Finite Domain Constraint Programming Systems

One of the main reasons why constraint programming quickly found its way into applications has been the early availability of usable constraint programming systems. Given the wide range of applications using constraint programming it is obvious that one of the key properties of constraint programming systems is their provision of widely reusable services for constructing constraint-based applications. A constraint programming system can be thought of as providing a set of reusable services. Common services include constraint propagation, search, and services for interfacing to the system. This chapter looks in more detail at which services are provided by a constraint programming system and in particular what are the key principles and techniques in constructing and coordinating these services. To give the chapter a clear focus and a reasonably uniform presentation, we mostly restrict our attention to propagation-based finite domain constraint programming systems. That is, systems that solve problems using constraint propagation involving variables ranging over some finite set of integers. The focus on finite domain constraint programming systems coincides with both practical relevance and known principles and techniques: systems at least offer services for finite domains; much of the known principles and techniques have been conceived and documented for finite domains. Essential for a system in providing the services mentioned above are some important abstractions (or objects) to be implemented by a system: variables, implementations for constraints, and so on. Important abstractions for propagation, search, and interfacing are as follows.