Conditional Directed Narrowing

. We present an implementation of directed narrowing extended to the conditional framework, which is complete for two classes of conditional term rewrite systems : confluent and decreasing on one hand, level-confluent and terminating on the other hand. 1 Introduction Narrowing was originally introduced for solving unification of terms modulo a theory represented by a term rewrite system (E-unification). Next it has been used as the operational semantics of functional logic programming languages (see [5] for a recent survey). In this framework, the program is often represented by a set of equational Horn clauses, i.e. a conditional term rewrite system (CTRS). However, conditional narrowing is inefficient for practical applications because the search space is huge and contains infinite branches. This is why many authors have proposed optimizations to the narrowing procedure : innermost, basic innermost, LSE, lazy, approximations, etc.... Many of them need some restrictions on the re..