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The Theory plug-in enables modellers to extend the mathematical modelling notation for Event-B, with accompanying support for reasoning about the extended language. Previous version of the Theory plug-in has been implemented based on Rodin 2.x. This presentation outline the main improvements to the The- ory plug-in, to be compatible with Rodin 3.x,...
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... directly, inductively or axiomatically. Fig. 3 shows the definitions of two operators list isEmpty (defined directly) and list length (defined inductively). An operator defined without any definition or INFIX (for operator with two or more arguments). Further properties can be declared for operators include associativity and commutativity. Fig. 4 shows the declaration for three operators: sum, zero, and (unary) minus. In particular, sum is declared to be an infix operator which is associative and commutative. The axioms are the assumption about these operators that can be used to defined ...
Citations
... We also investigated on the Rodin capabilities in case of a continuous domain model of the environment. We modeled the continous parts of the system using the plug-in Theory [18] integrated within the Rodin platform. Since Event-B has no inbuilt Fig. 4. Event-B abstract machine for e-Bike cruise control system generated with iUML continuous facilities, a considerable amount of continuous infrastructure had to be built behind the scenes using this plug-in of the Rodin tool. ...
Formal modelling is essential for precisely defining, understanding and reasoning when designing complex systems, such as cyberphysical systems. In this paper we present a formal specification using Event-B and Rodin platform for a case study of a cruise control system for a hybrid propulsion vehicle and electric bicycle (e-Bike). Our work uses the EventB method, a formal approach for reliable systems specification and verification, being supported by the Rodin platform, based on theorem proving, allowing a stepwise specification process based on refinement. We also use, from the same platform, the ProB model checker for the verification of the B-Machine and iUML plug-in to visualize our model. This approach shows the benefits of using a formal modelling platform, in the context of cyberphysical systems, which provides multiple ways of analysing a system.
Static type checking helps catch errors in manipulating variables values early on, and most specification languages, like Event-B, are strongly typed. However, the type system of Event-B language is relatively simple and provides only a way to specify discrete behaviour using Integer type. There is no possibility to model continuous behaviour, which would have helped analyse hybrid systems. More precisely, the Event-B language doesn’t consider in its type-checking system the possibility of defining such behaviours and checking the correctness of the values of the continuous variables within the Event-B models. In this article, we propose to extend the type-checking system of Event-B to include Float variables by specifying a floating point numbers theory using the theory plugin.
The B landscape can be confusing to formal methods outsiders, especially due to the fact that it is partitioned into classical B for software and Event-B for systems modelling. In this article we shed light on commonalities and differences between these formalisms, based on our experience in building tools that support both of them. In particular, we examine not so well-known pitfalls. For example, despite sharing a common mathematical foundation in predicate logic, set theory and arithmetic, there are formulas that are true in Event-B and false in classical B, and vice-versa.
This paper presents an Event-B meta-modelisation of an Event-B project restricted to its context hierarchy which introduces the functional part of a development through sets, constants, axioms and theorems. We study the proposal of a new mechanism for Event-B. It consists in allowing to instantiate in a new context an already proved theorem in a given context. We investigate the validation of the instantiation mechanism in order to prove the validity of imported theorems. We also compare the proposal with similar mechanisms available within some existing theorem provers.
Hybrid and cyber-physical systems pose new challenges for formal construction of systems. In hybrid systems, the states evolve over continuous time according to related laws of continuous and discrete dynamics. Thus, timing constraints and synchronous signals play important roles. Moreover, in the development of complex hybrid systems, refinement, and composition of timing constraints are in need. However, the existing formal approaches of Event-B have difficulties in refinement and composition of hybrid systems. Therefore, in this article, we propose a formal hybrid approach to solve this problem. Our approach of modeling is based on the Event-B method, and uses the Rodin platform and its plugin Theory.
