IN THE PREVIOUS chapters we discussed various aspects of constraint programming. We did it by concentrating on the relevant ingredients of this programming style separately. In principle we could put them together using the general framework of Section 3.2. There are, however, other issues that naturally arise when one tries to incorporate these techniques in a programming language or system. In this chapter we shall discuss these matters and also shed light on the resulting programming style. At the same time we shall provide a short summary of various research topics currently pursued in constraint programming.

We discuss in turn the issues concerned with modeling (in Section 9.1), constraint programming languages (in Section 9.2), constraint propagation (in Section 9.3), constraint solvers (in Section 9.4), search (in Section 9.5) and over-constrained problems (in Section 9.6). Finally, at the end of the chapter, in the bibliographic remarks, we provide pointers to a number of useful surveys that should allow the reader to embark on research in constraint programming. As the final bibliography is just ‘next door’ we do not list the, rather extensive, list of references at the end of this chapter.

Modeling

Recall that in Chapter 1 we formulated the following principle: