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\title{State Spaces: The Locale Way}
\author{Norbert Schirmer}
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\section{Introduction}

These theories introduce a new command called \isacommand{statespace}.
It's usage is similar to \isacommand{record}s. However, the command
does not introduce a new type but an abstract specification based on
the locale infrastructure. This leads to extra flexibility in
composing state space components, in particular multiple inheritance
and renaming of components.

The state space infrastructure basically manages the following things:
\begin{itemize}
\item distinctness of field names
\item projections~/ injections from~/ to an abstract \emph{value} type
\item syntax translations for lookup and update, hiding the
  projections and injections
\item simplification procedure for lookups~/ updates, similar to
  records
\end{itemize}


\paragraph{Overview}
In Section \ref{sec:DistinctTreeProver} we define distinctness of the
nodes in a binary tree and provide the basic prover tools to support
efficient distinctness reasoning for field names managed by state
spaces. The state is represented as a function from (abstract) names
to (abstract) values as introduced in Section \ref{sec:StateFun}. The
basic setup for state spaces is in Section
\ref{sec:StateSpaceLocale}. Some syntax for lookup and updates is
added in Section \ref{sec:StateSpaceSyntax}. Finally Section
\ref{sec:Examples} explains the usage of state spaces by examples.


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