Zenon: An Extensible Automated Theorem Prover Producing Checkable Proofs

  • Richard Bonichon
  • David Delahaye
  • Damien Doligez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4790)

Abstract

We present Zenon, an automated theorem prover for first order classical logic (with equality), based on the tableau method. Zenon is intended to be the dedicated prover of the Focal environment, an object-oriented algebraic specification and proof system, which is able to produce OCaml code for execution and Coq code for certification. Zenon can directly generate Coq proofs (proof scripts or proof terms), which can be reinserted in the Coq specifications produced by Focal. Zenon can also be extended, which makes specific (and possibly local) automation possible in Focal.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Barendregt, H., Barendsen, E.: Autarkic Computations in Formal Proofs. Journal of Automated Reasoning (JAR) 28(3), 321–336 (2002)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bezem, M., Hendriks, D.H., de Nivelle, H.: Automated Proof Construction in Type Theory Using Resolution. Journal of Automated Reasoning (JAR) 29(3–4), 253–275 (2002)MATHCrossRefGoogle Scholar
  3. 3.
    Delahaye, D., Étienne, J.-F., Donzeau-Gouge, V.V.: Certifying Airport Security Regulations using the Focal Environment. In: Misra, J., Nipkow, T., Sekerinski, E. (eds.) FM 2006. LNCS, vol. 4085, pp. 48–63. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Delahaye, D., Étienne, J.-F., Donzeau-Gouge, V.V.: Reasoning about Airport Security Regulations using the Focal Environment. In: International Symposium on Leveraging Applications of Formal Methods, Verification and Validation (ISoLA), Paphos (Cyprus) (November 2006)Google Scholar
  5. 5.
    Hurd, J.: Integrating Gandal and HOL. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs 1999. LNCS, vol. 1690, pp. 311–322. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  6. 6.
    Jaume, M., Morisset, C.: Formalisation and Implementation of Access Control Models. In: Information Assurance and Security (IAS), International Conference on Information Technology (ITCC), Las Vegas (USA), pp. 703–708. IEEE Computer Society Press, Los Alamitos (2005)Google Scholar
  7. 7.
    Leisenring, A.C.: Mathematical Logic and Hilbert’s ε-Symbol. MacDonald Technical and Scientific, London (1969) ISBN 0356026795Google Scholar
  8. 8.
    McCune, W., Shumsky, O.: System Description: IVY. In: McAllester, D. (ed.) CADE-17. LNCS, vol. 1831, pp. 401–405. Springer, Heidelberg (2000)Google Scholar
  9. 9.
    Paulson, L.C., Susanto, K.W.: Source-Level Proof Reconstruction for Interactive Theorem Proving. In: Theorem Proving in Higher Order Logics (TPHOLs). LNCS, Springer, Heidelberg (2007)Google Scholar
  10. 10.
    The  EDEMOI Project (2003), http://www-lsr.imag.fr/EDEMOI/
  11. 11.
    Sutcliffe, G.: CASC-J3 - The 3rd IJCAR ATP System Competition. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 572–573. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Sutcliffe, G., Suttner, C.B.: The TPTP Problem Library: CNF Release v1.2.1. Journal of Automated Reasoning (JAR) 21(2), 177–203 (1998)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    The Coq Development Team. Coq, version 8.1. INRIA (November 2006), available at: http://coq.inria.fr/
  14. 14.
    The Cristal Team. Objective Caml, version 3.10. INRIA (May 2007), available at: http://caml.inria.fr/
  15. 15.
    The Focal Development Team. Focal, version 0.3.1. CNAM/INRIA/LIP6 (May 2005), available at: http://focal.inria.fr/
  16. 16.
    The HELM Team. Matita, version 0.1.0. Computer Science Department, University of Bologna (July 2006), available at: http://matita.cs.unibo.it/

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Richard Bonichon
    • 1
  • David Delahaye
    • 2
  • Damien Doligez
    • 3
  1. 1.LIP6/Paris 6, ParisFrance
  2. 2.CEDRIC/CNAM, ParisFrance
  3. 3.INRIA, RocquencourtFrance

Personalised recommendations