Towards declarative diagnosis of constraint programs over finite domains

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The paper proposes a theoretical approach of the debugging of constraint programs based on a notion of explanation tree. The proposed approach is an attempt to adapt algorithmic debugging to constraint programming. In this theoretical framework for domain reduction, explanations are proof trees explaining value removals. These proof trees are defined by inductive definitions which express the removals of values as consequences of other value removals. Explanations may be considered as the essence of constraint programming. They are a declarative view of the computation trace. The diagnosis consists in locating an error in an explanation rooted by a symptom.