A Formal Proof of Dickson’s Lemma in ACL2

  • F. J. Martın-Mateos
  • J. A. Alonso
  • M. J. Hidalgo
  • J. L. Ruiz-Reina
Conference paper

DOI: 10.1007/978-3-540-39813-4_3

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2850)
Cite this paper as:
Martın-Mateos F.J., Alonso J.A., Hidalgo M.J., Ruiz-Reina J.L. (2003) A Formal Proof of Dickson’s Lemma in ACL2. In: Vardi M.Y., Voronkov A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2003. Lecture Notes in Computer Science, vol 2850. Springer, Berlin, Heidelberg

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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