Streamlining Proof Integration Through Elaboration on Demand

Objective

Automated reasoning (AR) systems, such as Satisfiability Modulo Theory (SMT) solvers and theorem provers, decide verification conditions without human interaction. However, formal verification systems need irrefutable assurance that the answer of the AR system is correct. To provide this assurance, AR systems produce proof certificates that can be replayed in proof assistants, or checked by formally verified proof checkers. Unfortunately, the adaption of proof certificates is limited, because the implementation of verified proof checkers and proof replay pipelines is labor intensive. The Panproof project tackles this problem by elaborating proof rules specific to an AR system to standard proof rules. This allows proof consumers to support multiple AR systems by only implementing the standard rules. To control proof size growth, the consumer can control which rules should be elaborated. For example, if a system specific rule is common, the consumer could implement support for it so that elaboration is not needed. Panproof represents proof rules with three components: a function that computes the conclusions of steps, a function that elaborates steps, and a mechanized proof that these two functions are equivalent. Since Panproof will be implemented in Agda, a consequence of the equivalency proof is that Panproof can also be used as a formally verified proof checker. The Panproof project will develop programming techniques to implement the elaboration functions and the equivalence proofs. It will also develop a library of standard rules based on empirical studies of the proof rules used by real-world AR systems, and will integrate with multiple AR systems and consumers. Overall, Panproof will make it easier to integrate AR systems in verification pipelines. This will make it faster to verify software systems, and ultimately result in safer software.