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Add trivial identity {b}=b and !{b}=!b for any Boolean formula b.

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* src/ltlast/unop.cc: Perform the simplification.
* src/ltlast/unop.hh, doc/tl/tl.tex: Document it.
* src/ltltest/equals.test: Adjust test cases.
This commit is contained in:
Alexandre Duret-Lutz 2011-11-07 11:30:27 +01:00
parent 98f67973eb
commit 77d704ea9e
4 changed files with 28 additions and 18 deletions
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20
doc/tl/tl.tex
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@ -794,17 +794,17 @@ while $f$ is a PSL formula.
\begin{align*}
\sigma\vDash \ratgroup{r}\Esuffix f &\iff \exists k\ge 0, (\sigma^{0..k}\VDash r)\land(\sigma^{k..}\vDash f)\\
\sigma\vDash \ratgroup{r}\Asuffix f &\iff \forall k\ge 0, (\sigma^{0..k}\VDash r)\limplies (\sigma^{k..}\vDash f)\\
\sigma\vDash \ratgroup{r} & \iff (\exists k\ge 0, \sigma^{0..k}\VDash r)\lor(\forall k\ge 0,\,\exists \pi\in(\B^\AP)^\star,\, (\sigma^{0..k}\prec \pi)\land(\pi\VDash r))\\
\sigma\vDash \nratgroup{r} & \iff (\forall k\ge 0, \sigma^{0..k}\nVDash r)\land(\exists k\ge 0,\,\exists \forall\in(\B^\AP)^\star,\, (\sigma^{0..k}\prec \pi)\limplies(\pi\nVDash r))\\
\sigma\vDash \ratgroup{r} & \iff (\exists k\ge 0, \sigma^{0..k}\VDash r)\lor(\forall k\ge 0,\,\exists\pi\in(\B^\AP)^\star,\, (\sigma^{0..k}\prec \pi)\land(\pi\VDash r))\\
\sigma\vDash \nratgroup{r} & \iff (\forall k\ge 0, \sigma^{0..k}\nVDash r)\land(\exists k\ge 0,\,\forall\pi\in(\B^\AP)^\star,\, (\sigma^{0..k}\prec \pi)\limplies(\pi\nVDash r))\\
\end{align*}
The $\prec$ symbol should be read as ``\emph{is a prefix of}''. So
the semantic for `$\sigma\vDash \ratgroup{r}$' is that either there is
a finite prefix of $\sigma$ that is a model of $r$, or any prefix of
$\sigma$ can be extended into a finite sequence $\pi$ that is a model
of $r$. An infinite sequence $\texttt{a;a;a;a;a;}\ldots$ is therefore a
model of the formula \samp{$\ratgroup{a\PLUS{};\NOT a}$} even though
it never sees \samp{$\NOT a$}.
a (non-empty) finite prefix of $\sigma$ that is a model of $r$, or any
prefix of $\sigma$ can be extended into a finite sequence $\pi$ that
is a model of $r$. An infinite sequence $\texttt{a;a;a;a;a;}\ldots$
is therefore a model of the formula \samp{$\ratgroup{a\PLUS{};\NOT
a}$} even though it never sees \samp{$\NOT a$}.
\subsection{Syntactic Sugar}
@ -842,10 +842,12 @@ formula $b$, the following rewritings are systematically performed
& \ratgroup{\eword}\Esuffix f&\equiv \0
& \ratgroup{\eword} & \equiv \0
& \nratgroup{\eword} & \equiv \1 \\
\ratgroup{b}\Asuffix f&\equiv b\IMPLIES f
& \ratgroup{b}\Esuffix f&\equiv b\AND f
& \ratgroup{b} &\equiv b
& \nratgroup{b} &\equiv \NOT b\\
\ratgroup{r}\Asuffix \1&\equiv \1
& \ratgroup{r}\Esuffix \0&\equiv \0 \\
\ratgroup{b}\Asuffix f&\equiv b\IMPLIES f
& \ratgroup{b}\Esuffix f&\equiv b\AND f \\
\end{align*}
\chapter{Grammar}