Skip to main content
Log in

A decidability criterion for van Wijngaarden grammars

  • Published:
Acta Informatica Aims and scope Submit manuscript

Summary

Van Wijngaarden grammars are a very useful instrument for syntactically describing even the most complex languages. This is illuminated specifically by describing the language of valid formulas of first order logic by a van Wijngaarden grammar.

Normal forms of van Wijngaarden grammars and restrictions which guarantee decidability are discussed and ALGOL 68 is considered under these views.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Baker, J. L.: Grammars with structured vocabulary: A model for the ALGOL 68-definition. Information and Control 20, 351–395 (1972)

    Google Scholar 

  2. Greibach, S. A.: Some restrictions on W-grammars. ACM, Proceedings of the 6th Symposium on the Theory of Computing, Seattle, May 1974

  3. Heilbrunner, S.: Gleichungssysteme für Zeichenreichen. TU München, Abtlg. Mathematik, Bericht Nr. 7311, 1973

  4. Maurer, H.: Theoretische Grundlagen der Programmiersprachen; Mannheim: Bibliographisches Institut 1969

    Google Scholar 

  5. Naur, P. (ed.): Revised Report on the Algorithmic Language ALGOL 60. Numerische Mathematik 4, 420–453 (1963)

  6. Pair, C.: Concerning the syntax of ALGOL 68. ALGOL Bull. 31, 16–27 (1970)

    Google Scholar 

  7. Schneider, H.-J.: Ein formales Verfahren zur maschinellen Sprachanalyse. Dissertation, Hannover 1965

  8. Schneider, H.-J.: Die Berücksichtigung von Kasus, Genus und anderen Spezifikationen bei formalen Grammatiken natürlicher Sprachen. Elektronische Datenverarbeitung 5, 245–248 (1966)

    Google Scholar 

  9. Sintzoff, M.: Existence of a van Wijngaarden syntax for every recursively enumerable set. Annales de la Société Scientifique de Bruxelles, T. 81, II (1967)

    Google Scholar 

  10. Smullyan, R. M.: First order logic. Berlin-Heidelberg-New York: Springer 1968

    Google Scholar 

  11. van Wijngaarden A. (ed.): Report on the Algorithmic Language ALGOL 68. Numerische Mathematik 14, 79–218 (1969)

  12. van Wijngaarden, A., et al. (eds.): Revised Report on the Algorithmic Language ALGOL 68. Supplement to ALGOL BULLETTIN 36 and Dep. Comp. Sc., University of Alberta, Edmonton, Technical Report TR 74-3, March 1974

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deussen, P. A decidability criterion for van Wijngaarden grammars. Acta Informatica 5, 353–375 (1975). https://doi.org/10.1007/BF00264566

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00264566

Keywords

Navigation