ACL2 Verification of Simplicial Degeneracy Programs in the Kenzo System

  • Authors:

  • Francisco-Jesus Martín-Mateos;Julio Rubio;Jose-Luis Ruiz-Reina

  • Affiliations:

  • Computational Logic Group Dept. of Computer Science and Artificial Intelligence, University of Seville, E.T.S.I. Informática, Sevilla, Spain 41012;Dept. of Mathematics and Computation, University of La Rioja, Logroño, Spain 26004;Computational Logic Group Dept. of Computer Science and Artificial Intelligence, University of Seville, E.T.S.I. Informática, Sevilla, Spain 41012

  • Venue:
  • Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
  • Year:
  • 2009

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Abstract

Kenzo is a Computer Algebra system devoted to Algebraic Topology, and written in the Common Lisp programming language. It is a descendant of a previous system called EAT (for Effective Algebraic Topology). Kenzo shows a much better performance than EAT due, among other reasons, to a smart encoding of degeneracy lists as integers. In this paper, we give a complete automated proof of the correctness of this encoding used in Kenzo. The proof is carried out using ACL2, a system for proving properties of programs written in (a subset of) Common Lisp. The most interesting idea, from a methodological point of view, is our use of EAT to build a model on which the verification is carried out. Thus, EAT, which is logically simpler but less efficient than Kenzo, acts as a mathematical model and then Kenzo is formally verified against it.