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ACL2 Verification of Simplicial Degeneracy Programs in the Kenzo System

  • Francisco-Jesus Martín-Mateos
  • Julio Rubio
  • Jose-Luis Ruiz-Reina
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5625)

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.

Keywords

Simplicial Complex Algebraic Topology Simplicial Topology Common Lisp Binary Notation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Francisco-Jesus Martín-Mateos
    • 1
  • Julio Rubio
    • 2
  • Jose-Luis Ruiz-Reina
    • 1
  1. 1.Computational Logic Group Dept. of Computer Science and Artificial IntelligenceUniversity of Seville, E.T.S.I. InformáticaSevillaSpain
  2. 2.Dept. of Mathematics and ComputationUniversity of La RiojaLogroñoSpain

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