On the Completeness of Object - CreatingDatabase Transformation Languages 1

Object-oriented applications of database systems require database transformations involving non-standard functionalities such as set manipulation and object creation, i.e., the introduction of new domain elements. To deal with these functionalities, Abiteboul and Kanellakis introduced the \determinate" transformations as a generalization of the standard domain-preserving transformations. The obvious extensions of complete standard database programming languages, however, are not complete for the determinate transformations. To remedy this mismatch, the \constructive" transformations are proposed. It is shown that the constructive transformations are precisely the transformations that can be expressed in said extensions of complete standard languages. Thereto, a close correspondence between object creation and the construction of hereditarily nite sets is established. A restricted version of the main completeness result for the case where only list (as opposed to general set) manipulations are involved is also presented.