Paper: added an example of IRE construction.

diff --git a/re2c/doc/tdfa_v2/img/trees.tex b/re2c/doc/tdfa_v2/img/trees.tex
index c26a9cd77d5b9e9dc2bd2d24ec96840538ee8dd8..34ff56ecc9cd0e8f76a8fdce0b69f7473d5ebf1a 100644 (file)
--- a/re2c/doc/tdfa_v2/img/trees.tex
+++ b/re2c/doc/tdfa_v2/img/trees.tex
@@ -9,13 +9,14 @@
 \usegdlibrary{trees}
 \usepackage{stix}
 
+\newcommand{\IRE}{I\!RE}
 
 \begin{document}
 
 %\begin{tikzpicture}[>=stealth, every node/.style={rectangle, rounded corners, draw, minimum size=0.1in}]
 \begin{tikzpicture}[>=stealth, every node/.style={draw=none, minimum size=0.1}]
 
-\begin{scope}[xshift=2in]
+\begin{scope}[xshift=2.5in]
 %    \node [rectangle, rounded corners, draw, minimum width=3.7in, minimum height=1.9in, yshift=-0.7in] {};
 %    \node[yshift=0.3in, draw=none] {$t_1: T(T(\varnothing, T(a)), T(\varnothing))$};
     \graph [tree layout, grow=down, fresh nodes] {
@@ -36,20 +37,9 @@
     };
     \node[xshift=0in, yshift=-1.5in, draw=none]
     {\small{$
-    \Big(1, 1,
-        \big(2, 2,
-            (0, 0, \epsilon ) \mid
-            (0, 0,
-                (0, 0, a)^{0, \infty}
-            )
-        \big) \cdot
-        \big(3, 0,
-            (4, 3,
-                (0, 0, a) \mid
-                (0, 0, \epsilon)
-            )^{0, \infty}
-        \big)
-    \Big)$}};
+    \IRE ((\epsilon|a^{0,\infty})(\epsilon|a)^{0,\infty} )) = (1,1,(2,2,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty}))
+        \cdot (3,0,(4,3,(0,0,\epsilon) \mid (0,0,a))^{0,\infty}))
+    $}};
 %    \node[xshift=0in, yshift=-1.7in, draw=none] {$(\epsilon | a^{0,\infty})(a | \epsilon)^{0,\infty}$};
 \end{scope}
 

diff --git a/re2c/doc/tdfa_v2/part_1_tnfa.tex b/re2c/doc/tdfa_v2/part_1_tnfa.tex
index ee2fac6456318f1743e2745575aeb02d8c7c4b6c..69f6ca9b6213f1c11f8bc23afe6b3d161f08c60d 100644 (file)
--- a/re2c/doc/tdfa_v2/part_1_tnfa.tex
+++ b/re2c/doc/tdfa_v2/part_1_tnfa.tex
@@ -407,29 +407,92 @@ we can transform IRE back to RE
 by erasing all indices
 and adding parentheses around subexpressions with nonzero explicit submatch index.
 Therefore RE and IRE are equivalent representations.
-\\
+%
+Below is an example of IRE construction for RE $(\epsilon|a^{0,\infty})(\epsilon|a)^{0,\infty} )$
+(the resulting IRE can be seen on figure \ref{fig_parse_trees}):
 
