\usepackage{euler}
\usepackage{amssymb}
\usepackage{stmaryrd}
+\usepackage{wasysym}
-\title{A MathML Editor Based on \TeX{} Syntax\\Formal Specification}
+\title{\EdiTeX: a MathML Editor Based on \TeX{} Syntax\\\small Description and Formal Specification}
\author{Paolo Marinelli\\Luca Padovani\\\small\{{\tt pmarinel},{\tt lpadovan}\}{\tt @cs.unibo.it}\\\small Department of Computer Science\\\small University of Bologna}
\date{}
+\newcommand{\EdiTeX}{Edi\TeX}
+
\newcommand{\tmap}[1]{\llbracket#1\rrbracket}
\newcommand{\tadvance}{\vartriangle}
\newcommand{\tnext}{\rhd}
\newcommand{\NNODE}{\texttt{n}}
\newcommand{\ONODE}{\texttt{o}}
\newcommand{\CNODE}{\texttt{c}}
+\newcommand{\TABLE}{\texttt{table}}
\newcommand{\SP}{\texttt{sp}}
\newcommand{\SB}{\texttt{sb}}
\newcommand{\CELL}{\texttt{cell}}
\newcommand{\ROW}{\texttt{row}}
-\newcommand{\SLDROP}{\hookleftarrow}
-\newcommand{\NLDROP}{\leftarrow}
+\newcommand{\SLDROP}{\blacktriangleleft}
+\newcommand{\NLDROP}{\vartriangleleft}
+\newcommand{\RDROP}{\vartriangleright}
\begin{document}
\maketitle
+\section{Introduction}
+
+MathML~\cite{MathML1,MathML2,MathML2E} is an XML application for the
+representation of mathematical expressions. As most XML applications,
+MathML is unsuitable to be hand-written, except for the simplest
+cases, because of its verbosity. In fact, the MathML specification
+explicitly states that
+\begin{quote}
+``While MathML is human-readable, it is anticipated that, in all but
+the simplest cases, authors will use equation editors, conversion
+programs, and other specialized software tools to generate MathML''
+\end{quote}
+
+The statement about human readability of MathML is already too strong,
+as the large number of mathematical symbols, operators, and
+diacritical marks that are used in mathematical notation cause MathML
+documents to make extensive use of Unicode characters that typically
+are not in the ``visible'' range of common text editors. Such
+characters may appear as entity references, whose name indicates
+somehow the kind of symbol used, or character references or they are
+directly encoded in the document encoding scheme (for instance,
+UTF-8).
+
+It is thus obvious that authoring MathML documents assumes the
+assistance of dedicated tools. As of today, such tools can be
+classified into two main categories:
+\begin{enumerate}
+ \item WYSIWYG (What You See Is What You Get) editors that allow the
+ author to see the formatted document on the screen as it is
+ composed;
+ \item conversion tools that generate MathML markup from different
+ sources, typically other markup languages for scientific
+ documents, such as \TeX.
+\end{enumerate}
+
+While the former tools are certainly more appealing, especially to the
+unexperienced user, as they give a direct visual feedback, the
+existance of tools in the second category takes into account the large
+availability of existing documents in \TeX{} format, and also the fact
+that experienced or ``lazy'' users may continue to prefer the use of a
+markup language other than MathML for editing, and generate MathML
+only as a final step of the authoring process. The ``laziness'' is not
+really intended as a way of being reluctant towards a new technology,
+but rather as a justified convincement that WYSIWYG editors are ``nice
+to look at'' but after all they may slow down the authoring process.
+WYSIWYG editors often involve the use of menus, palettes of symbols,
+and, in general, an extensive use of the pointing device (the mouse)
+for completing most operations. The use of shortcuts is of little
+help, as it implies very soon a challenging exercise for the fingers
+and the mind. Moreover, authors \emph{cannot improve} their authoring
+speed with time. On the other side, the gap between the syntax of any
+markup language for mathematics and mathematical notation may be
+relevant, especially for large, non-trivial formulas and authoring is
+a re-iterated process in which the author repeadtedly types the markup
+in the editor, compiles, and looks at the result inside a pre-viewer.
+
+\EdiTeX{} tries to synthesize the ``best of both worlds'' in a single
+tool. The basic idea is that of creating a WYSIWYG editor in which
+editing is achieved by typing \TeX{} markup as the author would do in
+a text editor. The \TeX{} markup is tokenized and parsed on-the-fly
+and a corresponding MathML representation is created and
+displayed. This way, the author can see the rendered document as it
+changes. The advantages of this approach can be summarized as follows:
+\begin{itemize}
+ \item the document is rendered concurrently with the editing, the
+ user has an immediate feedback hence it is easier to spot errors;
+ \item the author types in a concrete (and likely familiar) syntax
+ improving the editing speed;
+ \item the usual WYSIWYG mechanisms are still available. In
+ particular, it is possible to select \emph{visually} a fragment of
+ the document that needs re-editing, or that was left behind for
+ subsequent editing.
+\end{itemize}
+
+\paragraph{The Name of the Game:} there is no reference to MathML in
+the name ``\EdiTeX.'' In fact, the architecture of the editor is not
+tied to MathML markup. Although we focus on MathML editing, by
+changing a completely modularized component of the editor it is
+virtually possible to generate any other markup language.
+
+\paragraph{Acknowledgments.} Stephen M. Watt and Igor Rodionov for
+their work on the \TeX{} to MathML conversion tool; Stan Devitt for an
+illuminating discussion about the architecture of \TeX{} to XML
+conversion tools; Claudio Sacerdoti Coen for the valuable feedback and
+uncountable bug reports.
+
+\section{Architecture}
+
+\section{Customization}
+
+\subsection{Short and Long Identifiers}
+
+\subsection{The Dictionary}
+
+\subsection{Stylesheets and Trasformations}
+
+\subsection{Rendering}
+
+\section{XML Representation of \TeX{} Markup}
+
\section{Tokens}
The following tokens are defined:
\end{tabular}
%$
-%% \section{Description and Semantics of the Pattern Language}
+\section{Description and Semantics of the Pattern Language}
%% \begin{eqnarray*}
%% \mathit{NodeTest} & ::= & \mathtt{*} \\
%% & | & \mathit{AttributeName}\mathtt{='}\mathit{Text}\mathtt{'}
%% \end{eqnarray*}
+\begin{table}
+\[
+\begin{array}{rcl@{\hspace{3em}}rcl@{\hspace{3em}}rcl}
+ C &::=& Q\verb+/+ & Q &::=& T & P &::=& P' \\
+ &|& Q\verb+//+ & &|& Q\verb+[@+n\verb+=+v\verb+]+ & &|& \verb+^+P'\\
+ &|& \verb+(+C\verb+)+ & &|& Q\verb+[!@+n\verb+=+v\verb+]+ & &|& P'\verb+$+\\%$
+ &|& (\alpha\verb+=+C) & &|& Q\verb+[@+n\verb+]+ & &|& \verb+^+P'\verb+$+\\%$
+ &|& C_1 \verb+&+ C_2 & &|& Q\verb+[+P\verb+]+ & & &\\
+ &|& C_1 \verb+|+ C_2 & & & & P' &::=& P''\\
+ &|& C\verb.+. & T &::=& N & &|& P''\verb+#+P''\\
+ &|& C\verb+*+ & &|& C N & & &\\
+ &|& C\verb+?+ & & & & P'' &::=& \\
+ &|& C_1~C_2 & N &::=& \verb+<*>+ & &|& T\;P''\\
+ &|& \verb+!+C & &|& \verb+<+n_1\verb+|+\cdots\verb+|+n_2\verb+>+ & & &\\
+ & & & &|& \verb+<!+n_1\verb+|+\cdots\verb+|+n_2\verb+>+ & & &\\
+\end{array}
+\]
+\caption{Syntax of the pattern language. $n$, $n_i$ denote names, $v$
+denotes a string enclosed in single or double quotes}
+\end{table}
+
+
\section{Insert Rules}
\paragraph{Begin Group:} $\{$
\paragraph{Normal Left Drop:} $\NLDROP$
\begin{description}
- \item{\verb+/cursor+}\\
- error.
- \item{\verb+math/cursor+}\\
- nothing to drop.
- \item{\verb+g[!@id][_*#_]/cursor+}\\
- replace the cursor with the $\NLDROP$.
- \item{\verb+g[!@id][^#$]/cursor+}\\
- replace the cursor with the $\NLDROP$
- \item{\verb+g[@id][_*#_]/cursor+}\\
- replace the cursor with the $\NLDROP$.
- \item{\verb+g[@id][^#$]/cursor+}\\
- replace the cursor with the $\NLDROP$.
- \item{\verb+c[_*#_]/cursor+}\\
- replace the cursor with the $\NLDROP$.
- \item{\verb+sp[^*#$]/cursor+}\\
- replace the cursor with the $\NLDROP$.
- \item{\verb+c/p/cursor+}\\
+
+ \item{\verb+cursor+}\\
replace the cursor with the $\NLDROP$.
+
\end{description}
\paragraph{Special Left Drop:} $\SLDROP$
+
\begin{description}
- \item{\verb+/cursor+}\\
- error.
- \item{\verb+math/cursor+}\\
- nothing to drop.
- \item{\verb+g[!@id][_*#_]/cursor+}\\
- replace the cursor with the $\SLDROP$.
- \item{\verb+g[!@id][^#$]/cursor+}\\
- replace the cursor with the $\SLDROP$
- \item{\verb+g[@id][_*#_]/cursor+}\\
- replace the cursor with the $\SLDROP$.
- \item{\verb+g[@id][^#$]/cursor+}\\
- replace the cursor with the $\SLDROP$.
- \item{\verb+c[_*#_]/cursor+}\\
- replace the cursor with the $\SLDROP$.
- \item{\verb+sp[^*#$]/cursor+}\\
+
+ \item{\verb+cursor+}\\
replace the cursor with the $\SLDROP$.
- \item{\verb+c[p#]/cursor+}\\
- remove the cursor and append the $\SLDROP$ to the \PNODE{} node.
