On Decision Procedures for Set-Value Fields

An important feature of object-oriented programming languages is the ability todynamically instantiate user-defined container data structures such as lists, trees,and hash tables. Programs implement such data structures using references todynamically allocated objects, which allows data structures to store unboundednumbers of objects, but makes reasoning about programs more difficult. Reasoningabout object-oriented programs with complex data structures is simplified if datastructure operations are specified in terms of abstract sets of objects associatedwith each data structure. For example, an insertion into a data structure in thisapproach becomes simply an insertion into a dynamically changing set-valued fieldof an object, as opposed to a manipulation of a dynamically linked structure linkedto the object.In this paper we explore reasoning techniques for programs that manipulate datastructures specified using set-valued abstract fields associated with container objects.We compare the expressive power and the complexity of specification languagesbased on 1) decidable prefix vocabulary classes of first-order logic, 2) twovariablelogic with counting, and 3) Nelson-Oppen combinations of multisortedtheories. Such specification logics can be used for verification of object-orientedprograms with supplied invariants. Moreover, by selecting an appropriate subsetof properties expressible in such logic, the decision procedures for these logics yieldautomated computation of lattice operations in abstract interpretation domain, aswell as automated computation of abstract program semantics