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simplify: more rules for first_match

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* spot/tl/simplify.cc: Implement the rules.
* tests/core/reduccmp.test: Test them.
* doc/tl/tl.tex: Document them.
This commit is contained in:
Alexandre Duret-Lutz 2019-05-10 22:54:55 +02:00
parent c6605e951d
commit e325289a12
3 changed files with 118 additions and 12 deletions
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12
doc/tl/tl.tex
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@ -1590,9 +1590,17 @@ SERE.
\begin{align*}
\FIRSTMATCH\code(b\STAR{\mvar{i}..\mvar{j}}\code) &\equiv b\STAR{\mvar{i}} \\
\FIRSTMATCH\code(r\STAR{\mvar{i}..\mvar{j}}\code) &\equiv \FIRSTMATCH\code(r\STAR{\mvar{i}}\code) \\
\FIRSTMATCH\code(r_1\CONCAT{}r_2\STAR{\mvar{i}..\mvar{j}}\code) &\equiv \FIRSTMATCH(r_1\CONCAT\mathrlap{r_2\STAR{\mvar{i}})} \\
\FIRSTMATCH\code(r\FSTAR{\mvar{i}..\mvar{j}}\code) &\equiv \FIRSTMATCH\code(r\FSTAR{\mvar{i}}\code) \\
\FIRSTMATCH\code(r_1\CONCAT{}r_2\STAR{\mvar{i}..\mvar{j}}\code) &\equiv \FIRSTMATCH\code(r_1\CONCAT{}r_2\STAR{\mvar{i}}\code) \\
\FIRSTMATCH\code(r_1\CONCAT{}r_2\FSTAR{\mvar{i}..\mvar{j}}\code) &\equiv \FIRSTMATCH\code(r_1\CONCAT{}r_2\FSTAR{\mvar{i}}\code) \\
\FIRSTMATCH\code(r_1\FUSION{}r_2\STAR{\mvar{i}..\mvar{j}}\code) &\equiv \FIRSTMATCH\code(r_1\FUSION{}r_2\STAR{\mvar{\max(i,1)}}\code) \\
\FIRSTMATCH\code(r_1\FUSION{}r_2\FSTAR{\mvar{i}..\mvar{j}}\code) &\equiv \FIRSTMATCH\code(r_1\FUSION{}r_2\FSTAR{\mvar{i}}\code) \\
\FIRSTMATCH\code(b\CONCAT{}r\code) &\equiv b\CONCAT\FIRSTMATCH\code(r\code) \\
\FIRSTMATCH\code(r_1\CONCAT{}r_2\code) &\equiv\FIRSTMATCH(r_1)\mathrlap{\quad\text{if~} \varepsilon\VDash r_2}
\FIRSTMATCH\code(b\STAR{\mvar{i}..\mvar{j}}\CONCAT{}r\code) &\equiv b\STAR{\mvar{i}}\CONCAT\FIRSTMATCH\code(b\STAR{0..\mvar{j-i}}\CONCAT r\code) \\
\FIRSTMATCH\code(b\STAR{\mvar{i}..\mvar{j}}\FUSION{}r\code) &\equiv b\STAR{\mvar{i-1}}\CONCAT\FIRSTMATCH\code(b\STAR{1..\mvar{j-i+1}}\FUSION r\code)\quad\text{if~}i>1\\
\FIRSTMATCH\code(r_1\CONCAT{}r_2\code) &\equiv\FIRSTMATCH\code(r_1\code)\quad\text{if~} \varepsilon\VDash r_2\\
\FIRSTMATCH\code(\FIRSTMATCH\code(r_1\code)\CONCAT{}r_2\code) &\equiv\FIRSTMATCH\code(r_1\code)\CONCAT\FIRSTMATCH\code(r_2\code)\\
\FIRSTMATCH\code(\FIRSTMATCH\code(r_1\code)\FUSION{}r_2\code) &\equiv\FIRSTMATCH\code(r_1\code)\FUSION\FIRSTMATCH\code(\1\FUSION{}r_2\code)
\end{align*}
Starred subformulas are rewritten in Star Normal