Automatic Invariant Synthesis for Arrays in Simple Programs

This paper proposes a way of using abstract interpretation for discovering properties about array contents in programs which manipulate arrays by sequential traversal. The method summarizes an array property as a universally quantified property. It directly treats invariant properties (including universally quantified formulas and atomic formulas) as abstract domains. Our method is sound and converges in finite time, and it is flexible. The method has been used to automatically discover nontrivial invariants for several examples. In particular, the method can represent and process multidimensional array properties.