Automated Provers doing (Higher-Order) Proof search: A Case Study in the Verification of Pointer Programs

We would like to present results obtained after doing a case study on the possibilities of doing proof search in a higher-order logic using existing automated proof tools. A commonly occurring type of proof obligation necessary to prove the correctness of the Schorr-Waite algorithm in the interactive prover Isabelle/HOL is given as a problem to the automated prover haRVey. Preliminary experimental results are encouraging. In [10], Shankar argues that decision procedures for various decidable fragments of a higher-order Logic (HOL) can be put to productive use in the context of interactive theorem provers. Among others, he advocates the use of “ground decision procedures” in PVS [8]. A ground decision procedure is a procedure capable of deciding the satisfiability problem for ground formulae in some (decidable) theory of first-order logic (FOL). According to the seminal work of Boyer and Moore [2], Shankar remarks that integrating decision procedures in more general reasoning activities (such as rewriting or finding suitable instances of quantified variables) is far from being a trivial task. The main difficulty is that proof obligations generated in many verification problems contains user-defined symbols whose meaning is not known to the available decision procedures. A näıve approach would be to treat user-defined function symbols as uninterpreted and use well-known combination schemas (such as Nelson-Oppen [5]) to build procedures for a combination of theories, decided by the available procedure and the theory of equality. Unfortunately, for some interesting verification problems such as program verification, this approach