Finite Countermodel Based Verification for Program Transformation (A Case Study)
This work addresses the integration of verification techniques into program transformation for researchers in formal methods, but it is incremental as it builds on existing supercompilation and verification approaches.
The paper investigates how finite countermodels from safety verification can be applied to Turchin's supercompilation method to solve reachability problems in program transformation, demonstrating the use of an external countermodel finder for specific sub-algorithms.
Both automatic program verification and program transformation are based on program analysis. In the past decade a number of approaches using various automatic general-purpose program transformation techniques (partial deduction, specialization, supercompilation) for verification of unreachability properties of computing systems were introduced and demonstrated. On the other hand, the semantics based unfold-fold program transformation methods pose themselves diverse kinds of reachability tasks and try to solve them, aiming at improving the semantics tree of the program being transformed. That means some general-purpose verification methods may be used for strengthening program transformation techniques. This paper considers the question how finite countermodels for safety verification method might be used in Turchin's supercompilation method. We extract a number of supercompilation sub-algorithms trying to solve reachability problems and demonstrate use of an external countermodel finder for solving some of the problems.