用强化搜索提升Lean 4的自动定理证明效率
Pantograph: A Machine-to-Machine Interaction Interface for Advanced Theorem Proving, High Level Reasoning, and Data Extraction in Lean 4
- 引入蒙特卡洛树搜索等算法优化证明路径探索
- 增强对Lean 4推导步骤的鲁棒处理能力
- 适合想研究智能证明系统的研究者
机器辅助定理证明是指通过结构化推理自动生成数学定理的证明。近年来，结合机器学习模型与证明助手进行该任务的兴趣显著上升。本文提出Pantograph，一个面向Lean 4证明助手的多功能接口，支持基于蒙特卡洛树搜索等强大算法的高效证明搜索。此外，Pantograph通过改进对Lean 4推导步骤的处理，提升了高层推理能力。文中介绍了其架构与功能，并展示了一个应用案例：利用机器学习模型与证明草图完成Lean 4定理的证明。Pantograph的创新特性为更复杂的机器学习模型开展高阶证明搜索和推理铺平道路，助力未来研究人员构建更通用、强大的定理证明系统。
原文摘要 · Abstract (English)
Machine-assisted theorem proving refers to the process of conducting structured reasoning to automatically generate proofs for mathematical theorems. Recently, there has been a surge of interest in using machine learning models in conjunction with proof assistants to perform this task. In this paper, we introduce Pantograph, a tool that provides a versatile interface to the Lean 4 proof assistant and enables efficient proof search via powerful search algorithms such as Monte Carlo Tree Search. In addition, Pantograph enables high-level reasoning by enabling a more robust handling of Lean 4's inference steps. We provide an overview of Pantograph's architecture and features. We also report on an illustrative use case: using machine learning models and proof sketches to prove Lean 4 theorems. Pantograph's innovative features pave the way for more advanced machine learning models to perform complex proof searches and high-level reasoning, equipping future researchers to design more versatile and powerful theorem provers.
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