Singular and Plural Functions for Functional Logic Programming

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)Comment: 53 pages, 5 figure

Semantics for interactive high-order functional-logic programming

本研究の目的はインタラクションのある高階関数論理型の操作的、代数的、論理的、圏論的意味論を与えることである。それぞれの意味論は以下の目的のために重要であり、しかもそれぞれのそれぞれに対する正当性 ...Thesis (Ph. D. in Engineering)--University of Tsukuba, (A), no. 1911, 1998.3.2

A Concurrent Operational Semantics for Constraint Functional Logic Programming

In this paper we describe a sound and complete concurrent operational semantics for constraint functional logic programming languages which allows to model declarative applications in which the interaction between demand-driven narrowing and constraint solving helps to prune the search space, leading to shorter goal derivations. We encode concurrency into the generic CFLP(D) scheme, a uniform foundation for the operational semantics of constraint functional logic programming systems parameterized by a constraint solver over the given domain D. In this concurrent version of the CFLP(D) scheme, goal solving processes can be executed concurrently and cooperate together to perform their specific tasks via demand-driven narrowing and declarative residuation guided by constrained definitional trees, constraint solving, and communication by synchronization on logical variables

Liberal Typing for Functional Logic Programs

We propose a new type system for functional logic programming which is more liberal than the classical Damas-Milner usually adopted, but it is also restrictive enough to ensure type soundness. Starting from Damas-Milner typing of expressions we propose a new notion of well-typed program that adds support for type-indexed functions, existential types, opaque higher-order patterns and generic functions-as shown by an extensive collection of examples that illustrate the possibilities of our proposal. In the negative side, the types of functions must be declared, and therefore types are checked but not inferred. Another consequence is that parametricity is lost, although the impact of this flaw is limited as "free theorems" were already compromised in functional logic programming because of non-determinism