Singular and Plural Functions for Functional Logic Programming

TL;DR

This paper introduces two new compositional plural semantics for functional logic programming that differ from run-time choice, enhancing the understanding and practical use of non-deterministic functions with pattern matching.

Contribution

It proposes novel plural semantics for constructor systems that are compositional, studies their properties, and demonstrates their practical application in a combined semantics language implemented in Maude.

Findings

New plural semantics are compositional and form a hierarchy based on computed values.

A syntactic criterion identifies programs where semantics behave identically.

A language combining call-time choice and plural semantics improves declarative programming capabilities.

Abstract

Functional logic programming (FLP) languages use non-terminating and non-confluent constructor systems (CS's) as programs in order to define non-strict non-determi-nistic 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 properties---mainly 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 we propose two novel compositional plural semantics for CS's that are different from run-time choice. We study 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 computed values. We have also identified a class of programs characterized by a syntactic criterion for which the proposed plural semantics behave the same, and a program transformation that can be used to simulate one of them by term rewriting. At the practical level, we study how to use the expressive capabilities of these semantics for improving the declarative flavour of programs. We also propose a language which combines call-time choice and our plural semantics, that we have implemented in Maude. The resulting interpreter is employed to test several significant examples showing the capabilities of the combined semantics. To appear in Theory and Practice of Logic Programming (TPLP)