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This paper proposes an efficient method for evaluationof deductive queries over constraint databases. The method isbased on a combination of the top-down resolution with memoingand the closed form bottom-up evaluation. In this way the top-downevaluation is guaranteed to terminate for all queries for whichthe bottom-up evaluation terminates. The main advantage of theproposed method is the direct use of the information presentin partially instantiated queries without the need for rewritingof the original program. The evaluation algorithm automaticallypropagates the necessary constraints during the computation.In addition, the top-down evaluation potentially allows the useof compilation techniques, developed for compilers of logic programminglanguages, which can make the query evaluation very efficient.