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  • Cited by 4
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Dowek, Gilles and Gabbay, Murdoch J. 2012. PNL to HOL: From the logic of nominal sets to the logic of higher-order functions. Theoretical Computer Science, Vol. 451, p. 38.


    Gabbay, M. J. 2012. Meta-variables as infinite lists in nominal terms unification and rewriting. Logic Journal of IGPL, Vol. 20, Issue. 6, p. 967.


    Gabbay, Murdoch J. 2012. Finite and infinite support in nominal algebra and logic: nominal completeness theorems for free. The Journal of Symbolic Logic, Vol. 77, Issue. 03, p. 828.


    Gabbay, Murdoch J. and Mulligan, Dominic P. 2011. Nominal Henkin Semantics: simply-typed lambda-calculus models in nominal sets. Electronic Proceedings in Theoretical Computer Science, Vol. 71, p. 58.


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  • Mathematical Structures in Computer Science, Volume 21, Issue 5
  • October 2011, pp. 997-1033

Two-level nominal sets and semantic nominal terms: an extension of nominal set theory for handling meta-variables

  • MURDOCH J. GABBAY (a1)
  • DOI: http://dx.doi.org/10.1017/S0960129511000272
  • Published online: 27 May 2011
Abstract

Nominal sets are a sets-based first-order denotation for variables in logic and programming. In this paper we extend nominal sets to two-level nominal sets. These preserve much of the behaviour of nominal sets, including notions of variable and abstraction, but they include a denotation for both variables and meta-variables. Meta-variables are interpreted as infinite lists of distinct variable symbols. We use two-level sets to define, amongst other things, a denotation for meta-variable abstraction, and nominal style datatypes of syntax-with-binding with meta-variables. We discuss the connections between this and nominal terms and prove a soundness result.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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