Narrowing and Basic Forward Closures

While the leftmost-innermost narrowing algorithm is incomplete, basic narrowing contains redundancies. We remove these redundancies by introducing a new narrowing procedure, called left-to-right basic narrowing algorithm. For each leftmost-innermost rewriting derivation from (s), there is an equivalent left-to-right basic rewriting derivation , which in turn can be projected on a left-to-right basic narrowing derivation from s, thus establishing the completeness of this new procedure. Aside from the improved eeciency, left-to-right basic derivations are a valuable device in the development of specialized narrowing procedures. We introduce the notion of basic forward closures and show their relationship to left-to-right basic rewriting derivations. Where such a closure is nite, it leads to a terminating and complete narrowing algorithm.