Event-B is a formal method for system-level modelling and analysis. Key features of Event-B are the use of set theory as a modelling notation, the use of refinement to represent systems at different abstraction levels and the use of mathematical proof to verify consistency between refinement levels. In this article we present the Rodin modelling tool that seamlessly integrates modelling and proving. We outline how the Event-B language was designed to facilitate proof and how the tool has been designed to support changes to models while minimising the impact of changes on existing proofs. We outline the important features of the prover architecture and explain how well-definedness is treated. The tool is extensible and configurable so that it can be adapted more easily to different application domains and development methods.

/pdf/rodin-an-open-toolset-for-modelling-and-reasoning-in-event-b-10h3ppr9tv.pdf

Rodin: an open toolset for modelling and reasoning in Event-B

The B Book

We present PROB, an animation and model checking tool for the B method PROB's animation facilities allow users to gain confidence in their specifications, and unlike the animator provided by the B-Toolkit, the user does not have to guess the right values for the operation arguments or choice variables PROB contains a model checker and a constraint-based checker, both of which can be used to detect various errors in B specifications We present our first experiences in using PROB on several case studies, highlighting that PROB enables users to uncover errors that are not easily discovered by existing tools

ProB: A model checker for B

https://onlinelibrary.wiley.com/doi/pdf/10.1002/stvr.247

Problem frames: analyzing and structuring software development problems. By Michael Jackson. Published by Addison‐Wesley, Boston, Massachusetts, U.S.A., ACM Press Series, 2001. ISBN: 0‐201‐59627‐X, 390 pages. Price: U.K. ?32.95, U.S.A. $49.99, soft cover.

We consider modelling indispensable for the development of complex systems. Modelling must be carried out in a formal notation to reason and make meaningful conjectures about a model. But formal modelling of complex systems is a difficult task. Even when theorem provers improve further and get more powerful, modelling will remain difficult. The reason for this that modelling is an exploratory activity that requires ingenuity in order to arrive at a meaningful model. We are aware that automated theorem provers can discharge most of the onerous trivial proof obligations that appear when modelling systems. In this article we present a modelling tool that seamlessly integrates modelling and proving similar to what is offered today in modern integrated development environments for programming. The tool is extensible and configurable so that it can be adapted more easily to different application domains and development methods.

/pdf/an-open-extensible-tool-environment-for-event-b-1cn2inogdu.pdf

An open extensible tool environment for event-b

Two methods have been identified for Event-B model decomposition: shared variable and shared event. The purpose of this paper is to introduce the two approaches and the respective tool support in the Rodin platform. Besides alleviating the complexity for large systems and respective proofs, decomposition allows team development in parallel over the same Event-B project which is very attractive in the industrial environment. Copyright © 2011 John Wiley & Sons, Ltd.

/pdf/decomposition-tool-for-event-b-4pltktjxv1.pdf

Decomposition tool for event-B

Event-B has given developers the opportunity to construct models of complex systems that are correct-by-construction. However, there is no systematic approach, especially in terms of reuse, which could help with the construction of these models. We introduce the notion of design patterns within the framework of Event-B to shorten this gap. Our approach preserves the correctness of the models, which is critical in formal methods and also reduces the proving effort. Within our approach, an Event-B design pattern is just another model devoted to the formalisation of a typical sub-problem. As a result, we can use patterns to construct a model which can subsequently be used as a pattern to construct a larger model. We also present the interaction between developers and the tool support within the associated RODIN Platform of Event-B. The approach has been applied successfully to some medium-size industrial case studies.

/pdf/event-b-patterns-and-their-tool-support-20s5hoqijf.pdf

Event-B patterns and their tool support

Event-B is a formal method which is widely used in modelling safety critical systems. So far, the main properties of interest in Event-B are safety related. Even though some liveness properties, e,g, termination, are already within the scope of Event-B, more general liveness properties, e.g. progress or persistence, are currently unsupported. We present in this paper proof rules to reason about important classes of liveness properties. We illustrate our proof rules by applying them to prove liveness properties of realistic examples. Our proof rules are based on several proof obligations that can be implemented in a tool support such as the Rodin platform.

/pdf/reasoning-about-liveness-properties-in-event-b-lrzqx4a0gn.pdf

Reasoning about liveness properties in event-B

Event-B is a notation and method for discrete systems modelling by refinement. We introduce a small but very useful construction: qualitative probabilistic choice. It extends the expressiveness of Event-B allowing us to prove properties of systems that could not be formalised in Event-B before. We demonstrate this by means of a small example, part of a larger Event-B development that could not be fully proved before. An important feature of the introduced construction is that it does not complicate the existing Event-B notation or method, and can be explained without referring to the underlying more complicated probabilistic theory. The necessary theory [18] itself is briefly outlined in this article to justify the soundness of the proof obligations given. We also give a short account of alternative constructions that we explored, and rejected.

/pdf/qualitative-probabilistic-modelling-in-event-b-4xdplud2la.pdf

Thai Son Hoang

Papers

Rodin: an open toolset for modelling and reasoning in Event-B

Decomposition tool for event-B

Event-B patterns and their tool support

Reasoning about liveness properties in event-B

Qualitative probabilistic modelling in event-B