Introduction to Constraint Programming

Constraint programming is a highly declarative paradigm in which concepts are described in a general way. A constraint can be summarized as a logical relation between the variables involved in a constraint satisfaction problem (CSP). A global constraint allows the expression of the underlying logical relation between a subset, of any size, of the variables involved in a CSP. The propagation algorithm is stopped when the set of constraints “to propagate” is empty. To be able to characterize the behavior of a constraint’s filtering algorithm, this chapter presents the notion of consistency level, and the definitions relative to the two highest levels of consistencies reachable by a constraint, in the case of both single integer variables and where integer and set variables are jointly used. The chapter also presents the overall pattern of articulation to describe completely what a constraint solver is.