Diff of /trunk/doc/typing/typing.tex

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	revision 65, Thu May 13 21:04:35 2010 UTC	revision 66, Thu May 13 23:12:28 2010 UTC
#	Line 28	Line 28
28	This document looks at the rules for typechecking Diderot.	This document looks at the rules for typechecking Diderot.
29
30	\section{Types}	\section{Types}
31		\begin{displaymath}
32		\begin{array}{rclr}
33		\nu & ::= & n & \text{dimension ($n > 0$)} \\
34		& \mid & \phi & \text{dimension variable} \\
35		\sigma & ::= & \epsilon & \text{empty sequence of dimensions} \\[1em]
36		& \mid & \rho & \text{shape variable} \\
37		& \mid & \sigma,\nu & \text{shape extension} \\[1em]
38		\kappa & ::= & n & \text{$n$ levels of differentiation ($n \geq 0$)} \\
39		& \mid & \kappa-n & \text{}
40		\end{array}
41		\end{displaymath}%
42
43	The syntax of Diderot types is given in \figref{fig:types}.	The syntax of Diderot types is given in \figref{fig:types}.
44	\begin{figure}[t]	\begin{figure}[t]
45	\begin{displaymath}	\begin{displaymath}
46	\begin{array}{rclr}	\begin{array}{rclr}
47	\iota & ::= & \TYconst & \text{type constants} \\	\tau & ::= & \TYconst & \text{type constants} \\
	& \mid & \TYint & \text{integers} \\[1em]
	\tau & ::= & \iota \\
48	& \mid & \theta \\	& \mid & \theta \\
49	& \mid & \TYmatrix{n}{m} & \text{$n\times{}m$ matrix} \\	%           & \mid & \TYmatrix{n}{m} & \text{$n\times{}m$ matrix} \\
50	& \mid & \TYimage{d}{\mu} & \text{$d$-dimension image of $\mu$ values}\\	& \mid & \TYimage{\nu}{\sigma} & \text{$d$-dimension image of $\mu$ values}\\
51	& \mid & \TYkern{k} & \text{convolution kernel with $k$ derivatives} \\	& \mid & \TYkern{k} & \text{convolution kernel with $k$ derivatives} \\
52	& \mid & \TYfield{k}{d}{\theta} & \text{$d$-dimension field of $\theta$ values with $k$ derivatives} \\	& \mid & \TYfield{k}{\nu}{\sigma} & \text{field} \\
53	\sigma & ::= \	\sigma & ::= \
54	\end{array}%	\end{array}%
55	\end{displaymath}%	\end{displaymath}%

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