Value withdrawal explanations: a theoretical tool for programming environments

Abstract. Constraint logic programming combines declarativity and ef-ficiency thanks to constraint solvers implemented for specific domains. Value withdrawal explanations have been efficiently used in several con-straints programming environments but there does not exist any formal-ization of them. This paper is an attempt to fill this lack. Furthermore, we hope that this theoretical tool could help to validate some program-ming environments. A value withdrawal explanation is a tree describing the withdrawal of a value during a domain reduction by local consistency notions and labeling. Domain reduction is formalized by a search tree us-ing two kinds of operators: for local consistency notions and for labeling. These operators are defined by sets of rules. Proof trees are built with respect to these rules. For each removed value, there exists such a proof tree which is the withdrawal explanation of this value.