Goal-Directed Abstraction

A critical component of an abstract interpretation algorithm is the abstract domain, and traditionally, it is manually defined. Recently, automatic abstract interpretation techniques have emerged. A prominent technique, called Counter Example Guided Abstraction Refinement (CEGAR), and is based on an iterative process given a target property. Beginning with an abstract domain with a low level of detail, failure to prove the property gives rise a process of abstraction refinement so that the next iteration can use a new abstract domain with a higher level of detail. The idea is to build the final abstract domain with just the right amount of detail. In this paper, we present a complementary approach: we abstract on demand, as opposed to refine on demand. Starting with no abstraction at all, our algorithm iteratively builds, if needed, abstract domains with lesser detail. We demonstrate advantages of our algorithm over CEGAR.