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* doc/tl/tl.tex: Document operator precedence.

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Alexandre Duret-Lutz 2011-11-29 18:51:51 +01:00
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@ -864,29 +864,71 @@ operator, even if the operator has multiple synonyms (like \samp{|},
\mathit{atomic\_prop} ::=&\, \text{see section~\ref{sec:ap}} & \mid&\,\tsamp{(}\,\mathit{tformula}\,\tsamp{)} \\
\mathit{bformula} ::=&\, \mathit{constant} & \mid&\,\msamp{\NOT}\,\mathit{tformula}\,\\
\mid&\,\mathit{atomic\_prop} & \mid&\,\mathit{tformula}\,\msamp{\AND}\,\mathit{tformula} \\
\mid&\,\tsamp{(}\,\mathit{bformula}\,\tsamp{)} & \mid&\,\mathit{tformula}\,\msamp{\OR}\,\mathit{tformula} \\
\mid&\,\msamp{\NOT}\,\mathit{bformula} & \mid&\,\mathit{tformula}\,\msamp{\IMPLIES}\,\mathit{tformula} \\
\mid&\,\mathit{bformula}\,\msamp{\AND}\,\mathit{bformula} & \mid&\,\mathit{tformula}\,\msamp{\XOR}\,\mathit{tformula} \\
\mid&\,\mathit{bformula}\,\msamp{\OR}\,\mathit{bformula} & \mid&\,\mathit{tformula}\,\msamp{\EQUIV}\,\mathit{tformula} \\
\mid&\,\mathit{bformula}\,\msamp{\IMPLIES}\,\mathit{bformula} & \mid&\,\msamp{\X}\,\mathit{tformula}\\
\mid&\,\mathit{bformula}\,\msamp{\XOR}\,\mathit{bformula} & \mid&\,\msamp{\F}\,\mathit{tformula}\\
\mid&\,\mathit{bformula}\,\msamp{\EQUIV}\,\mathit{bformula} & \mid&\,\msamp{\G}\,\mathit{tformula}\\
\mathit{rformula} ::=&\, \mathit{bformula} & \mid&\,\mathit{tformula}\,\msamp{\U}\,\mathit{tformula} \\
\mid&\,\tsamp{\{}\mathit{rformula}\tsamp{\}} & \mid&\,\mathit{tformula}\,\msamp{\W}\,\mathit{tformula} \\
\mid&\,\mathit{rformula}\msamp{\OR}\mathit{rformula} & \mid&\,\mathit{tformula}\,\msamp{\R}\,\mathit{tformula} \\
\mid&\,\mathit{rformula}\msamp{\AND}\mathit{rformula} & \mid&\,\mathit{tformula}\,\msamp{\M}\,\mathit{tformula} \\
\mid&\,\mathit{rformula}\msamp{\ANDALT}\mathit{rformula} & \mid&\,\tsamp{\{}\mathit{rformula}\tsamp{\}}\,\msamp{\Asuffix}\,\mathit{tformula}\\
\mid&\,\mathit{rformula}\msamp{\CONCAT}\mathit{rformula} & \mid&\,\tsamp{\{}\mathit{rformula}\tsamp{\}}\,\msamp{\AsuffixEQ}\,\mathit{tformula}\\
\mid&\,\mathit{rformula}\msamp{\FUSION}\mathit{rformula} & \mid&\,\tsamp{\{}\mathit{rformula}\tsamp{\}}\,\msamp{\Esuffix}\,\mathit{tformula}\\
\mid&\,\mathit{rformula}\msamp{\STAR{\mvar{i}..\mvar{j}}} & \mid&\,\tsamp{\{}\mathit{rformula}\tsamp{\}}\,\msamp{\EsuffixEQ}\,\mathit{tformula} \\
\mid&\,\mathit{rformula}\msamp{\PLUS} & \mid&\,\tsamp{\{}\mathit{rformula}\tsamp{\}} \\
\mid&\,\mathit{rformula}\msamp{\EQUAL{\mvar{i}..\mvar{j}}} & \mid&\,\tsamp{\{}\mathit{rformula}\tsamp{\}}\msamp{\NOT} \\
\mid&\,\mathit{atomic\_prop}\code{=0} & \mid&\,\mathit{tformula}\,\msamp{\OR}\,\mathit{tformula} \\
\mid&\,\mathit{atomic\_prop}\code{=1} & \mid&\,\mathit{tformula}\,\msamp{\IMPLIES}\,\mathit{tformula} \\
\mid&\,\tsamp{(}\,\mathit{bformula}\,\tsamp{)} & \mid&\,\mathit{tformula}\,\msamp{\XOR}\,\mathit{tformula} \\
\mid&\,\msamp{\NOT}\,\mathit{bformula} & \mid&\,\mathit{tformula}\,\msamp{\EQUIV}\,\mathit{tformula} \\
\mid&\,\mathit{bformula}\,\msamp{\AND}\,\mathit{bformula} & \mid&\,\msamp{\X}\,\mathit{tformula}\\
