Advertisement

A type-coercion problem in computer algebra

  • Andreas Weber
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 737)

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.

Keywords

Computer algebra type systems subtyping type coercion type inference order-sorted rewriting universal algebra 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    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.Google Scholar
  2. 2.
    J. H. Davenport and B. M. Trager. Scratchpad's view of algebra I: Basic commutative algebra. In Miola [10]., pages 40–54.Google Scholar
  3. 3.
    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.Google Scholar
  4. 4.
    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.Google Scholar
  5. 5.
    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.Google Scholar
  6. 6.
    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.Google Scholar
  7. 7.
    A. Fortenbacher. Efficient type inference and coercion in computer algebra. In Miola [10]., pages 56–60.Google Scholar
  8. 8.
    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.Google Scholar
  9. 9.
    G. Grätzer. Universal Algebra. Springer-Verlag, New York-Heidelberg-Berlin, second edition, 1979.Google Scholar
  10. 10.
    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.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Andreas Weber
    • 1
  1. 1.Wilhelm-Schickard-InstitutUniversität TübingenTübingenGermany

Personalised recommendations