Verifying Array Manipulating Programs by Tiling

Abstract

Formally verifying properties of programs that manipulate arrays in loops is computationally challenging. In this paper, we focus on a useful class of such programs, and present a novel property-driven verification method that first infers array access patterns in loops using simple heuristics, and then uses this information to compositionally prove universally quantified assertions about arrays. Specifically, we identify tiles of array access patterns in a loop, and use the tiling information to reduce the problem of checking a quantified assertion at the end of a loop to an inductive argument that checks only a slice of the assertion for a single iteration of the loop body. We show that this method can be extended to programs with sequentially composed loops and nested loops as well. We have implemented our method in a tool called $\textsc {Tiler}$. Initial experiments show that $\textsc {Tiler}$ outperforms several state-of-the-art tools on a suite of interesting benchmarks.