Discovery of invariants through automated theory formation

Abstract

Refinement is a powerful mechanism for mastering the complexities that arise when formally modelling systems. Refinement also brings with it additional proof obligations - requiring a developer to discover properties relating to their design decisions. With the goal of reducing this burden, we have investigated how a general purpose automated theory formation tool, HR, can be used to automate the discovery of such properties within the context of the Event-B formal modelling framework. This gave rise to an integrated approach to automated invariant discovery. In addition to formal modelling and automated theory formation, our approach relies upon the simulation of system models as a key input to the invariant discovery process. Moreover we have developed a set of heuristics which, when coupled with automated proof-failure analysis, have enabled us to effectively tailor HR to the needs of Event-B developments. Drawing in part upon case study material from the literature, we have achieved some promising experimental results. While our focus has been on Event-B, we believe that our approach could be applied more widely to formal modelling frameworks which support simulation. © 2012 British Computer Society.