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, 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 often 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.
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References
Arkoudas, K., et al.: Verifying a file system implementation. In: Davies, J., Schulte, W., Barnett, M. (eds.) ICFEM 2004. LNCS, vol. 3308, pp. 8–12. Springer, Heidelberg (2004)
Barendregt, H.P.: Lambda calculi with types. In: Handbook of Logic in Computer Science, vol. II, Oxford University Press, Oxford (2001)
Barnett, M., Leino, K.R.M., Schulte, W.: The Spec# programming system: An overview. In: Barthe, G., et al. (eds.) CASSIS 2004. LNCS, vol. 3362, Springer, Heidelberg (2005)
Bouillaguet, C., Kuncak, V., Wies, T., Zee, K., Rinard, M.: On using first-order theorem provers in a data structure verification system. Technical Report MIT-CSAIL-TR-2006-072, MIT (November 2006), http://hdl.handle.net/1721.1/34874
de Roever, W.-P., Engelhardt, K.: Data Refinement: Model-oriented proof methods and their comparison. Cambridge University Press, Cambridge (1998)
Hurd, J.: An LCF-style interface between HOL and first-order logic. In: Voronkov, A. (ed.) Automated Deduction - CADE-18. LNCS (LNAI), vol. 2392, Springer, Heidelberg (2002)
Kuncak, V.: Modular Data Structure Verification. PhD thesis, EECS Department, Massachusetts Institute of Technology (February 2007)
Kuncak, V., Nguyen, H.H., Rinard, M.: Deciding Boolean Algebra with Presburger Arithmetic. J. of Automated Reasoning (2006), http://dx.doi.org/10.1007/s10817-006-9042-1
Leino, K.R.M., Müller, P.: A verification methodology for model fields. In: Sestoft, P. (ed.) ESOP 2006 and ETAPS 2006. LNCS, vol. 3924, Springer, Heidelberg (2006)
Lev-Ami, T., Reps, T., Sagiv, M., Wilhelm, R.: Putting static analysis to work for verification: A case study. In: Int. Symp. Software Testing and Analysis (2000)
Manzano, M.: Extensions of First-Order Logic. Cambridge University Press, Cambridge (1996)
Meng, J., Paulson, L.C.: Experiments on supporting interactive proof using resolution. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol. 3097, Springer, Heidelberg (2004)
Meng, J., Paulson, L.C.: Lightweight relevance filtering for machine-generated resolution problems. In: ESCoR: Empirically Successful Computerized Reasoning (2006)
Meng, J., Paulson, L.C.: Translating higher-order problems to first-order clauses. In: ESCoR: Empir. Successful Comp. Reasoning, pp. 70–80 (2006)
Nguyen, H.H., et al.: Automated verification of shape, size and bag properties via separation logic. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, Springer, Heidelberg (2007)
Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)
Reineke, J.: Shape analysis of sets. Master’s thesis, Universität des Saarlandes, Germany (June 2005)
Rugina, R.: Quantitative shape analysis. In: Giacobazzi, R. (ed.) SAS 2004. LNCS, vol. 3148, Springer, Heidelberg (2004)
Sagiv, M., Reps, T., Wilhelm, R.: Parametric shape analysis via 3-valued logic. ACM TOPLAS 24(3), 217–298 (2002)
Schulz, S.: E–A Brainiac Theorem Prover. Journal of AI Communications 15(2–3), 111–126 (2002)
Sutcliffe, G., Suttner, C.B.: The tptp problem library: Cnf release v1.2.1. Journal of Automated Reasoning 21(2), 177–203 (1998)
Weidenbach, C.: Combining superposition, sorts and splitting. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. II, chapter 27, pp. 1965–2013. Elsevier, Amsterdam (2001)
Wies, T., Kuncak, V., Lam, P., Podelski, A., Rinard, M.: Field constraint analysis. In: Proc. Int. Conf. Verification, Model Checking, and Abstract Interpratation (2006)
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Bouillaguet, C., Kuncak, V., Wies, T., Zee, K., Rinard, M. (2007). Using First-Order Theorem Provers in the Jahob Data Structure Verification System. In: Cook, B., Podelski, A. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2007. Lecture Notes in Computer Science, vol 4349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69738-1_5
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DOI: https://doi.org/10.1007/978-3-540-69738-1_5
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