Skip to main content

Coinductive Constraint Logic Programming

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7294)

Abstract

Constraint logic programming (CLP) has been proposed as a declarative paradigm for merging constraint solving and logic programming. Recently, coinductive logic programming has been proposed as a powerful extension of logic programming for handling (rational) infinite objects and reasoning about their properties. Coinductive logic programming does not include constraints while CLP’s declarative semantics is given in terms of a least fixed-point (i.e., it is inductive) and cannot directly support reasoning about (rational) infinite objects and their properties. In this paper we combine constraint logic programming and coinduction to obtain co-constraint logic programming (co-CLP for brevity). We present the declarative semantics of co-CLP in terms of a greatest fixed-point and its operational semantics based on the coinductive hypothesis rule. We prove the equivalence of these two semantics for programs with rational terms.

Keywords

  • Logic Program
  • Logic Programming
  • Function Symbol
  • Operational Semantic
  • Constraint Logic

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barwise, J., Moss, L.: Vicious circles: on the mathematics of non-wellfounded phenomena. CSLI, Stanford (1996)

    MATH  Google Scholar 

  2. Colmerauer, A.: Prolog and infinite trees. In: Clark, K.L., Tärnlund, S.-A. (eds.) Logic Programming, pp. 231–251. Academic Press, London (1982)

    Google Scholar 

  3. Gupta, G., Saeedloei, N., DeVries, B., Min, R., Marple, K., Kluźniak, F.: Infinite Computation, Co-induction and Computational Logic. In: Corradini, A., Klin, B., Cîrstea, C. (eds.) CALCO 2011. LNCS, vol. 6859, pp. 40–54. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  4. Gupta, R.: Programming models and methods for spatiotemporal actions and reasoning in cyber-physical systems. In: NSF Workshop on CPS (2006)

    Google Scholar 

  5. Heitmeyer, C.L., Lynch, N.A.: The generalized railroad crossing: A case study in formal verification of real-time systems. In: IEEE RTSS, pp. 120–131 (1994)

    Google Scholar 

  6. Henzinger, T.A., Ho, P.-H.: Hytech: The Cornell Hybrid Technology Tool. In: Antsaklis, P.J., Kohn, W., Nerode, A., Sastry, S.S. (eds.) HS 1994. LNCS, vol. 999, pp. 265–293. Springer, Heidelberg (1995)

    CrossRef  Google Scholar 

  7. Jaffar, J., Maher, M.J.: Constraint logic programming: A survey. J. Log. Program. 19/20, 503–581 (1994)

    CrossRef  MathSciNet  Google Scholar 

  8. Lee, E.A.: Cyber-physical systems: Design challenges. In: ISORC (May 2008)

    Google Scholar 

  9. Lloyd, J.W.: Foundations of logic programming, 2nd extended edn. Springer, Berlin (1987)

    Google Scholar 

  10. Saeedloei, N.: Modeling and Verification of Real-Time and Cyber-Physical Systems. PhD thesis, University of Texas at Dallas, Richardson, Texas (2011)

    Google Scholar 

  11. Saeedloei, N., Gupta, G.: Verifying Complex Continuous Real-Time Systems with Coinductive CLP(R). In: Dediu, A.-H., Fernau, H., Martín-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 536–548. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  12. Saeedloei, N., Gupta, G.: A logic-based modeling and verification of CPS. SIGBED Rev. 8, 31–34 (2011)

    CrossRef  Google Scholar 

  13. Simon, L.: Coinductive Logic Programming. PhD thesis, University of Texas at Dallas, Richardson, Texas (2006)

    Google Scholar 

  14. Simon, L., Bansal, A., Mallya, A., Gupta, G.: Co-Logic Programming: Extending Logic Programming with Coinduction. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 472–483. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  15. Sterling, L., Shapiro, E.: The art of Prolog: advanced programming techniques, 2nd edn. MIT Press, Cambridge (1994)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Saeedloei, N., Gupta, G. (2012). Coinductive Constraint Logic Programming. In: Schrijvers, T., Thiemann, P. (eds) Functional and Logic Programming. FLOPS 2012. Lecture Notes in Computer Science, vol 7294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29822-6_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-29822-6_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29821-9

  • Online ISBN: 978-3-642-29822-6

  • eBook Packages: Computer ScienceComputer Science (R0)