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Proof Certificates for Algebra and Their Application to Automatic Geometry Theorem Proving

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Automated Deduction in Geometry (ADG 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6301))

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Abstract

Integrating decision procedures in proof assistants in a safe way is a major challenge. In this paper, we describe how, starting from Hilbert’s Nullstellensatz theorem, we combine a modified version of Buchberger’s algorithm and some reflexive techniques to get an effective procedure that automatically produces formal proofs of theorems in geometry. The method is implemented in the Coq system but, since our specialised version of Buchberger’s algorithm outputs explicit proof certificates, it could be easily adapted to other proof assistants.

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Author information

Authors and Affiliations

  1. Marelle Project, INRIA Sophia Antipolis, France

    Benjamin Grégoire, Loïc Pottier & Laurent Théry

Authors
  1. Benjamin Grégoire
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  2. Loïc Pottier
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  3. Laurent Théry
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Editor information

Editors and Affiliations

  1. Max-Planck-Institut für Informatik, RG 1: Automation of Logic, 66123, Saarbrücken, Germany

    Thomas Sturm

  2. Wilhelm-Schickard-Institut für Informatik, Symbolic Computation Group, Universität Tübingen, 72076, Tübingen, Germany

    Christoph Zengler

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Grégoire, B., Pottier, L., Théry, L. (2011). Proof Certificates for Algebra and Their Application to Automatic Geometry Theorem Proving. In: Sturm, T., Zengler, C. (eds) Automated Deduction in Geometry. ADG 2008. Lecture Notes in Computer Science(), vol 6301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21046-4_3

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  • DOI: https://doi.org/10.1007/978-3-642-21046-4_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21045-7

  • Online ISBN: 978-3-642-21046-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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