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tl: add some simplifications for first_match

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Following a discussion with Victor Khomenko.

* doc/tl/tl.tex: Document those rules.
* spot/tl/simplify.cc: Implement them.
* tests/core/reduccmp.test: Test them.
This commit is contained in:
Alexandre Duret-Lutz 2019-05-08 15:05:47 +02:00
parent b7cd475632
commit c6605e951d
3 changed files with 73 additions and 20 deletions
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28
doc/tl/tl.tex
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@ -801,7 +801,8 @@ $b_1$, $b_2$ are assumed to be Boolean formulas.
&&
f\FSTAR{\mvar{i}..\mvar{j}}\FSTAR{\mvar{k}..\mvar{l}} &\equiv f\FSTAR{\mvar{ik}..\mvar{jl}}\text{~if~}i(k+1)\le jk+1 \\
f\FSTAR{0}&\equiv \1 & f\FSTAR{1}&\equiv f\text{~if~}\varepsilon\nVDash f\\
\FIRSTMATCH\code(b\code) &\equiv b & \FIRSTMATCH\code(f\code) &\equiv \eword\text{~if~}\varepsilon\VDash f
\FIRSTMATCH\code(b\code) &\equiv b & \FIRSTMATCH\code(f\code) &\equiv \eword\text{~if~}\varepsilon\VDash f \\
&& \FIRSTMATCH\code(\FIRSTMATCH\code(f\code)\code) &\equiv \FIRSTMATCH\code(f\code)
\end{align*}
\noindent
@ -995,22 +996,6 @@ operator, even if the operator has multiple synonyms (like \samp{|},
\end{align*}
\section{Operator precedence}
The following operator precedence describes the current parser of
@ -1600,7 +1585,14 @@ SERE.
\sere{b_1\FUSION r_1}\ANDALT\sere{b_2\FUSION r_2} &\equiv \sere{b_1\ANDALT b_2}\FUSION\sere{r_1\ANDALT r_2} &
\sere{r_1\FUSION b_1}\ANDALT\sere{r_2\FUSION b_2} &\equiv \sere{r_1\ANDALT r_2}\FUSION\sere{b_1\ANDALT b_2} \\
\sere{b_1\CONCAT r_1}\AND \sere{b_2\CONCAT r_2} &\equiv \sere{b_1\ANDALT b_2}\CONCAT\sere{r_1\AND r_2} \\
\sere{b_1\FUSION r_1}\AND \sere{b_2\FUSION r_2} &\equiv \sere{b_1\ANDALT b_2}\FUSION\sere{r_1\AND r_2} \mathrlap{\quad\text{if~}\varepsilon\nVDash r_1\land\varepsilon\nVDash r_2}\\
\sere{b_1\FUSION r_1}\AND \sere{b_2\FUSION r_2} &\equiv \sere{b_1\ANDALT b_2}\FUSION\sere{r_1\AND r_2} \mathrlap{\quad\text{if~}\varepsilon\nVDash r_1\land\varepsilon\nVDash r_2}
\end{align*}
\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(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}
\end{align*}
Starred subformulas are rewritten in Star Normal