Problem
Research questions and friction points this paper is trying to address.
autoformalization
general topology
Isabelle/HOL
LLM-assisted formalization
mathematical formalization
Munkres' General Topology Autoformalized in Isabelle/HOL
🤖 AI Summary
This work addresses the challenge of efficiently and comprehensively formalizing the general topology content from Chapters 2–8 of the classic textbook *Munkres’ Topology* into machine-verifiable proofs. By integrating large language models (ChatGPT 5.2 and Claude Opus 4.6) with the Isabelle/HOL proof assistant, the authors employ an innovative declarative workflow—initially inserting “sorry” placeholders and subsequently filling them in batches—to formalize all 39 sections and 806 theorems within 24 active days, yielding over 85,000 lines of fully completed proof code. This constitutes the first fully automated, “sorry”-free formalization of an entire classical topology textbook, encompassing landmark results such as Tychonoff’s theorem and the Baire category theorem, thereby demonstrating the substantial advantages of LLM-assisted formalization in terms of efficiency, cost, and reliability.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
LLM-assisted autoformalization
Isabelle/HOL
declarative proof workflow
Sledgehammer
formal mathematics
🔎 Similar Papers
No similar papers found.
