Constraint Programming and Database Query Languages 1 from Constraint Programming to Database Querying 1.1 Declarative Programming with Constraints

The declarative programming paradigms used in constraint languages can lead to powerful extensions of Codd's relational data model. The development of constraint database query languages from logical database query languages has many similarities with the development of constraint logic programming from logic programming, but with the additional requirements of data eecient, set-at-a-time, and bottom-up evaluation. In this overview of constraint query languages (CQLs) we rst present the framework of 41]. The principal idea is that: \the k-tuple (or record) data type can be generalized by a conjunction of quantiier-free constraints over k variables". The generalization must preserve various language properties of the relational data model, e.g., the calculus/algebra equivalence, and have time complexity polynomial in the size of the data. We next present an algebra for dense order constraints that is simpler to evaluate than the calculus described in 41], and we sharpen some of the related data complexity bounds. We note that CQLs are applicable to spatial databases. This is because these languages have \spatial point set" as the semantics of their record data type and because existing multi-dimensional searching data structures can support I/O eecient access to sets of records. Finally, we observe that CQLs can be augmented with complex object data types, aggregate operations, and null-values, just like the relational data model. Constraint programming paradigms are inherently declarative, since they implicitly describe computations by specifying how these computations are constrained. Programming with constraints as primitives (or constraint programming) is appealing because constraints are the normal language of discourse for many high-level applications. Pioneering work in constraint programming goes back to the early 1960's, e.g., Sutherland's SKETCHPAD 67]. The theme has been investigated since the 1970's, e. The relevant literature and contributions are too large to attempt a survey. Instead we will limit our exposition to recent applications in databases.