Equivalence of the Quotient Term Model and the Least Complete Herbrand Model for a Functional Logic Language

use journal articles in a variety of ways, limited only as required to insure fair attribution to authors and the journal, and to prohibit use in a competing commercial product. See the journal's World Wide Web site for further details. The Journal of Functional and Logic Programming is a peer-reviewed and electronically published scholarly journal that covers a broad scope of topics from functional and logic programming. In particular, it focuses on the integration of the functional and the logic paradigms as well as their common foundations. Abstract This paper addresses the semantics of a rst-order functional logic language , from the viewpoint of conditional equational logic. A functional logic program is regarded as a set of nonlogical axioms of conditional equational logic that are interpreted as deening a function. A query is considered to be an existentially quantiied equation, and solving the query proves the existentially quantiied equation by obtaining a witness. This is justiied by showing equivalence of three models for the functional logic program, i.e., the quotient term model, the least complete Herbrand model, and the operational model of narrowing.