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1 :	jhr	329	%!TEX root = report.tex
2 :			%
3 :			\chapter{The Diderot Language}
4 :			\label{chap:lang}
5 :
6 :			%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
7 :	jhr	2636	\section{Program structure}
8 :
9 :			\begin{Grammar}
10 :			\ProgramRULES{}
11 :			\end{Grammar}%
12 :
13 :			%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
14 :	jhr	329	\section{Global declarations}
15 :
16 :	jhr	2636	\begin{Grammar}
17 :			\GlobalDeclRULES{}
18 :			\end{Grammar}%
19 :
20 :			\subsection{Global variable declarations}
21 :
22 :			\begin{Grammar}
23 :			\VarDeclRULES{}
24 :			\end{Grammar}%
25 :
26 :			\subsection{Input variable declarations}
27 :
28 :			\begin{Grammar}
29 :			\InputDeclRULES{}
30 :			\end{Grammar}%
31 :
32 :			\subsection{Function declarations}
33 :			\begin{Grammar}
34 :			\FuncDeclRULES{}
35 :			\ParamsRULES{}
36 :			\ParamRULES{}
37 :			\end{Grammar}%
38 :
39 :	jhr	329	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
40 :	jhr	1116	\section{Strand definitions}
41 :	jhr	329
42 :	jhr	2636	\begin{Grammar}
43 :			\StrandDeclRULES{}
44 :			\end{Grammar}%
45 :
46 :	jhr	1116	\subsection{Strand state}
47 :	jhr	329
48 :	jhr	2636	\begin{Grammar}
49 :			\StrandStateDeclRULES{}
50 :			\end{Grammar}%
51 :
52 :	jhr	329	\subsection{The update method}
53 :
54 :			\subsection{The stabilize method}
55 :
56 :			%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
57 :			\section{Initialization}
58 :	jhr	330
59 :			%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
60 :			\section{Statements}
61 :	jhr	473
62 :	jhr	2636	\begin{Grammar}
63 :			\BlockRULES{}
64 :			\StmtRULES{}
65 :			\end{Grammar}%
66 :
67 :	jhr	473	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
68 :			\section{Expressions}
69 :
70 :	jhr	1116	In this section, we describe Diderot's expression syntax.
71 :			The section is organized from lowest to highest precedence.
72 :
73 :	jhr	473	\subsection{Conditional expressions}
74 :			There are three conditional expression forms in Diderot:
75 :			\emph{if-else} expressions, \emph{or-else} expressions, and \emph{and-also}
76 :			expressions.
77 :			The syntax of these is given by the following grammar fragment:
78 :			\begin{Grammar}
79 :			\ExprRULES{}
80 :	jhr	2636	\OrExprRULES{}
81 :	jhr	473	\AndExprRULES{}
82 :			\end{Grammar}%
83 :
84 :			\subsubsection{If-else expressions}
85 :			The if-else expression has the following typing rule:
86 :			\begin{displaymath}
87 :			\infer{
88 :			\HasTy{\ENV}{e_1\;\mkw{if}\;e_2\;\mkw{else}\;e_3}{\tau}
89 :			}{
90 :			\HasTy{\ENV}{e_1}{\tau} \quad
91 :			\HasTy{\ENV}{e_2}{\TYbool} \quad
92 :			\HasTy{\ENV}{e_3}{\tau} \quad
93 :			}
94 :			\end{displaymath}%
95 :			Its semantics are that it evaluates $e_2$ first.
96 :			If the value is true, then it evaluate $e_1$, otherwise it evaluates $e_3$.
97 :
98 :			\subsubsection{Or-else expressions}
99 :			\begin{displaymath}
100 :			\infer{
101 :			\HasTy{\ENV}{e_1\;\mkw{||}\;e_2}{\TYbool}
102 :			}{
103 :			\HasTy{\ENV}{e_1}{\TYbool} \quad
104 :			\HasTy{\ENV}{e_2}{\TYbool}
105 :			}
106 :			\end{displaymath}%
107 :			The or-else form is derived from the if-else form as follows:
108 :			\begin{displaymath}
109 :			e_1\;\mkw{||}\;e_2 \quad \equiv \quad \mkw{true}\;\mkw{if}\;e_1\;\mkw{else}\;e_2
110 :			\end{displaymath}%
111 :
112 :	jhr	2636	\subsubsection{And-also expressions}
113 :	jhr	473	\begin{displaymath}
114 :			\infer{
115 :			\HasTy{\ENV}{e_1\;\mkw{\&\&}\;e_2}{\TYbool}
116 :			}{
117 :			\HasTy{\ENV}{e_1}{\TYbool} \quad
118 :			\HasTy{\ENV}{e_2}{\TYbool}
119 :			}
120 :			\end{displaymath}%
121 :			The and-also form is derived from the if-else form as follows:
122 :			\begin{displaymath}
123 :			e_1\;\mkw{\&\&}\;e_2 \quad \equiv \quad e_2\;\mkw{if}\;e_1\;\mkw{else}\;\mkw{false}
124 :			\end{displaymath}%
125 :
126 :			\subsection{Binary expressions}
127 :			\begin{Grammar}
128 :			\CmpExprRULES{}
129 :	jhr	1116	\CmpOpRULES{}
130 :	jhr	473	\AddExprRULES{}
131 :	jhr	1116	\AddOpRULES{}
132 :	jhr	473	\MulExprRULES{}
133 :			\MulOpRULES{}
134 :	jhr	1116	\PowerExprRULES{}
135 :	jhr	473	\ProbeExprRULES{}
136 :			\end{Grammar}%
137 :
138 :	jhr	1116	\subsection{Prefix-operator expressions}
139 :	jhr	473	\begin{Grammar}
140 :			\PrefixExprRULES{}
141 :			\end{Grammar}%
142 :
143 :	jhr	1116	\subsection{Suffix-operator expressions}
144 :	jhr	473	\begin{Grammar}
145 :	jhr	1116	\SuffixExprRULES{}
146 :			\SuffixRULES{}
147 :	jhr	473	\IndexRULES{}
148 :			\end{Grammar}%
149 :
150 :	jhr	1116	\subsection{Derivative expressions}
151 :			\begin{Grammar}
152 :			\DerivExprRULES{}
153 :			\end{Grammar}%
154 :
155 :	jhr	473	\subsection{Atomic expressions}
156 :			\begin{Grammar}
157 :	jhr	1116	\AtomExprRULES{}
158 :	jhr	473	\ArgumentsRULES{}
159 :			\end{Grammar}%

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