Safe Folding/Unfolding with Conditional Narrowing

Author

María Alpuente, Moreno Falaschi, Ginés Moreno, and Germán Vidal

Abstract

Functional logic languages with a complete operational semantics are based on narrowing, a generalization of term rewriting where unification replaces matching. In this paper, we study the semantic properties of a general transformation technique called unfolding in the context of functional logic languages. Unfolding a program is defined as the application of narrowing steps to the calls in the program rules in some appropriate form. We show that, unlike the case of pure logic or pure functional programs, where unfolding is correct w.r.t. practically all available semantics, unrestricted unfolding using narrowing does not preserve program meaning, even when we consider the weakest notion of semantics the program can be given. We single out the conditions which guarantee that an equivalent program w.r.t. the semantics of computed answers is produced. Then, we study the combination of this technique with a folding transformation rule in the case of innermost conditional narrowing, and prove that the resulting transformation still preserves the computed answer semantics of the initial program, under the usual conditions for the completeness of innermost conditional narrowing. We also discuss a relationship between unfold/fold transformations and partial evaluation of functional logic programs.

Keywords

integration of functional and logic programming, narrowing, partial evaluation, term rewriting systems, program transformation.