Skip to main content

Abstract specification of mathematical structures and methods

  • Symbolic And Algebraic Computation — Implementation Methods And Techniques
  • Conference paper
  • First Online:
Design and Implementation of Symbolic Computation Systems (DISCO 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 429))

Abstract

This paper presents several methodological and technological aspects for the treatment of mathematical objects by very high level abstract specification of data and methods. A homogeneus environment is defined for the design and implementation at the highest abstract level. The presentation is developed from the point of view of both formal specification and implementation languages. Indeed specification and programming are considered as uniform actions under the same general conceptual model. The conceptual model is completely supported by the Object-Oriented methodology. Particular interest is devoted to Algorithmic Logic, as a logic specification language, and to Loglan as an innovative Object-Oriented programming language.

Research partially supported by MURST: “Calcolo Algebrico, Sistemi di Manipolazione Algebrica”; CNR: “Matematica Computazionale”, Progetto Finalizzato “Sistemi Informatici e Calcolo Parallelo”; Olivetti System and Networks.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. CIONI, A. SALWICKI (Eds): Advanced Programming Methodologies, Academic Press (1989).

    Google Scholar 

  2. J.W. GOODWIN: Why Programming Environments Need Dynamic Data Types, IEEE Trans. on Software Eng. SE-7, 5, (1981).

    Google Scholar 

  3. W.M. BARTOL et al: Report on the Programming Language LOGLAN 82, Polish Scient. Publ. Warsaw (1984).

    Google Scholar 

  4. B. LISKOV: Data Abstraction and Hierarchy, Proc. OOPSLA '87 (1987).

    Google Scholar 

  5. B. MEYER: Object Oriented Software Construction, Prentice Hall (1988).

    Google Scholar 

  6. A. MIOLA, D.Y. YUN Computational Aspects of Hensel Type Univariate Polynomial GCD, ACM Proc. EUROSAM (1974).

    Google Scholar 

  7. G. MIRKOWSKA, A. SALWICKI: Algorithmic Logic, Polish Scient. Publ. Warsaw (1987).

    Google Scholar 

  8. A.SNYDER: Inheritance and the Development of Encapsulated Software Systems, In “Research Directions in Object Oriented Programming”, MIT Press, C.S. Series (1987).

    Google Scholar 

  9. M. TEMPERINI, R. VITALE: A Formal approach to the specification and manipulation of mathematical objects, R.251 IASI-CNR Roma (1988).

    Google Scholar 

  10. P. THOMAS, H. ROBINSON-J. EMMS: Abstract Data Types — Their Specification, Representation, and Use, Clarendon Press, Oxford (1988).

    Google Scholar 

  11. P.WEGNER: The Object Oriented Classification Paradigm, In “Research Directions in Object Oriented Programming”, MIT Press, C.S. Series (1987).

    Google Scholar 

  12. D.Y.Y. YUN: Algebraic algorithms using P-adic construction, ACM Proc. SYMSAC (1976).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Alfonso Miola

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Limongelli, C., Beatrice Mele, M., Regio, M., Temperini, M. (1990). Abstract specification of mathematical structures and methods. In: Miola, A. (eds) Design and Implementation of Symbolic Computation Systems. DISCO 1990. Lecture Notes in Computer Science, vol 429. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52531-9_125

Download citation

  • DOI: https://doi.org/10.1007/3-540-52531-9_125

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52531-8

  • Online ISBN: 978-3-540-47014-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics