One of the continuing challenges in abstract interpretation is the creation of abstractions that yield analyses that are both tractable and precise enough to prove interesting properties about real-world programs. One source of diffi- culty is the need to handle programs with different behaviors along different execution paths. Disjunctive (powerset) abstractions capture such distinctions in a natural way. However, in general, powerset abstractions increase space and time costs by an exponential factor. Thus, powerset abstractions are generally perceived as very costly.
In this paper, we partially address this challenge by presenting and empirically evaluating a new heap abstraction. The new heap abstraction works by merging shape descriptors according to a partial isomorphism similarity criteria, resulting in a partially disjunctive abstraction. We implemented this abstraction in TVLA—a generic system for implementing program analyses.We conducted an empirical evaluation of the new abstraction and compared it with the powerset heap abstraction. The experiments show that analyses based on the partially disjunctive heap abstraction are as precise as the ones based on the powerset heap abstraction. In terms of performance, analyses based on the partially disjunctive heap abstraction are often superior to analyses based on the powerset heap abstraction. The empirical results show considerable speedups, up to 2 orders of magnitude, enabling previously non-terminating analyses, such as verification of the Deutsch-Schorr-Waite scanning algorithm, to terminate with no negative effect on the overall precision. Indeed, experience indicates that the partially disjunctive shape abstraction improves performance across all TVLA analyses uniformly, and in many cases is essential for making precise shape analysis feasible.