Loop Leaping with Closures

Loop leaping is the colloquial name given to a form of program analysis in which summaries are derived for nested loops starting from the innermost loop and proceeding in a bottom-up fashion considering one more loop at a time. Loop leaping contrasts with classical approaches to finding loop invariants that are iterative; loop leaping is compositional requiring each stratum in the nest of loops to be considered exactly once. The approach is attractive in predicate abstraction where disjunctive domains are increasingly used that present long ascending chains. This paper proposes a simple and an efficient approach for loop leaping for these domains based on viewing loops as closure operators.