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


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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J. R. Hindley and J. P. Seldin (2008) Lambda-Calculus and Combinators, An Introduction, 2nd editionCambridge University Press.

N. Tzevelekos (2007) Full abstraction for nominal general references. In: Proceedings of the 22nd IEEE Symposium on Logic in Computer Science (LICS 2007), IEEE Computer Society Press399410.

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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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