1. Verification of behavioural elements of UML models using B Truong, Ninh-Thuan and Souquieres, Jeanine. 2005. In Proceedings of the 2005 ACM Symposium on Applied Computing Santa Fe, New Mexico, March 13 - 17, 2005 Presented by: James T. O’Hara SE 510, Fall 2005

2. 1 A Tale of Two Tools … The application of formal methods allows the rigorous definition and analysis of the functionality and the behavior of a system. It is capable of showing that the system is correct. B is a method for specifying, designing and coding software systems. UML is a widely accepted modeling language that can be used to visualize, specify, construct and document the artifacts of a software system.

3. 2 Combining UML with B The derivation from UML specification into the B formal method is considered as an appropriate way to jointly use UML and B in practical, unified and rigorous software development. The aim of the study was to use B support tools to analyze UML model properties.

4. 3 THE B METHOD B is a formal software development method, originally developed by J.R. Abrial. The B notation is based on set theory, the language of generalized substitutions and first order logic. Specifications are composed of abstract machines that are similar to modules or classes.

5. 4 The UML Metamodel The UML metamodel defines the complete semantics for representing object models using UML. Abstract Syntax Well-Formedness Rules Semantics

6. 5 TRANSFORMATION OF UML TO B The transformation of an attribute of a UML class to a variable of a B abstract machine can be performed as follows:

7. 6 What is a UML Collaboration Diagram A collaboration diagram describes interactions among objects in terms of sequenced messages. Collaboration diagrams represent a combination of information taken from class, sequence, and use case diagrams describing both the static structure and dynamic behavior of a system.

8. 7 UML Collaboration Diagram UML collaboration diagrams, are used to explore the dynamic nature of your software. Source: http://www.agilemodeling.com/style/collaborationDiagram.htm

9. 8 TRANSFORMATION OF THE COLLABORATION PACKAGE TO B The Collaboration package is a sub-package of the Behavioral Elements package

10. 9 What is a UML State Diagram UML state machine diagrams depict the various states that an object may be in and the transitions between those states. Figure 1. A seminar during registration. Source: http://www.agilemodeling.com/artifacts/stateMachineDiagram.htm

11. 10 TRANSFORMATION OF THE STATE MACHINE PACKAGE TO B The State Machine package is a sub- package of the Behavioral Elements package.

12. 11 A CASE STUDY Modeling of a printing system. This system can be described as follows: the printing system is a system to print a file from a computer. The use gives a command to print a file, and the system will respond according to its messages. Figure 3. Collaboration diagram of the printing system.

13. 12 Interaction B Abstract Machine

14. 13 Verification of UML Model Properties The well-formedness rules of the Messages class applied on the Collaboration package and their B machines counterparts can be evaluated for completeness and consistency. UML well-formedness rules can be represented by system invariants.

15. 14 CONCLUSION In this paper, the author’s have presented a technique to transform the UML behavioral diagrams to a B specification. With the contribution of the transformation of UML metamodel and their well- formedness rules into B, the semantics of the UML models can be translated into B properties. Formal methods can then be used to specify and verify object-oriented systems.

16. 15 Additional References The B-Book: Assigning Programs to Meanings, Cambridge University Press 1996. ISBN 0-521-49619-5 The Object Primer: Agile Model- Driven Development with UML 2.0 Scott Ambler, Cambridge University Press, Paperback, 3rd edition, 2004