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Get rid of bunop::Equal and bunop::Goto.

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* src/ltlast/bunop.hh, src/ltlast/bunop.cc, src/ltlvisit/randomltl.cc,
src/ltlvisit/simplify.cc, src/ltlvisit/tostring.cc,
src/tgbaalgos/ltl2tgba_fm.cc: Remove all traces of these two
operators since they are not handled like sugar.
* doc/tl/tl.tex: Adjust documentation to reflect the fact that these
two operators are sugar.
This commit is contained in:
Alexandre Duret-Lutz 2012-04-15 00:13:42 +02:00
parent 210723e30c
commit abaf102746
7 changed files with 38 additions and 272 deletions
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65
doc/tl/tl.tex
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@ -580,22 +580,6 @@ denote arbitrary SERE and $b$ denotes a Boolean formula.
& $f\STAR{\mvar{i}:}$
& $f\STAR{\mvar{i} to}$
& $f\STAR{\mvar{i},}$\\
bounded occurrence & $b\EQUAL{\mvar{i}..\mvar{j}}$
& $b\EQUAL{\mvar{i}:\mvar{j}}$
& $b\EQUAL{\mvar{i} to \mvar{j}}$
& $b\EQUAL{\mvar{i},\mvar{j}}$\\
unbounded occurrence & $b\EQUAL{\mvar{i}..}$
& $b\EQUAL{\mvar{i}:}$
& $b\EQUAL{\mvar{i} to}$
& $b\EQUAL{\mvar{i},}$\\
bounded goto & $b\GOTO{\mvar{i}..\mvar{j}}$
& $b\GOTO{\mvar{i}:\mvar{j}}$
& $b\GOTO{\mvar{i} to \mvar{j}}$
& $b\GOTO{\mvar{i},\mvar{j}}$\\
unbounded goto & $b\GOTO{\mvar{i}..}$
& $b\GOTO{\mvar{i}:}$
& $b\GOTO{\mvar{i} to}$
& $b\GOTO{\mvar{i},}$\\
\end{tabular}
\end{center}
@ -642,15 +626,7 @@ $b$ is a Boolean formula.
\text{or} & \mvar{i}>0 \land (\exists k\in\N,\,
(\sigma^{0..k-1}\VDash f) \land (\sigma^{k..}
\VDash f\STAR{\mvar{i-1}..}))\\
\end{cases}\\
\sigma\VDash b\EQUAL{\mvar{i}..\mvar{j}} & \iff
\sigma\VDash\mathtt{\{\{}\NOT b\,\mathtt\}\STAR{0..}\CONCAT\ b\,\mathtt\}\STAR{\mvar{i}..\mvar{j}}\CONCAT\mathtt\{\NOT b\,\mathtt\}\STAR{0..}\\
\sigma\VDash b\EQUAL{\mvar{i}..} & \iff
\sigma\VDash\mathtt{\{\{}\NOT b\,\mathtt\}\STAR{0..}\CONCAT\ b\,\mathtt\}\STAR{\mvar{i}..}\CONCAT\mathtt\{\NOT b\,\mathtt\}\STAR{0..}\\
\sigma\VDash b\GOTO{\mvar{i}..\mvar{j}} & \iff
\sigma\VDash\mathtt{\{\{}\NOT b\,\mathtt\}\STAR{0..}\CONCAT\ b\,\mathtt\}\STAR{\mvar{i}..\mvar{j}}\\
\sigma\VDash b\GOTO{\mvar{i}..} & \iff
\sigma\VDash\mathtt{\{\{}\NOT b\,\mathtt\}\STAR{0..}\CONCAT\ b\,\mathtt\}\STAR{\mvar{i}..}\\
\end{cases}
\end{align*}}
Notes:
@ -667,9 +643,16 @@ operands are Boolean formul\ae.
The syntax on the left is equivalent to the syntax on the right.
