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1 :	jhr	101	%!TEX root = report.tex
2 :			%
3 :			\chapter{Types}
4 :			\label{chap:types}
5 :
6 :			The grammar of Diderot types is as follows:
7 :			\begin{Grammar}
8 :			\TypeRULES{}
9 :			\end{Grammar}%
10 :
11 :			\section{Value types}
12 :			Diderot supports four types of concrete values: booleans, integers, strings, and tensors.
13 :			The grammar of these types is
14 :			\begin{Grammar}
15 :			\ValueTypeRULES{}
16 :			\DimensionsRULES{}
17 :			\end{Grammar}%
18 :
19 :			The tensor type \mbox{\kw{tensor}\kw{[}$d_1,\ldots{},d_n$\kw{]}} is the of type order-$n$ tensors
20 :			with shape $d_1,\ldots{},d_n$.
21 :			Tensors include scalars (order-0) and vectors (order-1).
22 :			Because these types are frequently used, Diderot supports the following predefined type definitions:
23 :			\begin{center}
24 :			\begin{tabular}{r@{$\quad\equiv\quad$}l}
25 :			\kw{real} & \texttt{\kw{tensor}\kw{[}\kw{]}} \\
26 :			\kw{vec2} & \texttt{\kw{tensor}\kw{[}2\kw{]}} \\
27 :			\kw{vec3} & \texttt{\kw{tensor}\kw{[}3\kw{]}} \\
28 :			\kw{vec4} & \texttt{\kw{tensor}\kw{[}4\kw{]}}
29 :			\end{tabular}
30 :			\end{center}%
31 :
32 :			\section{Images}
33 :
34 :			\section{Fields}
35 :
36 :			\section{Kernels}
37 :			Kernels are abstract types that represent the \emph{convolution kernels} used
38 :			to reconstruct continuous fields from image data.
39 :			The syntax of a kernel type is \mbox{\kw{kernel}\kw{\#}$k$}, where
40 :			$k \geq 0$ gives the number of levels of differentiation supported by the
41 :			kernel.

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