Skip to main content
SpringerLink
Log in
Book cover

Workshop on the Specification of Abstract Data Types

Workshop of the ESPRIT Basic Research Working Group COMPASS

ADT 1994, COMPASS 1994: Recent Trends in Data Type Specification pp 307–318Cite as

Defining equations in terminal coalgebras

  • Contributed Papers
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 906))

Abstract

Defining equations on constructors of abstract data types (with initial semantics) are used to express that different combinations of constructors generate equal values. In this paper we will study the role of equations on the destructors of terminal coalgebras for the specification of behavior classes. It turns out that equations on the destructors may be used to constrain the behavior by defining subcoalgebras of terminal coalgebras. Defining equations on destructors may be used to formalize safety properties, i.e. properties that have to be invariant with respect to changes of states.

This work has been partially supported by ESPRIT — BRA WG n. 6112 COMPASS.

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. Barr, M.: Terminal coalgebras in well-founded set theory. Theoretical Computer Science 114 (1993), 299–315.

    Article  Google Scholar 

  2. Dauchy,P., Gaudel, M.C.: Algebraic Specifications with Implicit State. Techn. Report, n 887 (1994) Univ. Paris-Sud.

    Google Scholar 

  3. Ehrig, H.: Dynamic Abstract Data Types, An Informal Proposal. Bull. EATCS 53 (1994).

    Google Scholar 

  4. Gabriel, P., Ulmer, F.: Lokal präsentierbare Kategorien. Springer Lect. Notes Math. 221 (1971): 1–200.

    Google Scholar 

  5. Gurevitch, Y.: EvoMng Algebras, A Tutorial Introduction. Bull. EATCS 43 (1991), pp.264–284.

    Google Scholar 

  6. Lawvere,F.W.:Functorial Semantics of Algebraic Theories. Proc. Nat. Acad. Sci. USA, 1963

    Google Scholar 

  7. Milner.R.: The Polyadic π-Calculus, A Tutorial. In: Bauer, F.L., Brauer,W., Schwichtenberg,H. (eds): Logic and Algebra of Specification, NATO ASI Series, Series F: Computer and Systems Science, Vol. 94, Springer-Verlag, 1993.

    Google Scholar 

  8. Poigné, A.: Basic Category Theory. In: Abramsky, S., Gabbay, Dov M., Maibaum, T.S.E. (eds): Handbook of Logic in Computer Science, Vol. 1, Oxford Science Publications, Clarendon Press, Oxford, 1992.

    Google Scholar 

  9. Reichel, H.: Initial Computability, Algebraic Specifications, and Partial Algebras. Oxford Science Publications, 1987.

    Google Scholar 

  10. Reichel,H.: An Approach to Object Semantics based on Terminal Co-algebras. Mathematical Structures in Computer Science (in print)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Informatik, Technische Universität Dresden, Mommsenstraße 13, D-01069, Dresden, Germany

    Ulrich Hensel & Horst Reichel

Authors
  1. Ulrich Hensel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Horst Reichel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Egidio Astesiano Gianna Reggio Andrzej Tarlecki

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hensel, U., Reichel, H. (1995). Defining equations in terminal coalgebras. In: Astesiano, E., Reggio, G., Tarlecki, A. (eds) Recent Trends in Data Type Specification. ADT COMPASS 1994 1994. Lecture Notes in Computer Science, vol 906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014435

Download citation

  • DOI: https://doi.org/10.1007/BFb0014435

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59132-0

  • Online ISBN: 978-3-540-49198-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation