A Methodological View of Constraint Solving

Constraints are an effective tool to define sets of data by means of logical formulae. Our goal here is to survey the notion of constraint system and to give examples of constraint systems operating on various domains, such as natural, rational or real numbers, finite domains, and term domains. We classify the different methods used for solving constraints, syntactic methods based on transformations, semantic methods based on adequate representations of constraints, hybrid methods combining transformations and enumerations. The concepts and methods are illustrated via examples. We also discuss applications of constraints to various fields, such as programming, operations research, and theorem proving.