Introducing external functions in constraint query languages

Constraint databases use constraints to model and query data. In particular, constraints allow a finite representation of infinite sets of relational tuples (also called generalized tuples). The choice of different logical theories to express constraints inside relational languages leads to the definition of constraint languages with different expressive power. Practical constraint database languages typically use linear constraints. This choice allows the use of efficient algorithms but, at the same time, some useful queries, needed by the considered application, may not be represented inside the resulting languages (for example, the convex hull cannot be computed [19]). These additional queries can only be modeled by changing the theory (thus, loosing the advantages of the linear theory), or extending the language, or using external functions. In this paper we consider the last approach and we propose an algebra and a calculus for constraint relational databases extended with external functions, formally proving their equivalence. In doing that, we use an approach similar to the one used by Klug to prove the equivalence between the relational algebra and the relational calculus extended with aggregate functions [14]. As far as we know, this is the first approach to introduce external functions in constraint query languages.