An association algebra for processing object-oriented databases

An association algebra (A-algebra) is presented for manipulating object-oriented (O-O) databases which is analogous to the relational algebra for relational databases. In this algebra, objects and their associations in an O-O database are uniformly represented by association patterns and are manipulated by a number of operators. These operators are defined to operate on association patterns of both heterogeneous and homogeneous structures. Very complex structures (e.g. network structures of object associations across several classes) can be directly manipulated by these operators. Therefore, the association algebra has greater expressive powers than the relational algebra which manipulates on relations of compatible structures. Some mathematical properties of these operators are described together with their application in query decomposition and optimization. The algebra has been used as the basis for the design and implementation of an O-O query language called OQL and a knowledge rule specification language