Lazy narrowing with simplification

Abstract

Languages that integrate functional and logic programming styles with a complete operational semantics are based on narrowing. In order to avoid useless computations, lazy narrowing strategies have been proposed in the past. This paper presents an improvement of lazy narrowing by incorporating deterministic simplification steps into lazy narrowing derivations. These simplification steps reduce the search space so that in some cases infinite search spaces are reduced to finite ones. We consider two classes of programs where this strategy can be applied. Firstly, we show soundness and completeness of our strategy for functional logic programs based on ground confluent and terminating rewrite systems. Then, we show similar results for constructor-based weakly orthogonal (not necessarily terminating) rewrite systems. Finally, we demonstrate the improved operational behavior by means of several examples. Since most functional logic languages are based on programs belonging to one of these classes, our result is a significant step to improve the operational semantics of existing functional logic languages.