A Complete Narrowing Calculus for Higher-Order Functional Logic Programming

Using higher-order functions is standard practice in functional programming, but most functional logic programming languages that have been described in the literature lack this feature. The natural way to deal with higher-order functions in the framework of (first-order) term rewriting is through so-called applicative term rewriting systems. In this paper we argue that existing calculi for lazy narrowing either do not apply to applicative systems or handle applicative terms very inefficiently. We propose a new lazy narrowing calculus for applicative term rewriting systems and prove its completeness.