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An abstract of the thesis of Bobbi J. Barry for the Master of Science in Computer Science presented June 12, 1996. Title: Needed Narrowing as the Computational Strategy of Evaluable Functions in an Extension of Goedel. A programming language that combines the best aspects of both the functional and logic paradigms with a complete evaluation strategy has been a goal of a Portland State University project team for the last several years. I present the third in a series of modifications to the compiler of the logic programming language Goedel which reaches this goal. This enhancement of Goedel's compiler translates user-defined functions in the form of rewrite rules into code that performs evaluation of these functions by the strategy of needed narrowing. In addition, Goedel's mechanism that evaluates predicates is supplemented so that needed narrowing is still maintained as the evaluation strategy when predicates possess functional arguments. NEEDED NARROWING AS THE COMPUTATIONAL STRATEGY OF EVALUABLE FUNCTIONS IN AN EXTENSION OF GOEDEL