An object-oriented query model: An algebraic approach with closure

An object algebra is presented as a formal query model for object-oriented databases. The algebra serves not only to access and manipulate the structure and behavior of objects, but also supports the creation of new objects and the introduction of new relationships into the schema. It provides a more powerful and flexible tool than do messages for effectively dealing with complex situations and meeting associative access equirements. Operands as well as the results of operations in the proposed algebra are formally characterized as pairs of sets - a set of objects capturing the states and a set of message expressions comprised of sequences of messages modeling the object behavior. The closure property is achieved in a natural way by letting the results of operations possess the same characteristics as do the operands in an algebra expression. Some operators of the algebra resemble those of the relational algebra but with different syntax and semantics. Additional operators are introduced to complement them. A class is shown to possess the properties of an operand by defining a set of objects and deriving a set of message expressions for it. Furthermore, the result of an object algebra expression is shown to have the characteristics of a class whose superclass/subclass relationships with its operand class(es) can be established, thus providing a mechanism to properly and persistently place it in the class lattice (schema).