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Formalising Liveness Properties in Event-B with the Reflexive EB4EB Framework

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NASA Formal Methods (NFM 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13903))

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Abstract

The correct-by-construction state-based Event-B formal method lacks the ability to express liveness properties using temporal logic. To address this challenge, two approaches can be envisioned. First, embed Event-B models in another formal method supporting liveness properties verification. This method is cumbersome and error-prone, and the verification result is not guaranteed on the source model. Second, extend Event-B to support the expression of and reasoning on liveness properties, and more generally temporal properties. Following the second approach, in [20], J.-R. Abrial and T. S. Hoang proposed an axiomatisation of linear temporal logic (LTL) for Event-B with a set of proof obligations (POs) allowing to verify these properties. These POs are mathematically formalised, but are neither implemented nor generated automatically. In this paper, using the reflexive EB4EB framework [37, 38] allowing for manipulation of the core concepts of Event-B, we propose to formalise and operationalise the automatic generation of proof obligations associated to liveness properties expressed in LTL. Furthermore, relying on trace-based semantics, we demonstrate the soundness of this formalisation, and provide a set of intermediate and generic theorems to increase the rate of proof automation for these properties. Finally, a case study is proposed to demonstrate the use of the defined operators for expressing and proving liveness properties.

The authors thank the ANR-19-CE25-0010 EBRP:EventB-Rodin-Plus project.

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Notes

  1. 1.

    https://www.irit.fr/~Peter.Riviere/models/.

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Authors and Affiliations

  1. INPT-ENSEEIHT/IRIT, University of Toulouse, Toulouse, France

    P. Rivière, N. K. Singh, Y. Aït-Ameur & G. Dupont

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  1. P. Rivière
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  2. N. K. Singh
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  3. Y. Aït-Ameur
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Correspondence to P. Rivière , N. K. Singh , Y. Aït-Ameur or G. Dupont .

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Editors and Affiliations

  1. Iowa State University, Ames, IA, USA

    Kristin Yvonne Rozier

  2. University of Texas at Austin, Austin, TX, USA

    Swarat Chaudhuri

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Rivière, P., Singh, N.K., Aït-Ameur, Y., Dupont, G. (2023). Formalising Liveness Properties in Event-B with the Reflexive EB4EB Framework. In: Rozier, K.Y., Chaudhuri, S. (eds) NASA Formal Methods. NFM 2023. Lecture Notes in Computer Science, vol 13903. Springer, Cham. https://doi.org/10.1007/978-3-031-33170-1_19

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  • DOI: https://doi.org/10.1007/978-3-031-33170-1_19

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