\mid&\,\mathit{bformula}\,\msamp{\OR}\,\mathit{bformula} & \mid&\,\msamp{\F}\,\mathit{tformula}\\
\mid&\,\mathit{bformula}\,\msamp{\IMPLIES}\,\mathit{bformula} & \mid&\,\msamp{\G}\,\mathit{tformula}\\
\mid&\,\mathit{bformula}\,\msamp{\XOR}\,\mathit{bformula} & \mid&\,\mathit{tformula}\,\msamp{\U}\,\mathit{tformula} \\
\mid&\,\mathit{bformula}\,\msamp{\EQUIV}\,\mathit{bformula} & \mid&\,\mathit{tformula}\,\msamp{\W}\,\mathit{tformula} \\
\mathit{rformula} ::=&\, \mathit{bformula} & \mid&\,\mathit{tformula}\,\msamp{\R}\,\mathit{tformula} \\
\mid&\,\tsamp{\{}\mathit{rformula}\tsamp{\}} & \mid&\,\mathit{tformula}\,\msamp{\M}\,\mathit{tformula} \\
\mid&\,\mathit{rformula}\msamp{\OR}\mathit{rformula} & \mid&\,\tsamp{\{}\mathit{rformula}\tsamp{\}}\,\msamp{\Asuffix}\,\mathit{tformula}\\
\mid&\,\mathit{rformula}\msamp{\AND}\mathit{rformula} & \mid&\,\tsamp{\{}\mathit{rformula}\tsamp{\}}\,\msamp{\AsuffixEQ}\,\mathit{tformula}\\
\mid&\,\mathit{rformula}\msamp{\ANDALT}\mathit{rformula} & \mid&\,\tsamp{\{}\mathit{rformula}\tsamp{\}}\,\msamp{\Esuffix}\,\mathit{tformula}\\
\mid&\,\mathit{rformula}\msamp{\CONCAT}\mathit{rformula} & \mid&\,\tsamp{\{}\mathit{rformula}\tsamp{\}}\,\msamp{\EsuffixEQ}\,\mathit{tformula} \\
\mid&\,\mathit{rformula}\msamp{\FUSION}\mathit{rformula} & \mid&\,\tsamp{\{}\mathit{rformula}\tsamp{\}} \\
\mid&\,\mathit{rformula}\msamp{\STAR{\mvar{i}..\mvar{j}}} & \mid&\,\tsamp{\{}\mathit{rformula}\tsamp{\}}\msamp{\NOT} \\
\mid&\,\mathit{rformula}\msamp{\PLUS} \\
\mid&\,\mathit{rformula}\msamp{\EQUAL{\mvar{i}..\mvar{j}}} \\
\mid&\,\mathit{rformula}\msamp{\GOTO{\mvar{i}..\mvar{j}}} \\
\end{align*}
\section{Operator precedence}
\ltltodo[inline]{Document operator precedence.}
\spottodo[inline]{The following operator precedence describe the
current parser of Spot, but this is not what we want eventually.
For instance $\IMPLIES$ should be right associative. $\U$ and $\W$
would probably make more sense as right associative operators too.\\
%
Tools that have $\U$, $\R$, $\W$, and $\M$ operators as left
associative: Spin, ltl2ba (same parser as spin), Wring, psl2ba,
Spot, Modella, NuSMV.\\
%
Tools (and doc) that have these operators as right associative: Goal
(hence Büchi Store), PSL reference manual, LTL2AUT, LTL2Büchi (from
JavaPathFinder).\\
%
Tools that have these operators as non-associative (parentheses are
required): Vis, LBTT.\\
%
While compiling these lists I have also discovered that not all
people aggreed on the associativity of $\IMPLIES$ and $\EQUIV$.
Some have both left-assoc, or both right-assoc, other have only
$\IMPLIES$ as right-assoc.\\
%
We want to get closer to the PSL standard eventually.}
\begin{center}
\begin{tabular}{cll}
assoc. & operators & priority \\
\hline
left & $\Asuffix,\,\AsuffixEQ,\,\Esuffix,\,\EsuffixEQ$ & lowest \\
left & $\CONCAT,\,\FUSION$ & \\
left & $\IMPLIES,\,\EQUIV$ & \\
left & $\XOR$ & \\
left & $\OR$ & \\
left & $\AND,\,\ANDALT$ & \\
left & $\U,\,\W,\,\M,\,\R$ & \\
& $\F,\,\G$ & \\
& $\X$ & \\
& $\STAR{\mvar{i}..\mvar{j}},\,\PLUS,\,\EQUAL{\mvar{i}..\mvar{j}},\,\GOTO{\mvar{i}..\mvar{j}}$ & \\
& $\NOT$ & \\
& $\code{=0},\,\code{=1}$ & highest \\
\end{tabular}
\end{center}
\chapter{Properties}