Results 1 to 10 of about 169,062 (163)
A FORMAL PROOF OF THE KEPLER CONJECTURE [PDF]
Forum of Mathematics, Pi, 2017 This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the official published account of the now completed Flyspeck project.
THOMAS HALES +21 more
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A Formal Proof of the Irrationality of $\zeta(3)$ [PDF]
Logical Methods in Computer Science, 2021 This paper presents a complete formal verification of a proof that the evaluation of the Riemann zeta function at 3 is irrational, using the Coq proof assistant.
Assia Mahboubi, Thomas Sibut-Pinote
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Towards Formal Proof Metrics [PDF]
Lecture Notes in Computer Science, 2016 Recent years have seen increasing success in building large formal proof developments using interactive theorem provers ITPs. Some proofs have involved many authors, years of effort, and resulted in large, complex interdependent sets of proof "source code" files.
Cezary Kaliszyk +2 more
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Formal proof of a program: Find
Science of Computer Programming, 2007 AbstractIn 1971, C.A.R. Hoare gave the proof of correctness and termination of a rather complex algorithm, in a paper entitled Proof of a program: Find. It is a handmade proof, where the program is given together with its formal specification and where each step is fully justified by mathematical reasoning.
Jean-Christophe Filliatre
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A full formal representation of Arrow's impossibility theorem. [PDF]
PLoS ONERevised proofs of Kenneth Arrow's impossibility theorem, one of the most influential theorems in economics, political science, and philosophy, have been presented in prose form, incorporating novel ideas such as decisive sets and pivotal voters.
Kazuya Yamamoto
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Swarms of Mobile Robots: Towards Versatility with Safety [PDF]
Leibniz Transactions on Embedded Systems, 2022 We present Pactole, a formal framework to design and prove the correctness of protocols (or the impossibility of their existence) that target mobile robotic swarms.
Courtieu, Pierre +3 more
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Is Mathematical Logic Really Necessary in Teaching Mathematical Proofs? [PDF]
Athens Journal of Education, 2020 As it is already observed by mathematicians and educators, there is a discrepancy between the formal techniques of mathematical logic and the informal techniques of mathematics in regards to proof.
Michael Aristidou
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Principia: An International Journal of Epistemology, 2022 When adopting a sound logical system, reasonings made within this system are correct. The situation with reasonings expressed, at least in part, with natural language is much more ambiguous. One way to be certain of the correctness of these reasonings is
Mario Bacelar Valente
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Logic for exact real arithmetic [PDF]
Logical Methods in Computer Science, 2021 Continuing earlier work of the first author with U. Berger, K. Miyamoto and H. Tsuiki, it is shown how a division algorithm for real numbers given as a stream of signed digits can be extracted from an appropriate formal proof.
Helmut Schwichtenberg +1 more
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A new coinductive confluence proof for infinitary lambda calculus [PDF]
Logical Methods in Computer Science, 2020 We present a new and formal coinductive proof of confluence and normalisation of B\"ohm reduction in infinitary lambda calculus. The proof is simpler than previous proofs of this result.
Łukasz Czajka
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