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Trivially reduce f;f to f[*2], f[*1..3];f to f[*2..4], etc.

Browse source 
* src/ltlast/multop.cc (instance): Implement the reduction.
* src/ltlast/multop.hh, doc/tl/tl.tex: Document it.
* src/ltltest/equals.test: Add a test.
This commit is contained in:
Alexandre Duret-Lutz 2012-04-25 15:14:14 +02:00
parent 4a775a17a3
commit e7cf7b422d
4 changed files with 88 additions and 8 deletions
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24
doc/tl/tl.tex
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@ -687,7 +687,7 @@ $b_1$, $b_2$ are assumed to be Boolean formul\ae.
\0\STAR{\mvar{i}..\mvar{j}} &\equiv \0 \text{~if~}i>0 \\
\eword\STAR{\var{i}..\mvar{j}} &\equiv \eword&
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 \\
f\STAR{0}&\equiv \eword &
f\STAR{1}&\equiv f\\
\end{align*}
@ -697,9 +697,6 @@ The following rules are all valid with the two arguments swapped.
%\samp{$\FUSION$}.)
\begin{align*}
f\AND f &\equiv f&
f\ANDALT f &\equiv f &
f\OR f &\equiv f \\
\0\AND f &\equiv \0 &
\0\ANDALT f &\equiv \0 &
\0\OR f &\equiv f &
@ -715,22 +712,33 @@ The following rules are all valid with the two arguments swapped.
\1 \FUSION f & \equiv f\mathrlap{\text{~if~}\varepsilon\nVDash f}\\
&&
\STAR{} \AND f &\equiv f &
\STAR{} \OR f &\equiv \1\STAR{} &
\STAR{} \OR f &\equiv \1\mathrlap{\STAR{}} &
&&
\STAR{} \CONCAT f &\equiv \STAR{}\mathrlap{\text{~if~}\varepsilon\VDash f}& \\
\eword\AND f &\equiv f &
\eword\ANDALT f &\equiv
\begin{cases}
\eword &\mathrlap{\text{if~} \varepsilon\VDash f} \\
\0 &\mathrlap{\text{if~} \varepsilon\nVDash f} \\
\mathrlap{\eword\text{~if~} \varepsilon\VDash f} \\
\0\mathrlap{\phantom{\STAR{}}\text{~if~} \varepsilon\nVDash f} \\
\end{cases} &
&&
\eword \FUSION f &\equiv \0 &
\eword \CONCAT f &\equiv f\\
f\AND f &\equiv f&
f\ANDALT f &\equiv f &
f\OR f &\equiv f&
&&
f\CONCAT f&\equiv f\STAR{2}\\
b_1 \AND b_2 &\equiv b_1\ANDALT b_2 &
&&
&&
b_1:b_2 &\equiv b_1\ANDALT b_2\\
b_1:b_2 &\equiv b_1\ANDALT b_2 &
f\STAR{\mvar{i}..\mvar{j}}\CONCAT f&\equiv f\STAR{\mvar{i+1}..\mvar{j+1}}\\
&&
&&
&&
&&
\mathllap{f\STAR{\mvar{i}..\mvar{j}}}\CONCAT f\STAR{\mvar{k}..\mvar{l}}&\equiv f\STAR{\mvar{i+k}..\mvar{j+l}}\\
\end{align*}
\section{SERE-LTL Binding Operators}