Inductive Invariants That Spark Joy: Using Invariant Taxonomies to Streamline Distributed Protocol Proofs

Proving the correctness of a distributed protocol is a challenging endeavor. Central to this task is finding an inductive invariant for the protocol. Currently, automated invariant inference algorithms require developers to describe protocols using a restricted logic. If the developer wants to prove a protocol expressed without these restrictions, they must devise an inductive invariant manually.

We propose an approach that simplifies and partially automates finding the inductive invariant of a distributed protocol, as well as proving that it really is an invariant. The key insight is to identify an invariant taxonomy that divides invariants into Regular Invariants, which have one of a few simple lowlevel structures, and Protocol Invariants, which capture the higher-level host relationships that make the protocol work.

Building on the insight of this taxonomy, we describe the Kondo methodology for proving the correctness of a distributed protocol modeled as a state machine. The developer first manually devises the Protocol Invariants by proving a synchronous version of the protocol correct. In this simpler version, sends and receives are replaced with atomic variable assignments. The Kondo tool then automatically generates the asynchronous protocol description, Regular Invariants, and proofs that the Regular Invariants are inductive on their own. Finally, Kondo combines these with the synchronous proof into a draft proof of the asynchronous protocol, which may then require a small amount of user effort to complete. Our evaluation shows that Kondo reduces developer effort for a wide variety of distributed protocols.