  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 accesses 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
Tiler. Initial experiments show that Tiler outperforms several state-of-the-art
tools on a suite of interesting benchmarks.
