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.
Preview
Unable to display preview. Download preview PDF.
References
G. CIONI, A. SALWICKI (Eds): Advanced Programming Methodologies, Academic Press (1989).
J.W. GOODWIN: Why Programming Environments Need Dynamic Data Types, IEEE Trans. on Software Eng. SE-7, 5, (1981).
W.M. BARTOL et al: Report on the Programming Language LOGLAN 82, Polish Scient. Publ. Warsaw (1984).
B. LISKOV: Data Abstraction and Hierarchy, Proc. OOPSLA '87 (1987).
B. MEYER: Object Oriented Software Construction, Prentice Hall (1988).
A. MIOLA, D.Y. YUN Computational Aspects of Hensel Type Univariate Polynomial GCD, ACM Proc. EUROSAM (1974).
G. MIRKOWSKA, A. SALWICKI: Algorithmic Logic, Polish Scient. Publ. Warsaw (1987).
A.SNYDER: Inheritance and the Development of Encapsulated Software Systems, In “Research Directions in Object Oriented Programming”, MIT Press, C.S. Series (1987).
M. TEMPERINI, R. VITALE: A Formal approach to the specification and manipulation of mathematical objects, R.251 IASI-CNR Roma (1988).
P. THOMAS, H. ROBINSON-J. EMMS: Abstract Data Types — Their Specification, Representation, and Use, Clarendon Press, Oxford (1988).
P.WEGNER: The Object Oriented Classification Paradigm, In “Research Directions in Object Oriented Programming”, MIT Press, C.S. Series (1987).
D.Y.Y. YUN: Algebraic algorithms using P-adic construction, ACM Proc. SYMSAC (1976).
Author information
Authors and Affiliations
Editor information
Rights 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