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\title{Typechecking Diderot}
\author{
Gordon Kindlmann \\
University of Chicago \\
{\small\tt{}glk@cs.uchicago.edu} \\
\and
John Reppy \\
University of Chicago \\
{\small\tt{}jhr@cs.uchicago.edu} \\
}
\date{\today}
\begin{document}
\maketitle
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\section{Introduction}
This document looks at the rules for typechecking Diderot.
\section{Types}
The syntax of Diderot types is given in \figref{fig:types}.
\begin{figure}[t]
\begin{displaymath}
\begin{array}{rclr}
\iota & ::= & \TYconst & \text{type constants} \\
& \mid & \TYint & \text{integers} \\[1em]
\tau & ::= & \iota \\
& \mid & \theta \\
& \mid & \TYmatrix{n}{m} & \text{$n\times{}m$ matrix} \\
& \mid & \TYimage{d}{\mu} & \text{$d$-dimension image of $\mu$ values}\\
& \mid & \TYkern{k} & \text{convolution kernel with $k$ derivatives} \\
& \mid & \TYfield{k}{d}{\theta} & \text{$d$-dimension field of $\theta$ values with $k$ derivatives} \\
\sigma & ::= \
\end{array}%
\end{displaymath}%
where $o\in\Nat$ is the tensor order, $d,n,m\in\SET{2,3}$ are dimensions,
and $k\in\Nat$ is the differentiability of a field.
\caption{Diderot types}
\label{fig:types}
\end{figure}%
\end{document}