Lean Refactor: Multi-Objective Controllable Proof Optimization via Agentic Strategy Search
摘要
We present Lean Refactor, a plug-and-play retrieval-augmented agentic framework for multi-objective, controllable, and version-robust refactoring of Lean proofs. LLM-generated proofs are notoriously correct-but-verbose and brittle across library versions, yet existing refactoring works overlook three practical challenges: 1) Lean refactoring is natively multi-objective (proof length, compilation cost, and version compatibility are often in tension); 2) Lean repositories have fragile compatibility, whereas LLM releases are unaware of Lean/Mathlib versions; 3) Training-based pipelines require repeated fine-tuning with each new LLM release, scaling neither with model churn nor with Lean's release cycle. Lean Refactor steers a frozen agentic LLM with retrievals from a curated database of multi-objective refactoring strategies, each densely annotated with metadata such as supported Lean/Mathlib versions and expected compilation-cost reduction. Experiments show over token-level compression on competition benchmarks, over on research repositories, and up to compilation-time reduction, outperforming prior work and Claude Code. Version-filtered retrieval further improves compression on the target Lean version, and refactored miniF2F proofs exhibit stronger zero-shot version transfer to future Lean releases than their unrefactored counterparts.
引用
@article{arxiv.2605.20244,
title = {Lean Refactor: Multi-Objective Controllable Proof Optimization via Agentic Strategy Search},
author = {Jialin Lu and Soonho Kong and Rodrigo Stehling and Kaiyu Yang and Zhangyang Wang and Weiran Sun and Wuyang Chen},
journal= {arXiv preprint arXiv:2605.20244},
year = {2026}
}