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

Published online by Cambridge University Press:  27 May 2011

MURDOCH J. GABBAY
MURDOCH J. GABBAY*
Affiliation:
School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, Scotland
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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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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 21 , Issue 5 , October 2011 , pp. 997 - 1033
Copyright
Copyright © Cambridge University Press 2011

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