A Framework for Array Invariants Synthesis in Induction-Loop Programs

Abstract interpretation is capable of inferring a wide variety of quantifier-free program invariants. In this paper, we propose a general framework for building universally quantified abstract domains that leverage existing quantifier-free domains in induction-loop programs. This method is sound and converges in finite time. We instantiate this framework using two quantifier-free domains: difference-bound matrices with disequality constraints (dDBM) domain and polynomial equations domain. The experiments on a variety of programs using arrays demonstrate the feasibility of the approach.