Abstract

Set-based analysis (SBA) produces good predictions about the behavior of functional and objectoriented programs. The analysis proceeds by inferring constraints that characterize the data flow relationships of the analyzed program. Experiences with MrSpidey, a static debugger based on SBA, indicate that SBA can adequately deal with programs of up to a couple of thousand lines of code. SBA fails, however, to cope with larger programs because it generates systems of constraints that are at least linear, and possibly quadratic, in the size of the analyzed program. This article presents theoretical and practical results concerning methods for reducing the size of constraint systems. The theoretical results include a proof-theoretic characterization of the observable behavior of constraint systems for program components, and a complete algorithm for deciding the observable equivalence of constraint systems. In the course of this development we establish a close connection between the observable equivalence of constraint systems and the equivalence of regular-tree grammars. We then exploit this connection to adapt a variety of algorithms for simplifying grammars to the problem of simplifying constraint systems. Based on the resulting algorithms, we have developed componential set-based analysis, a modular and polymorphic variant of SBA. Experimental results verify the effectiveness of the simplification

Citations