Skip to main content
SpringerLink
Log in

On typed calculi with a merge operator

  • Semantics
  • Conference paper
  • First Online:
Foundation of Software Technology and Theoretical Computer Science (FSTTCS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 880))

Abstract

Extensions of the simply typed lambda calculus with a merge operator are defined and investigated. A merge of functions denotes a function which can be applied to more than one type and computes the result by merging the results of the component functions. We propose first two calculi in which the inconsistency between the return values of the component functions is solved using a non-symmetric rule, and show that they do not have good proof-theoretic properties: one does not have the Strong Normalization Property, and the other does not have the Transitivity of Coercions Property. Then, using the type system, we restrict the two calculi in a way that terms which may cause inconsistency are excluded, and show that the two calculi become equivalent and have all the desired properties.

A merge of functions in object oriented programming corresponds to writing a method in a subclass by modifying those in superclasses, and the above restriction corresponds to only allowing adding some behaviors in the modification. This result conforms with the programming methodology in which one should write a subclass method so that it does not override the behavior of superclass methods.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Castagna. A meta-language for typed object-oriented languages. In 13th Conference on the Foundations of Software Technology and Theoretical Computer Science, number 761 in LNCS, Bombay, India, 1993.

    Google Scholar 

  2. F. Cardone and M. Coppo. Two extensions of curry's type inference system. In Logic and Computer Science, pp. 19–66. Academic Press, 1990.

    Google Scholar 

  3. Giuseppe Castagna, Giorgio Ghelli, and Giuseppe Longo. A calculus for overloaded functions with subtyping. Information and Computation, Vol. to appear, 1994.

    Google Scholar 

  4. R. Hasegawa. Parametricity of extensionally collapsed term models of polymorphism and their categorical properties. In Theoretical Aspects of Computer Software, volume 526 of Lecture Notes in Computer Science, pp. 495–512, 1991.

    Google Scholar 

  5. R. Harper and B. Pierce. A record calculus based on symmetric concatenation. In Proc. The Eighteenth Annual Symp. on Principles of Programming Languages, pp. 131–142, 1991.

    Google Scholar 

  6. R. Milner. Fully abstract models of typed λ-calculus. Theoret. Corn-put. Sci, Vol. 4, pp. 1–22, 1977.

    Google Scholar 

  7. Gennaro Monteleone. Generalized conjunctive types. In Proc. The Sixteenth Annual Symposium on Principles of Programming Languages, pp. 242–249. ACM, 1989.

    Google Scholar 

  8. A. Ohori and P. Buneman. Type inference in a database programming language. In Proc. AC Conf. on LISP and Functional Programming, pp. 174–183, 1988.

    Google Scholar 

  9. Didier Remy. Typing record concatenation for free. In Proc. The Nineteenth Annual Symposium on Principles of Programming Languages, pp. 166–176. ACM, 1992.

    Google Scholar 

  10. J. C. Reynolds. Using category theory to design implicit conversions and generic operators. In Lecture Notes in Computer Science, 94. Springer-Verlag, 1981.

    Google Scholar 

  11. J. C. Reynolds. Types, abstraction, and parametric polymorphism. In R. E. A. Mason, editor, Information Processing 83, pp. 513–523. North-Holland, 1983.

    Google Scholar 

  12. John C. Reynolds. Preliminary design of the programming language Forsythe. Technical Report CMU-CS-88-159, Carnegie Mellon University, June 1988.

    Google Scholar 

  13. Hideki Tsuiki. A Record Calculus with a Merge Operator. PhD thesis, Keio University, 1992.

    Google Scholar 

  14. Hideki Tsuiki, A normalizing calculus with overloading and subtyping. In 2'nd Int. Symp. on Theoretical Aspects of Computer Software, LNCS 789, pp. 273–295, 1994.

    Google Scholar 

  15. Mitchell Wand. Type inference for record concatenation and multiple inheritance. In Proc. Fourth IEEE Annual Symp. on Logic in Computer Science, pp. 92–97, 1989.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Kyoto-Sangyo University Kamigamo Motoyama, Kita-ku, Kyoto 606, Japan

    Hideki Tsuiki

Authors
  1. Hideki Tsuiki
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

P. S. Thiagarajan

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Tsuiki, H. (1994). On typed calculi with a merge operator. In: Thiagarajan, P.S. (eds) Foundation of Software Technology and Theoretical Computer Science. FSTTCS 1994. Lecture Notes in Computer Science, vol 880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58715-2_117

Download citation

  • DOI: https://doi.org/10.1007/3-540-58715-2_117

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58715-6

  • Online ISBN: 978-3-540-49054-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation