Perspicuity and Granularity in Refinement

TL;DR

This paper explores the relationship between different methods of action refinement in formal systems, distinguishing perspicuous actions from granularity changes, and analyzes their compatibility with refinement relations.

Contribution

It provides a detailed analysis of how various action refinement techniques relate to the fundamental refinement relation, highlighting incompatibilities and implications for Event-B.

Findings

Refining skip is incompatible with failures-based refinement.

Distinction between perspicuous actions and granularity changes.

Implications for designing Event-B refinement processes.

Abstract

This paper reconsiders refinements which introduce actions on the concrete level which were not present at the abstract level. It draws a distinction between concrete actions which are "perspicuous" at the abstract level, and changes of granularity of actions between different levels of abstraction. The main contribution of this paper is in exploring the relation between these different methods of "action refinement", and the basic refinement relation that is used. 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 entangled.