--- trunk/doc/typing/typing.tex 2010/05/13 21:04:35 65 +++ trunk/doc/typing/typing.tex 2010/05/13 23:12:28 66 @@ -28,18 +28,28 @@ This document looks at the rules for typechecking Diderot. \section{Types} +\begin{displaymath} + \begin{array}{rclr} + \nu & ::= & n & \text{dimension ($n > 0$)} \\ + & \mid & \phi & \text{dimension variable} \\ + \sigma & ::= & \epsilon & \text{empty sequence of dimensions} \\[1em] + & \mid & \rho & \text{shape variable} \\ + & \mid & \sigma,\nu & \text{shape extension} \\[1em] + \kappa & ::= & n & \text{$n$ levels of differentiation ($n \geq 0$)} \\ + & \mid & \kappa-n & \text{} + \end{array} +\end{displaymath}% + 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 \\ + \tau & ::= & \TYconst & \text{type constants} \\ & \mid & \theta \\ - & \mid & \TYmatrix{n}{m} & \text{$n\times{}m$ matrix} \\ - & \mid & \TYimage{d}{\mu} & \text{$d$-dimension image of $\mu$ values}\\ +% & \mid & \TYmatrix{n}{m} & \text{$n\times{}m$ matrix} \\ + & \mid & \TYimage{\nu}{\sigma} & \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} \\ + & \mid & \TYfield{k}{\nu}{\sigma} & \text{field} \\ \sigma & ::= \ \end{array}% \end{displaymath}%
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The output has ended thus: ield{k}{\nu}{\sigma} & \text{field} \\ \sigma & ::= \ \end{array}% \end{displaymath}%