In Modular Design higher-level modules shouldn’t depend on lower-level modules. That’s because abstract modules shouldn’t be limited by concrete solutions. Another reason is testability - modules that have direct dependencies to lower-level modules are harder to test.
At this point, my assume only crazy people are reading this, so go buy a hat so you can hold onto it.
，推荐阅读同城约会获取更多信息
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.
Мужчина ворвался в прямой эфир телеканала и спустил штаны20:53。91视频是该领域的重要参考
Фото: Majid Asgaripour / WANA (West Asia News Agency) via Reuters，推荐阅读im钱包官方下载获取更多信息
Суд приговорил мужчину к 12 годам колонии строгого режима с отбыванием первых трех лет в тюрьме.