Abstract
Shape analyses are often imprecise in their numerical reasoning, whereas numerical static analyses are often largely unaware of the shape of a program’s heap. In this paper we propose a lazy method of combining a shape analysis based on separation logic with an arbitrary arithmetic analysis. When potentially spurious counterexamples are reported by our shape analysis, the method constructs a purely arithmetic program whose traces over-approximate the set of counterexample traces. It then uses this arithmetic program together with the arithmetic analysis to construct a refinement for the shape analysis. Our method is aimed at proving properties that require comprehensive reasoning about heaps together with more targeted arithmetic reasoning. Given a sufficient precondition, our technique can automatically prove memory safety of programs whose error-free operation depends on a combination of shape, size, and integer invariants. We have implemented our algorithm and tested it on a number of common list routines using a variety of arithmetic analysis tools for refinement.
This research was sponsored by the International Collaboration for Advancing Security Technology (iCAST), the Gigascale Systems Research Center (GSRC), the Semiconductor Research Corporation (SRC) under grant TJ-1366, the National Science Foundation (NSF) under grant no. CCR-9803774, the Office of Naval Research (ONR), the Naval Research Laboratory (NRL) under contract no. N00014-01-1-0796, the Defense Advanced Research Projects Agency, the Army Research Office (ARO) under contract no. DAAD19-01-1-0485, and the General Motors Collaborative Research Lab at CMU. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution.
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Magill, S., Berdine, J., Clarke, E., Cook, B. (2007). Arithmetic Strengthening for Shape Analysis . In: Nielson, H.R., Filé, G. (eds) Static Analysis. SAS 2007. Lecture Notes in Computer Science, vol 4634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74061-2_26
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