Munkres' General Topology Autoformalized in Isabelle/HOL
About
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--\v{C}ech 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.
Related benchmarks
| Task | Dataset | Result | Rank | |
|---|---|---|---|---|
| Autoformalization | Munkres’ Topology (Sections 12–50 (39)) | Active days24 | 2 | |
| Formal proof size measurement | Urysohn lemma 33.1 | Direct287 | 1 | |
| Formal proof size measurement | Urysohn metriz. 34.1 | Direct Proof Size1.20e+3 | 1 | |
| Formal proof size measurement | Tietze extension 35.1 | Direct Component Size324 | 1 | |
| Formal proof size measurement | Tychonoff 37.3 | Direct Size198 | 1 | |
| Formal proof size measurement | Nagata–Smirnov | Direct Size968 | 1 | |
| Formal proof size measurement | Smirnov metriz. 42.1 | Direct Proof Size83 | 1 | |
| Formal proof size measurement | Space-filling curve 44.1 | Direct Proof Size325 | 1 | |
| Formal proof size measurement | Ascoli general | Direct372 | 1 | |
| Formal proof size measurement | Baire category 48.2 | Direct Proof Size62 | 1 |