Singular and plural functions for functional logic programming

Abstract

Modern functional logic programming (FLP) languages use non-terminating and nonconfluent constructor systems (CS's) as programs in order to define non-strict non-deterministic functions. Two semantic alternatives have been usually considered for parameter passing with this kind of functions: call-time choice and run-time choice. While the former is the standard choice of modern FLP languages, the latter lacks some basic propertiesmainly compositionality-that have prevented its use in practical FLP systems. Traditionally it has been considered that call-time choice induces a singular denotational semantics, while run-time choice induces a plural semantics. We have discovered that this latter identification is wrong when pattern matching is involved, and thus in this paper we propose two novel compositional plural semantics for CS's that are different from run-time choice.We investigate the basic properties of our plural semantics-compositionality, polarity, monotonicity for substitutions, and a restricted form of the bubbling property for constructor systems-and the relation between them and to previous proposals, concluding that these semantics form a hierarchy in the sense of set inclusion of the set of values computed by them. Besides, we have identified a class of programs characterized by a simple syntactic criterion for which the proposed plural semantics behave the same, and a program transformation that can be used to simulate one of the proposed plural semantics by term rewriting. At the practical level, we study how to use the new expressive capabilities of these semantics for improving the declarative flavour of programs. As call-time choice is the standard semantics for FLP, it still remains the best option for many common programming patterns. Therefore we propose a language which combines call-time choice and our plural semantics, that we have implemented in the Maude system. The resulting interpreter is then employed to develop and test several significant examples showing the capabilities of the combined semantics.

Functional Logic Programming in Maude

“…See [36] for elaborated interactions on non-determinism and non-right-linear equations (or rules). Some bizarre behaviours are still possible when combining it with demand-driven evaluation and solutions have been recently developed [40].…”

Synthesizing Set Functions

“…The notion of "plural function" is also used in[22] to define a "plural" semantics for functional logic programs. Although the type of their plural functions is identical to ours, their semantics is quite different.…”