An Interval-Based Approach to Modelling Time in Event-B

Abstract

Abstract. Our work was inspired by our modelling and verification of a cardiac pacemaker, which includes concurrent aspects and a set of interdependent and cyclic timing constraints. To model timing constraints in such systems, we present an approach based on the concept of timing interval. We provide a template-based timing constraint modelling scheme that could potentially be applicable to a wide range of modelling scenarios. We give a notation and Event-B semantics for the interval. The Event-B coding of the interval is decoupled from the application logic of the model, therefore a generative design of the approach is possible. We demonstrate our interval approach and its refinement through a small example. The example is verified, model-checked and animated (manually validated) with the ProB animator.

Modelling Complex Timing Requirements with Refinement

“…We build our contribution of timing interval refinement transformations on our timing interval approach [16]. The timing interval (1) is a higher level abstraction that builds on Sarshogh's original Delay and Deadline timing properties [14].…”

“…The system may have a number of timing intervals, each identified by a unique name. There may be multiple active instances of a given interval that occur independently from each other [16].…”

“…We start this section by using the abstract machine of the example model [19] to explain the underlying Event-B semantics and the dynamics of the timing interval [16] 2 . Interval approach improvements -index recycling and relative timing -are briefly covered on the way.…”

“…The tiGen tool code generation is based on generic code templates and comprises several steps [16]: (i) each specification element is assigned a predefined generic Event-B code template, (ii) the generic code variables are instantiated by prefixing them with the interval name, and (iii) the instantiated code is then injected into the model locations based on the specification and template-specific injection rules.…”

“…Our contribution is a set of refinement transformations that build on our timing interval approach [16], and the tiGen tool that facilitates the use thereof. The transformations enable further elaboration of the timing interval in a methodical and reusable manner.…”