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International Workshop on Types for Proofs and Programs

TYPES 2002: Types for Proofs and Programs pp 220–239Cite as

Weak Transitivity in Coercive Subtyping

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2646))

Abstract

Coercive subtyping is a general approach to subtyping, inheritance and abbreviation in dependent type theories. A vital requirement for coercive subtyping is that of coherence which essentially says that coercions between any two types must be unique. Another important task for coercive subtyping is to prove the admissibility or elimination of transitivity and substitution. In this paper, we propose and study the notion of Weak Transitivity, consider suitable subtyping rules for certain parameterised inductive types and prove its coherence and the admissibility of substitution and weak transitivity in the coercive subtyping framework.

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References

  1. P. Aczel. Simple overloading for type theories. Draft, 1994.

    Google Scholar 

  2. B. Barras et al. The Coq Proof Assistant Reference Manual (Version 6.3.1). INRIA-Rocquencourt, 2000.

    Google Scholar 

  3. A. Bailey. The Machine-checked Literate Formalisation of Algebra in Type Theory. PhD thesis, University of Manchester, 1998.

    Google Scholar 

  4. V. Breazu-Tannen, T. Coquand, C. Gunter, and A. Scedrov. Inheritance and explicit coercion. Information and Computation, 93, 1991.

    Google Scholar 

  5. G. Barthe and M.J. Frade. Constructor subtyping. Proceedings of ESOP’99, LNCS 1576, 1999.

    Google Scholar 

  6. G. Barthe and F. van Raamsdonk. Constructor subtyping in the calculus of inductive constructions. Proceedings of FOSSACS’00, LNCS 1784, 2000.

    Google Scholar 

  7. G. Chen. Subtyping, Type Conversion and Transitivity Elimination. PhD thesis, University of Paris VII, 1998.

    Google Scholar 

  8. P. Callaghan and Z. Luo. An implementation of LF with coercive subtyping and universes. Journal of Automated Reasoning, 27(1):3–27, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  9. P. C. Callaghan, Z. Luo, and J. Pang. Object languages in a type-theoretic meta-framework. Workshop of Proof Transformation and Presentation and Proof Complexities (PTP’01), 2001.

    Google Scholar 

  10. R. Harper, F. Honsell, and G. Plotkin. A framework for defining logics. Proc. 2nd Ann. Symp. on Logic in Computer Science. IEEE, 1987.

    Google Scholar 

  11. A. Jones, Z. Luo, and S. Soloviev. Some proof-theoretic and algorithmic aspects of coercive subtyping. Types for proofs and programs (eds, E. Gimenez and C. Paulin-Mohring), Proc. of the Inter. Conf. TYPES’96, LNCS 1512, 1998.

    Chapter  Google Scholar 

  12. Z. Luo and P. Callaghan. Coercive subtyping and lexical semantics (extended abstract). LACL’98, 1998.

    Google Scholar 

  13. Y. Luo and Z. Luo. Coherence and transitivity in coercive subtyping. In R. Nieuwenhuis and A. Voronkov, editors, 8th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, volume 2250 of LNAI, pages 249–265. Springer-Verlag, 2001.

    Google Scholar 

  14. G. Longo, K. Milsted, and S. Soloviev. A logic of subtyping. In Proc. of LICS’95, 1995.

    Google Scholar 

  15. Z. Luo and R. Pollack. LEGO Proof Development System: User’s Manual. LFCS Report ECS-LFCS-92-211, Department of Computer Science, University of Edinburgh, 1992.

    Google Scholar 

  16. Z. Luo and S. Soloviev. Dependent coercions. The 8th Inter. Conf. on Category Theory and Computer Science (CTCS’99), Edinburgh, Scotland. Electronic Notes in Theoretical Computer Science, 29, 1999.

    Google Scholar 

  17. Z. Luo. Computation and Reasoning: A Type Theory for Computer Science. Oxford University Press, 1994.

    Google Scholar 

  18. Z. Luo. Coercive subtyping in type theory. Proc. of CSL’96, the 1996 Annual Conference of the European Association for Computer Science Logic, Utrecht. LNCS 1258, 1997.

    Google Scholar 

  19. Z. Luo. Coercive subtyping. Journal of Logic and Computation, 9(1):105–130, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  20. P. Martin-Löf. Intuitionistic Type Theory. Bibliopolis, 1984.

    Google Scholar 

  21. B. Nordström, K. Petersson, and J. Smith. Programming in Martin-Löf’s Type Theory: An Introduction. Oxford University Press, 1990.

    Google Scholar 

  22. A. Saibi. Typing algorithm in type theory with inheritance. Proc of POPL’97, 1997.

    Google Scholar 

  23. S. Soloviev and Z. Luo. Coercion completion and conservativity in coercive subtyping. Annals of Pure and Applied Logic, 2002.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Durham, South Road, Durham, DH1 3LE, UK

    Yong Luo & Zhaohui Luo

  2. IRIT Univ. Paul Sabatier (Toulouse -III), 118 route de Narbonne, 31000, Toulouse, France

    Sergei Soloviev

Authors
  1. Yong Luo
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  2. Zhaohui Luo
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  3. Sergei Soloviev
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Nijmegen, Toernooiveld 1, 6525 ED, Nijmegen, The Netherlands

    Herman Geuvers  & Freek Wiedijk  & 

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© 2003 Springer-Verlag Berlin Heidelberg

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Luo, Y., Luo, Z., Soloviev, S. (2003). Weak Transitivity in Coercive Subtyping. In: Geuvers, H., Wiedijk, F. (eds) Types for Proofs and Programs. TYPES 2002. Lecture Notes in Computer Science, vol 2646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39185-1_13

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  • DOI: https://doi.org/10.1007/3-540-39185-1_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-14031-3

  • Online ISBN: 978-3-540-39185-2

  • eBook Packages: Springer Book Archive

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