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Coercive subtyping in type theory

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Book cover Computer Science Logic (CSL 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1258))

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Abstract

We propose and study coercive subtyping, a formal extension with subtyping of dependent type theories such as Martin-Löf's type theory [NPS90] and the type theory UTT [Luo94]. In this approach, subtyping with specified implicit coercions is treated as a feature at the level of the logical framework; in particular, subsumption and coercion are combined in such a way that the meaning of an object being in a supertype is given by coercive definition rules for the definitional equality. It is shown that this provides a conceptually simple and uniform framework to understand subtyping and coercion relations in type theories with sophisticated type structures such as inductive types and universes. The use of coercive subtyping in formal development and in reasoning about subsets of objects is discussed in the context of computer-assisted formal reasoning.

This work is partly supported by the UK EPSRC grant on ‘Subtyping, Inheritance and Reuse’ (GR/K79130).

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Authors and Affiliations

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

    Zhaohui Luo

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  1. Zhaohui Luo
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Dirk van Dalen Marc Bezem

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© 1997 Springer-Verlag Berlin Heidelberg

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Luo, Z. (1997). Coercive subtyping in type theory. In: van Dalen, D., Bezem, M. (eds) Computer Science Logic. CSL 1996. Lecture Notes in Computer Science, vol 1258. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63172-0_45

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  • DOI: https://doi.org/10.1007/3-540-63172-0_45

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  • Print ISBN: 978-3-540-63172-9

  • Online ISBN: 978-3-540-69201-0

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