A Correctness Proof for Warren's HO into FO Translation

In 16], Warren suggested a method for embedding higher-order (HO) programming constructs into Prolog, that can be viewed as a kind of higher-order into rst-order (FO) translation. This method has been used in diierent settings as a tool for the combination of functional and logic programming 3, 2, 1], or even for the reduction of the former to the later 4]. The present paper was motivated by our feeling that the semantic correctness of Warren's translation is not yet suuciently well understood. We give a formulation of the method in the framework of the HO functional logic language SFL 6, 7], which uses conditional narrowing as operational semantics and has also a well deened declarative semantics. We show that HO SFL programs can be translated into FO SFL programs in such a way that both the declarative and the narrowing semantics are preserved. As a consequence, narrowing strategies which are sound and complete for FO SFL programs can be automatically transferred to HO SFL programs, via the translation.