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International Conference on Intelligent Computer Mathematics

CICM 2015: Intelligent Computer Mathematics pp 55–70Cite as

Optimizing a Certified Proof Checker for a Large-Scale Computer-Generated Proof

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9150))

Abstract

In recent work, we formalized the theory of optimal-size sorting networks with the goal of extracting a verified checker for the large-scale computer-generated proof that 25 comparisons are optimal when sorting 9 inputs, which required more than a decade of CPU time and produced 27 GB of proof witnesses. The checker uses an untrusted oracle based on these witnesses and is able to verify the smaller case of 8 inputs within a couple of days, but it did not scale to the full proof for 9 inputs. In this paper, we describe several non-trivial optimizations of the algorithm in the checker, obtained by appropriately changing the formalization and capitalizing on the symbiosis with an adequate implementation of the oracle. We provide experimental evidence of orders of magnitude improvements to both runtime and memory footprint for 8 inputs, and actually manage to check the full proof for 9 inputs.

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Notes

  1. 1.

    The choice of Haskell as target language is pragmatic: preliminary experiments suggested that it was the fastest one for this project.

  2. 2.

    Throughout this presentation we will always show transcribed Coq code, which is almost completely computational and preserved by extraction.

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Acknowledgements

We would like to thank Pierre Letouzey for suggesting and helping with extracting to Haskell native types, Søren Haagerup for helping with profiling, and Michael Codish for his support and his enthusiasm about sorting networks.

The authors were supported by the Danish Council for Independent Research, Natural Sciences. Computational resources were generously provided by the Danish Center for Scientific Computing.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230, Odense M, Denmark

    Luís Cruz-Filipe & Peter Schneider-Kamp

Authors
  1. Luís Cruz-Filipe
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  2. Peter Schneider-Kamp
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Corresponding author

Correspondence to Luís Cruz-Filipe .

Editor information

Editors and Affiliations

  1. School of Computer Science, University of Birmingham, Birmingham, United Kingdom

    Manfred Kerber

  2. McMaster University, Hamilton, Ontario, Canada

    Jacques Carette

  3. University of Innsbruck, Innsbruck, Austria

    Cezary Kaliszyk

  4. Jacobs University Bremen, Bremen, Germany

    Florian Rabe

  5. University of Birmingham, Birmingham, United Kingdom

    Volker Sorge

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Cruz-Filipe, L., Schneider-Kamp, P. (2015). Optimizing a Certified Proof Checker for a Large-Scale Computer-Generated Proof. In: Kerber, M., Carette, J., Kaliszyk, C., Rabe, F., Sorge, V. (eds) Intelligent Computer Mathematics. CICM 2015. Lecture Notes in Computer Science(), vol 9150. Springer, Cham. https://doi.org/10.1007/978-3-319-20615-8_4

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  • DOI: https://doi.org/10.1007/978-3-319-20615-8_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20614-1

  • Online ISBN: 978-3-319-20615-8

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