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A domain-theoretic approach to functional and logic programming

Part of: JFP Research Articles

Published online by Cambridge University Press:  07 November 2008

Frank S. K. Silbermann  and
Bharat Jayaraman
Frank S. K. Silbermann
Affiliation:
Department of Computer Science, School of Engineering, 301 Stanley Thomas Hall, Tulane University, New Orleans, LA 70118, USA (fs@cs.tulane.edu)
Bharat Jayaraman
Affiliation:
Department of Computer Science, State University of New York at Buffalo, Buffalo, NY 14260, USA (bharat@cs.buffalo.edu)
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Abstract

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The integration of functional and logic programming languages has been a topic of great interest in the last decade. Many proposals have been made, yet none is completely satisfactory especially in the context of higher order functions and lazy evaluation. This paper addresses these shortcomings via a new approach: domain theory as a common basis for functional and logic programming. Our integrated language remains essentially within the functional paradigm. The logic programming capability is provided by set abstraction (via Zermelo-Frankel set notation), using the Herbrand universe as a set abstraction generator, but for efficiency reasons our proposed evaluation procedure treats this generator's enumeration parameter as a logical variable. The language is defined in terms of (computable) domain-theoretic constructions and primitives, using the lower (or angelic) powerdomain to model the set abstraction facility. The result is a simple, elegant and purely declarative language that successfully combines the most important features of both pure functional programming and pure Horn logic programming. Referential transparency with respect to the underlying mathematical model is maintained throughout. An implicitly correct operational semantics is obtained by direct execution of the denotational semantic definition, modified suitably to permit logical variables whenever the Herbrand universe is being generated within a set abstraction. Completeness of the operational semantics requires a form of parallel evaluation, rather than the more familiar left-most rule.

Type
Articles
Information
Journal of Functional Programming , Volume 2 , Issue 3 , July 1992 , pp. 273 - 321
Copyright
Copyright © Cambridge University Press 1992

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