Abstract
Formal development in Event-B generally requires the validation of a large number of proof obligations. Some automatic tools exist to automatically discharge a significant part of them, thus augmenting the efficiency of the formal development. We here investigate the use of SMT (Satisfiability Modulo Theories) solvers in addition to the traditional tools, and detail the techniques used for the cooperation between the Rodin platform and SMT solvers.
Our contribution is the definition of two approaches to use SMT solvers, their implementation in a Rodin plug-in, and an experimental evaluation on a large sample of industrial and academic projects. Adding SMT solvers to Atelier B provers reduces to one fourth the number of sequents that need to be proved interactively.
This work is partly supported by ANR project DECERT, CNPq/INRIA project SMT-SAVeS, and CNPq grants 560014/2010-4 and 573964/2008-4 (National Institute of Science and Technology for Software Engineering—INES, www.ines.org.br ).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Abrial, J.-R.: Modeling in Event-B: System and Software Engineering. Cambridge University Press (2010)
Armand, M., Faure, G., Grégoire, B., Keller, C., Théry, L., Werner, B.: A Modular Integration of SAT/SMT Solvers to Coq through Proof Witnesses. In: Jouannaud, J.-P., Shao, Z. (eds.) CPP 2011. LNCS, vol. 7086, pp. 135–150. Springer, Heidelberg (2011)
Barrett, C., Sebastiani, R., Seshia, S.A., Tinelli, C.: Satisfiability modulo theories. In: Biere, A., Heule, M.J.H., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185, ch. 26, pp. 825–885. IOS Press (February 2009)
Barrett, C., Stump, A., Tinelli, C.: The SMT-LIB Standard Version 2.0 (2010)
Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press (2009)
Bouton, T., de Oliveira, D.C.B., Déharbe, D., Fontaine, P.: veriT: An Open, Trustable and Efficient SMT-Solver. In: Schmidt, R.A. (ed.) CADE-22. LNCS, vol. 5663, pp. 151–156. Springer, Heidelberg (2009)
Coleman, J., Jones, C., Oliver, I., Romanovsky, A., Troubitsyna, E.: RODIN (Rigorous open Development Environment for Complex Systems). In: Fifth European Dependable Computing Conference: EDCC-5 supplementary volume, pp. 23–26 (2005)
Couchot, J.-F., Déharbe, D., Giorgetti, A., Ranise, S.: Scalable Automated Proving and Debugging of Set-Based Specifications. Journal of the Brazilian Computer Society 9, 17–36 (2003)
de Moura, L., Bjørner, N.: Z3: An Efficient SMT Solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)
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)
Déharbe, D.: Integration of SMT-solvers in B and Event-B development environments. Science of Computer Programming (March 2011)
Konrad, M., Voisin, L.: Translation from Set-Theory to Predicate Calculus. Technical report, ETH Zurich (2011)
Kröning, D., Rümmer, P., Weissenbacher, G.: A Proposal for a Theory of Finite Sets, Lists, and Maps for the SMT-LIB Standard. In: Informal proceedings, 7th Int’l Workshop on Satisfiability Modulo Theories (SMT) at CADE 22 (2009)
Métayer, C., Voisin, L.: The Event-B mathematical language (2009), http://deploy-eprints.ecs.soton.ac.uk/11/4/kernel_lang.pdf
Nelson, G., Oppen, D.C.: Simplifications by cooperating decision procedures. ACM Transactions on Programming Languages and Systems 1(2), 245–257 (1979)
Schmalz, M.: The logic of Event-B, Technical report 698, ETH Zürich, Information Security (2011)
Schulz, S.: E - A Brainiac Theorem Prover. AI Communications 15(2/3), 111–126 (2002)
The Eclipse Foundation. Eclipse SDK (2009)
Tinelli, C., Harandi, M.T.: A new correctness proof of the Nelson–Oppen combination procedure. In: Baader, F., Schulz, K.U. (eds.) Frontiers of Combining Systems (FroCoS), Applied Logic, pp. 103–120. Kluwer Academic Publishers (March 1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Déharbe, D., Fontaine, P., Guyot, Y., Voisin, L. (2012). SMT Solvers for Rodin. In: Derrick, J., et al. Abstract State Machines, Alloy, B, VDM, and Z. ABZ 2012. Lecture Notes in Computer Science, vol 7316. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30885-7_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-30885-7_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30884-0
Online ISBN: 978-3-642-30885-7
eBook Packages: Computer ScienceComputer Science (R0)