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\title{Abstract Rewriting}
\author{Christian Sternagel and Ren\'e Thiemann}
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\begin{abstract}
We present an Isabelle formalization of abstract rewriting (see, e.g.,
\cite{BaaderNipkow}). First, we define standard relations like
\emph{joinability}, \emph{meetability}, \emph{conversion}, etc. Then, we
formalize important properties of abstract rewrite systems, e.g.,
confluence and strong normalization. Our main concern is on strong
normalization, since this formalization is the basis of \cite{CeTA} (which
is mainly about strong normalization of term rewrite systems; see also
\isafor/\ceta's
website\footnote{\url{http://cl-informatik.uibk.ac.at/software/ceta}}).
Hence lemmas involving strong normalization, constitute by far the biggest
part of this theory. One of those is Newman's lemma.
\end{abstract}

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A description of this formalization will be available in
\cite{Sternagel2010}.

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