Interprocedural analyses: a comparison

We present a framework for program analysis of languages with procedures which is general enough to allow for a comparison of various approaches to interprocedural analysis. Our framework is based on a small-step operational semantics and subsumes both frameworks for imperative and for logic languages. We consider reachability analysis, that is, the problem of approximating the sets of program states reaching program points. We use our framework in order to clarify the impact of several independent design decisions on the precision of the analysis. Thus, we compare intraprocedural forward accumulation with intraprocedural backward accumulation. Furthermore, we consider both relational and functional approaches. While for relational analysis the accumulation strategy makes no difference in precision, we prove for functional analysis that forward accumulation may lose precision against backward accumulation. Concerning the relative precision of relational analyses and corresponding functional analyses, we exhibit scenarios where functional analysis does not lose precision. Finally, we explain why even an enhancement of functional analysis through disjunctive completion of the underlying abstract domain may sometimes lose precision against relational analysis.