Chapter

Logic for Programming, Artificial Intelligence, and Reasoning

Volume 2850 of the series Lecture Notes in Computer Science pp 49-58

A Formal Proof of Dickson’s Lemma in ACL2

  • F. J. Martın-MateosAffiliated withComputational Logic Group, Dept. of Computer Science and Artificial Intelligence, University of Seville, E.T.S.I. Informática
  • , J. A. AlonsoAffiliated withComputational Logic Group, Dept. of Computer Science and Artificial Intelligence, University of Seville, E.T.S.I. Informática
  • , M. J. HidalgoAffiliated withComputational Logic Group, Dept. of Computer Science and Artificial Intelligence, University of Seville, E.T.S.I. Informática
  • , J. L. Ruiz-ReinaAffiliated withComputational Logic Group, Dept. of Computer Science and Artificial Intelligence, University of Seville, E.T.S.I. Informática

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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.