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The guarantees of formally verified systems are only as strong as their trusted specifications (specs). As observed by previous studies, bugs in formal specs invalidate the assurances that proofs provide. Unfortunately, specs—by their very nature—cannot be proven correct. Currently, the only way to identify spec bugs is by careful, manual inspection. In this paper we introduce IronSpec, a framework of automatic and manual techniques to increase the reliability of formal specifications. IronSpec draws inspiration from classical software testing practices, which we adapt to the realm of formal specs. IronSpec facilitates spec testing with automated sanity checking, a methodology for writing SpecTesting Proofs (STPs), and automated spec mutation testing. We evaluate IronSpec on 14 specs, including six specs of real-world verified codebases. Our results show that IronSpec is effective at flagging discrepancies between the spec and the developer’s intent, and has led to the discovery of ten specification bugs across all six real-world verified systems. 

In this paper, we examine the Paxos protocol and demonstrate how the discrete numbering of ballots can be leveraged to weaken the conditions for learning. Specifically, we define the notion of consecutive ballots and use this to define Consecutive Quorums. Consecutive Quorums weaken the learning criterion such that a learner does not need matching accept messages sent in the same ballot from a majority of acceptors to learn a value. We prove that this modification preserves the original safety and liveness guarantees of Paxos. We define Consecutive Paxos which encapsulates the properties of discrete consecutive ballots. To establish the correctness of these results, in addition to a paper proof, we formally verify the correctness of a State Machine Replication Library built on top of an optimized version of Multi-Paxos modified to reflect Consecutive Paxos.