Skip to main content

Non-termination in Unifying Theories of Programming

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3929))

Abstract

Within the shape Unifying Theories of Programming framework, program initiation and termination has been modelled by introducing a pair of variables in order to satisfy the required algebraic properties. We replace these variables with the improper value ⊥ that is frequently used to denote undefinedness. Both approaches are proved isomorphic using the relation calculus, and the existing operations and laws are carried over. We split the isomorphism by interposing “intuitive” relations.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Hoare, C.A.R., He, J.: Unifying theories of programming. Prentice Hall Europe, Englewood Cliffs (1998)

    MATH  Google Scholar 

  2. Dunne, S.: Recasting Hoare and He’s unifying theory of programs in the context of general correctness. In: Butterfield, A., Strong, G., Pahl, C. (eds.) 5th Irish Workshop on Formal Methods. EWiC, The British Computer Society (2001)

    Google Scholar 

  3. Schmidt, G., Ströhlein, T.: Relationen und Graphen. Springer, Heidelberg (1989)

    Book  MATH  Google Scholar 

  4. Szász, G.: Introduction to Lattice Theory, 3rd edn. Academic Press, London (1963)

    MATH  Google Scholar 

  5. Hehner, E.C.R., Malton, A.J.: Termination conventions and comparative semantics. Acta Informatica 25(1), 1–14 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  6. Nelson, G.: A generalization of Dijkstra’s calculus. ACM Transactions on Programming Languages and Systems 11(4), 517–561 (1989)

    Article  Google Scholar 

  7. de Bakker, J.W.: Semantics and termination of nondeterministic recursive programs. In: Michaelson, S., Milner, R. (eds.) Third International Colloquium on Automata, Languages and Programming. Edinburgh University Press, pp. 435–477 (1976)

    Google Scholar 

  8. Broy, M., Gnatz, R., Wirsing, M.: Semantics of nondeterministic and noncontinuous constructs. In: Gerhart, S.L., Pair, C., Pepper, P.A., Wössner, H., Dijkstra, E.W., Guttag, J.V., Owicki, S.S., Partsch, H., Bauer, F.L., Gries, D., Griffiths, M., Horning, J.J., Wirsing, M. (eds.) Program Construction. LNCS, vol. 69, pp. 553–592. Springer, Heidelberg (1979)

    Chapter  Google Scholar 

  9. Berghammer, R., Zierer, H.: Relational algebraic semantics of deterministic and nondeterministic programs. Theoretical Computer Science 43(2-3), 123–147 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  10. Apt, K.R., Plotkin, G.D.: Countable nondeterminism and random assignment. Journal of the ACM 33(4), 724–767 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  11. Desharnais, J., Möller, B., Tchier, F.: Kleene under a modal demonic star. Journal of Logic and Algebraic Programming, special issue on Relation Algebra and Kleene Algebra (in press, 2005)

    Google Scholar 

  12. Guttmann, W., Möller, B.: Modal design algebra. In: First International Symposium on Unifying Theories of Programming (to appear, 2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Guttmann, W. (2006). Non-termination in Unifying Theories of Programming. In: MacCaull, W., Winter, M., Düntsch, I. (eds) Relational Methods in Computer Science. RelMiCS 2005. Lecture Notes in Computer Science, vol 3929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11734673_9

Download citation

  • DOI: https://doi.org/10.1007/11734673_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-33339-5

  • Online ISBN: 978-3-540-33340-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics