ACL2 Verification of Simplicial Degeneracy Programs in the Kenzo System
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.
KeywordsSimplicial Complex Algebraic Topology Simplicial Topology Common Lisp Binary Notation
Unable to display preview. Download preview PDF.
- 2.Andrés, M., Lambán, L., Rubio, J., Ruiz-Reina, J.L.: Formalizing Simplicial Topology in ACL2. In: ACL2 Workshop 2007, University of Austin, pp. 34–39 (2007)Google Scholar
- 8.Dousson, X., Rubio, J., Sergeraert, F., Siret, Y.: The Kenzo Program, Institut Fourier (1999), http://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/
- 10.Kaufmann, M., Manolios, P., Moore, J S.: Computer-Aided Reasoning: An Approach. Kluwer Academic Publishers, Dordrecht (2000)Google Scholar
- 11.Kaufmann, M., Moore, J S.: ACL2 Home Page, http://www.cs.utexas.edu/users/moore/acl2
- 13.Martín–Mateos, F.J., Ruiz–Reina, J.L., Rubio, J.: ACL2 verification of simplicial degeneracy programs in the Kenzo system, http://www.cs.us.es/~fmartin/acl2/kenzo
- 14.May, J.P.: Simplicial Objects in Algebraic Topology. Van Nostrand (1967)Google Scholar
- 15.Rubio, J., Sergeraert, F., Siret, Y.: EAT: Symbolic Software for Effective Homology Computation, Institut Fourier (1997), ftp://ftp-fourier.ujf-grenoble.fr/pub/EAT
- 16.Steele Jr., G.L.: Common Lisp The Language, 2nd edn. Digital Press (1990)Google Scholar