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\documentclass{svjour3}
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\usepackage{times}
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\usepackage{isabelle}
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\usepackage{isabellesym}
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\usepackage{amsmath}
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\usepackage{amssymb}
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\usepackage{mathabx}
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\usepackage{proof}
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\usepackage{longtable}
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\usepackage{graphics}
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\usepackage{pdfsetup}
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\urlstyle{rm}
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\isabellestyle{it}
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\renewcommand{\isastyle}{\isastyleminor}
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\renewcommand{\isacharunderscore}{\mbox{$\_\!\_$}}
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\renewcommand{\isasymbullet}{{\raisebox{-0.4mm}{\Large$\boldsymbol{\cdot}$}}}
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\def\dn{\,\stackrel{\mbox{\scriptsize def}}{=}\,}
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\renewcommand{\isasymequiv}{$\dn$}
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\renewcommand{\isasymiota}{}
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\renewcommand{\isasymrightleftharpoons}{}
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\renewcommand{\isasymemptyset}{$\varnothing$}
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\newcommand{\isasymallatoms}{\ensuremath{\mathbb{A}}}
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\newcommand{\rrh}{\mbox{\footnotesize$\rightrightharpoons$}}
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\newcommand{\numbered}[1]{\refstepcounter{equation}{\rm(\arabic{equation})}\label{#1}}
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\newcommand\new[0]{\reflectbox{\ensuremath{\mathsf{N}}}}
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\changenotsign
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\begin{document}
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\title{Implementing the Nominal Logic Work in Isabelle/HOL}
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\author{Christian Urban \and Brian Huffman}
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\institute{C.~Urban \at Technical University of Munich
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\and B.~Huffman \at Portland State University}
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\date{Received: date / Accepted: date}
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\maketitle
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\begin{abstract}
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In his nominal logic work, Pitts introduced a beautiful theory about names and
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binding based on the notions of atoms, permutations and support. The
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engineering challenge is to smoothly adapt this theory to a theorem prover
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environment, in our case Isabelle/HOL. For this we have to formulate the
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theory so that it is compatible with Higher-Order Logic, which the original formulation by
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Pitts is not. We achieve this by not requiring that every construction has
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to have finite support. We present a formalisation that is based on a
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unified atom type and that represents permutations by bijective functions from
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atoms to atoms. Interestingly, we allow swappings, which are permutations
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build from two atoms, to be ill-sorted. We also describe a reasoning infrastructure
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that automates properties about equivariance, and present a formalisation of
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two abstraction operators that bind sets of names.
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\end{abstract}
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% generated text of all theories
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\input{session}
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% optional bibliography
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\bibliographystyle{abbrv}
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\bibliography{root}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: t
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%%% End:
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