These rewritings are performed from left to right when parsing a
formula, and some are performed from right to left when writing it for
output.
formula, and \emph{some} are performed from right to left when writing
it for output. $b$ must be a Boolean formula.
\begin{align*}
b\GOTO{\mvar{i}..\mvar{j}} &\equiv \mathtt{\{\{}\NOT b\mathtt{\}}\STAR{0..}\CONCAT b\mathtt{\}}\STAR{\mvar{i}..\mvar{j}} &
b\EQUAL{\mvar{i}..\mvar{j}} &\equiv \mathtt{\{\{}\NOT b\mathtt{\}}\STAR{0..}\CONCAT b\mathtt{\}}\STAR{\mvar{i}..\mvar{j}}\CONCAT \mathtt{\{}\NOT b\mathtt{\}}\STAR{0..} \\
b\GOTO{\mvar{i}..} &\equiv \mathtt{\{\{}\NOT b\mathtt{\}}\STAR{0..}\CONCAT b\mathtt{\}}\STAR{\mvar{i}..} &
b\EQUAL{\mvar{i}..} &\equiv \mathtt{\{\{}\NOT b\mathtt{\}}\STAR{0..}\CONCAT b\mathtt{\}}\STAR{\mvar{i}..}\CONCAT \mathtt{\{}\NOT b\mathtt{\}}\STAR{0..}\text{~if~}i>0 \\
&& b\EQUAL{0..} &\equiv \mathtt{\{\{}\1\STAR{0..}\mathtt{\}}
\end{align*}
\begin{align*}
f\STARALT &\equiv f\STAR{0..}\\
f\STAR{} &\equiv f\STAR{0..} &
@ -701,22 +684,10 @@ $b_1$, $b_2$ are assumed to be Boolean formul\ae.
\begin{align*}
\0\STAR{0..\mvar{j}} &\equiv \eword &
\0\EQUAL{0..\mvar{j}} &\equiv \1\STAR{} &
\0\GOTO{0..\mvar{j}} &\equiv \eword \\
\0\STAR{\mvar{i}..\mvar{j}} &\equiv \0 \text{~if~}i>0 &
\0\EQUAL{\mvar{i}..\mvar{j}} &\equiv \0 \text{~if~}i>0&
\0\GOTO{\mvar{i}..\mvar{j}} &\equiv \0 \text{~if~}i>0\\
\0\STAR{\mvar{i}..\mvar{j}} &\equiv \0 \text{~if~}i>0 \\
\eword\STAR{\var{i}..\mvar{j}} &\equiv \eword&
\1\EQUAL{0} &\equiv\eword&
\1\GOTO{0} &\equiv\eword\\
f\STAR{0}&\equiv \eword &
\1\EQUAL{\mvar{i}..\mvar{j}}&\equiv \1\STAR{\mvar{i}..\mvar{j}}&
\1\GOTO{\mvar{i}..\mvar{j}}&\equiv \1\STAR{\mvar{i}..\mvar{j}}\\
f\STAR{\mvar{i}..\mvar{j}}\STAR{\mvar{k}..\mvar{l}} &\equiv f\STAR{\mvar{ik}..\mvar{jl}}&
b\EQUAL{0..}&\equiv 1\STAR{} &
b\GOTO{0}&\equiv \eword \\
&\drsh\text{~if~}i(k+1)\le jk+1 &
b\EQUAL{0}&\equiv (\NOT b)\STAR{} \\
f\STAR{\mvar{i}..\mvar{j}}\STAR{\mvar{k}..\mvar{l}} &\equiv f\STAR{\mvar{ik}..\mvar{jl}}\text{~if~}i(k+1)\le jk+1 \\
f\STAR{0}&\equiv \eword
\end{align*}
\noindent
@ -1396,16 +1367,6 @@ SERE.
b \ANDALT r &\text{if~} i\le 1\le j\\
\0 &\text{else}\\
\end{cases}\\
b \ANDALT r\EQUAL{\mvar{i}..\mvar{j}} &\equiv
\begin{cases}
b \ANDALT r &\text{if~} i\le 1\le j\\
\0 &\text{else}\\
\end{cases}\\
b \ANDALT r\GOTO{\mvar{i}..\mvar{j}} &\equiv
\begin{cases}
b \ANDALT r &\text{if~} i\le 1\le j\\
\0 &\text{else}\\
\end{cases}\\
b \ANDALT \sere{r_1 \FUSION \ldots \FUSION r_n} &\equiv b \ANDALT r_1 \ANDALT \ldots \ANDALT r_n \\
b \ANDALT \sere{r_1 \CONCAT \ldots \CONCAT r_n} &\equiv
\begin{cases}