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International Workshop on Computer Science Logic

CSL 2008: Computer Science Logic pp 446–460Cite as

Syntactic Metatheory of Higher-Order Subtyping

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5213))

Abstract

We present a new proof of decidability of higher-order subtyping in the presence of bounded quantification. The algorithm is formulated as a judgement which operates on beta-eta-normal forms. Transitivity and closure under application are proven directly and syntactically, without the need for a model construction or reasoning on longest beta-reduction sequences. The main technical tool is hereditary substitution, i.e., substitution of one normal form into another, resolving all freshly generated redexes on the fly. Hereditary substitutions are used to keep types in normal-form during execution of the subtyping algorithm. Termination of hereditary substitutions can be proven in an elementary way, by a lexicographic induction on the kind of the substituted variable and the size of the expression substituted into—this is what enables a purely syntactic metatheory.

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Authors and Affiliations

  1. Department of Computer Science, University of Munich, Oettingenstr. 67, D-80538, München, Germany

    Andreas Abel & Dulma Rodriguez

Authors
  1. Andreas Abel
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  2. Dulma Rodriguez
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Michael Kaminski Simone Martini

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© 2008 Springer-Verlag Berlin Heidelberg

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Abel, A., Rodriguez, D. (2008). Syntactic Metatheory of Higher-Order Subtyping. In: Kaminski, M., Martini, S. (eds) Computer Science Logic. CSL 2008. Lecture Notes in Computer Science, vol 5213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87531-4_32

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  • DOI: https://doi.org/10.1007/978-3-540-87531-4_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87530-7

  • Online ISBN: 978-3-540-87531-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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