Extending the EB4EB framework with parameterised events

Abstract

EB4EB, standing for Event-B for Event-B, is a framework that supports the formalisation of Event-B models using first-order logic and set-theory, so that it becomes possible to manipulate them as first-class objects. This framework relies on an Event-B algebraic theory, which serves as a meta-theory formalising, explicitly, all of the features of an Event-B machine. States, events, invariants, variants, etc... are formalised through data-types and operators. When this meta-theory is instantiated, an Event-B model becomes a first-order logic and set-theoretic formula, described in an Event-B context.

Because it can handle machine elements as terms in formulas, the EB4EB framework enables the definition of new specific proof obligations and analyses. Such analyses may then be applied to any EB4EB machines in order to establish advanced properties, not natively present in the Event-B method, such as deadlock-freeness or liveness requirements. These analyses are non-intrusive since they do not require to alter the machine in order to be performed.

In the previous formalisation of the EB4EB framework only states and events were handled, limiting the expressive reasoning power of the framework. This paper presents an extension of the EB4EB framework to support parameterised events, an important feature of Event-B. This extension is not straightforward in EB4EB. Indeed, the typing system supported by Event-B theories is not rich enough to describe such extension in a constructive manner as for the other Event-B features formalised in EB4EB. The proposed solution, described in this paper, consists in defining an axiomatic formalisation of event parameters definitions. We also show that the proof obligations and model analyses we have defined scale to handle event parameters. The approach is illustrated on different case studies we have developed.