- \item{\verb+c[<i|n|o|s|c>#]/cursor+}\\
- remove the cursor and append it before the \INODE{}, \NNODE{}, \ONODE{}, \SNODE{} or \CNODE{} node.
- \item{\verb+c/p/cursor+}\\
- repace the cursor with the $\SLDROP$.
+
\end{description}
\section{Right Drop Rules}
+\begin{description}
+
+ \item{\verb+cursor+}\\
+ replace the cursor with the $\RDROP$.
+
+\end{description}
+
\section{$\varepsilon$-rules}
\paragraph{Nromal Left Drop}
\begin{description}
- %drop_prev_script(false). The results aren't \NLDROP's parent dependent.
- \item{\verb+.[<sp|sb>#]/+$\NLDROP$}\\
- remove the $\NLDROP$ and append it to the preceding script.
-
- %drop_prev_group(false). The results are \NLDROP's parent independent.
- \item{\verb+.[g#]/+$\NLDROP$}\\
- remove the $\NLDROP$ and append it to the \G{} node.
-
- %drop_prev_macro(false). The results aren't \NLDROP's parent dependent, unless the macro is undefined.
- \item{\verb+.[c[@pattern+$\sim$\verb+')'][g$]#]/+$\NLDROP$}\\
- remove the $\NLDROP$ and append it to the \G{} node.
- \item{\verb+.[c[@pattern='(]'][^g[^$]$]#]/+$\NLDROP$}\\
- remove the \CNODE{} node.
- \item{\verb+.[c[@pattern='(]'][^g[_]$]#]/+$\NLDROP$}\\
- replace the \CNODE{} node with the content of the \G{} node.
- \item{\verb+.[c[*]#]/+$\NLDROP$}\\
- remove the $\NLDROP$ and append it to the \CNODE{} node.
- \item{\verb+.[c[^$]#]/+$\NLDROP$}\\
- remove the $\NLDROP$ and replace the \CNODE{} with the cursor.
-
- %drop_prev_macro(false), when the macro is undefined and the NLDROP's parent is not a group with id
- \item{\verb+<!g[@id]>[c[@undefined='1']#]/+$\NLDROP$}\\
- remove the $\NLDROP$ and replace the \CNODE{} node with the cursor.
-
- %drop_prev_macro(false), when the macro is undefined and the \NLDROP's parent is a group with id.
- \item{\verb+g[@id][^c[@undefined='1']#$]/+$\NLDROP$}\\
- remove the \CNODE{} node.
- \item{\verb+g[@id][^c[@undefined='1']#._]+$\NLDROP$}\\
- remove the $\NLDROP$ and replace the \CNODE{} node with the cursor.
- \item{\verb+g[@id][_.c[@undefined='1']#]/+$\NLDROP$}\\
- remove the $\NLDROP$ and replace the \CNODE{} node with the cursor.
-
- %drop_prev_token(false), when the \NLDROP's parent is not a group with id.
- \item{\verb+<!g[@id]>[_<i|n|o|s>#_]/+$\NLDROP$}\\
- replace the node preceding the $\NLDROP$ with the cursor and remove the $\NLDROP$.
-
- %drop_prev_token(false), when the cursor's parent is a group with id.
- \item{\verb+g[@id][^<i|n|o|s>#$]/+$\NLDROP$}\\
- remove the $\NLDROP$ and replace the \INODE{}, \NNODE{}, \ONODE{} or \SNODE{} with the $\NLDROP$.
- \item{\verb+g[@id][^<i|n|o|s>#._]/+$\NLDROP$}\\
- remove the $\NLDROP$ and replace the \INODE{}, \NNODE{}, \ONODE{} or \SNODE{} with the cursor.
- \item{\verb+g[@id][_.<i|n|o|s>#]/+$\NLDROP$}\\
- remove the $\NLDROP$ and replace the \INODE{}, \NNODE{}, \ONODE{} or \SNODE{} with the cursor.
-
- %rgreplace_father().
- \item{\verb+g[@id][^#$]/+$\NLDROP$}\\
+ \item{\verb+math/g[^#]/+$\NLDROP$}\\
+ repalce the $\NLDROP$ with the cursor.
+
+ %**************************************************************************************
+ %****************************** epsilon-rules with \NLDROP ****************************
+ %**************************************************************************************
+
+ %************** \NLDROP has neither preceding nor following nodes ********************
+
+ \item{\verb+math[^#$]/+$\NLDROP$}\\
+ replace the $\NLDROP$ with the cursor.
+
+ \item{\verb+g[^#$]/+$\NLDROP$}\\
replace the \G{} node with the $\NLDROP$.
- %situations where the \NLDROP is a script's child.
- \item{\verb+<sp|sb>[^g[^$]#$]/+$\NLDROP$}\\
- replace the \SP{} or \SB{} node with the $\NLDROP$.
- \item{\verb+<sp|sb>[^<!g[^$]#$>]/+$\NLDROP$}\\
- replace the \SP{} or \SB{} with the non-\G{} node and insert the $\NLDROP$ after it.
