Fast and Effective Well-Definedness Checking

Abstract

Well-Definedness is important for many formal methods. In B and Event-B it ensures that certain kinds of errors (e.g., division by 0) cannot appear and that proof rules based on two-valued logic are sound. For validation tools such as ProB, well-definedness is important for constraint solving. B and Event-B establish well-definedness by generating dedicated proof obligations (POs). Unfortunately, the standard provers are not always very good at discharging them. In this paper, we present a new integrated technique to simultaneously generate and discharge well-definedness POs. The implementation contains a dedicated rule-based prover written in Prolog supporting B, Event-B and extensions thereof for data validation. We show that the generation and discharging is significantly faster than existing implementations in rodin and Atelier-B and that a large number of POs are automatically discharged. The POs are fine-grained enough to provide precise source code feedback, and allow inspection of problematic POs within various editors.