Introducing extra operations in refinement

Abstract

Abstract This paper reconsiders refinements which introduce actions on the concrete level which were not present at the abstract level. It considers a range of different basic refinement relations, covering the standard ones for formalisms like Event-B, Z, action systems, and CSP. It also describes a number of ways in which new operations may be introduced: extended interfaces, internal actions, stuttering steps, and action refinement. The main contribution of this paper is in exploring the interaction between those two dimensions. In particular, it shows how the “refining skip” method is incompatible with failures-based refinement relations, and consequently some decisions in designing Event-B refinement are more entangled than previously highlighted.