+ % this rule is overridden by the two ones below
+ \item{\verb+c/p[^#$]/+$\NLDROP$}\\
+ remove the $\NLDROP$ and insert it before the \PNODE{} node.
+
+ \item{\verb+c[p[@left-open='1'][*]#$]/p[@right-open='1'][^#$]/+$\NLDROP$}\\
+ replace the \CNODE{} node with the content of the first \PNODE{} node and insert the $\NLDROP$ after this content
+
+ \item{\verb+c[p[@left-open='1'][!*]#$]/p[@right-open='1'][^#$]/+$\NLDROP$}\\
+ replace the \CNODE{} node with the $\NLDROP$.
+
+ \item{\verb+c[^#][!p(*)]/+$\NLDROP$}\\
+ replace the \CNODE{} node with the $\NLDROP$.
+
+ \item{\verb+cell[^#$]/+$\NLDROP$}\\
+ replace the cell with the $\NLDROP_n$.
+
+ \item{\verb+table[^#$]/+$\NLDROP$}\\
+ replace the \TABLE{} node with the $\NLDROP$.
+
+ %************************* \NLDROP has at least one preceding node *********************
+
+ % general rules
+
+ % this rule should also handles the case where the \NLDROP is the third (and last) child of a script.
+ \item{\verb+*[*#]/+$\NLDROP$}\\
+ remove the $\NLDROP$ and append it as the last child of its ex preceding brother.
+
+ % this rule overrides the one above
+ \item{\verb+*[(i|n|o|s|c[!*])#]/+$\NLDROP$}\\
+ remove the $\NLDROP$ and replace the token with the $\NLDROP_n$.
+
+ % special rules
- %situations where the \NLDROP is a macro's child.
+ \item{\verb+<sp|sb>[^*#$]+/$\NLDROP$}\\
+ replace the script node with its first child and insert the $\NLDROP$ after it.
+
+ % this rule overrides the one above.
+ \item{\verb+<sp|sb>[^g[!@id][!*]#$]/+$\NLDROP$}\\
+ replace the script with the cursor.
+
+ % this rule overrides the one above
+ \item{\verb+*[sp[!@id][^*g[!@id][^o[@name='prime']++\verb+o[@name='prime']$]]#]/+$\NLDROP$}\\
+ remove the last \ONODE{} node and replace the $\NLDROP$ with the cursor.%$\NLDROP_n$.
+
+ \item{\verb+*[sp[!@id][^*g[!@id][^o[@name='prime']$]]#]/+$\NLDROP$}\\
+ replace the script with its first child and replace the $\NLDROP$ with the cursor.%$\NLDROP_n$.
+
+ \item{\verb+c[(i|n|o|s|c[!*])#]/+$\NLDROP$}\\
+ move the $\NLDROP$ before the delimiter.
+
+ % this rule is true for both right-open and parameterized macros.
\item{\verb+c[p#]/+$\NLDROP$}\\
- remove the $\NLDROP$ and append it to the \PNODE{} node.
- \item{\verb+c[<i|n|o|s|c>#]/+$\NLDROP$}\\
- remove the $\NLDROP$ and insert it before the \INODE{}, \NNODE{}, \ONODE{}, \SNODE{} or the \CNODE node.
+ move the $\NLDROP$ into the \PNODE{} node.
+
+ %**************** \NLDROP has no preceding nodes, but has following nodes **************
+
+ % general rule
+ \item{\verb+*[^#*]/+$\NLDROP$}\\
+ remove the $\NLDROP$ and insert it before its parent.
+
+ % special rules
+
+ % this rule is applicable to all macros.
\item{\verb+c[^#][p[*]]/+$\NLDROP$}\\
- nothing to drop. Not all the parameters are empty.
- \item{\verb+c[!p[*]][^#]/+$NLDROP$}\\
- replace the macro with the $\NLDROP$.
-
- %situations where the cursor is a phantom group's child and has no preceding node.
- \item{\verb+math/g[!@id][^#$]/+$\NLDROP$}\\
- nothing to drop.
- \item{\verb+c[@pattern='()'][^g[^$]#$]/g[!@id][^#$]/+$\NLDROP$}\\
- replace the \CNODE{} node with the $\NLDROP$
- \item{\verb+c[@pattern='()'][^g[*]#$]/g[!@id][^#$]/+$\NLDROP$}\\
- remove the $\NLDROP$, insert the $\NLDROP$ after the \CNODE{} node replace the \CNODE{} node with the content of the first \G{} node.
- \item{\verb+c[@pattern='[)'][^#$]/g[!@id][^#$]/+$\NLDROP$}\\
- replace the \CNODE{} node with the $\NLDROP$.
- \item{\verb+c[@pattern='(]']/g[^#$]/+$\NLDROP$}\\
- error.
- \item{\verb+c[@table='1']/p[^#$]/row[^#$]/cell[^#$]/g[!@id][^#$]/+$\NLDROP$}\\
- replace the \CNODE{} with the cursor.
