LNCA: A Lazy Narrowing Calculus for Applicative Term Rewriting Systems

The integration of higher-order functions into functional logic programming is widely seen as a powerful and desirable feature. The natural way to deal with higher-order functions in the well-studied framework of first-order term rewriting is through so-called applicative term rewriting systems (ATRSs). We propose a new calculus, called LNCA, to deal efficiently with confluent ATRSs and prove its soundness and completeness