Abstract
The software system ALLTYPES provides an environment that is particularly designed for developing computer algebra software in the realm of differential equations. Its most important features may be described as follows: A set of about thirty parametrized algebraic types is defined. Data objects represented by these types may be manipulated by more than one hundred polymorphic functions. Reusability of code is achieved by genericity and inheritance. The user may extend the system by defining new types and polymorphic functions. A language comprising seven basic language constructs is defined for implementing mathematical algorithms. The easy manipulation of types is particularly supported by ALLTYPES. To this end a special portion of the language that is enclosed by a pair of absolute bars is dedicated to manipulating typed objects, i. e. user-defined or automatic type coercions. Type inquiries are also included in the language. A small amount of parallelism is supported in terms of two language constructs pand and por where the letter p indicates a parallel version of the respective logical function. Currently ALLTYPES is implemented in Reduce and Macsyma (to be completed soon). Software implemented on top of ALLTYPES should work independent of the underlying computer algebra language.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Booch, G, Object Oriented Design, Benjamin/Cummings Publishing, 1991.
Coad, P., Yourdon, E., Object-Oriented Analysis and Object-Oriented Design, both published by Yourdon Press, Englewood Cliffs, 1991.
Meyer, B., Object-oriented Software Construction, Prentice Hall, 1988.
Budd, T., Object-Oriented Programming, Addison-Wesley, 1991.
Cardelli, L., Wegner, P., On Understanding Types, Data Abstraction, and Polymorphism, Computing Surveys 17, 471–522 (1985).
Taivalsaari, A., On the Notion of Inheritance, ACM Computing Surveys 28, 438–479 (1996).
Buchberger, B., Symbolic Computation: Computer Algebra and Logic, Proceedings of the Frontiers in Combining System Conference, Munich, F. Baader and K. U. Schulz, eds, Applied Logic Series, Kluwer Academic Publishers, 1996.
Fedoraro, J. F., The Design of a Language for Algebraic Computation Systems, Thesis, Berkeley, 1983.
Hearn, A. C., Reduce User’s Manual, part of Reduce.
Jenks, R. D., Sutor, B., Axiom, Springer, 1992.
Scheller, D., ALLTYPES: The Reduce Implementation, GMD Report, 1998.
Weber, A., Structuring the Type System of a Computer Algebra System, Dissertation, UniversitÄt Tübingen, 1992.
Golden, J., private communication.
Schwarz, F., ALLTYPES: The User Manual, GMD Report, to appear.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schwarz, F. (1998). ALLTYPES: An algebraic language and TYPE system. In: Calmet, J., Plaza, J. (eds) Artificial Intelligence and Symbolic Computation. AISC 1998. Lecture Notes in Computer Science, vol 1476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055919
Download citation
DOI: https://doi.org/10.1007/BFb0055919
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64960-1
Online ISBN: 978-3-540-49816-2
eBook Packages: Springer Book Archive