Article

Providing declarative semantics for HH extended constraint logic programs

Authors:

Miguel García-Díaz,

Susana NievaAuthors Info & Claims

PPDP '04: Proceedings of the 6th ACM SIGPLAN international conference on Principles and practice of declarative programming

Pages 55 - 66

https://doi.org/10.1145/1013963.1013973

Published: 24 August 2004 Publication History

Abstract

This paper is focused on a double extension of traditional Logic Programming which enhances it following two different approaches. On one hand, extending Horn logic to hereditary Harrop formulas HH), in order to improve the expressive power; on the other, incorporating constraints, in order to increase the efficiency. For this combination, called HH(C), an operational semantics exists, but no declarative semantic for it has been defined so far.One of the main features of (Constraint) Logic Programming is that the algorithmic behavior of (constraint) logic programs and its mathematical interpretations agree with each other, in the sense that the declarative meaning of a program can be interpreted operationally as a goal-oriented search for solutions. Both operational (algorithmic) and declarative (mathematical) semantics for programs are useful and widely developed in the frame of Logic Programming as well as in its extension, Constraint Logic Programming.For these reasons, HH(C) was in need of a more mathematical interpretation of programs. In this paper some fixed point semantics for HH(C) are presented. Taking as a starting point the techniques used by Miller to interpret the fragment of HH that incorporates intuitionistic implication in goals, we have formulated two novel extensions capable of dealing with the whole HH logic, including universal quantifiers, as well as with the presence of constraints. Those semantics are proved to be sound and complete w.r.t. the operational semantics of HH(C).

References

[1]

G. Amato and J. Lipton. Indexed categories and bottom-up semantics of logic programs. In R. Nieuwenhuis and A. Voronkov, editors, LPAR'01, LNCS 2250, pages 438--454. Springer, 2001.]]

Digital Library

[2]

A. Bossi, M. Gabrielli, G. Levi, and M. C. Meo. A compositional semantics for logic programs. Theoretical Computer Science, 122(1-2):3--47, 1994.]]

Digital Library

[3]

M. Comini, G. Levi, and M. C. Meo. A theory of observables for logic programs. Information and Computation, 69(1--2):23--80, 2001.]]

Digital Library

[4]

M. de Marco. Intuitionistic Semantics for Hereditarily Harrop Logic Programming. PhD thesis, Wesleyan University, 1999.]]

[5]

S. E. Finkelstein, P. Freyd, and J. Lipton. A new framework for declarative programming. Theoretical Computer Science, 300(1--3):91--160, 2003.]]

Digital Library

[6]

M. Gabbrielli, G. M. Dore, and G. Levi. Observable semantics for constraint logic programs. Journal of Logic and Computation, 5(2):133--171, 1995.]]

[7]

M. García-Díaz and S. Nieva. Solving mixed quantified constraints over a domain based on real numbers and Herbrand terms. In Z. Hu and M. Rodríguez-Artalejo, editors, FLOPS'02, LNCS 2441, pages 103--118. Springer, 2002.]]

Digital Library

[8]

J. Jaffar and M. J. Maher. Constraint logic programming: a survey. Journal of Logic Programming, 19/20:503--581, 1994.]]

[9]

J. Jaffar, M. J. Maher, K. Marriott, and P. J. Stuckey. The semantics of constraint logic programs. Journal of Logic Programming, 37(1-3):1--46, 1998.]]

[10]

J. Leach and S. Nieva. A higher-order logic programming language with constraints. In H. Kuchen and K. Ueda, editors, FLOPS'01, LNCS 2024, pages 108--122. Springer, 2001.]]

Digital Library

[11]

J. Leach, S. Nieva, and M. Rodríguez-Artalejo. Constraint logic programming with hereditary Harrop formulas. Theory and Practice of Logic Programming, 1(4):409--445, 2001.]]

Digital Library

[12]

J. W. Lloyd. Foundations of logic programming. Springer-Verlag, 1987.]]

Digital Library

[13]

D. Miller. A logical analysis of modules in logic programming. Journal of Logic Programming, 6(1-2):79--108, 1989.]]

Digital Library

[14]

D. Miller, G. Nadathur, F. Pfenning, and A. Scedrov. uniform proofs as a foundation for logic programming. Annals of Pure and Applied Logic, 51:125--157, 1991.]]

[15]

G. Nadathur. A proof procedure for the logic of hereditary Harrop formulas. Journal of Automated Reasoning, 11:111--145, 1993.]]

[16]

G. Smolka and R. Treinen. Records for logic programming. Journal of Logic Programming, 18(3):229--258, 1994.]]

[17]

A. Tarski. A decision method for elementary algebra and geometry. University of California Press, 1951.]]

[18]

A. Tarski. A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics, 5:285--309, 1955.]]

[19]

M. H. van Emden and R. A. Kowalski. The semantics of predicate logic as a programming language. Journal of the ACM, 23(4):733--742, 1976.]]

