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Marcel Fabian Krüger 2024-10-19 10:09:17 +02:00
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support/luamml-algorithm.tex
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\newcommand\Luamml{\pkg{Luamml}} % \newcommand\Luamml{\pkg{Luamml}}
\newcommand\luamml{\pkg{luamml}} % \newcommand\luamml{\pkg{luamml}}
\newcommand\xmltag[1]{\texttt{<#1>}} % \newcommand\xmltag[1]{\texttt{<#1>}}
\section{\Luamml's representation of XML and MathML} % \section{\Luamml's representation of XML and MathML}
In the following I assume basic familiarity with both Lua\TeX's representation of math noads and MathML. % In the following I assume basic familiarity with both Lua\TeX's representation of math noads and MathML.
%
\subsection{Representation of XML elements} % \subsection{Representation of XML elements}
In many places, \luamml\ passes around XML elements. Every element is represented by a Lua table. % In many places, \luamml\ passes around XML elements. Every element is represented by a Lua table.
Element \texttt 0 must always be present and is a string representing the tag name. % Element \texttt 0 must always be present and is a string representing the tag name.
The positive integer elements of the table represent child elements (either strings for direct text content or nested tables for nested elements). % The positive integer elements of the table represent child elements (either strings for direct text content or nested tables for nested elements).
All string members which do not start with a colon are attributes, whose value is the result of applying \texttt{tostring} to the field value. % All string members which do not start with a colon are attributes, whose value is the result of applying \texttt{tostring} to the field value.
This implies that these values should almost always be strings, except that the value \texttt 0 (since it never needs a unit) can often be set as a number. % This implies that these values should almost always be strings, except that the value \texttt 0 (since it never needs a unit) can often be set as a number.
For example the XML document % For example the XML document
\begin{verbatim} % \begin{verbatim}
<math block="display"> % <math block="display">
<mn>0</mn> % <mn>0</mn>
<mo> &lt; </mo> % <mo> &lt; </mo>
<mi mathvariant="normal">x</mi> % <mi mathvariant="normal">x</mi>
</math> % </math>
\end{verbatim} % \end{verbatim}
would be represented by the Lua table % would be represented by the Lua table
\begin{verbatim} % \begin{verbatim}
{[0] = "math", block="display", % {[0] = "math", block="display",
{[0] = "mn", "0"}, % {[0] = "mn", "0"},
{[0] = "mo", "<"}, % {[0] = "mo", "<"},
{[0] = "mi", mathvariant="normal", "x"} % {[0] = "mi", mathvariant="normal", "x"}
} % }
\end{verbatim} % \end{verbatim}
%
\subsection{Expression cores} % \subsection{Expression cores}
MathML knows the concept of \enquote{embellished operators}: % MathML knows the concept of \enquote{embellished operators}:
\begin{blockquote} % \begin{blockquote}
The precise definition of an \enquote{embellished operator} is: % The precise definition of an \enquote{embellished operator} is:
\begin{itemize} % \begin{itemize}
\item an \xmltag{mo} element; % \item an \xmltag{mo} element;
\item or one of the elements \xmltag{msub}, \xmltag{msup}, \xmltag{msubsup}, \xmltag{munder}, \xmltag{mover}, \xmltag{munderover}, \xmltag{mmultiscripts}, \xmltag{mfrac}, or \xmltag{semantics} (§ 5.1 Annotation Framework), whose first argument exists and is an embellished operator; % \item or one of the elements \xmltag{msub}, \xmltag{msup}, \xmltag{msubsup}, \xmltag{munder}, \xmltag{mover}, \xmltag{munderover}, \xmltag{mmultiscripts}, \xmltag{mfrac}, or \xmltag{semantics} (§ 5.1 Annotation Framework), whose first argument exists and is an embellished operator;
\item or one of the elements \xmltag{mstyle}, \xmltag{mphantom}, or \xmltag{mpadded}, such that an mrow containing the same arguments would be an embellished operator; % \item or one of the elements \xmltag{mstyle}, \xmltag{mphantom}, or \xmltag{mpadded}, such that an mrow containing the same arguments would be an embellished operator;
\item or an \xmltag{maction} element whose selected sub-expression exists and is an embellished operator; % \item or an \xmltag{maction} element whose selected sub-expression exists and is an embellished operator;
\item or an \xmltag{mrow} whose arguments consist (in any order) of one embellished operator and zero or more space-like elements. % \item or an \xmltag{mrow} whose arguments consist (in any order) of one embellished operator and zero or more space-like elements.
\end{itemize} % \end{itemize}
\end{blockquote} % \end{blockquote}
For every embellished operator, MathML calls the \xmltag{mo} element defining the embellished operator the \enquote{core} of the embellished operator. % For every embellished operator, MathML calls the \xmltag{mo} element defining the embellished operator the \enquote{core} of the embellished operator.
