Theory and Practice of Constraint Handling Rules

Constraint Handling Rules (CHR) are our proposal to allow more exibility and application-oriented customization of constraint systems. CHR are a declarative language extension especially designed for writing user-deened constraints. CHR are essentially a committed-choice language consisting of multi-headed guarded rules that rewrite constraints into simpler ones until they are solved. In this broad survey we aim at covering all aspects of CHR as they currently present themselves. Going from theory to practice, we will deene syntax and semantics for CHR, introduce an important decidable property, connuence, of CHR programs and deene a tight integration of CHR with constraint logic programming languages. This survey then describes implementations of the language before we review several constraint solvers-both traditional and non-standard ones-written in the CHR language. Finally we introduce two innovative applications that beneeted from using CHR.