A Rewriting Logic for Declarative Programming

We propose an approach to declarative programming which integrates the functional and relational paradigms by taking possibly non-deterministic lazy functions as the fundamental notion. Programs in our paradigm are theories in a constructor-based conditional rewriting logic. We present proof calculi and a model theory for this logic, and we prove the existence of free term models which provide an adequate intended semantics for programs. Moreover, we develop a sound and strongly complete lazy narrowing calculus, which is able to support sharing without the technical overhead of graph rewriting and to identify safe cases for eager variable elimination.