Foundations for using linear temporal logic in Event-B refinement

Abstract

Abstract. In this paper we present a new way of reconciling Event-B refinement with linear temporal logic (LTL) properties. In particular, the results presented in this paper allow properties to be established for abstract system models, and identify conditions to ensure that the properties (suitably translated) continue to hold as those models are developed through refinement. There are several novel elements to this achievement: (1) we identify conditions that allow LTL properties to be mapped across refinement chains; (2) we provide translations of LTL predicates to reflect the introduction through refinement of new events and the renaming and splitting of existing events; (3) we do this for an extended version of LTL particularly suited to Event-B, including state predicates and enabledness of events, which can be model-checked at the abstract level. Our results are more general than any previous work in this area, covering liveness in the context of anticipated events, and relaxing constraints between adjacent refinement levels. The approach is illustrated with a case study. This enables designers to develop event based models and to consider their execution patterns so that liveness and fairness properties can be verified for Event-B systems.

A Time Refinement Framework Based on iUML-B State Machine

“…properties in the refinement process. As Hoang and Schneider said [34], " e challenge is to identify more natural ways of integrating Event-B and LTL so that LTL properties can be preserved by Event-B refinement, which is not the case in general." Our point is that it is better and easier to adopt an integrated formal method than to integrate Event-B and LTL properties verification by using the syntax and semantics of Event-B just like the work done by Iliasov and Vain et al e method proposed in this paper uses the iUML-B functional state machine to express the order of events at a particular refinement level and uses the ticker state machine to express the elapse of time.…”

Legislation-driven development of a Gift Aid system using Event-B

“…In particular, we aim to create interactive visualisations of our Event-B models using BMotionWeb, an extension of ProB for rapid creation of formal prototypes [LL16], or its successor VisB [WL20]. Further extensions of this work would be to utilise alternative means of capturing requirements and specifying behaviour that aids communication amongst all stakeholders while embedding Event-B modelling within a Behaviour-Driven Development, including Linear Temporal Logic (LTL) [HSTW16], and the iUML-B diagrammatic front-end for Event-B [SHD + 18].…”

“…Development in Event-B typically begins with developing a high level abstract model of the system and refining the model over a series of steps to incrementally develop a more detailed specification. As presented in [Abr10, HLP13, STW14] and [HSTW16], Event-B provides an effective and flexible refinement strategy, allowing events to be added, merged, forked and extended in steps. Refinement rules may extend functionality, add data values, strengthen event guards and introduce invariants.…”

Reasoning About Real-Time Systems in Event-B Models with Fairness Assumptions

“…Hoang et al extended work in [14] by covering liveness in the context of convergent events and relaxing constraints between adjacent refinement levels by using strong deadlock freedom with new events. However, the proof rules in [13]- [15] have not yet considered fairness assumptions in the verification step and the refinement step. There are also work that integrate Event-B with other formal methods for the verification of liveness properties.…”