Gadgil, S and Tadipatri, AR (2024) Formalizing Giles Gardam's Disproof of Kaplansky's Unit Conjecture. In: 13th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2024, in affiliation with the annual Symposium on Principles of Programming, Languages, ,POPL 2024, 15 - 16 January 2024, London, pp. 177-189.
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Abstract
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. © 2024 ACM.
| Item Type: | Conference Paper |
|---|---|
| Publication: | CPP 2024 - Proceedings of the 13th ACM SIGPLAN International Conference on Certified Programs and Proofs, Co-located with: POPL 2024 |
| Publisher: | Association for Computing Machinery, Inc |
| Additional Information: | The copyright for this article belongs to author. |
| Keywords: | Group theory, Automated theorem proving; Dependent type theory; Formalisation; Group rings; Interactive theorem proving; Kaplansky conjecture; Lean theorem prover; Proof assistant; Theorem provers; Verified computations, Theorem proving |
| Department/Centre: | Others |
| Date Deposited: | 01 Mar 2024 08:54 |
| Last Modified: | 01 Mar 2024 08:54 |
| URI: | https://eprints.iisc.ac.in/id/eprint/83935 |
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