Skip to main content
SpringerLink
Log in

Key extensions of abstract data types, final algebras, and database semantics

  • Part II Research Contributions
  • Chapter
  • First Online:
Category Theory and Computer Programming

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 240))

Abstract

The algebraic specification of abstract data types provides a number of features for structuring specifications in order to make them easier to write, to read, to understand, and to maintain. Among the most important such features are different kinds of extensions, based on initial, final, or behavioural semantics. This paper studies a new kind of extension called key extension, and its final algebra semantics. Key extensions model one of the essential steps in database specification where abstract object types are to be specified on the basis of given abstract data types. The intended standard semantics is a universe of "possible objects" that provides the basis for further database concepts like situations, states, etc. It is shown under which conditions final algebras exist that can serve as a natural standard semantics for key extensions. We also characterize rather a large class of constraints that can be used for keys in accordance with our semantics.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dosch,W./Mascari,G./Wirsing, M.: On the Algebraic Specification of Databases. Proc. 8th Int. Conf. on Very Large Data Bases, Mexico City 1982

    Google Scholar 

  2. Ehrich, H.-D.: Extensions and Implementations of abstract data type specifications. Proc. 7th Symp. MFCS 78 (J. Winkowski, ed.). LNCS 64, Springer-Verlag, Berlin 1978, 155–164

    Google Scholar 

  3. Ehrich, H.-D.: On the theory of specification, implementation and parameterization of abstract data types. Journal ACM 29 (1982), 206–227

    Google Scholar 

  4. Ehrich,H.-D.: Algebraic (?) Specification of Conceptual Database Schemata (Extended Abstract). Proc. 3rd Workshop on Theory and Application of Abstract Data Types (H.-J.Kreowski, ed.) (To appear as Informatik-Fachbericht, Springer-Verlag)

    Google Scholar 

  5. Ehrig,H./Kreowski,H.-J./Weber,H.: Algebraic Specification Schemes for Database Systems. Proc 4th Int. Conf. on Very Large Databases, Berlin 1978

    Google Scholar 

  6. Ehrich,H.-D./Lipeck,U.W./Gogolla,M.: Specification, Semantics, and Enforcement of Dynamic Database Constraints. Proc. 10th Int. Conf. on Very Large Databases, Singapore 1984

    Google Scholar 

  7. Ehrig, H./Mahr, B.: Fundamentals of Algebraic Specification 1. Springer-Verlag, Berlin 1985

    Google Scholar 

  8. Golshani,F./Maibaum,T.S.E./Sadler,M.R.: A Modal System of Algebras for Database Specification and Query/Update Language Support. Proc. 9th Int. Conf. on Very Large Data Bases, Florence 1983

    Google Scholar 

  9. Goguen, J.A./Thatcher, J.W./Wagner, E.G.: An initial algebra approach to the specification, correctness and implementation of abstract data types. Current Trends in Programming Methodology IV (R.T. Yeh, ed.), Prentice-Hall, Englewood Cliffs 1978, 80–149

    Google Scholar 

  10. Gogolla,M.: A Final Algebra Semantics for Errors and Exceptions. Proc. 3rd Workshop on Theory and Application of Abstract Data Types (H.-J.Kreowski, ed.). (To appear as Informatik-Fachbericht, Springer-Verlag)

    Google Scholar 

  11. Hupbach, U.L./Reichel, H.: On Behavioural Equivalence of Data Types, EIK 19 (1983), 297–305

    Google Scholar 

  12. Jantke,K.: The Recursive Power of Algebraic Semantics (submitted for publication)

    Google Scholar 

  13. Khosla, S./Maibaum, T.S.E./Sadler, M.: Database Specification. Proc. IFIP Working Conf.on Database Semantics (R. Meersman/T.B. Steel, eds.), North Holland, Amsterdam 1985

    Google Scholar 

  14. Lipeck, U.W./Ehrich, H.-D./Gogolla, M.: Specifying Admissibility of Dynamic Database Behaviour Using Temporal Logic. Proc. IFIP Working Conf. on Theoretical and Formal Aspects of Information Systems (A Sernadas et al., eds), North Holland, Amsterdam 1985

    Google Scholar 

  15. Lipeck,U.W.: Stepwise Specification of Dynamic Database Behaviour. (To appear)

    Google Scholar 

  16. Lipeck, U.W./Saake,G./Ehrich,H.-D.: Monitoring Dynamic Integrity Constraints by Transition Graphs (submitted for publication)

    Google Scholar 

  17. Saake,G.: Konstruktion von Transitionsgraphen aus temporalen Formeln zur Integritätsüberprüfung in Datenbanken. Diploma Thesis, Techn. Univ. Braunschweig 1985

    Google Scholar 

  18. Wand, M.: Final Algebra Semantics and Data Type Extensions. Journal of Computer and System Sciences 19 (1979), 27–44

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Inst. f. Informatik, TU Braunschweig, Postfach 33 29, D-3300, Braunschweig, West Germany

    H. -D. Ehrich

Authors
  1. H. -D. Ehrich
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

David Pitt Samson Abramsky Axel Poigné David Rydeheard

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Ehrich, H.D. (1986). Key extensions of abstract data types, final algebras, and database semantics. In: Pitt, D., Abramsky, S., Poigné, A., Rydeheard, D. (eds) Category Theory and Computer Programming. Lecture Notes in Computer Science, vol 240. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17162-2_135

Download citation

  • DOI: https://doi.org/10.1007/3-540-17162-2_135

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17162-1

  • Online ISBN: 978-3-540-47213-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation