A verified framework for symbolic execution in the ACL2 theorem prover

Abstract

Mechanized theorem proving is a promising means of formally establishing facts about complex systems. However, in applying theorem proving methodologies to industrial-scale hardware and software systems, a large amount of user interaction is required in order to prove useful properties. In practice, the human user tasked with such a verification must gain a deep understanding of the system to be verified, and prove numerous lemmas in order to allow the theorem proving program to approach a proof of the desired fact. Furthermore, proofs that fail during this process are a source of confusion: the proof may either fail because the conjecture was false, or because the prover required more help from the user in order to reach the desired conclusion.

We have implemented a symbolic execution framework inside the ACL2 theorem prover in order to help address these issues on certain problem domains. Our framework introduces a proof strategy that applies bit-level symbolic execution using BDDs to finite-domain problems. This proof strategy is a fully verified decision procedure for such problems, and on many useful problem domains its capacity vastly exceeds that of exhaustive testing. Our framework also produces counterexamples for conjectures that it determines to be false.

Our framework seeks to reduce the amount of necessary user interaction in proving theorems about industrial-scale hardware and software systems. By increasing the automation available in the prover, we allow the user to complete useful proofs while understanding less of the detailed implementation of the system. Furthermore, by producing counterexamples for falsified conjectures, our framework reduces the time spent by the user in trying to determine why a proof failed.