-Just like REs denote sets of PTs, IREs denote sets of \emph{IPTs} --- \emph{indexed parse trees},
-which are exactly like PTs except that each IPT is superscripted with
-the implicit submatch index inherited from the corresponding IRE node.
+    \begin{align*}
+    &\begin{aligned}
+        & mark ( (\epsilon|a^{0,\infty})(\epsilon|a)^{0,\infty} ) ) = \big[ \\
+        %
+        & \quad mark ( (\epsilon|a^{0,\infty}) ) = \big[ \\
+        & \quad mark ( \epsilon|a^{0,\infty} ) = \big[ \\
+        & \quad\quad\quad mark ( \epsilon ) = (0,0,\epsilon), \\
+        & \quad\quad\quad mark ( a^{0,\infty} ) = \big[ \\
+        & \quad\quad\quad\quad mark ( a ) = (0,0,a) \\
+        & \quad\quad\quad \big] = (0,0,(0,0,a)^{0,\infty}) \\
+        & \quad\quad \big] = (0,0,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \\
+        & \quad \big] = (1,1,(0,0,\epsilon)|(0,0,(0,0,a)^{0,\infty})) \\
+        %
+        & \quad mark ( (\epsilon|a)^{0,\infty} ) = \big[ \\
+        & \quad\quad mark ( (\epsilon|a) ) = \big[ \\
+        & \quad\quad\quad mark ( \epsilon|a ) = \big [ \\
+        & \quad\quad\quad\quad mark ( \epsilon ) = (0,0,\epsilon) \\
+        & \quad\quad\quad\quad mark ( a ) = (0,0,a) \\
+        & \quad\quad\quad \big] = (0,0,(0,0,\epsilon)|(0,0,a)) \\
+        & \quad\quad \big] = (1,1,(0,0,\epsilon) \mid (0,0,a)) \\
+        & \quad \big] = (1,0,(1,1,(0,0,\epsilon) \mid (0,0,a))^{0,\infty}) \\
+        %
+        & \big] = (1,1,
+           (1,1,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \\
+           & \quad\quad\quad \cdot (1,0,(1,1,(0,0,\epsilon) \mid (0,0,a))^{0,\infty})
+           )
+    \end{aligned}
+    %
+    &&\begin{aligned}
+        & enum (1,1,(1,1,
+            (1,1,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \\
+            & \quad\quad\quad\quad\quad \cdot (1,0,(1,1,(0,0,\epsilon) \mid (0,0,a))^{0,\infty}))) = \big[ \\
+        & \quad enum (2,2,(1,1,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty}))) = \big[ \\
+        & \quad\quad enum (3,3,(0,0,\epsilon)) = (3,3,(0,0,\epsilon)) \\
+        & \quad\quad enum (3,3,(0,0,(0,0,a)^{0,\infty})) = \big[ \\
+        & \quad\quad\quad enum (3,3,(0,0,a)) = (3,3,(0,0,a)) \\
+        & \quad\quad \big] = (3,3,(0,0,(0,0,a)^{0,\infty})) \\
+        & \quad \big] = (3,3,(2,2,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty}))) \\
+        %
+        & \quad enum (3,3, (1,0,(1,1,(0,0,\epsilon) \mid (0,0,a))^{0,\infty}) ) = \big[ \\
+        & \quad\quad enum (4,3, (1,1,(0,0,\epsilon) \mid (0,0,a)) ) = \big[ \\
+        & \quad\quad\quad enum (5,4, (0,0,\epsilon) ) = (0,0,\epsilon) \\
+        & \quad\quad\quad enum (5,4, (0,0,a) ) = (0,0,a) \\
+        & \quad\quad \big] = (5,4,(4,3,(0,0,\epsilon) \mid (0,0,a))) \\
+        & \quad \big] = (5,4,(3,0,(4,3,(0,0,\epsilon) \mid (0,0,a))^{0,\infty})) \\
+        %
+        & \big] = (5,4,(1,1,
+           (2,2,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \\
+           & \quad\quad\quad\quad\quad \cdot (3,0,(4,3,(0,0,\epsilon) \mid (0,0,a))^{0,\infty})
+           ))
+    \end{aligned}
+    \end{align*}
+
+Just like REs denote sets of PTs, IREs denote sets of \emph{IPTs} --- \emph{indexed parse trees}.
+The only difference between PTs and IPTs is that each node of an IPT has an associated number ---
+the implicit submatch index inherited from the corresponding IRE node (denoted with a superscript).
 Explicit submatch index is not used in IPTs.
-The set of all IPTs is denoted $\XIT$.
-%
-%    \begin{Xdef}
-%    \emph{Parse trees (PT)} over finite alphabet $\Sigma$, denoted $\XT_\Sigma$, are:
-%    \begin{enumerate}
-%        \item Atomic PT:
-%          \emph{nil tree} ${\varnothing}^i \in \XT_\Sigma$,
-%          \emph{empty tree} ${\epsilon}^i \in \XT_\Sigma$ and
-%          \emph{unit tree} ${\alpha}^i \in \XT_\Sigma$, where $\alpha \in \Sigma$ and $i \in \YZ$.
-%        \item Compound PT: if $t_1, \dots, t_n \in \XT_\Sigma$, where $n \geq 1$, and $i \in \YZ$, then
-%          ${T}^i(t_1, \dots, t_n) \in \XT_\Sigma$.
-%    \end{enumerate}
-%    \end{Xdef}
-%
-The operator $\IPT: \XIR_\Sigma \rightarrow 2^{\XIT_\Sigma}$ gives the set of all IPTs denoted by the given IRE
-(its definition is very similar to the one of operator $PT$):
 
+    \begin{Xdef}
+    \emph{Indexed parse trees (IPT)} over finite alphabet $\Sigma$, denoted $\XIT_\Sigma$, are:
+    \begin{enumerate}
+        \item Atomic IPTs:
+          \emph{nil tree} ${\varnothing}^i \in \XIT_\Sigma$,
+          \emph{empty tree} ${\epsilon}^i \in \XIT_\Sigma$ and
+          \emph{unit tree} ${\alpha}^i \in \XIT_\Sigma$, where $\alpha \in \Sigma$ and $i \in \YZ$.
+        \item Compound IPTs: if $t_1, \dots, t_n \in \XIT_\Sigma$, where $n \geq 1$, and $i \in \YZ$, then
+          ${T}^i(t_1, \dots, t_n) \in \XIT_\Sigma$.
+    \end{enumerate}
+    \end{Xdef}
+
+\iffalse
+\begin{figure}\label{fig_mark_enum}
+\includegraphics[width=\linewidth]{img/mark_enum.pdf}
+\caption{
+The process of constructing IRE for RE $(\epsilon|a^{0,\infty})(\epsilon|a)^{0,\infty} )$
+and the result visualized as a tree.
+}
+\end{figure}
+\fi
+
+The operator $\IPT: \XIR_\Sigma \rightarrow 2^{\XIT_\Sigma}$ gives the set of all IPTs denoted by the given IRE:
+%(its definition is very similar to the one of operator $PT$):
     \begin{align*}
         \IPT\big((i, \Xund, \epsilon)\big) &= \{ {\epsilon}^{i} \}
         \\