We present the first verification of full functional correctness for a range of linked data structure implementations, including mutable lists, trees, graphs, and hash tables. Specifically, we present the use of the Jahob verification system to verify formal specifications, written in classical higher-order logic, that completely capture the desired behavior of the Java data structure implementations (with the exception of properties involving execution time and/or memory consumption). Given that the desired correctness properties include intractable constructs such as quantifiers, transitive closure, and lambda abstraction, it is a challenge to successfully prove the generated verification conditions. Our Jahob verification system uses integrated reasoning to split each verification condition into a conjunction of simpler subformulas, then apply a diverse collection of specialized decision procedures,

We describe a technique that enables the focused application of multiple analyses to different modules in the same program. In our approach, each module encapsulates one or more data structures and uses membership in abstract sets to characterize how objects participate in data structures. Each analysis verifies that the implementation of the module 1) preserves important internal data structure consistency properties and 2) correctly implements an interface that uses formulas in a set algebra to characterize the effects of operations on the encapsulated data structures. Collectively, the analyses use the set algebra to 1) characterize how objects participate in multiple data structures and to 2) enable the inter-analysis communication required to verify properties that depend on multiple modules analyzed by different analyses.

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. Moreover, our experimental results show that the elimination of this 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. 1

Abstract. Termination of a heap-manipulating program generally depends on preconditions that express heap assumptions (i.e., assertions describing reachability, aliasing, separation and sharing in the heap). We present an algorithm for the inference of such preconditions. The algorithm exploits a unique interplay between counterexample-producing abstract termination checker and shape analysis. The shape analysis produces heap assumptions on demand to eliminate counterexamples, i.e., non-terminating abstract computations. The experiments with our prototype implementation indicate its practical potential. 1

Abstract. The process of verifying that a program conforms to its specification is often hampered by errors in both the program and the specification. A runtime checker that can evaluate formal specifications can be useful for quickly identifying such errors. This paper describes our preliminary experience with incorporating run-time checking into the Jahob verification system and discusses some lessons we learned in this process. One of the challenges in building a runtime checker for a program verification system is that the language of invariants and assertions is designed for simplicity of semantics and tractability of proofs, and not for run-time checking. Some of the more challenging constructs include existential and universal quantification, set comprehension, specification variables, and formulas that refer to past program states. In this paper, we describe how we handle these constructs in our runtime checker, and describe directions for future work. 1

Modular analyses of software systems rely on the specifications of the analyzed modules. In many analysis techniques (e.g. ESC/Java), the specifications have to be provided by users. This puts a considerable burden on users and thus limits the applicability of such techniques. To avoid this problem, some modular analysis techniques automatically extract module summaries that capture specific aspects of the modules ’ behaviors. However, such summaries are only useful in checking a restricted class of properties. We describe a static modular analysis that automatically extracts procedure specifications in order to check heap-manipulating programs against rich data structure properties. Extracted specifications are context-dependent; their precision depends on both the property being checked, and the calling context in which they are used. Starting from a rough over-approximation of the behavior of each call site, our analysis computes an abstraction of the procedure being analyzed and checks it against the property. Specifications are further refined, as needed, in response to spurious