Non-Monotonic Program Analysis

Traditionally, program analysis is formulated as computation of fixpoints using monotonic iteration of lattice-theoretic functions. Monotonicity is important because it ensures convergence of the analysis towards a fixpoint. Still, the idea of non-monotonic iteration is intriguing because such an analysis can cut short the search, potentially convergingmuch faster than monotonic iteration. In this paper, we answer the question whether non-monotonic analyses are a worthwhile pursuit. We consider several non-monotonic algorithms for the specific problem of solving systems of Horn clauses. Our algorithms have in common that they (1) use logical abduction to span the search space of nonmonotonic iteration sequences, and (2) bound the non-monotonic search by a monotone sequence of checkpoints to enforce overall convergence. The algorithms differ in their search strategies, where the most interesting one performs an A*-like search. We have implemented these algorithms and compared them against existing monotonic analyses for solving Horn clauses. Our evaluation indicates that non-monotonic fixpoint iteration is a promising complementary technique to traditional program analyses.