3 Search Results for "De Lon, Adrian"

Document
Short Paper
DOI: 10.4230/LIPIcs.ITP.2026.31
130k Lines of Formal Topology in Two Weeks: Simple and Cheap Autoformalization for Everyone? (Short Paper)

Authors: Josef Urban

Published in: LIPIcs, Volume 382, 17th International Conference on Interactive Theorem Proving (ITP 2026)

Abstract
This is a brief description of a project that has already autoformalized a large portion of the general topology from the Munkres textbook (which has in total 241 pages in 7 chapters and 39 sections). The project has been running since November 21, 2025 and has as of January 4, 2026, produced 160k lines of formalized topology. Most of it (about 130k lines) have been done in two weeks, from December 22 to January 4, for an LLM subscription cost of about $100. This includes a 3k-line proof of Urysohn’s lemma, a 2k-line proof of Urysohn’s Metrization theorem, over 10k-line proof of the Tietze extension theorem, and many more (in total over 1.5k lemmas/theorems). The approach is quite simple and cheap: build a long-running feedback loop between an LLM and a reasonably fast proof checker equipped with a core foundational library. The LLM is now instantiated as ChatGPT (mostly 5.2) or Claude Sonnet (4.5) run through the respective Codex or Claude Code command line interfaces. The proof checker is Chad Brown’s higher-order set theory system Megalodon, and the core library is Brown’s formalization of basic set theory and surreal numbers (including reals, etc). The rest is some prompt engineering and technical choices which we describe here. Based on the fast progress, low cost, virtually unknown ITP/library, and the simple setup available to everyone, we believe that (auto)formalization may become quite easy and ubiquitous in 2026, regardless of which proof assistant is used.
Cite as

Josef Urban. 130k Lines of Formal Topology in Two Weeks: Simple and Cheap Autoformalization for Everyone? (Short Paper). In 17th International Conference on Interactive Theorem Proving (ITP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 382, pp. 31:1-31:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{urban:LIPIcs.ITP.2026.31,
  author =	{Urban, Josef},
  title =	{{130k Lines of Formal Topology in Two Weeks: Simple and Cheap Autoformalization for Everyone?}},
  booktitle =	{17th International Conference on Interactive Theorem Proving (ITP 2026)},
  pages =	{31:1--31:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-436-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{382},
  editor =	{Komendantskaya, Ekaterina and Nipkow, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2026.31},
  URN =		{urn:nbn:de:0030-drops-270052},
  doi =		{10.4230/LIPIcs.ITP.2026.31},
  annote =	{Keywords: Autoformalization, Automated reasoning, Interactive theorem proving, Formal proof assistants, Machine learning, Language Models}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.6
A Natural Language Formalization of Perfectoid Rings in ℕaproche

Authors: Peter Koepke

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
This paper describes an experiment to formalize sophisticated mathematics in the ℕaproche proof assistant which uses natural language input and a first-order internal logic. We view this as a contribution to the ongoing discussion whether formal systems for research mathematics require complex, computer-orientated type systems or whether approaches closer to traditional mathematical practices are possible. The formalization also explores the limits of the current ℕaproche system and avenues for further development.
Cite as

Peter Koepke. A Natural Language Formalization of Perfectoid Rings in ℕaproche. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{koepke:LIPIcs.ITP.2025.6,
  author =	{Koepke, Peter},
  title =	{{A Natural Language Formalization of Perfectoid Rings in \mathbb{N}aproche}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{6:1--6:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.6},
  URN =		{urn:nbn:de:0030-drops-246054},
  doi =		{10.4230/LIPIcs.ITP.2025.6},
  annote =	{Keywords: formal mathematics, formalization, perfectoid rings, controlled natural language, Naproche}
}
Document
DOI: 10.4230/LIPIcs.ITP.2021.16
A Natural Formalization of the Mutilated Checkerboard Problem in Naproche

Authors: Adrian De Lon, Peter Koepke, and Anton Lorenzen

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
Naproche is an emerging natural proof assistant that accepts input in a controlled natural language for mathematics, which we have integrated with LaTeX for ease of learning and to quickly produce high-quality typeset documents. We present a self-contained formalization of the Mutilated Checkerboard Problem in Naproche, following a proof sketch by John McCarthy. The formalization is embedded in detailed literate style comments. We also briefly describe the Naproche approach.
Cite as

Adrian De Lon, Peter Koepke, and Anton Lorenzen. A Natural Formalization of the Mutilated Checkerboard Problem in Naproche. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 16:1-16:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{delon_et_al:LIPIcs.ITP.2021.16,
  author =	{De Lon, Adrian and Koepke, Peter and Lorenzen, Anton},
  title =	{{A Natural Formalization of the Mutilated Checkerboard Problem in Naproche}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{16:1--16:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.16},
  URN =		{urn:nbn:de:0030-drops-139112},
  doi =		{10.4230/LIPIcs.ITP.2021.16},
  annote =	{Keywords: checkerboard, formalization, formal mathematics, controlled language}
}
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