Systematic explanation of indexical constraints

Several constraint solvers over finite domains, such as GNU-Prolog or SICStus Prolog, use indexicals to define their primitive constraints. An indexical specifies a set of consistent values for a given variable and can be compiled into an efficient filtering algorithm. The explanation of a value withdrawal is a set of constraints that is sufficient to justify this withdrawal. Explanations enable the handling of over-constrained or dynamic problems, and allow the development of new search methods. Traditionally, an explanation algorithm has to be designed for each filtering algorithm. This paper shows that explanation algorithms can be automatically derived from indexical constraints. In the case of SICStus Prolog, explanation computation can also benefit from the existing implementation