean-grounded proof context whose representation may evolve but whose groundedness is enforced. We run the coevolving trajectory and a fixed-benchmark baseline for 15 active generations and compare them on a held-out miniF2F test split. The best coevolving agent reaches a 45.1% held-out solve rate, versus 12.7% for the seed and 32.0% for the best fixed-benchmark agent, showing that verifier-grounded self-evolution can improve Lean proof workflows under a coevolving benchmark.

Problem

• Lean proof agents
• self-evolution
• formal mathematical reasoning
• benchmark coevolution
• verifier-grounded

Innovation

• self-evolving agents
• coevolution
• Lean verification
• verifier-grounded learning
• proof automation