Tool support for qualitative reasoning in event-B

Abstract

Event-B is a notation and method for modelling discrete transition systems by re nement. The standard reasoning in Event-B is based on nondeterminism, however some system behaviours are more appropriately modelled probabilistically. Earlier work has extended Event-B with means for reasoning about qualitative probability. The extension provides proof obligations to prove almost-certain termination of systems and does not complicate the existing Event-B notation or method. However, this early work does not mention the preservation of qualitative reasoning in the case of re nement. Within our work we discuss how qualitative probabilistic reasoning can be maintained during re nement and propose some restrictions and conditions for almost-certain termination on re nement. We continue the above investigation with the integration of qualitative probabilistic reasoning into Event-B further towards the direction of having a tool support. We extend the Rodin Platform to support proving almost-certain termination and using our new developed tool support we model some example algorithms terminating almost-certainly. In passing by, we formalise a non-trivial algorithm, namely Rabin's choice coordination. Our correctness reasoning is a combination of termination proofs in terms of probabilistic convergence and standard invariants techniques with re nement. We use the technique of splitting/merging the events to avoid having complicated proofs.