Abstract
An important feature of modem computer algebra systems is the support of a rich type system with the possibility of type inference.
Basic features of such a type system are polymorphism and coercion between types. Recently the use of order-sorted rewrite systems was proposed as a general framework.
We will give a quite simple example of a family of types arising in computer algebra whose coercion relations cannot be captured by a finite set of first-order rewrite rules.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
R. S. Sutor and R. D. Jenks. The type inference and coercion facilities in the Scratchpad II interpreter. ACM SIGPLAN Notices, 22(7):56–63, 1987. SIGPLAN '87 Symposium on Interpreters and Interpretive Techniques.
J. H. Davenport and B. M. Trager. Scratchpad's view of algebra I: Basic commutative algebra. In Miola [10]., pages 40–54.
S. K. Abdali, G. W. Cherry, and N. Soiffer. A Smalltak system for algebraic manipulation. ACM SIGPLAN Notices, 21(11):277–283, November 1986. OOPSLA '86 Conference Proceedings, Portland, Oregon.
D. L. Rector. Semantics in algebraic computation. In E. Kaltofen and S. M. Watt, editors, Computers and Mathematics, pages 299–307, Massachusetts Institute of Technology, June 1989. Springer-Verlag.
G. Baumgartner and R. Stansifer. A proposal to study type systems for computer algebra. Technical Report 90-07.0, Research Institute for Symbolic Computation Linz, A-4040 Linz, Austria, March 1990.
H. Comon, D. Lugiez, and Ph. Schnoebelen. A rewrite-based type discipline for a subset of computer algebra. Journal of Symbolic Computation, 11:349–368, 1991.
A. Fortenbacher. Efficient type inference and coercion in computer algebra. In Miola [10]., pages 56–60.
N. Dershowitz and J.-P. Jouannaud. Rewrite systems. In J. van Leeuwen, editor, Formal Models and Semantics, volume B of Handbook of Theoretical Computer Science, chapter 6, pages 243–320. Elsevier, Amsterdam, 1990.
G. Grätzer. Universal Algebra. Springer-Verlag, New York-Heidelberg-Berlin, second edition, 1979.
A. Miola, editor. Design and Implementation of Symbolic Computation Systems (DISCO '90), volume 429 of Lecture Notes in Computer Science, Capri, Italy, April 1990. Springer-Verlag.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Weber, A. (1993). A type-coercion problem in computer algebra. In: Calmet, J., Campbell, J.A. (eds) Artificial Intelligence and Symbolic Mathematical Computing. AISMC 1992. Lecture Notes in Computer Science, vol 737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57322-4_13
Download citation
DOI: https://doi.org/10.1007/3-540-57322-4_13
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57322-7
Online ISBN: 978-3-540-48063-1
eBook Packages: Springer Book Archive