Munkres《一般拓扑学》在Isabelle/HOL中的自动形式化 / Munkres' General Topology Autoformalized in Isabelle/HOL
1️⃣ 一句话总结
这篇论文展示了利用大型语言模型辅助,在24天内将Munkres的《一般拓扑学》教科书几乎全部内容自动形式化为超过8.5万行可验证的代码,证明了这种方法是可行、快速且成本较低的。
We describe an experiment in LLM-assisted autoformalization that produced over 85,000 lines of Isabelle/HOL code covering all 39 sections of Munkres' Topology (general topology, Chapters 2--8), from topological spaces through dimension theory. The LLM-based coding agents (initially ChatGPT 5.2 and then Claude Opus 4.6) used 24 active days for that. The formalization is complete: all 806 formal results are fully proved with zero sorry's. Proved results include the Tychonoff theorem, the Baire category theorem, the Nagata--Smirnov and Smirnov metrization theorems, the Stone--Čech compactification, Ascoli's theorem, the space-filling curve, and others. The methodology is based on a "sorry-first" declarative proof workflow combined with bulk use of sledgehammer - two of Isabelle major strengths. This leads to relatively fast autoformalization progress. We analyze the resulting formalization in detail, analyze the human--LLM interaction patterns from the session log, and briefly compare with related autoformalization efforts in Megalodon, HOL Light, and Naproche. The results indicate that LLM-assisted formalization of standard mathematical textbooks in Isabelle/HOL is quite feasible, cheap and fast, even if some human supervision is useful.
Munkres《一般拓扑学》在Isabelle/HOL中的自动形式化 / Munkres' General Topology Autoformalized in Isabelle/HOL
这篇论文展示了利用大型语言模型辅助,在24天内将Munkres的《一般拓扑学》教科书几乎全部内容自动形式化为超过8.5万行可验证的代码,证明了这种方法是可行、快速且成本较低的。
源自 arXiv: 2604.07455