- \item{\verb+c[@table='1']/p[row[cell[^g[!@id]$]$]#_]/row[^#$]/cell[^#$]/g[!@id][^#$]/+$\NLDROP$}\\
- remove the \ROW{} node in which the $\NLDROP$ is and append the cursor to the \G{} node.
- \item{\verb+c[@table='1']/p[^#row_]/row[^#$]/cell[^#$]/g[!@id][^#$]/+$\NLDROP$}\\
- nothing to drop.
- \item{\verb+row[_cell[^g[!@id]$]#_]/cell[^#$]/g[!@id][^#$]/+$\NLDROP$}\\
- remove the cell in which the $\NLDROP$ is and append the cursor to the \G{} node of the preceding \CELL{} node.
- \item{\verb+row[^#cell_]/cell[^#$]/g[!@id][^#$]/+$\NLDROP$}\\
- nothing to drop.
- \item{\verb+sp[^*#$]/g[^#$]/+$\NLDROP$}\\
- replace the \SP{} node with it's first child and insert the cursor after it.
- \item{\verb+sp[^*#$]/g[o#_]/+$\NLDROP$}\\
- remove the \ONODE{}, remove the $\NLDROP$ and insert the cursor after the \SP{} node.
-
- %situations where \NLDROP is a p's child
- \item{\verb+c/p[^#$]/+$\NLDROP$}\\
- remove the $\NLDROP$ and insert it before the \PNODE{} node.
+ remove the $\NLDROP$ and insert it before the \CNODE{} node.
\end{description}
\begin{description}
- %drop_prev_script(true). The results aren't cursor's parent dependent.
- \item{\verb+.[<sp|sb>#]/+$\SLDROP$}\\
- remove the $\SLDROP$ and append it to the preceding script.
-
- %drop_prev_group(true). The results are cursor's parent independent.
- \item{\verb+.[g#]/+$\SLDROP$}\\
- remove the $\SLDROP$ and append it to the \G{} node.
-
- %drop_prev_macro(true). The results aren't cursor's parent dependent.
- \item{\verb+.[c[undefined='1']#]/+$\SLDROP$}\\
- remove the $\SLDROP$ and replace the \CNODE{} with the cursor.
- \item{\verb+.[c[@pattern~')'][g$]#]/+$\SLDROP$}\\
- remove the $\SLDROP$ and append the cursor to the \G{} node.
- \item{\verb+.[c[@pattern='(]'][^g[^$]$]#]/+$\SLDROP$}\\
- remove the \CNODE{} node and replace the $\SLDROP$ with the cursor.
- \item{\verb+.[c[@pattern='(]'][^g[_]$]#]/+$\SLDROP$}\\
- replace the \CNODE{} node with the content of the \G{} node and replace the $\SLDROP$ with the cursor.
- \item{\verb+.[c[*]#]/+$\SLDROP$}\\
- remove the $\SLDROP$ and append it to the \CNODE{} node.
- \item{\verb+.[c[^$]#]/+$\SLDROP$}\\
- remove the $\SLDROP$ and replace the \CNODE{} with the cursor.
- %here, we have to return the macro's name to the lexer.
-
- %drop_prev_token(true). The results aren't \SLDROP's parent dependent.
- \item{\verb+.[_<i|n|o|s>#_]/+$\SLDROP$}\\
- replace the node preceding the $\SLDROP$ with the cursor and remove the $\SLDROP$.
-
- %situations where the \SLDROP is a script's child.
- \item{\verb+<sp|sb>[^g[@id][^$]#$]/+$\SLDROP$}\\
- replace the \SP{} or \SB{} node with the \G{} node and insert the cursor after it.
- \item{\verb+<sp|sb>[^<g[!@id][^$]#$>]/+$\SLDROP$}\\
- replace the \SP{} or \SB{} with the cursor.
- \item{\verb+<sp|sb>[^*#$]/+$\SLDROP$}\\
- replace the \SP{} or \SB{} node with it's first child and insert the cursor after it.
-
- %situations where the \SLDROP is a macro's child.
- \item{\verb+c[p#]/+$\SLDROP$}\\
- remove the $\SLDROP$ and append it to the \PNODE{} node.
- \item{\verb+c[<i|n|o|s|c>#]/+$\SLDROP$}\\
- remove the $\SLDROP$ and insert the cursor before the \INODE{}, \NNODE{}, \ONODE{}, \SNODE{} or the \CNODE node.
- \item{\verb+c[^#][p[*]]/+$\SLDROP$}\\
- nothing to drop. Not all the parameters are empty.
- \item{\verb+c[!p[*]][^#]/+$SLDROP$}\\
- replace the macro with the cursor.
-
- %situations where the \SLDROP is a phantom group's child and has no preceding node.
- \item{\verb+math/g[!@id][^#$]/+$\SLDROP$}\\
- nothing to drop.
- \item{\verb+c[@pattern='()'][^g[^$]#$]/g[!@id][^#$]/+$\SLDROP$}\\
- replace the \CNODE{} node with the cursor.
- \item{\verb+c[@pattern='()'][^g[*]#$]/g[!@id][^#$]/+$\SLDROP$}\\
- replace the \CNODE{} with the content of the first group and insert the cursor after it.
