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

  • Benjamin Grégoire
  • Loïc Pottier
  • Laurent Théry
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6301)


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.


decision procedure Nullstellensatz geometry theorem proving proof assistant 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Benjamin Grégoire
    • 1
  • Loïc Pottier
    • 1
  • Laurent Théry
    • 1
  1. 1.Marelle Project, INRIA Sophia AntipolisFrance

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