A Formal Proof of Dickson’s Lemma in ACL2

  • F. J. Martın-Mateos
  • J. A. Alonso
  • M. J. Hidalgo
  • J. L. Ruiz-Reina
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2850)

Abstract.

Dickson’s Lemma is the main result needed to prove the termination of Buchberger’s algorithm for computing Gröbner basis of polynomial ideals. In this case study, we present a formal proof of Dickson’s Lemma using the ACL2 system. Due to the limited expressiveness of the ACL2 logic, the classical non-constructive proof of this result cannot be done in ACL2. Instead, we formalize a proof where the termination argument is justified by the multiset extension of a well-founded relation.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • F. J. Martın-Mateos
    • 1
  • J. A. Alonso
    • 1
  • M. J. Hidalgo
    • 1
  • J. L. Ruiz-Reina
    • 1
  1. 1.Computational Logic Group, Dept. of Computer Science and Artificial IntelligenceUniversity of Seville, E.T.S.I. InformáticaSevillaSpain

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