Abstract
Programs written in modern languages perform intricate manipulations of containers such as arrays, lists, dictionaries, and sets. We present an abstract interpretation-based framework for automatically inferring relations between the set of values stored in these containers. Relations include inclusion relations over unions and intersections, as well as quantified relationships with scalar variables. We develop an abstract domain constructor that builds a container domain out of a Quantified Union-Intersection Constraint (QUIC) graph parameterized by an arbitrary base domain. We instantiate our domain with a polyhedral base domain and evaluate it on programs extracted from the Python test suite. Over traditional, non-relational domains, we find significant precision improvements with minimal performance cost.
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
Aiken, A., Kozen, D., Vardi, M., Wimmers, E.: The complexity of set constraints. In: Pacholski, L., Tiuryn, J. (eds.) CSL 1994. LNCS, vol. 832, pp. 1–17. Springer, Heidelberg (1995)
Aiken, A., Fähndrich, M., Foster, J.S., Su, Z.: A toolkit for constructing type- and constraint-based program analyses. In: Leroy, X., Ohori, A. (eds.) TIC 1998. LNCS, vol. 1473, pp. 78–96. Springer, Heidelberg (1998)
Bouajjani, A., Drăgoi, C., Enea, C., Sighireanu, M.: Abstract domains for automated reasoning about list-manipulating programs with infinite data. In: Kuncak, V., Rybalchenko, A. (eds.) VMCAI 2012. LNCS, vol. 7148, pp. 1–22. Springer, Heidelberg (2012)
Bradley, A.R., Manna, Z., Sipma, H.B.: What’s decidable about arrays? In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 427–442. Springer, Heidelberg (2006)
Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL (1977)
Cousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: POPL (1979)
Cousot, P., Cousot, R., Logozzo, F.: A parametric segmentation functor for fully automatic and scalable array content analysis. In: POPL (2011)
de Moura, L., Bjørner, N.: Generalized, efficient array decision procedures. In: Conference on Formal Methods in Computer Aided Design, FMCAD (2009)
Dillig, I., Dillig, T., Aiken, A.: Fluid updates: Beyond strong vs. Weak updates. In: Gordon, A.D. (ed.) ESOP 2010. LNCS, vol. 6012, pp. 246–266. Springer, Heidelberg (2010a)
Dillig, I., Dillig, T., Aiken, A.: Symbolic heap abstraction with demand-driven axiomatization of memory invariants. In: OOPSLA (2010b)
Dillig, I., Dillig, T., Aiken, A.: Precise reasoning for programs using containers. In: POPL (2011)
Flanagan, C.: Effective Static Debugging via Componential Set-Based Analysis. PhD thesis, Rice University (1997)
Gopan, D., Reps, T., Sagiv, M.: A framework for numeric analysis of array operations. In: POPL (2005)
Gulwani, S., McCloskey, B., Tiwari, A.: Lifting abstract interpreters to quantified logical domains. In: POPL (2008)
Halbwachs, N., Péron, M.: Discovering properties about arrays in simple programs. In: PLDI (2008)
Jhala, R., McMillan, K.L.: Array abstractions from proofs. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 193–206. Springer, Heidelberg (2007)
Kovács, L., Voronkov, A.: Finding loop invariants for programs over arrays using a theorem prover. In: Chechik, M., Wirsing, M. (eds.) FASE 2009. LNCS, vol. 5503, pp. 470–485. Springer, Heidelberg (2009)
Kuncak, V.: Modular Data Structure Verification. PhD thesis, EECS Department, Massachusetts Institute of Technology (2007)
Lam, P., Kuncak, V., Rinard, M.: Hob: a tool for verifying data structure consistency. In: Bodik, R. (ed.) CC 2005. LNCS, vol. 3443, pp. 237–241. Springer, Heidelberg (2005)
Marron, M., Stefanovic, D., Hermenegildo, M., Kapur, D.: Heap analysis in the presence of collection libraries. In: PASTE (2007)
Marron, M., Méndez-Lojo, M., Hermenegildo, M., Stefanovic, D., Kapur, D.: Sharing analysis of arrays, collections, and recursive structures. In: PASTE (2008)
McMillan, K.L.: Quantified invariant generation using an interpolating saturation prover. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 413–427. Springer, Heidelberg (2008)
Pham, T.-H., Trinh, M.-T., Truong, A.-H., Chin, W.-N.: FixBag: A fixpoint calculator for quantified bag constraints. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 656–662. Springer, Heidelberg (2011)
Python. Python 2.7.3 test suite (2012), http://www.python.org
Seghir, M.N., Podelski, A., Wies, T.: Abstraction refinement for quantified array assertions. In: Palsberg, J., Su, Z. (eds.) SAS 2009. LNCS, vol. 5673, pp. 3–18. Springer, Heidelberg (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cox, A., Chang, BY.E., Sankaranarayanan, S. (2013). QUIC Graphs: Relational Invariant Generation for Containers. In: Castagna, G. (eds) ECOOP 2013 – Object-Oriented Programming. ECOOP 2013. Lecture Notes in Computer Science, vol 7920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39038-8_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-39038-8_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39037-1
Online ISBN: 978-3-642-39038-8
eBook Packages: Computer ScienceComputer Science (R0)