Advertisement

Verifying B Proof Rules Using Deep Embedding and Automated Theorem Proving

  • Mélanie Jacquel
  • Karim Berkani
  • David Delahaye
  • Catherine Dubois
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7041)

Abstract

We propose a formal and mechanized framework which consists in verifying proof rules of the B method, which cannot be automatically proved by the elementary prover of Atelier B and using an external automated theorem prover called Zenon. This framework contains in particular a set of tools, named BCARe and developed by Siemens SAS I MO, which relies on a deep embedding of the B theory within the logic of the Coq proof assistant and allows us to automatically generate the required properties to be checked for a given proof rule. Currently, this tool chain is able to automatically verify a part of the derived rules of the B-Book, as well as some added rules coming from Atelier B and the rule database maintained by Siemens SAS I MO.

Keywords

B Method Proof Rules Verification Deep Embedding Automated Theorem Proving Coq zenon 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abrial, J.-R.: The B-Book, Assigning Programs to Meanings. Cambridge University Press, Cambridge, UK (1996) ISBN 0521496195CrossRefzbMATHGoogle Scholar
  2. 2.
    Abrial, J.-R., Mussat, L.: On Using Conditional Definitions in Formal Theories. In: Bert, D., et al. (eds.) B 2002 and ZB 2002. LNCS, vol. 2272, pp. 242–269. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Berkani, K., Dubois, C., Faivre, A., Falampin, J.: Validation des règles de base de l’Atelier B. Technique et Science Informatiques (TSI) 23(7), 855–878 (2004)CrossRefGoogle Scholar
  4. 4.
    Bodeveix, J.-P., Filali, M., Muñoz, C.: A Formalization of the B-Method in Coq and PVS. B Users Group Meeting, Toulouse, France (September 1999)Google Scholar
  5. 5.
    Bonichon, R., Delahaye, D., Doligez, D.: Zenon: An Extensible Automated Theorem Prover Producing Checkable Proofs. In: Dershowitz, N., Voronkov, A. (eds.) LPAR 2007. LNCS (LNAI), vol. 4790, pp. 151–165. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Chartier, P.: Formalisation of B in Isabelle/HOL. In: Bert, D. (ed.) B 1998. LNCS, vol. 1393, pp. 66–82. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  7. 7.
    Cirstea, H., Kirchner, C.: Using Rewriting and Strategies for Describing the B Predicate Prover. In: Strategies in Automated Deduction, Lindau, Germany, pp. 25–36 (July 1998)Google Scholar
  8. 8.
    ClearSy. Atelier B 4.0 (February 2009), http://www.atelierb.eu/
  9. 9.
    Couchot, J.-F., Dadeau, F., Déharbe, D., Giorgetti, A., Ranise, S.: Proving and Debugging Set-Based Specifications. In: Workshop on Formal Methods, Campina Grande, Brazil. ENTCS, vol. 95, pp. 189–208. Elsevier (October 2003)Google Scholar
  10. 10.
    Déharbe, D.: Automatic Verification for a Class of Proof Obligations with SMT-Solvers. In: Frappier, M., Glässer, U., Khurshid, S., Laleau, R., Reeves, S. (eds.) ABZ 2010. LNCS, vol. 5977, pp. 217–230. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Delahaye, D.: A Tactic Language for the System Coq. In: Parigot, M., Voronkov, A. (eds.) LPAR 2000. LNCS (LNAI), vol. 1955, pp. 85–95. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  12. 12.
    Jaeger, É., Dubois, C.: Why would you trust B? In: Dershowitz, N., Voronkov, A. (eds.) LPAR 2007. LNCS (LNAI), vol. 4790, pp. 288–302. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Le Lay, É.: Automatiser la validation des règles. Master’s thesis, INSA (Rennes), Siemens SAS I MO (September 2008)Google Scholar
  14. 14.
    Mikhailov, L., Butler, M.: An Approach to Combining B and Alloy. In: Bert, D., Bowen, J.P., Henson, M.C., Robinson, K. (eds.) B 2002 and ZB 2002. LNCS, vol. 2272, pp. 140–161. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    The Coq Development Team. Coq, version 8.3. INRIA (October 2010), http://coq.inria.fr/

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Mélanie Jacquel
    • 1
  • Karim Berkani
    • 1
  • David Delahaye
    • 2
  • Catherine Dubois
    • 3
  1. 1.Siemens SAS I MOChâtillonFrance
  2. 2.CEDRIC/CNAMParisFrance
  3. 3.CEDRIC/ENSIIEÉvryFrance

Personalised recommendations