A formal background to build constraint objects

Constraint databases exploit a fundamental duality: (i) a constraint (first-order formula) with free variables is interpreted as a set of database tuples that satisfy it; (ii) conversely, a database object can be viewed as a constraint. This enables us to use constraints as basic data types in the underlying DBMS and to enjoy the expressiveness of first-order logic and most of the advantages of constraint programming. Most existing frameworks consider the relational data model as a basic data representation model and use linear constraints to represent complex objects. This is not always efficient. Moreover, modern DBMSs offer much more than a simple set of relational tables. Therefore, we focus on the definition and formal background for an implementation of a constraint data model to be built on top of an object-relational DBMS. As an illustration, our approach is capable of exploiting existing spatial tools (like the one from Oracle 8) yielding the declarativeness and expressiveness of constraint programming.