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\begin{document}

\title{Proof Pearl: A New Foundation for Nominal Isabelle}

\author{Brian Huffman\inst{1} and Christian Urban\inst{2}}

\institute{Portland State University \and Technical University of Munich}

\maketitle

\begin{abstract}

Pitts et al introduced a beautiful theory about names and binding based on the

notions of permutation and support. The engineering challenge is to smoothly

adapt this theory to a theorem prover environment, in our case Isabelle/HOL.

We present a formalisation of this work that differs from our earlier approach

in two important respects: First, instead of representing permutations as

lists of pairs of atoms, we now use a more abstract representation based on

functions.  Second, whereas the earlier work modeled different sorts of atoms

using different types, we now introduce a unified atom type that includes all

sorts of atoms. Interestingly, we allow swappings, that is permutations build up by

two atoms, to be ill-sorted.  As a result of these design changes, we can iron

out inconveniences for the user, considerably simplify proofs and also

drastically reduce the amount of custom ML-code. Furthermore we can extend the

capabilities of Nominal Isabelle to deal with variables that carry additional

information. We end up with a pleasing and formalised theory of permutations

and support, on which we can build an improved and more powerful version of

Nominal Isabelle.

\end{abstract}

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\end{document}

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