A CSP Account of Event-B Refinement

TL;DR

This paper introduces a CSP-based semantics for Event-B, clarifying the behavior-oriented relationship between systems and their refinements, including complex steps like event splitting and anticipation.

Contribution

It provides the first CSP account of Event-B refinement, encompassing event splitting and anticipation, and formalizes the refinement process as CSP refinement.

Findings

CSP semantics for Event-B is defined.

Event-B refinement steps are captured as CSP refinement.

The approach clarifies the behavioral relationship between systems and their refinements.

Abstract

Event-B provides a flexible framework for stepwise system development via refinement. The framework supports steps for (a) refining events (one-by-one), (b) splitting events (one-by-many), and (c) introducing new events. In each of the steps events can moreover possibly be anticipated or convergent. All such steps are accompanied with precise proof obligations. Still, it remains unclear what the exact relationship - in terms of a behaviour-oriented semantics - between an Event-B machine and its refinement is. In this paper, we give a CSP account of Event-B refinement, with a treatment for the first time of splitting events and of anticipated events. To this end, we define a CSP semantics for Event-B and show how the different forms of Event-B refinement can be captured as CSP refinement.