On Using First-Order Theorem Provers in the Jahob Data Structure Verification System

Abstract

This paper presents our integration of efficient resolution-based theorem provers into the Jahob data structure verification system. Our experimental results show that this approach enables Jahob to automatically verify the correctness of a range of complex dynamically instantiable data structures, including data structures such as hash tables and search trees, without the need for interactive theorem proving or techniques tailored to individual data structures. Our primary technical results include: (1) a translation from higher-order logic to first-order logic that enables the application of resolution-based theorem provers and (2) a proof that eliminating type (sort) information in formulas is both sound and complete, even in the presence of a generic equality operator. Our experimental results show that the elimination of type information dramatically decreases the time required to prove the resulting formulas. These techniques enabled us to verify complex correctness properties of Java programs such as a mutable set implemented as an imperative linked list, a finite map implemented as a functional ordered tree, a hash table with a mutable array, and a simple library system example that uses these container data structures. Our system verifies (in a matter of minutes) that data structure operations correctly update the finite map, that they preserve data structure invariants (such as ordering of elements, membership in appropriate hash table buckets, or relationships between sets and relations), and that there are no run-time errors such as null dereferences or array out of bounds accesses.