Digital Library

[20]

D. A. Wolfram. A semantics for λ-prolog. Theoretical Computer Science, 136:277--288, 1994.]]

Digital Library

Cited By

Nieva SSánchez-Hernández JSáenz-Pérez F(2008)Formalizing a constraint deductive database language based on hereditary Harrop formulas with negationProceedings of the 9th international conference on Functional and logic programming10.5555/1788446.1788476(289-304)Online publication date: 14-Apr-2008
https://dl.acm.org/doi/10.5555/1788446.1788476
Nieva SSánchez-Hernández JSáenz-Pérez F(2008)Formalizing a Constraint Deductive Database Language Based on Hereditary Harrop Formulas with NegationFunctional and Logic Programming10.1007/978-3-540-78969-7_21(289-304)Online publication date: 2008
https://doi.org/10.1007/978-3-540-78969-7_21
Lipton JNieva S(2007)Higher-order logic programming languages with constraintsProceedings of the 8th international conference on Typed lambda calculi and applications10.5555/1770203.1770223(272-289)Online publication date: 26-Jun-2007
https://dl.acm.org/doi/10.5555/1770203.1770223
Show More Cited By

Index Terms

Providing declarative semantics for HH extended constraint logic programs
1. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
      1. Semantics
    2. General programming languages
      1. Language types
        Constraint and logic languages
        Multiparadigm languages
2. Theory of computation
  1. Logic
    1. Constraint and logic programming
    2. Programming logic
  2. Semantics and reasoning
    1. Program reasoning
    2. Program semantics
      1. Denotational semantics

Recommendations

Constraint Logic Programming with Hereditary Harrop formulas

Constraint Logic Programming (CLP) and Hereditary Harrop formulas (HH) are two well known ways to enhance the expressivity of Horn clauses. In this paper, we present a novel combination of these two approaches. We show how to enrich the syntax and proof ...
Solving Mixed Quantified Constraints over a Domain Based on Real Numbers and Herbrand Terms
FLOPS '02: Proceedings of the 6th International Symposium on Functional and Logic Programming

Combining the logic of hereditary Harrop formulas HH with a constraint system, a logic programming language is obtained that extends Horn clauses in two different directions, th us enhancing substantially the expressivity of Prolog. The implementation ...
Proof theory of Nelson's paraconsistent logic: A uniform perspective

The aim of this paper is to obtain a theoretical foundation of inconsistency-tolerant (or paraconsistent) reasoning by presenting a comprehensive study of the structural proof-theory of David Nelson's paraconsistent logic. Inconsistency handling has a ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

PPDP '04: Proceedings of the 6th ACM SIGPLAN international conference on Principles and practice of declarative programming

August 2004

260 pages

ISBN:1581138199

DOI:10.1145/1013963

General Chair:
Eugenio Moggi
University of Genova, Italy
,
Program Chair:
David S. Warren
Stony Brook University & XSB, Inc., USA

Copyright © 2004 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 24 August 2004

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Article

Conference

PPDP04

Sponsor:

PPDP04: Principles and Practice of Declarative Programming 2004

August 24 - 26, 2004

Verona, Italy

Acceptance Rates

Overall Acceptance Rate 230 of 486 submissions, 47%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

5
Total Citations
View Citations
112
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 03 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

Nieva SSánchez-Hernández JSáenz-Pérez F(2008)Formalizing a constraint deductive database language based on hereditary Harrop formulas with negationProceedings of the 9th international conference on Functional and logic programming10.5555/1788446.1788476(289-304)Online publication date: 14-Apr-2008
https://dl.acm.org/doi/10.5555/1788446.1788476
Nieva SSánchez-Hernández JSáenz-Pérez F(2008)Formalizing a Constraint Deductive Database Language Based on Hereditary Harrop Formulas with NegationFunctional and Logic Programming10.1007/978-3-540-78969-7_21(289-304)Online publication date: 2008
https://doi.org/10.1007/978-3-540-78969-7_21
Lipton JNieva S(2007)Higher-order logic programming languages with constraintsProceedings of the 8th international conference on Typed lambda calculi and applications10.5555/1770203.1770223(272-289)Online publication date: 26-Jun-2007
https://dl.acm.org/doi/10.5555/1770203.1770223
Lipton JNieva S(2007)Higher-Order Logic Programming Languages with Constraints: A SemanticsTyped Lambda Calculi and Applications10.1007/978-3-540-73228-0_20(272-289)Online publication date: 2007
https://doi.org/10.1007/978-3-540-73228-0_20
Jagadeesan RNadathur GSaraswat V(2005)Testing concurrent systemsProceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science10.1007/11590156_42(517-528)Online publication date: 18-Dec-2005
https://dl.acm.org/doi/10.1007/11590156_42

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents