吉尔斯-加尔丹对卡普兰斯基单位猜想的形式化反证

Proceedings of the 13th ACM SIGPLAN International Conference on Certified Programs and Proofs Pub Date : 2024-01-09 DOI:10.1145/3636501.3636947

Siddhartha Gadgil, Anand Tadipatri

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引用次数: 1

摘要

我们描述了在精益 4 中对吉尔斯-加达姆反证卡普兰斯基单位猜想的形式化。这结合了演绎证明和形式化验证计算，利用了 Lean 4 作为编程语言的特性，它同时也是一种证明助手。除了对具体结果进行形式化之外，我们在这项工作中的目标是展示在当前技术水平下的可能性，并说明如何实现这一目标。具体来说，我们展示了一个重要数学结果的实时形式化，以及 Lean 4 中证明和计算的无缝集成。

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Formalizing Giles Gardam’s Disproof of Kaplansky’s Unit Conjecture

We describe a formalization in Lean 4 of Giles Gardam's disproof of Kaplansky's Unit Conjecture. This makes use of a combination of deductive proving and formally verified computation, using the nature of Lean 4 as a programming language which is also a proof assistant. Our goal in this work, besides formalization of the specific result, is to show what is possible with the current state of the art and illustrate how it can be achieved. Specifically we illustrate real time formalization of an important mathematical result and the seamless integration of proofs and computations in Lean 4.

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Proceedings of the 13th ACM SIGPLAN International Conference on Certified Programs and Proofs

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