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A type system for computer algebra

  • Philip S. Santas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 722)

Abstract

We examine type systems for support of subtypes and categories in computer algebra systems. By modelling representation of instances in terms of existential types instead of recursive types, we obtain not only a simplified model, but we build a basis for defining subtyping among algebraic domains. The introduction of metaclasses, facilitates the task, by allowing the inference of type classes. By means of type classes and existential types we construct subtype relations without involving coercions.

Keywords

Type System Type Class Computer Algebra System Class Intersection Type Inference 
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.

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References

  1. [BrMi92]
    K. Bruce, J. Mitchell. PER models of subtyping, recursive types and higher order poly morphism. 19th ACM Symposium on Principles of Programming Languages. New Mexico, Jan.1992.Google Scholar
  2. [Car88]
    L. Cardelli. Structural Subtyping and the notion of Power Type. 15th ACM Sumposium POPL. CA, Jan. 1988.Google Scholar
  3. [Car92]
    L. Cardelli. Typed Foundations for object-oriented programming. Tutorial at POPL, Jan. 1992.Google Scholar
  4. [CaWe85]
    L. Cardelli, P. Wegner. On understanding types, data abstraction, and polymorphism. Computing Surveys. 17(4). 1985.Google Scholar
  5. [CoHiC90]
    W. Cook, W. Hill, P. Canning. Inheritance is not Subtyping. 17thPOPL, ACM Press, Jan 1990.Google Scholar
  6. [Ghe91]
    G. Ghelli. Modelling features of object-oriented languages in second order functional languages with subtypes. in Foundations of OOP. Lecture Notes in Computer Science (489). Springer Verlag, 1991.Google Scholar
  7. [Gold89]
    A. Goldberg. Smalltalk-80. second edition, Addison-Wesley, 1989.Google Scholar
  8. [Gro91]
    P. Grogono. The Dee Report. Technical Report. CS, Concordia U. Montreal, Canada. Jan. 1991.Google Scholar
  9. [GrSa93]
    P. Grogono, P.S. Santas. On Equality and Abstractions. To be published at JOOP.Google Scholar
  10. [JeSu92]
    R.D. Jenks, R.S. Sutor. Axiom: The Scientific Computation System. NAG. Springer Ve rlag. 1992.Google Scholar
  11. [JTWS85]
    R.D. Jenks, B. Trager, S. M. Watt, R S. Sutor. Scratchpad II Programming Language Manual, IBM, 1985.Google Scholar
  12. [Mey91]
    B. Meyer. Eiffel: The language. Prentice Hall. 1991.Google Scholar
  13. [Mit88]
    J. Mitchell. Polymorphic type Inference and containement. Information and Computation (76). 1988.Google Scholar
  14. [MiMM91]
    J. Mitchell, S. Meldal, N. Madhav. An extension of SML modules with subtyping and inheritance. 18th Sumposium POPL, FL, Jan. 1991.Google Scholar
  15. [MiPl88]
    J. Mitchell, G. Plotkin. Abstract Types have Existential Type. ACM Transactions on Programming Languages and Systems. 10(3), 1988.Google Scholar
  16. [Pier91]
    B. Pierce. Programming with Intersection Types and Bounded Polymorphism. PhD thesis, CMU. Dec 1991.Google Scholar
  17. [PiTu92]
    B. Pierce, D. Turner. Type Theoretic Foundations for OOP. Report. Dept of CS, U. of Edinbourgh. 1992.Google Scholar
  18. [San93]
    P.S. Santas. Classes and Metaclasses. tech. report, Dept. of CS, ETH Zurich. 1993.Google Scholar
  19. [San92]
    P.S. Santas. Multiple Subclassing and Subtyping for Symbolic Computation. Proc. of Workshop on Multiple Inheritance and Multiple Subtyping. ECOOP 92. Utrecht, Netherlands. June 1992.Google Scholar
  20. [SuJe87]
    R.S. Sutor, R.D.Jenks. The Type Inference and Coercion facilities of the Scratchpad II Interpreter. IBM Tech. Report. March 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Philip S. Santas
    • 1
  1. 1.Institute of Scientific ComputationETH ZurichSwitzerland

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