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Subtyping Union Types

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Computer Science Logic (CSL 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3210))

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Abstract

Subtyping can be fairly complex for union types, due to interactions with other types, such as function types. Furthermore, these interactions turn out to depend on the calculus considered: for instance, a call-by-value calculus and a call-by-name calculus will have different possible subtyping rules. In order to abstract ourselves away from this dependence, we consider a fairly large class of calculi. This allows us to find a subtyping relation which is both robust (it is sound for all calculi) and precise (it is complete with respect to the class of calculi).

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References

  1. Damm, F.: Subtyping with union types, intersection types and recursive types II. Research Report 2259, INRIA Rennes (1994)

    Google Scholar 

  2. Vouillon, J.: Subtyping union types (extended version). Manuscript (2004), available from http://www.pps.jussieu.fr/~vouillon/publi/#union

  3. Vouillon, J., Melliès, P.A.: Semantic types: A fresh look at the ideal model for types. In: Proceedings of the 31th ACM Conference on Principles of Programming Languages, Venezia, Italia, pp. 52–63. ACM Press, New York (2004)

    MATH  Google Scholar 

  4. Melliès, P.A., Vouillon, J.: Recursive polymorphic types and parametricity in an operational framework. Preprint PPS//04/06//no 30 (2004), available from http://www.pps.jussieu.fr/~vouillon/publi/#semtypes2

  5. Girard, J.Y.: Interprétation fonctionelle et élimination des coupures dans l’arithm étique d’ordre supérieur. Th‘ese de doctorat d’État, University of Paris VII (1972)

    Google Scholar 

  6. Coq Development Team: The Coq Proof Assistant Reference Manual – Version V7.4 (2003), Available from http://coq.inria.fr/doc/main.html

  7. MacQueen, D., Plotkin, G., Sethi, R.: An ideal model for recursive polymorphic types. Information and Control 71, 95–130 (1986)

    Article  MathSciNet  Google Scholar 

  8. Girard, J.Y.: Linear logic. Theoretical Computer Science 50, 1–102 (1987)

    Article  MathSciNet  Google Scholar 

  9. Danos, V., Krivine, J.L.: Disjunctive tautologies and synchronisation schemes. In: Clote, P.G., Schwichtenberg, H. (eds.) CSL 2000. LNCS, vol. 1862, pp. 292–301. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  10. Krivine, J.L.: Typed lambda-calculus in classical Zermelo-Fraenkel set theory. Archive of Mathematical Logic 40, 189–205 (2001)

    Article  MathSciNet  Google Scholar 

  11. Pitts, A.M.: Parametric polymorphism and operational equivalence. Mathematical Structures in computer Science 10, 321–359 (2000)

    Article  MathSciNet  Google Scholar 

  12. Frisch, A., Castagna, G., Benzaken, V.: Semantic subtyping. In: 17th IEEE Symposium on Logic in Computer Science, pp. 137–146. IEEE Computer Society Press, Los Alamitos (2002)

    Google Scholar 

  13. Hosoya, H., Vouillon, J., Pierce, B.C.: Regular expression types for XML. In: Proceedings of the International Conference on Functional Programming, ICFP (2000)

    Google Scholar 

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Author information

Authors and Affiliations

  1. CNRS and Université Paris 7, Case 7014, 2 Place Jussieu, 75251 Cedex 05, Paris, France

    Jérôme Vouillon

Authors
  1. Jérôme Vouillon
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Editor information

Editors and Affiliations

  1. Wroclaw University, Poland

    Jerzy Marcinkowski

  2. Polish Academy of Sciences, Institute of Computer Science, Poland

    Andrzej Tarlecki

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© 2004 Springer-Verlag Berlin Heidelberg

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Vouillon, J. (2004). Subtyping Union Types. In: Marcinkowski, J., Tarlecki, A. (eds) Computer Science Logic. CSL 2004. Lecture Notes in Computer Science, vol 3210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30124-0_32

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  • DOI: https://doi.org/10.1007/978-3-540-30124-0_32

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23024-3

  • Online ISBN: 978-3-540-30124-0

  • eBook Packages: Springer Book Archive

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