Skip to main content
SpringerLink
Log in

Relating Abstract Datatypes and Z-Schemata

  • Conference paper
Recent Trends in Algebraic Development Techniques (WADT 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1827))

Included in the following conference series:

Abstract

In this paper we investigate formally the relationship between the notion of abstract datatypes in an arbitrary institution, found in algebraic specification languages like Clear, ASL, and CASL; and the notion of schemata from the model-oriented specification language Z. To this end the institution \({\cal S}\) of the logic underlying Z is defined, and a translation of Z-schemata to abstract datatypes over \({\cal S}\) is given. The notion of a schema is internal to the logic of Z, and thus specification techniques of Z relying on the notion of a schema can only be applied in the context of Z. By translating Z-schemata to abstract datatypes, these specification techniques can be transformed to specification techniques using abstract datatypes. Since the notion of abstract datatypes is institution independent, this results in a separation of these specification techniques from the specification language Z and allows them to be applied in the context of other, e.g. algebraic, specification languages.

This research has been partially supported by ESPRIT working group 29432 (CoFI WG).

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

Access this chapter

Log in via an institution
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baumeister, H.: Relations as abstract datatypes: An institution to specify relations between algebras. In: Mosses, P.D., Nielsen, M., Schwartzbach, M.I. (eds.) CAAP 1995, FASE 1995, and TAPSOFT 1995. LNCS, vol. 915, pp. 756–771. Springer, Heidelberg (1995)

    Google Scholar 

  2. Baumeister, H.: Using algebraic specification languages for model-oriented specifications. Technical Report MPI-I-96-2-003, Max-Planck-Institut für Informatik, Saarbrücken, Germany (February 1996)

    Google Scholar 

  3. Baumeister, H.: Relations between Abstract Datatypes modeled as Abstract Datatypes. PhD thesis, Universität des Saarlandes, Saarbrücken (May 1999)

    Google Scholar 

  4. Burstall, R.M., Goguen, J.A.: The semantics of Clear, a specification language (February 1980)

    Google Scholar 

  5. Ehrig, H., Orejas, F.: Dynamic abstract data types, an informal proposal. Bulletin of the EATCS 53, 162–169 (1994)

    MATH  Google Scholar 

  6. Goguen, J.A., Burstall, R.: Institutions: Abstract model theory for specification and programming. Journal of the Association for Computing Machinery 39(1), 95–146 (1992)

    MathSciNet  MATH  Google Scholar 

  7. Gurevich, Y.: Evolving algebras: An attempt to discover semantics. Bulletin of the EATCS 43, 264–284 (1991)

    MATH  Google Scholar 

  8. Hennicker, R., Wirsing, M., Bidoit, M.: Proof systems for structured specifications with observability operators. Theoretical Computer Science 173(2), 393–443 (1996)

    Article  MathSciNet  Google Scholar 

  9. Mossakowski, T.: Specifications in an arbitrary institution with symbols. In: Bert, D., Choppy, C. (eds.) WADT 1999. LNCS, vol. 1827, pp. 252–270. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  10. Mosses, P.D.: CoFI: The common framework initiative for algebraic specification and development. In: Bidoit, M., Dauchet, M. (eds.) CAAP 1997, FASE 1997, and TAPSOFT 1997. LNCS, vol. 1214. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  11. Sannella, D., Wirsing, M.: A kernel language for algebraic specification and implementation. In: Karpinski, M. (ed.) FCT 1983. LNCS, vol. 158, pp. 413–427. Springer, Berlin (1983)

    Google Scholar 

  12. Spivey, J.M.: Understanding Z: A Specification Language and its Formal Semantics, Cambridge tracts in theoretical computer science, vol. 3. Cambridge Univ. Press, Cambridge, GB, repr. (1992) edn. (1988)

    Google Scholar 

  13. Z notation, final committee draft, cd 13568.2, August 24 (1999), Available at http://web.comlab.ox.ac.uk/oucl/research/groups/zstandards/index.html

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Munich, Oettingenstr. 67, D-80358, Munich, Germany

    Hubert Baumeister

Authors
  1. Hubert Baumeister
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Laboratoire Logiciels, Systèmes, Réseaux - IMAG, B.P. 72, F-38402, Saint Martin d’Hères Cedex, France

    Didier Bert

  2. LIPN, Institut Galilée, Université Paris XIII, France

    Christine Choppy

  3. Department of Computer Science, Swansea University, UK

    Peter D. Mosses

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Baumeister, H. (2000). Relating Abstract Datatypes and Z-Schemata. In: Bert, D., Choppy, C., Mosses, P.D. (eds) Recent Trends in Algebraic Development Techniques. WADT 1999. Lecture Notes in Computer Science, vol 1827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44616-3_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-44616-3_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67898-4

  • Online ISBN: 978-3-540-44616-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation