Skip to main content

Verifying properties of module construction in type theory

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 711))

Abstract

This paper presents a comparison between algebraic specifications-in-the-large and a type theoretical formulation of modular specifications, called deliverables. It is shown that the laws of module algebra can be translated to laws about deliverables which can be proved correct in type theory. The adequacy of the Extended Calculus of Constructions as a possible implementation of type theory is discussed and it is explained how the reformulation of the laws is influenced by this choice.

This work was partially sponsored by the BMFT-project KORSO

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. A. Bergstra, J. Heering, P. Klint: Algebraic Specification. ACM Press, New York, 1989.

    Google Scholar 

  2. R.M. Burstall, J.A. Goguen: The semantics of Clear, a specification language. In: Proc. Advanced Course on Abstract Software Specification. LNCS 86, Springer, Berlin, 1980.

    Google Scholar 

  3. R.M. Burstall, J. McKinna: Deliverables: a categorical approach to program development in type theory. ECS-LFCS-92-242, Dept. of Computer Science, Edinburgh University, 1992.

    Google Scholar 

  4. J. McKinna: Deliverables: a categorical approach to program development in type theory. Ph.D. Thesis, University of Edinburgh, 1992. Also appeared as ECS-LFCS-92-247, Dept. of Computer Science, Edinburgh University, 1992.

    Google Scholar 

  5. J. Leszczylowski, M. Wirsing: Polymorphism, Parameterisation and Typing: An Algebraic Specification Perspective. In: Proc. of the 8th STACS, LNCS 480, Springer, Berlin, p. 1–15.

    Google Scholar 

  6. Z. Luo: ECC, an Extended Calculus of Constructions. In: Proc. of the Fourth Ann. Symp. on Logic in Computer Science (LICS), IEEE, 1989, p. 385–395.

    Google Scholar 

  7. Z. Luo: Program specification and data refinement in type theory. In: Proc. of the Fourth Intern. Conf. on the Theory and Practice of Software Development (TAPSOFT), LNCS 493, Springer, Berlin, 1991, p. 143–168.

    Google Scholar 

  8. Z. Luo: private communication.

    Google Scholar 

  9. Z. Luo, R. Pollack: LEGO Proof Development System: Users' Manual. ECS-LFCS-92-211, Dept. of Computer Science, Edinburgh University, 1992.

    Google Scholar 

  10. B. Norström, K. Petersson, J.M. Smith: Programming in Martin Löf's Type Theory. Oxford University Press, Oxford, 1990.

    Google Scholar 

  11. T. Streicher: Semantics of Type Theory — Correctness, Completeness and Independence Results. Birkhäuser, Boston, 1991.

    Google Scholar 

  12. T. Streicher, M. Wirsing: Dependent types considered necessary for algebraic specification languages. In: Recent Trends in Data Type Specification, Proc. 7th International Workshop on Specification of Abstract Data Types. LNCS 534, Springer, Berlin, 1990, p. 323–340.

    Google Scholar 

  13. M. Wirsing: Structured algebraic specifications: a kernel language. Theoretical Computer Science 42, 1986, p. 123–249.

    Google Scholar 

  14. M. Wirsing: Algebraic Specification in J.V. Leeuwen (ed.): Handbook of Theoretical Computer Science, Volume B, Elsevier, Amsterdam, 1990, p. 675–788.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Andrzej M. Borzyszkowski Stefan Sokołowski

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Reus, B., Streicher, T. (1993). Verifying properties of module construction in type theory. In: Borzyszkowski, A.M., Sokołowski, S. (eds) Mathematical Foundations of Computer Science 1993. MFCS 1993. Lecture Notes in Computer Science, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57182-5_57

Download citation

  • DOI: https://doi.org/10.1007/3-540-57182-5_57

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57182-7

  • Online ISBN: 978-3-540-47927-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics