Dominance: Modeling Heap Structures with Sharing

A number of papers have used predicate languages over sets of abstract locations to model the heap (decorating a heap graph with the predicates, or in conjunction with an access path abstraction). In this work we introduce a new predicate, dominance, which is a generalization of aliasing and is used to model how objects are shared in the heap (e.g. do two lists contain the same set of objects?) and how sharing influences the results of destructive updates (e.g. if all the objects in one list are modified does that imply that all the objects in another list are modified?). The dominance relation is introduced in the context of a graph-based heap model but the concept is general and can be incorporated in other frameworks as a high-level primitive. The motivation for introducing a higher-order predicate to model sharing is based on the success of existing approaches which use connectivity, reachability, and sharing predicates to perform shape analysis using high-level graph-based models. Our approach provides an analysis technique that is efficient and scalable while retaining a high level of accuracy. This is in contrast to proposals in the literature based on using logical languages (usually built on top of first-order predicate logic) which either are highly expressive and very general (resulting in a computationally expensive analysis) or utilize only fragments of the full logic (which reduces the computational cost but results in a much less powerful analysis). The approach presented in this paper has been implemented and run on a variation of the Jolden benchmarks. The information extracted using the analysis has been used to parallelize these programs with a near optimal speedup for 7 of the 9 benchmarks. The runtimes are small enough to make the analysis practical (a few seconds for each program).