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\title{Affine Arithmetic}
\author{Fabian Immler}

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\begin{abstract}

We give a formalization of affine forms~\cite{Stolfi2004,Girard2005} as abstract
representations of zonotopes. We provide affine operations as well as overapproximations of some
non-affine operations like multiplication and division. Expressions involving those operations can
automatically be turned into (executable) functions approximating the original expression in
affine arithmetic.

Moreover we give a verified implementation of a functional algorithm to compute the intersection of
a zonotope with a hyperplane, as described in the paper~\cite{Immler}.

\end{abstract}

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