# Jean-Raymond Abrial

A practical text suitable for an introductory or advanced course in formal methods, this book presents a mathematical approach to modeling and designing systems using an extension of the B formalism: Event-B. Based on the idea of refinement, the author’s systematic approach allows the user to construct models gradually and to facilitate a systematic(More)
• International Journal on Software Tools for…
• 2010
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(More)
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• Fundam. Inform.
• 2007
We argue that formal modeling should be the starting point for any serious development of computer systems. This claim poses a challenge for modeling: at first it must cope with the constraints and scale of serious developments. Only then it is a suitable starting point. We present three techniques, refinement, decomposition, and instantiation, that we(More)
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(More)
In B, the expression of dynamic constraints is notoriously missing. In this paper, we make various proposals for introducing them. They all express, in di erent complementary ways, how a system is allowed to evolve. Such descriptions are independent of the proposed evolutions of the system, which are de ned, as usual, by means of a number of operations.(More)
• TPHOLs
• 2003
In this article, we first briefly present a proof assistant called the Predicate Prover, which essentially offers two functionalities: (1) an automatic semi-decision procedure for First Order Predicate Calculus, and (2) a systematic translation of statements written within Set Theory into equivalent ones in First Order Predicate Calculus. We then show that(More)
In this article, I present an “event approach” used to formally develop sequential programs. It is based on the formalism of Action Systems [6] (and Guarded Commands[7]), which is encoded within B [2]. This approach has already been used to develop distributed programs [4]. In the first part, I present the basic concepts. In the second part, I develop a(More)
• Formal Aspects of Computing
• 2003
The IEEE 1394 tree identify protocol illustrates the adequacy of the event-driven approach used together with the B Method. This approach provides a complete framework for developing mathematical models of distributed algorithms. A specific development is made of a series of more and more refined models. Each model is made of a number of static properties(More)
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