Abstract
The formalisation of mathematics by use of theorem provers has reached the stage where previously questioned mathematical proofs have been formalised. However, sceptics will argue that lingering doubts remain about the efficacy of these formalisations. In this paper we motivate and describe a capability for addressing such concerns. We concentrate on the nearly-complete Flyspeck Project, which uses the HOL Light system to formalise the Kepler Conjecture proof. We first explain why a sceptic might doubt the formalisation. We go on to explain how the formal proof can be ported to the highly-trustworthy HOL Zero system and then independently audited, thus resolving any doubts.
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References
Hales, T.: Introduction to the Flyspeck Project. In: Mathematics, Algorithms, Proofs. Dagstuhl Seminar Proceedings, vol. 05021. Internationales Begegnungs- und Forschungszentrum für Informatik (2006)
Harrison, J.: HOL Light: An Overview. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 60–66. Springer, Heidelberg (2009)
Gordon, M.: An Introduction to the HOL System. In: Proceedings of the 1991 International Workshop on the HOL Theorem Proving System and its Applications. IEEE Computer Society Press (1992)
Pollack, R.: How to Believe a Machine-Checked Proof. In: Twenty Five Years of Constructive Type Theory. Oxford University Press (1998)
Wiedijk, F.: Pollack-Inconsistency. Electronic Notes in Theoretical Computer Science, vol. 285. Elsevier Science (2012)
Gordon, M., Milner, R., Wadsworth, C.P.: Edinburgh LCF. LNCS, vol. 78. Springer, Heidelberg (1979)
Proof Technologies Ltd. website, http://www.proof-technologies.com/
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Adams, M. (2014). Flyspecking Flyspeck. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_3
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DOI: https://doi.org/10.1007/978-3-662-44199-2_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44198-5
Online ISBN: 978-3-662-44199-2
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