Object-Orientation Axiomatised by Dynamic Logic

The eld of object-oriented databases is su ering from the lack of a|widely agreed upon|formal model. In this paper we develop the basics of a formal model for an object-oriented data model (kernel). The formalization is based on dynamic logic: combining many-sorted algebras with states and state transitions. The many-sorted algebras are utilized to model the static aspects, i.e., the value-oriented part of the object model. The state transitions account for the dynamic behavior of the object base due to object modi cations. The main dynamic features that we incorporate in the formal model comprise (object) attribute assignment, object creation, object deletion, and set object manipulation, i.e., removing and inserting elements. The virtues of the proposed model are demonstrated on three sample applications. Dangling references may lead a given program to nonterminate|we will show this fact. Second, a desirable property of a program will be veri ed. Last, the semantics of a simple declarative language for our object model will be speci ed. Utilizing the formal model we are able to prove the correctness of a particular query evaluation plan|called the \nested loop" evaluation.