The imprecision of the definitions of UML2.0 sequence diagrams, given by the Object Management Group (OMG), does not allow the obtention of all the possible valid behaviours for a given distributed system, when communicating objects are independent. We choose the causal semantics, which is suitable for this kind of systems; we propose its extension to support complex behaviours, expressed with combined fragments. We propose the implementation of our approach with Event-B in order to check later on some properties of safety, liveness and fairness.

Combined Fragments (CF) are the new features added to UML2.0 sequence diagrams (SD). They have widely increased its expressiveness power, permitting to model complex behaviours, they can be nested to allow more sophisticated behaviours. We focus on the most popular CF of control-flow ALT, OPT, LOOP, SEQ allowing to model respectively alternative, optional, iterative and sequential behaviours. They require a meticulous processing for the generation of partial order between their events. We proposed in a previous work, a causal semantics based on partial order theory, which is suitable for deriving of all possible valid traces for sequence diagrams with CF modelling behaviours of distributed systems. In this work, to deal with nested CF, we first update the formalization of sequence diagram, then we extend this semantics.

Abstract:Refinement process applied to UML2.0 Sequence Diagrams (SD) is adopted to deal with the complexity of modeling distributed systems. The various steps leading to the checking of the refinement of SDs theoretically as well as practically are explained. A refinement relation possessing the necessary properties, is formalized; its implementation in the Event-B method is proposed in order to check the correctness of the refinement of SDs, and to verify some safety, liveness properties and the termination of the new introduced events.

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