Functional Logic Programming with Failure: A Set-Oriented View

Finite failure of computations plays an important role as programming construct in the logic programming paradigm, and it has been shown that this also extends to the case of the functional logic programming paradigm. In particular we have considered CRWLF, a previous proof-theoretic semantic framework able to deduce negative (failure) information from functional logic programs. The non-deterministic nature of functions considered in CRWLF leads naturally to set-valued semantic description of expressions. Here we reformulate the framework to stress that set flavour, both at syntactic and semantic levels. The given approach, for which we obtain equivalence results with respect to the previous one, increases the expressiveness for writing programs and (hopefully) clarifies the understanding of the semantics given to nondeterministic functions, since classical mathematical notions like union of sets or families of sets are used. An important step in the reformulation is a useful program transformation which is proved to be correct within the framework.