用AI打造可验证的数学证明辅导系统，让错误率高的语言模型与严谨的定理证明器互补。
LeanTutor: Towards a Verified AI Mathematical Proof Tutor
- 结合大模型与定理证明器，实现自然语言与形式化证明的双向转换。
- 在371个皮亚诺算术证明上验证，系统能准确生成下一步推理。
- 适合数学教育者、形式化验证研究者使用，提升教学可信度。
本文致力于开发一个基于人工智能的可验证正确性的数学证明辅导系统。尽管大型语言模型（LLMs）能实现自然语言的无缝沟通，但其易出错；而定理证明器如Lean虽能保证正确性，却对学生而言难以学习。我们提出一个概念验证系统LeanTutor，通过整合LLMs与定理证明器的优势，构建了三个模块：(i) 自动形式化/证明检查器，(ii) 下一步推理生成器，(iii) 自然语言反馈生成器。为评估该系统，我们引入PeanoBench数据集，包含371个来自自然数游戏（Natural Numbers Game）的人类撰写自然语言与形式化语言双语证明。
原文摘要 · Abstract (English)
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for provable-correctness, but these are hard for students to learn. We present a proof-of-concept system (LeanTutor) by combining the complementary strengths of LLMs and theorem provers. LeanTutor is composed of three modules: (i) an autoformalizer/proof-checker, (ii) a next-step generator, and (iii) a natural language feedback generator. To evaluate the system, we introduce PeanoBench, a dataset of 371 Peano Arithmetic proofs in human-written natural language and formal language, derived from the Natural Numbers Game.
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