Abstract
The paper presents an approach that enables the elaboration of an automatic prover dedicated to the refinement of database applications. The approach is based on a strategy of proof reuse and on the specific characteristics of such applications. The problem can be stated as follows. Having established a set of basic refinement proofs associated to a set of refinement rules, the issue is to study how these basic proofs can be reused to establish more elaborate refinements. Elaborate refinements denote refinements that require the application of more than one refinement rule. We consider the B refinement process. In B, substitutions are inductively built using constructors. For each B constructor, we have formally defined the necessary and sufficient conditions that enable the reuse of the basic proofs. An application of our approach to data-intensive applications is presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Abrial, J.R.: The B-Book. Cambridge University Press, Cambridge (1996)
Clearsy: Atelier B, manuel de référence, Available at http://www.atelierb.societe.com
B-Core. B-Toolkit, on-line manual. Oxford, UK, Available at http://www.b-core.com
Barras, B., et al.: The Coq Proof Assistant, Reference Manual (7.1), INRIA Rocquencourt (2001)
Barthe, G., Pons, O.: Type Isomorphisms and Proof Reuse in Dependent Type Theory. In: Honsell, F., Miculan, M. (eds.) FOSSACS 2001. LNCS, vol. 2030, pp. 57–71. Springer, Heidelberg (2001)
Blaha, M., Premerlani, W.: Object-Oriented Modeling and Design for Database Applications. Prentice-Hall, Englewood Cliffs (1998)
Burdy, L., Meynadier, J.-M.: Automatic Refinement, BUG Meeting. In: FM 1999, Toulouse, France (September 1999)
Ceri, S.: Methodologies and Tools for Database Design. Elsevier Science, Amsterdam (1983)
Laleau, R.: On the interest of combining UML with the B formal method for the specification of database applications. In: ICEIS2000: 2nd International Conference on Enterprise Information Systems, Stafford, UK (July 2000)
Laleau, R., Mammar, A.: A Generic Process to Refine a B Specification into a Relational Database Implementation. In: Bowen, J.P., Dunne, S., Galloway, A., King, S. (eds.) B 2000, ZUM 2000, and ZB 2000. LNCS, vol. 1878, p. 22. Springer, Heidelberg (2000); Extended version in the CEDRIC research report N 86
Laleau, R., Mammar, A.: An overview of a method and its support tool for generating B specifications from UML notations. In: ASE: 15th IEEE Conference on Automated Software Engineering, Grenoble, France, September 2000. IEEE Computer Society Press, Los Alamitos (2000)
Laleau, R., Polack, F.: Specification of integrity-preserving operations in information systems by using a formal UML- based language. Information and Software Technology 43, 693–704 (2001)
Laleau, R.: Conception et développement formels d’applications bases de données. Habilitation Thesis, CEDRIC Laboratory, Évry, France (2002), Available at http://cedric.cnam.fr/PUBLIS/RC424.ps.gz
Luo, Z.: Coercive Subtyping in Type Theory. In: CSL book, pp. 276-296 (1996), Also available from citeseer.nj.nec.com/luo96coercive.html
Magaud, N., Bertot, Y.: Changement de Représentation de Données dans le Calcul des Constructions Inductives. Research report, RR-4039, INRIA, France (October 2000)
Magaud, N., Bertot, Y.: Changement de Représentation de Structures de Données dans Coq: le cas des entiers naturels. In: Proceedings of JFLA 2001 (2001)
Mammar, A.: Un environnement formel pour le développement d’applications bases de données. PhD thesis, CEDRIC Laboratory, CNAM, Evry, France (November 2002), Available at http://cedric.cnam.fr/PUBLIS/RC392.ps.gz
Pons, O.: Generalization in Type Theory Based Proof Assistants. In: Callaghan, P., Luo, Z., McKinna, J., Pollack, R. (eds.) TYPES 2000. LNCS, vol. 2277, p. 217. Springer, Heidelberg (2002)
Walther, C., Kolbe, T.: Proving Theorem by Reuse. Artificial Intelligence 116, 17–66 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mammar, A., Laleau, R. (2003). Design of an Automatic Prover Dedicated to the Refinement of Database Applications. In: Araki, K., Gnesi, S., Mandrioli, D. (eds) FME 2003: Formal Methods. FME 2003. Lecture Notes in Computer Science, vol 2805. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45236-2_45
Download citation
DOI: https://doi.org/10.1007/978-3-540-45236-2_45
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40828-4
Online ISBN: 978-3-540-45236-2
eBook Packages: Springer Book Archive