On the expressive power of query languages

Two main topics are addressed. First, an algebraic approach is presented to define a general notion of expressive power. Heterogeneous algebras represent information systems and morphisms represent the correspondences between the instances of databases, the correspondences between answers, and the correspondences between queries. An important feature of this new notion of expressive power is that query languages of different types can be compared with respect to their expressive power. In the case of relational query languages, the new notion of expressive power is shown to be equivalent to the notion used by Chandra and Harel. In the case of nonrelational query languages, the versatility of the new notion of expressive power is demonstrated by comparing the fixpoint query languages with an object-oriented query language called FQL. The expressive power of the Functional Query Language FQL is the second main topic of this paper. The specifications of FQL functions can be recursive or even mutually recursive, FQL has a fixpoint semantics based on a complete lattice consisting of bag functions. The query language FQL is shown to be more expressive than the fixpoint query languages. This result implies that FQL is also more expressive than Datalog with stratified negation. Examples of recursive FQL functions are given that determine the ancestors of persons and the bill of materials.