{41 () Constraint Query Algebras

Constraint query languages are natural extensions of relational database query languages. A framework for their declarative speciication (constraint calculi) and eecient implementation (low data complexity and secondary storage indexing) was presented in Kanellakis et al., 1995. Constraint query algebras form a procedural language layer between high-level declarative calculi and low-level indexing methods. Just like the relational algebra, this intermediate layer can be very useful for program optimization. In this paper, we study properties of constraint query algebras, which we present through three concrete examples. The dense order constraint algebra illustrates how the appropriate canonical form can simplify expensive operations, such as projection, and facilitate interaction with updates. The monotone two-variable linear constraint algebra illustrates the concept of strongly polynomial operations. Finally, the lazy evaluation of (non)linear constraint algebras illustrates how large numbers of (non)linear constraints could be implemented with only a small amount of costly symbolic processing.