Cooperation and coordination of constraint solvers

Declarative programming languages base on the idea that programs should be as close as possible to the problem specification and domain. Programs of these languages usually consist of directly formulated mathematical objects, i.e. relations and functions. Accordingly, declarative languages are distinguished into logic, functional, functional-logic, and constraint programming languages. Even if constraint programming is a young development in declarative programming languages, meanwhile, there is a wide range of constraint programming languages, and many domains and associated constraint solving mechanisms have been investigated. Using constraint programming, problems are specified by means of constraints. A constraint is usually a first order formula which describes properties of objects or relations between them. Problems described by constraints are handled by constraint solvers, i.e. specific algorithms for particular domains which mostly allow to check satisfiability of constraints, i.e. to solve constraints, to compute entailed constraints, and even to find variable assignments such that the constraints specifying the problem are satisfied. Though the paradigm of constraint programming offers efficient mechanisms to handle constraints of various domains, one constraint solver can only handle constraints of a particular constraint system. Thus, it is often desirable and advantageous to combine several constraint systems and the associated constraint solving techniques because this combination makes it possible to solve problems that none of the single solvers can handle alone. In this work, we propose a general scheme for the cooperation of constraint solvers. The base of our system is a uniform interface for constraint solvers which allows a fine-grain formal specification of information exchange between constraint solvers. On top of this interface, we develop an open and flexible combination mechanism for constraint solvers. The combination is open in the sense that whenever a new constraint system with associated constraint solver (satisfying certain properties) arises, it can be easily incorporated into the overall system independently of its domain and the language in which the constraint solver is implemented. It is flexible because