Shape Analysis with Reference Set Dominance

Precise modeling of the structure of the heap and how objects are shared between various arrays or data structures is fundamental to understanding the behavior of a program. This paper introduces a novel higher order relation, reference set dominance, which subsumes the concept of aliasing and enables existing shape analysis techniques to, efficiently and accurately, model many types of containment properties without the use of explicit quantification or specialized logics for containers/sets. We extend an existing shape analysis to model the concept of reference set dominance. This concept allows the analysis to track a number of important relations (must =, and must ⊆) between the sets of objects that are the targets of two given sets of references (variables or pointers). In combination with shape properties, an analysis that tracks reference dominance information can precisely reason about sharing properties on the heap (are the contents of one array a subset of another array?), and how sharing influences the results of destructive updates (does modifying all the objects in one array imply that all the objects in another array are modified as well?). Precisely and efficiently reasoning about these kinds of sharing properties has been beyond the abilities of previous analyses. We show that shape analysis augmented with dominance information is able to precisely model sharing for a large range of data structures in real programs and in contrast to more expressive proposals based on logic languages (e.g., extensions of first-order predicate logic with transitive closure), dominance properties can be efficiently implemented in a shape analyzer.