- \item{\verb+c[@pattern='[)'][^#$]/g[!@id][^#$]/+$\SLDROP$}\\
+ %********************************************************************************************************
+ %************************************ epsilon-rules with \SLDROP ****************************************
+ %********************************************************************************************************
+
+ \item{\verb+math/+$\SLDROP$}\\
+ replace the $\SLDROP$ with the cursor.
+
+ \item{\verb+math/g[^#]/+$\NLDROP$}\\
+ replace the $\NLDROP$ with the cursor.
+
+ %************************ \SLDROP has neither preceding nor following nodes *****************************
+
+ \item{\verb+g[^#$]/+$\SLDROP$}\\
+ replace the \G{} node with the cursor.
+
+ \item{\verb+c[p[@left-open='1'][*]#$]/p[@right-open='1'][^#$]/+$\SLDROP$}\\
+ replace the \CNODE{} node with the content of the first \PNODE{} node and insert the cursor after this content
+
+ \item{\verb+c[p[@left-open='1'][!*]#$]/p[@right-open='1'][^#$]/+$\SLDROP$}\\
replace the \CNODE{} node with the cursor.
- \item{\verb+c[@pattern='(]']/g[^#$]/+$\SLDROP$}\\
- error.
- \item{\verb+c[@table='1']/p[^#$]/row[^#$]/cell[^#$]/g[!@id][^#$]/+$\SLDROP$}\\
- replace the \ROW{} with the cursor.
- \item{\verb+c[@table='1']/p[row[cell[^g[!@id]$]$]#_]/row[^#$]/cell[^#$]/g[!@id][^#$]/+$\SLDROP$}\\
- remove the \ROW{} node in which the $\SLDROP$ is and append the cursor to the \G{} node.
- \item{\verb+c[@table='1']/p[^#row_]/row[^#$]/cell[^#$]/g[!@id][^#$]/+$\SLDROP$}\\
- nothing to drop.
- \item{\verb+row[_cell[^g[!@id]$]#_]/cell[^#$]/g[!@id][^#$]/+$\SLDROP$}\\
- remove the cell in which the $\SLDROP$ is and append the cursor to the \G{} node of the preceding \CELL{} node.
- \item{\verb+row[^#cell_]/cell[^#$]/g[!@id][^#$]/+$\SLDROP$}\\
- nothing to drop.
- \item{\verb+sp[^*#$]/g[^#$]/+$\SLDROP$}\\
- replace the \SP{} node with it's first child and insert the cursor after it.
- \item{\verb+sp[^*#$]/g[o#_]/+$\SLDROP$}\\
- remove the \ONODE{}, remove the $\SLDROP$ and insert the cursor after the \SP{} node.
-
- %situations where the \SLDROP is a p's child
+
\item{\verb+c/p[^#$]/+$\SLDROP$}\\
- remove the $\SLDROP$ and insert it before the \PNODE{}.
+ remove the $\SLDROP$ and insert it before the \PNODE{} node.
+
+ \item{\verb+c[^#][!p(*)]/+$\SLDROP$}\\
+ replace the \CNODE{} node with the cursor.
+
+ \item{\verb+cell[^#$]/+$\SLDROP$}\\
+ replace the cell with the $\NLDROP_n$.
+
+ \item{\verb+table[^#$]/+$\SLDROP$}\\
+ replace the \TABLE{} node with the cursor.
+
+ %*********************** \SLDROP has at least one preceding node ***********************************
+
+ \item{\verb+*[sp[!@id][^*g[!@id][^o[@name='prime']++\verb+o[@name='prime']$]]#]/+$\SLDROP$}\\
+ remove the last \ONODE{} node and replace the $\SLDROP$ with the cursor.
+
+ \item{\verb+*[sp[!@id][^*g[!@id][^o[@name='prime']$]]#]/+$\SLDROP$}\\
+ replace the script with its first child and replace the $\SLDROP$ with the cursor.%$\NLDROP_n$.
+
+ \item{\verb+<sp|sb>[^g[!@id][!*]#$]/+$\SLDROP$}\\
+ replace the script with the cursor.
+
+ % this rule is overridden by the three rules above.
+ \item{\verb+<sp|sb>[^*#$]+/$\SLDROP$}\\
+ replace the script node with its first child and insert the cursor after it.
+
+ \item{\verb+c[(i|n|o|s|c[!*])#]/+$\SLDROP$}\\
+ remove the $\SLDROP$ and insert the cursor before the delimiter.
+
+ \item{\verb+c[p#(i|n|o|s|c[!*])]/+$\SLDROP$}\\
+ remove the $\SLDROP$ and insert the cursor into the \PNODE{} node.
+
+ \item{\verb+c[p[@right-open='1']#]+}\\
+ remove the $\SLDROP$ and append the curor as last child of the \PNODE{} node.
+
+ % this rule is overridden by the two ones above.
+ \item{\verb+c[p#]/+$\SLDROP$}\\
+ move the $\SLDROP$ into the \PNODE{} node.
