Decision Procedures for Set-Valued Fields

In this paper we explore reasoning techniques for programs that manipulate data structures specified using set-valued abstract fields associated with container objects. We compare the expressive power and the complexity of specification languages based on 1) decidable prefix vocabulary classes of first-order logic, 2) two-variable logic with counting, and 3) Nelson-Oppen combinations of multisorted theories. Such specification logics can be used for verification of object-oriented programs with supplied invariants. Moreover, by selecting an appropriate subset of properties expressible in such logic, the decision procedures for these logics enable automated computation of lattice operations in an abstract interpretation domain, as well as automated computation of abstract program semantics.