Copyright © 1997-2026 by www.people.com.cn all rights reserved
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.
。关于这个话题，WPS下载最新地址提供了深入分析
15:28, 27 февраля 2026Ценности
16:58, 4 марта 2026Интернет и СМИ
，详情可参考体育直播
Из-за ударов США и Израиля в Иране разрушено 20 школ, 120 учеников и учителей пострадали. Об этом сообщила Isna со ссылкой на министра образования Исламской Республики Алиреза Каземи.。heLLoword翻译官方下载对此有专业解读
浙商证券首席经济学家李超表示，除“苏超”、“贵州村超、村 BA”、“湘超”等群众体育赛事外，2026年各地两会释放的服务消费发力点广泛分布在文旅演艺、入境与免税消费、新消费业态、民生服务消费、数字与科技消费、特色场景消费、宠物消费等多个领域，未来各地或将持续释放服务消费潜力。