+
+ \item{\verb+*[(i|n|o|s|c[!*])#]/+$\SLDROP$}\\
+ remove the $\SLDROP$ and replace the token with the cursor.
+
+ \item{\verb+*[table#]/+$\SLDROP$}\\
+ remove the $\SLDROP$ and append the $\NLDROP_n$ as the last child of the \TABLE{} node.
+
+ \item{\verb+*[c#]/+$\SLDROP$}\\
+ move the $\SLDROP$ into the \CNODE{} node.
+
+ \item{\verb+*[g#]/+$\SLDROP$}\\
+ remove the $\SLDROP$ and append the cursor as the last child of the \G{} node.
+
+ %********** \SLDROP has no preceding node, but has following ones **************
+
+ \item{\verb+c[^#p][p(*)]/+$\SLDROP$}\\
+ remove the $\SLDROP$ and insert the cursor before the \CNODE{} node.
+
+ % general rule
+ \item{\verb+*[^#*]/+$\SLDROP$}\\
+ remove the $\SLDROP$ and insert the cursor before its parent.
+
+\end{description}
+
+\paragraph{Normalize Left Drop}
+
+\begin{description}
+
+ %****************************************************************************************
+ %***************************** epsilon-rules with \NLDROP_n *****************************
+ %****************************************************************************************
+
+ \item{\verb+*[*#]/+$\NLDROP_n$}\\
+ replace the $\NLDROP_n$ with the cursor.
+
+ \item{\verb+row[cell#]/+$\NLDROP_n$}\\
+ remove the $\NLDROP_n$ and append the cursor as the last child of the \CELL{} node.
+
+ \item{\verb+row[^#$]/+$\NLDROP_n$}\\
+ replace the \ROW{} node with the $\NLDROP_n$
+
+ \item{\verb+table[row#]/+$\NLDROP_n$}\\
+ remove the $\NLDROP_n$ and append it as last child of the \ROW{} node.
+
+ \item{\verb+table[^#$]/+$\NLDROP_n$}\\
+ replace the \TABLE{} with the cursor.%$\NLDROP_n$.
+
+ \item{\verb+g[@id][^#$]/+$\NLDROP_n$}\\
+ replace the \G{} node with the $\NLDROP_n$.
+
+ \item{$\NLDROP_n$}\\
+ replace the $\NLDROP_n$ with the cursor.
+
+\end{description}
+
+\paragraph{Right Drop}
+
+\begin{description}
+
+ %************************* \RDROP has at least a following node ****************************************
+
+ \item{\verb+c[#(i|n|o|s|c[!*])]/+$\RDROP$}\\
+ remove the $\RDROP$ and append it after the delimiter
+
+ \item{\verb+*[#(i|n|o|s|c[!*])]/+$\RDROP$}\\
+ remove the token and replace the $\RDROP$ with the cursor $\RDROP_n$.
+
+ % this rule is overridden by those ones above.
+ \item{\verb+*[#*]/+$\RDROP$}\\
+ remove the $\RDROP$ and append it as the first child of the following node.
+
+ %************************** \RDROP has neither following nor preceding nodes ******************************
+
+ \item{\verb+c[#$][!p[*]]/+$\RDROP$}\\
+ replace the \CNODE{} with the $\RDROP$.
+
+ \item{\verb+p[^#$]/+$\RDROP$}\\
+ move the $\RDROP$ after the \PNODE{} node.
+
+ \item{\verb+g[^#$]/+$\RDROP$}\\
+ replace the \G{} node with the $\RDROP$.
+
+\end{description}
+
+\paragraph{Normalize Right Drop}
+
+\begin{description}
+
+ % at the moment it's the only rule, defined for this symbol.
+ \item{\verb+g[@id][^#$]/+$\RDROP_n$}\\
+ replace the \G{} node with the $\RDROP_n$.
+
+ \item{$\RDROP_n$}\\
+ replace the $\RDROP$ with the cursor.
