Abstract
We show that the idea of predicates on heap objects can be cast in the framework of predicate abstraction. This leads to an alternative view on the underlying concepts of three-valued shape analysis by Sagiv, Reps and Wilhelm. Our construction of the abstract post operator is analogous to the corresponding construction for classical predicate abstraction, except that predicates over objects on the heap take the place of state predicates, and boolean heaps (sets of bitvectors) take the place of boolean states (bitvectors). A program is abstracted to a program over boolean heaps. For each command of the program, the corresponding abstract command is effectively constructed by deductive reasoning, namely by the application of the weakest precondition operator and an entailment test. We thus obtain a symbolic framework for shape analysis.
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
Balaban, I., Pnueli, A., Zuck, L.: Shape analysis by predicate abstraction. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 164–180. Springer, Heidelberg (2005)
Ball, T., Majumdar, R., Millstein, T., Rajamani, S.: Automatic predicate abstraction of C programs. In: Programming language design and implementation (PLDI 2001). ACM SIGPLAN Notices, vol. 36, pp. 203–213 (2001)
Ball, T., Podelski, A., Rajamani, S.: Boolean and cartesian abstraction for model checking C programs. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 268–283. Springer, Heidelberg (2001)
Cousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: Symposium on Principles of Programming Languages (POPL 1979), pp. 269–282 (1979)
Dams, D., Namjoshi, K.: Shape Analysis through Predicate Abstraction and Model Checking. In: Zuck, L.D., Attie, P.C., Cortesi, A., Mukhopadhyay, S. (eds.) VMCAI 2003. LNCS, vol. 2575, pp. 310–323. Springer, Heidelberg (2002)
Graf, S., Saïdi, H.: Construction of Abstract State Graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72–83. Springer, Heidelberg (1997)
Immerman, N., Rabinovich, A., Reps, T., Sagiv, M., Yorsh, G.: The boundary between decidability and undecidability for transitive-closure logics. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol. 3210, pp. 160–174. Springer, Heidelberg (2004)
Immerman, N., Rabinovich, A., Reps, T., Sagiv, M., Yorsh, G.: Verification via structure simulation. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 281–294. Springer, Heidelberg (2004)
Klarlund, N., Schwartzbach, M.: Graph types. In: Symposium on Principles of Programming Languages (POPL’93), pp. 196–205 (1993)
Kuncak, V., Rinard, M.: Boolean algebra of shape analysis constraints. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 59–72. Springer, Heidelberg (2004)
Manevich, R., Yahav, E., Ramalingam, G., Sagiv, M.: Predicate abstraction and canonical abstraction for singly-linked lists. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 181–198. Springer, Heidelberg (2005)
Møller, A., Schwartzbach, M.: The pointer assertion logic engine. In: Programming language design and implementation (PLDI 2001), pp. 221–231 (2001)
Sagiv, M., Reps, T., Wilhelm, R.: Parametric shape analysis via 3-valued logic. ACM Transactions on Programming Languages and Systems (TOPLAS) 24(3), 217–298 (2002)
Wies, T.: Symbolic Shape Analysis. Diploma thesis, Universität des Saarlandes, Saarbrücken, Germany (2004)
Yorsh, G.: Logical Characterizations of Heap Abstractions. Master’s thesis, Tel-Aviv University, Tel-Aviv, Israel (2003)
Yorsh, G., Reps, T., Sagiv, M.: Symbolically computing most-precise abstract operations for shape analysis. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 530–545. Springer, Heidelberg (2004)
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
Podelski, A., Wies, T. (2005). Boolean Heaps. In: Hankin, C., Siveroni, I. (eds) Static Analysis. SAS 2005. Lecture Notes in Computer Science, vol 3672. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11547662_19
Download citation
DOI: https://doi.org/10.1007/11547662_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28584-7
Online ISBN: 978-3-540-31971-9
eBook Packages: Computer ScienceComputer Science (R0)