Local Reasoning for Parameterized First Order Protocols

Abstract

First Order Logic (FOL) is a powerful reasoning tool for program verification. Recent work on Ivy shows that FOL is well suited for verification of parameterized distributed systems. However, specifying many natural objects, such as a ring topology, in FOL is unexpectedly inconvenient. We present a framework based on FOL for specifying distributed multi-process protocols in a process-local manner together with an implicit network topology. In the specification framework, we provide an auto-active analysis technique to reason about the protocols locally, in a process-modular way. Our goal is to mirror the way designers often describe and reason about protocols. By hiding the topology behind the FOL structure, we simplify the modelling, but complicate the reasoning. To deal with that, we use an oracle for the topology to develop a sound and relatively complete proof rule that reduces reasoning about the implicit topology back to pure FOL. This completely avoids the need to axiomatize the topology. Using the rule, we establish a property that reduces verification to a fixed number of processes bounded by the size of local neighbourhoods. We show how to use the framework on a few examples, including leader elections on rings and trees.