Calculi and Eeciency Measures for Narrowing Techniques

Narrowing serves as operational semantics of functional{logic programming languages. Over the past two decades a vast variety of narrowing techniques have been proposed, diiering from each other in the class of equational theories they are applicable to and in their eeciency to evaluate a given goal. On the latter part, i.e., the eeciency, merely vague statements can be found in the existing literature and hardly any formal investigation has been carried out comparing diierent narrowing techniques. In this paper we use the concept of calculi which allows us to formalize various narrowing techniques in a uniform way. Based on this concept we introduce four eeciency measures and apply two of them to two diierent pairs of narrowing techniques. The results make clear statements about the diierence in eeciency for the narrowing techniques involved.