\end{description}
% g[@id][^#$]/cursor <- cursor
% (!g[@id][^#$])[A#B]/(g[@id][^#$]/)+cursor <- (!g[@id][^#$])[A#B]/cursor
+\clearpage
+\appendix
+\section{Semantics of the Regular Context Language}
+
+\newcommand{\CSEM}[2]{\mathcal{C}\llbracket#1\rrbracket#2}
+\newcommand{\QSEM}[2]{\mathcal{Q}\llbracket#1\rrbracket#2}
+\newcommand{\TSEMUP}[2]{\mathcal{T}^\uparrow\llbracket#1\rrbracket#2}
+\newcommand{\TSEMDOWN}[2]{\mathcal{T}_\downarrow\llbracket#1\rrbracket#2}
+\newcommand{\NSEM}[2]{\mathcal{N}\llbracket#1\rrbracket#2}
+\newcommand{\PSEM}[2]{\mathcal{P}\llbracket#1\rrbracket#2}
+\newcommand{\PPSEM}[2]{\mathcal{P'}\llbracket#1\rrbracket(#2)}
+\newcommand{\PARENT}[1]{\mathit{parent}(#1)}
+\newcommand{\CHILDREN}[1]{\mathit{children}(#1)}
+\newcommand{\ANCESTORS}[1]{\mathit{ancestors}(#1)}
+\newcommand{\DESCENDANTS}[1]{\mathit{descendants}(#1)}
+\newcommand{\HASATTRIBUTE}[2]{\mathit{hasAttribute}(#1,#2)}
+\newcommand{\HASNOATTRIBUTE}[2]{\mathit{hasNoAttribute}(#1,#2)}
+\newcommand{\ATTRIBUTE}[2]{\mathit{attribute}(#1,#2)}
+\newcommand{\ISELEMENT}[1]{\mathit{isElement}(#1)}
+\newcommand{\NAME}[1]{\mathit{name}(#1)}
+\newcommand{\PREV}[1]{\mathit{prev}(#1)}
+\newcommand{\NEXT}[1]{\mathit{next}(#1)}
+
+\[
+\begin{array}{rcl}
+ \CSEM{.}{x} &=& \{x\}\\
+ \CSEM{..}{x} &=& \PARENT{x}\\
+ \CSEM{/}{x} &=& \CHILDREN{x}\\
+ \CSEM{q}{x} &=& \{x_1\mid x_1\in\{x\} \wedge \QSEM{q}{x_1}\}\\
+ \CSEM{(c)}{x} &=& \CSEM{c}{x}\\
+ \CSEM{\alpha(c)}{x} &=& \CSEM{c}{x}, \mbox{bind $\alpha$ to $x$}\\
+ \CSEM{c_1\&c_2}{x} &=& \CSEM{c_1}{x} \cap \CSEM{c_2}{x}\\
+ \CSEM{c_1\mid c_2}{x} &=& \CSEM{c_1}{x} \cup \CSEM{c_2}{x}\\
+ \CSEM{c+}{x} &=& \CSEM{c}{x} \cup \CSEM{c+}{\CSEM{c}{x}}\\
+ \CSEM{c?}{x} &=& \CSEM{.\mid c}{x}\\
+ \CSEM{c*}{x} &=& \CSEM{{c+}?}{x}\\
+ \CSEM{c_1\;c_2}{x} &=& \CSEM{c_2}{\CSEM{c_1}{x}}\\[3ex]
+ \QSEM{\langle*\rangle}{x} &=& \ISELEMENT{x}\\
+ \QSEM{\langle!*\rangle}{x} &=& \neg\QSEM{\langle*\rangle}{x}\\
+ \QSEM{\langle n_1\mid\cdots\mid n_k\rangle}{x} &=& \exists i\in\{1,\dots,k\}:\NAME{x}=n_i\\
+ \QSEM{\langle !n_1\mid\cdots\mid n_k\rangle}{x} &=& \neg\QSEM{\langle n_1\mid\cdots\mid n_k\rangle}{x}\\
+ \QSEM{q[@n]}{x} &=& \QSEM{q}{x} \wedge \HASATTRIBUTE{x}{n}\\
+ \QSEM{q[!@n]}{x} &=& \QSEM{q}{x} \wedge \HASNOATTRIBUTE{x}{n}\\
+ \QSEM{q[@n=v]}{x} &=& \QSEM{q}{x} \wedge \ATTRIBUTE{x}{n}= v\\
+ \QSEM{q[!@n=v]}{x} &=& \QSEM{q}{x} \wedge \ATTRIBUTE{x}{n}\ne v\\
+ \QSEM{q[p]}{x} &=& \QSEM{q}{x} \wedge \PSEM{p}{x}\\
+ \QSEM{q[!p]}{x} &=& \QSEM{q}{x} \wedge \neg\PSEM{p}{x}\\[3ex]
+ \PSEM{p_1\#p_2}{x} &=& \PPSEM{p_1}{*,x}\wedge\PPSEM{p_2}{x,*}\\
+ \PSEM{\cent p_1\#p_2}{x} &=& \PPSEM{p_1}{\cent,x}\wedge\PPSEM{p_2}{x,*}\\
+ \PSEM{p_1\#p_2\$}{x} &=& \PPSEM{p_1}{*,x}\wedge\PPSEM{p_2}{x,\$}\\
+ \PSEM{\cent p_1\#p_2\$}{x} &=& \PPSEM{p_1}{\cent,x}\wedge\PPSEM{p_2}{x,\$}\\[3ex]
+ \PPSEM{}{*,x} &=& \mathit{true}\\
+ \PPSEM{}{\cent,x} &=& \PREV{x}=\emptyset\\
+ \PPSEM{}{x,*} &=& \mathit{true}\\
+ \PPSEM{}{x,\$} &=& \NEXT{x}=\emptyset\\
+ \PPSEM{p\;c}{\alpha,x} &=& \CSEM{c}{\PREV{x}}\ne\emptyset\wedge\PPSEM{p}{\alpha,\PREV{x}}\\
+ \PPSEM{c\;p}{x,\alpha} &=& \CSEM{c}{\NEXT{x}}\ne\emptyset\wedge\PPSEM{p}{\NEXT{x},\alpha}\\
+\end{array}
+\]
+
\end{document}
projects / helm.git / blobdiff