Abstract
We present an implementation of symbolic reachability analysis with the features of compositionality, and intermittent abstraction, in the sense of pefrorming approximation only at selected program points, if at all. The key advantages of compositionality are well known, while those of intermittent abstraction are that the abstract domain required to ensure convergence of the algorithm can be minimized, and that the cost of performing abstractions, now being intermittent, is reduced.
We start by formulating the problem in CLP, and first obtain compositionality. We then address two key efficiency challenges. The first is that reasoning is required about the strongest-postcondition operator associated with an arbitrarily long program fragment. This essentially means dealing with constraints over an unbounded number of variables describing the states between the start and end of the program fragment at hand. This is addressed by using the variable elimination or projection mechanism that is implicit in CLP systems. The second challenge is termination, that is, to determine which subgoals are redundant. We address this by a novel formulation of memoization called coinductive tabling.
We finally evaluate the method experimentally. At one extreme, where abstraction is performed at every step, we compare against a model checker. At the other extreme, where no abstraction is performed, we compare against a program verifier. Of course, our method provides for the middle ground, with a flexible combination of abstraction and Hoare-style reasoning with predicate transformers and loop-invariants.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ball, T., Majumdar, R., Millstein, T., Rajamani, S.K.: Automatic predicate abstraction of C programs. In: 15th PLDI, May 2001. SIGPLAN Notices, vol. 36(5), pp. 203–213 (2001)
Ball, T., Millstein, T., Rajamani, S.K.: Polymorphic predicate abstraction. ACM Transactions on Programming Languages and Systems 27(2), 314–343 (2005)
Barras, B., Boutin, S., Cornes, C., Courant, J., Filliatre, J., Giménez, E., Herbelin, H., Huet, G., Noz, C.M., Murthy, C., Parent, C., Paulin, C., Saïbi, A., Werner, B.: The Coq proof assistant reference manual—version v6.1. Technical Report 0203, INRIA (1997)
Bossi, A. (ed.): LOPSTR 1999. LNCS, vol. 1817. Springer, Heidelberg (2000)
Chaki, S., Clarke, E., Groce, A., Jha, S., Veith, H.: Modular verification of software components in C. IEEE Transactions on Software Engineering 30(6), 388–402 (2004)
Cok, D.R., Kiniry, J.: ESC/Java2: Uniting ESC/Java and JML. In: Barthe, G., Burdy, L., Huisman, M., Lanet, J.-L., Muntean, T. (eds.) CASSIS 2004. LNCS, vol. 3362, pp. 108–128. Springer, Heidelberg (2005)
Cousot, P., Cousot, R.: Comparing the Galois connection and widening/narrowing approaches to abstract interpretation. In: Bruynooghe, M., Wirsing, M. (eds.) PLILP 1992. LNCS, vol. 631. Springer, Heidelberg (1992)
Das, S., Dill, D.L., Park, S.: Experience with predicate abstraction. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 160–171. Springer, Heidelberg (1999)
Delzanno, G., Podelski, A.: Model checking in CLP. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 223–239. Springer, Heidelberg (1999)
Du, X., Ramakrishnan, C.R., Smolka, S.A.: Tabled resolution + constraints: A recipe for model checking real-time systems. In: 21st RTSS. IEEE Computer Society Press, Los Alamitos (2000)
Burdy, L., et al.: Java applet correctness: A developer-oriented approach. In: Araki, K., Gnesi, S., Mandrioli, D. (eds.) FME 2003. LNCS, vol. 2805. Springer, Heidelberg (2003)
Ramakrishna, Y.S., et al.: Efficient model checking using tabled resolution. In: Grumberg [16]
Fioravanti, F., Pettorossi, A., Proietti, M.: Verifying CTL properties of infinite-state systems by specializing constraint logic programs. In: Leuschel, M., Podelski, A., Ramakrishnan, C.R., Ultes-Nitsche, U. (eds.) 2nd VCL, pp. 85–96 (2001)
Fribourg, L.: Constraint logic programming applied to model checking. In: Bossi [4], pp. 30–41
Graf, S., Saïdi, H.: Construction of abstract state graphs of infinite systems with PVS. In: Grumberg [16], pp. 72–83
Grumberg, O. (ed.): CAV 1997. LNCS, vol. 1254. Springer, Heidelberg (1997)
Gupta, G., Pontelli, E.: A constraint-based approach for specification and verification of real-time systems. In: 18th RTSS, pp. 230–239. IEEE Computer Society Press, Los Alamitos (1997)
Harrison, J.: HOL light: A tutorial introduction. In: Srivas, M., Camilleri, A. (eds.) FMCAD 1996. LNCS, vol. 1166, pp. 265–269. Springer, Heidelberg (1996)
Henzinger, T.A., Jhala, R., Majumdar, R.: Lazy abstraction. In: 29th POPL. SIGPLAN Notices, vol. 37(1), pp. 58–70. ACM Press, New York (2002)
Holzmann, G.J.: The Spin Model Checker: Primer and Reference Manual. Add.-Wesley, Reading (2003)
Jaffar, J., Maher, M., Stuckey, P., Yap, R.: Projecting CLP(\(\cal R\)) constraints. In: New Generation Computing, vol. 11, pp. 449–469. Ohmsha and Springer, Heidelberg (1993)
Jaffar, J., Michaylov, S., Stuckey, P.J., Yap, R.H.C.: The CLP(\(\cal R\)) language and system. ACM TOPLAS 14(3), 339–395 (1992)
Leuschel, M., Massart, T.: Infinite-state model checking by abstract interpretation and program specialization. In: Bossi [4]
Marché, C., Paulin-Mohring, C., Urbain, X.: The KRAKATOA tool for certification of JAVA/JAVACARD programs annotated in JML. J. Log. and Alg. Prog. 58(1–2), 89–106 (2004)
Nielson, F., Nielson, H.R., Hankin, C.: Principles of Program Analysis. Springer, Heidelberg (1999)
Nilsson, U., Lübcke, J.: Constraint logic programming for local and symbolic model checking. In: Palamidessi, C., Moniz Pereira, L., Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 384–398. Springer, Heidelberg (2000)
Owre, S., Shankar, N., Rushby, J.: PVS: A prototype verification system. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 748–752. Springer, Heidelberg (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jaffar, J., Santosa, A.E., Voicu, R. (2005). A CLP Method for Compositional and Intermittent Predicate Abstraction. In: Emerson, E.A., Namjoshi, K.S. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2006. Lecture Notes in Computer Science, vol 3855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11609773_2
Download citation
DOI: https://doi.org/10.1007/11609773_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31139-3
Online ISBN: 978-3-540-31622-0
eBook Packages: Computer ScienceComputer Science (R0)