We study a powerful class of logic programs which terminate for a large class of goals. Both classes are characterized in a natural way in terms of mappings from variable-free atoms to natural numbers. We present a technique based on this idea which improves the termination behavior and allows a more multidirectional use of Prolog programs. The class of logic programs is shown to be strong enough to compute every total recursive function. The class of goals considerably extends the variable-free ones. © 1993.
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