Advertisement

An algebraic implementation of packages

  • Snorri Agnarsson
  • M. S. Krishnamoorthy
  • B. David Saunders
Computer Algebra Systems Implementation I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 204)

Abstract

An implementation of packages is described. The implementation is based on viewing packages as substitutions. Using a few operations on packages it is possible to build any package, from a small collection of basic packages. Generic packages can be built, that can be used as building blocks for new packages. The packages defined by the model lend themselves well to algebraic manipulation.

Keywords

Variable Node Regular Tree Generic Package Finite Tree Euclidean Domain 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

8. References

  1. [Ada-80]
    Ada Programming Language, MIL-STD-1815, 10 December 1980.Google Scholar
  2. [Agnarsson-85a]
    Agnarsson, S. and M. S. Krishnamoorthy, Towards a Theory of Packages, to appear in proceedings of SIGPLAN '85, 1985.Google Scholar
  3. [Agnarsson-85b]
    Agnarsson, S., Packages as Substitutions, Forthcoming Ph.D. Thesis, RPI, Troy, NY, April 1985.Google Scholar
  4. [Bloom-80]
    Bloom, Stephen L., Calvin C. Elgot and Jesse B. Wright, Solutions of the Iteration Equation and Extensions of the Scalar Iteration Operation, SIAM Journal of Computing, 9, No. 1, February 1980.Google Scholar
  5. [Bloom-83a]
    Bloom, Stephen L., James W. Thatcher, Eric G. Wagner and Jesse B. Wright, Recursion and Iteration in Continuous Theories: The "M-Construction", Journal of Computer and System Sciences, 27 (1983) 148–164.Google Scholar
  6. [Bloom-83b]
    Bloom, Stephen L., All Solutions of a System of Recursion Equations in Infinite Trees and Other Contraction Theories, Journal of Computer and System Sciences, 27 (1983) 225–255.Google Scholar
  7. [Burstall-84a]
    Burstall, R., Programming with Modules as Typed Functional Programming, Proc. International Conference on Fifth Generation Computing Systems, Tokyo, November 1984.Google Scholar
  8. [Burstall-84b]
    Burstall, R. and B. Lampson, A Kernel Language for Abstract Data Types and Modules, Lecture Notes in Computer Science, Vol. 173, Springer-Verlag, New York, 1984.Google Scholar
  9. [Courcelle-78]
    Courcelle, B., A representation of trees by languages, Theoretical Computer Science, 6 (1978) 225–279 and 7 (1978) 25–55.Google Scholar
  10. [Courcelle-79]
    Courcelle, B., Infinite Trees in Normal Form and Recursive Equations Having a Unique Solution, Mathematical Systems Theory, 13 (1979) 131–180.CrossRefGoogle Scholar
  11. [Courcelle-83]
    Courcelle, B., Fundamental Properties of Infinite Trees, Theoretical Computer Science, 25 (1983) 95–169.CrossRefGoogle Scholar
  12. [Demers-80a]
    Demers, A. J., and J. E. Donahue, "Type Completeness" as a Language Principle, Proceedings Seventh Annual Principles of Programming Languages Symposium, 1980, pp. 234–244.Google Scholar
  13. [Demers-80b]
    Demers, A. J., and J. E. Donahue, Data Types, Parameters and Type Checking, Proceedings Seventh Annual Principles of Programming Languages Symposium, 1980, pp. 12–23.Google Scholar
  14. [Gallier-81]
    Gallier, J. DPDA's in’ atomic normal form’ and applications to the equivalence problems, Theoretical Computer Science, 14 (1981) 155–186.Google Scholar
  15. [Ginali-79]
    Ginali, Susanna, Regular Trees and the Free Iterative Theory, Journal of Computer and System Sciences, 18 (1979) 228–242.Google Scholar
  16. [Goguen-84]
    Goguen, Joseph A., Parameterized Programming, IEEE Transactions on Software Engineering, Vol. SE-10, 5, September 1984.Google Scholar
  17. [Jenks-84]
    Jenks, R. D., A Primer: 11 Keys to New Scratchpad, Lecture Notes in Computer Science, Vol. 174. Springer-Verlag, New York, 1984.Google Scholar
  18. [Liskov-81]
    Liskov, Barbara, Russell Atkinson, Toby Bloom, Eliot Moss, J. Craig Schaffert, Robert Scheifler and Alan Snyder, CLU Reference Manual, Lecture Notes in Computer Science, Vol. 114, Springer-Verlag, New York, 1981.Google Scholar
  19. [Milner-78]
    Milner, R., A Theory of Type Polymorphism in Programming. Journal of Computer and System Sciences 17, 348–375 (1978).CrossRefGoogle Scholar
  20. [Reynolds-70]
    Reynolds, John C., GEDANKEN — A Simple Typeless Language Based on the Principle of Completeness and the Reference Concept, Communications of the ACM 17, no. 5, pp. 308–319, May, 1970.Google Scholar
  21. [Wirth-83]
    Wirth, Niklaus, Programming in MODULA-2, Springer-Verlag, New York, 1983.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Snorri Agnarsson
    • 1
  • M. S. Krishnamoorthy
    • 1
  • B. David Saunders
    • 2
  1. 1.Department of Computer ScienceRensselaer Polytechnic InstituteTroyUSA
  2. 2.Department of Computer and Information SciencesUniversity of DelawareNewarkUSA

Personalised recommendations