Skip to main content

Hiord: A Type-Free Higher-Order Logic Programming Language with Predicate Abstraction

  • Conference paper
Advances in Computer Science - ASIAN 2004. Higher-Level Decision Making (ASIAN 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3321))

Included in the following conference series:

Abstract

A new formalism, called Hiord, for defining type-free higher-order logic programming languages with predicate abstraction is introduced. A model theory, based on partial combinatory algebras, is presented, with respect to which the formalism is shown sound. A programming language built on a subset of Hiord, and its implementation are discussed. A new proposal for defining modules in this framework is considered, along with several examples.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Miller, D., Nadathur, G., Pfenning, F., Scedrov, A.: Uniform proofs as a foundation for logic programming. Annals of Pure and Applied Logic 51, 125–157 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  2. Nadathur, G., Miller, D.: Higher-order horn clauses. Journal of the ACM 37, 777–814 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  3. Miller, D.: λprolog: an introduction to the language and its logic (2002), Manuscript available at http://www.cse.psu.edu/~dale

  4. Chen, W., Kifer, M., Warren, D.S.: Hilog: JuneA Foundation for Higher-Order Logic Programming. Journal of Logic Programming (1989)

    Google Scholar 

  5. Beeson, M.: Foundations of Constructive Mathematics. Springer, Heidelberg (1985)

    Google Scholar 

  6. Lawvere, F.W.: Diagonal arguments and cartesian-closed categories. In: Category Theory, Homology Theory and their Applications. Springer, Heidelberg (1969)

    Google Scholar 

  7. Huwig, H., Poigné, A.: A Note on Inconsistencies Caused by Fixpoints in a Cartesian Closed Categories. Theoretical Computer Science 73, 101–112 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  8. Miller, D.: A logic programming language with lambda-abstraction, function variables, and simple unification. Journal of Logic and Computation 1, 497–536 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  9. Curry, H.B., Feys, R.: Combinatory Logic. North-Holland, Amsterdam (1958)

    MATH  Google Scholar 

  10. Cabeza, D.: An Extensible, Global Analysis Friendly Logic Programming System. PhD thesis, Dept. of Computer Science, Technical University of Madrid, Spain, Madrid, Spain (2004)

    Google Scholar 

  11. Bueno, F., Cabeza, D., Carro, M., Hermenegildo, M., López-García, P. (eds.): G.P.: The Ciao System. Reference Manual (v1.10). The ciao system documentation series–TR, School of Computer Science, Technical University of Madrid, UPM (2002), System and on-line version of the manual, available at http://clip.dia.fi.upm.es/Software/Ciao/

  12. Warren, D.H.: Higher-order extensions to prolog: are they needed? In: Hayes, J., Michie, D., Pao, Y.H. (eds.) Machine Intelligence 10, pp. 441–454. Ellis Horwood Ltd., Chicester (1982)

    Google Scholar 

  13. Naish, L.: Higher-order logic programming. Technical Report 96/2, Department of Computer Science, University of Melbourne, Melbourne, Australia (1996)

    Google Scholar 

  14. McDowell, R., Miller, D.: A logic for reasoning with higher-order abstract syntax. In: Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science, p. 434. IEEE Computer Society Press, Los Alamitos (1997)

    Google Scholar 

  15. Miller, D.: Abstract syntax and logic programming. In: Proceedings of the Second Russian Conference on Logic Programming. Springer, Heidelberg (1991)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cabeza, D., Hermenegildo, M., Lipton, J. (2004). Hiord: A Type-Free Higher-Order Logic Programming Language with Predicate Abstraction. In: Maher, M.J. (eds) Advances in Computer Science - ASIAN 2004. Higher-Level Decision Making. ASIAN 2004. Lecture Notes in Computer Science, vol 3321. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30502-6_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30502-6_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24087-7

  • Online ISBN: 978-3-540-30502-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics