Lean Refactor: Multi-Objective Controllable Proof Optimization via Agentic Strategy Search
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Computer Science > Logic in Computer Science
Title:Lean Refactor: Multi-Objective Controllable Proof Optimization via Agentic Strategy Search
Abstract: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 $70\%$ token-level compression on competition benchmarks, over $20\%$ on research repositories, and up to $60\%$ 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.
| Subjects: | Logic in Computer Science (cs.LO); Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Machine Learning (cs.LG); Software Engineering (cs.SE) |
| Cite as: | arXiv:2605.20244 [cs.LO] |
| (or arXiv:2605.20244v1 [cs.LO] for this version) | |
| https://doi.org/10.48550/arXiv.2605.20244
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