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Implicit coercions in type systems

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Types for Proofs and Programs (TYPES 1995)

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Abstract

We propose a notion of pure type system with implicit coercions. In our framework, judgements are extended with a context of coercions Δ and the application rule is modified so as to allow coercions to be left implicit. The setting supports multiple inheritance and can be applied to all type theories with Π-types. One originality of our work is to propose a computational interpretation for implicit coercions. In this paper, we demonstrate how this interpretation allows a strict control on the logical properties of pure type systems with implicit coecions.

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References

  1. P. Aczel. A notion of class for type theory. Note, 1995.

    Google Scholar 

  2. D. Aspinall and A. Compagnoni. Subtyping dependent types. In Proceedings of LICS'96. IEEE Computer Society Press, 1996. To appear.

    Google Scholar 

  3. A. Bailey. Lego with classes. Note, 1995.

    Google Scholar 

  4. G. Barthe. Formalising algebra in type theory: fundamentals and applications to group theory. Manuscript. An earlier version appeared as technical report CSI-R9508, University of Nijmegen, under the title ‘Formalising mathematics in type theory: fundamentals and case studies', 1995.

    Google Scholar 

  5. G. Betarte and A. Tasistro. Extension of Martin-Löf's theory of types with record types and subtyping: motivation, rules and type checking. Manuscript, 1995.

    Google Scholar 

  6. G. Betarte and A. Tasistro. Formalisation of systems of algebras using dependent record types and subtyping: an example. Manuscript, 1995.

    Google Scholar 

  7. R.L. Constable, S.F. Allen, H.M. Bromley, W.R. Cleaveland, J.F. Cremer, R.W. Harper, D.J. Howe, T.B. Knoblock, N.P. Mendler, P. Panangaden, J.T. Sasaki, and S.F. Smith. Implementing Mathematics with the NuPrl Development System. Prentice-Hall, inc., Englewood Cliffs, New Jersey, first edition, 1986.

    Google Scholar 

  8. N.G. de Bruijn. The mathematical vernacular, a language for mathematics with typed sets. In R. Nederpelt, H. Geuvers, and R. de Vrijer, editors, Selected papers on Automath, volume 133 of Studies in Logic and the Foundations of Mathematics, pages 865–935. North-Holland, Amsterdam, 1994.

    Google Scholar 

  9. C.A. Gunter and J.C. Mitchell. Theoretical Aspects of Object-Oriented Programming: Types, Semantics and Language Design. The MIT Press, 1994.

    Google Scholar 

  10. P. Hudak, S.L. Peyton Jones, P.L. Wadler, Arvind, B. Boutel, J. Fairbairn, J. Fasel, K. Guzman, K. Hammond, J. Hughes, T. Johnsson, R. Kieburtz, R.S. Nikhil, W. Partain, and J. Peterson. Report on the functional programming language Haskell, version 1.2. Special Issue of SIGPLAN Notices, 27, 1992.

    Google Scholar 

  11. M. Jones. Introduction to Gofer. Included as part of the Gofer distribution. Available by anonymous ftp from nebula.cs.yale.edu in the directory pub/haskell/gofer, 1991.

    Google Scholar 

  12. M. Jones. A system of constructor classes: overloading and implicit higher-order polymorphism. Journal of Functional Programming, pages 1–25, January 1995.

    Google Scholar 

  13. Z. Luo. Computation and Reasoning: A Type Theory for Computer Science. Number 11 in International Series of Monographs on Computer Science. Oxford University Press, 1994.

    Google Scholar 

  14. Z. Luo. Coercive subtyping. Draft, 1995.

    Google Scholar 

  15. F. Pfenning. Refinement types for logical frameworks. In H. Geuvers, editor, Informal Proceedings of TYPES'93, pages 285–299, 1993. Available from http://www.dcs.ed.ac.uk/lfcsinfo/research/types-bra/proc/index.html.

    Google Scholar 

  16. R. Pollack. Implicit syntax. In G. Huet and G. Plotkin, editors, Informal Proceedings of First Workshop on Logical Frameworks, Antibes, May 1990.

    Google Scholar 

  17. L. S. van Benthem Jutting. Typing in pure type systems. Information and Computation, 105(1):30–41, July 1993.

    Google Scholar 

  18. P. Wadler and S. Blott. How to make ad hoc polymorphism less ad hoc. In Proceedings of POPL'89, pages 60–76. ACM Press, 1989.

    Google Scholar 

  19. A. Wikström. Functional Progrmmaming using Standard ML. Interntional Series in Computer Science. Prenctice Hall, 1987.

    Google Scholar 

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Stefano Berardi Mario Coppo

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© 1996 Springer-Verlag Berlin Heidelberg

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Barthe, G. (1996). Implicit coercions in type systems. In: Berardi, S., Coppo, M. (eds) Types for Proofs and Programs. TYPES 1995. Lecture Notes in Computer Science, vol 1158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61780-9_58

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  • DOI: https://doi.org/10.1007/3-540-61780-9_58

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61780-8

  • Online ISBN: 978-3-540-70722-6

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