A simple abstraction of arrays and maps by program translation

TL;DR

This paper introduces a static analysis method for array programs by translating them into scalar programs, enabling the use of existing analysis techniques to derive array invariants.

Contribution

It proposes a simple, automatic program transformation approach that simplifies array analysis by leveraging scalar analysis techniques and translating invariants back to arrays.

Findings

Successfully analyzed array algorithms like the Dutch flag problem

Provides a systematic way to derive array invariants from scalar invariants

Applicable to various static analysis techniques

Abstract

We present an approach for the static analysis of programs handling arrays, with a Galois connection between the semantics of the array program and semantics of purely scalar operations. The simplest way to implement it is by automatic, syntactic transformation of the array program into a scalar program followed analysis of the scalar program with any static analysis technique (abstract interpretation, acceleration, predicate abstraction,.. .). The scalars invariants thus obtained are translated back onto the original program as universally quantified array invariants. We illustrate our approach on a variety of examples, leading to the " Dutch flag " algorithm.