Decoupling the Ascending and Descending Phases in Abstract Interpretation

Abstract Interpretation approximates the semantics of a program by mimicking its concrete fixpoint computation on an abstract domain 𝔸 . The abstract (post-) fixpoint computation is classically divided into two phases: the ascending phase, using widenings as extrapolation operators to enforce termination, is followed by a descending phase, using narrowings as interpolation operators, so as to mitigate the effect of the precision losses introduced by widenings. In this paper we propose a simple variation of this classical approach where, to more effectively recover precision, we decouple the two phases: in particular, before starting the descending phase, we replace the domain 𝔸 with a more precise abstract domain 𝔻. The correctness of the approach is justified by casting it as an instance of the AI2 framework. After demonstrating the new technique on a simple example, we summarize the results of a preliminary experimental evaluation, showing that it is able to obtain significant precision improvements for several choices of the domains 𝔸 and 𝔻.