Software & Systems Modeling

, Volume 14, Issue 1, pp 101–119 | Cite as

Verifying B proof rules using deep embedding and automated theorem proving

  • Mélanie Jacquel
  • Karim Berkani
  • David Delahaye
  • Catherine Dubois
Special Section Paper
  • 135 Downloads

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 IC-MOL, which relies on a deep embedding of the B theory within the logic of the Coq proof assistant. This toolkit 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 IC-MOL.

Keywords

B Method Proof rules Verification  Deep embedding Automated theorem proving Coq Zenon 

Notes

Acknowledgments

The authors wish to thank the anonymous reviewers for their helpful comments and suggestions. They also thank Éric Dubois for his help in the production of the graphics for the benchmarks, as well as Hélène and Dalton Nelson for their careful reading.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Mélanie Jacquel
    • 1
  • Karim Berkani
    • 1
  • David Delahaye
    • 2
  • Catherine Dubois
    • 3
  1. 1.Siemens IC-MOLChâtillonFrance
  2. 2.CEDRIC/CNAMParisFrance
  3. 3.INRIA/CEDRIC/ENSIIEParisFrance

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