Towards Automatic Inference of Inductive Invariants

Abstract

Distributed systems are notoriously difficult to design and implement correctly. Formal verification provides correctness proofs, and has recently been successfully applied to various distributed systems. At the heart of a typical formal verification is a computer-checked proof with an inductive invariant. Finding this inductive invariant is the hardest part of the proof: a part that is currently undertaken manually by the developer and is responsible for most of the effort associated with formal verification. In this paper, we present a new approach: Incremental Inference of Inductive Invariants (I4), to automatically generate inductive invariants for distributed protocols. We start from a simple idea: the inductive invariant of a finite instance of the protocol must be an instance of a general inductive invariant for the infinite distributed protocol. In I4, we instantiate a finite instance of the protocol, work out the finite inductive invariant of this instance, then figure out the general inductive invariant as a generalization of the finite invariant. Our experiments show that I4 can finish the general proof of correctness of several systems with minimal human effort.