%
\Luamml\ makes this slightly more general: Every expression is represented by a pair of two elements: The expression and it's core. % \Luamml\ makes this slightly more general: Every expression is represented by a pair of two elements: The expression and it's core.
The core is always a \xmltag{mo}, \xmltag{mi}, or \xmltag{mn}, \texttt{nil} or s special marker for space like elements. % The core is always a \xmltag{mo}, \xmltag{mi}, or \xmltag{mn}, \texttt{nil} or s special marker for space like elements.
%
If and only if the element is a embellished operator the core is a \xmltag{mo} element representing the core of the embellished operator. % If and only if the element is a embellished operator the core is a \xmltag{mo} element representing the core of the embellished operator.
The core is a \xmltag{mi} or a \xmltag{mn} element if and only if the element would be an embellished operator with this core if this element where a \xmltag{mo} element. % The core is a \xmltag{mi} or a \xmltag{mn} element if and only if the element would be an embellished operator with this core if this element where a \xmltag{mo} element.
The core is the special space like marker for space like elements. Otherwise the core is \texttt{nil}. % The core is the special space like marker for space like elements. Otherwise the core is \texttt{nil}.
%
\subsection{Translation of math noads} % \subsection{Translation of math noads}
A math lists can contain the following node types: noad, fence, fraction, radical, accent, style, choice, ins, mark, adjust, boundary, whatsit, penalty, disc, glue, and kern. The \enquote{noads} % A math lists can contain the following node types: noad, fence, fraction, radical, accent, style, choice, ins, mark, adjust, boundary, whatsit, penalty, disc, glue, and kern. The \enquote{noads}
%
\subsubsection{Translation of kernel noads} % \subsubsection{Translation of kernel noads}
The math noads of this list contain nested kernel noads. So in the first step, we look into how kernel nodes are translated to math nodes. % The math noads of this list contain nested kernel noads. So in the first step, we look into how kernel nodes are translated to math nodes.
%
\paragraph{\texttt{math_char} kernel noads} % \paragraph{\texttt{math_char} kernel noads}
First the family and character value in the \texttt{math_char} are used to lookup the Unicode character value of this \texttt{math_char}. % First the family and character value in the \texttt{math_char} are used to lookup the Unicode character value of this \texttt{math_char}.
(For \texttt{unicode-math}, this is usually just the character value. Legacy maths has to be remapped based on the family.) % (For \texttt{unicode-math}, this is usually just the character value. Legacy maths has to be remapped based on the family.)
Then there are two cases: The digits \texttt{0} to \texttt{9} are mapped to \xmltag{mn} elements, everything else becomes a \xmltag{mi} element with \texttt{mathvariant} set to \texttt{normal}. % Then there are two cases: The digits \texttt{0} to \texttt{9} are mapped to \xmltag{mn} elements, everything else becomes a \xmltag{mi} element with \texttt{mathvariant} set to \texttt{normal}.
(The \texttt{mathvariant} value might get suppressed if the character defaults to mathvariant \texttt{normal}.) % (The \texttt{mathvariant} value might get suppressed if the character defaults to mathvariant \texttt{normal}.)
In either case, the \texttt{tex:family} attribute is set to the family number if it's not \texttt{0}. % In either case, the \texttt{tex:family} attribute is set to the family number if it's not \texttt{0}.
%
The core is always set to the expression itself. E.g.\ the \texttt{math_char} kernel noad \verb+\fam3 a+ would become (assuming no remapping for this family) % The core is always set to the expression itself. E.g.\ the \texttt{math_char} kernel noad \verb+\fam3 a+ would become (assuming no remapping for this family)
\begin{verbatim} % \begin{verbatim}
{[0] = 'mi', % {[0] = 'mi',
mathvariant = 'normal', % mathvariant = 'normal',
["tex:family"] = 3, % ["tex:family"] = 3,
"a" % "a"
} % }
\end{verbatim} % \end{verbatim}
%
\subsubsection{\texttt{sub_box} kernel noads} % \subsubsection{\texttt{sub_box} kernel noads}
I am open to suggestions how to convert them properly. % I am open to suggestions how to convert them properly.
%
\subsubsection{\texttt{sub_mlist} kernel noads} % \subsubsection{\texttt{sub_mlist} kernel noads}
The inner list is converted as a \xmltag{mrow} element, with the core being the core of the \xmltag{mrow} element. See the rules for this later. % The inner list is converted as a \xmltag{mrow} element, with the core being the core of the \xmltag{mrow} element. See the rules for this later.
%
\subsubsection{\texttt{delim} kernel noads} % \subsubsection{\texttt{delim} kernel noads}
If the \texttt{small_char} is zero, these get converted as space like elements of the form % If the \texttt{small_char} is zero, these get converted as space like elements of the form
\begin{verbatim} % \begin{verbatim}
{[0] = 'mspace', % {[0] = 'mspace',
width = '1.196pt', % width = '1.196pt',
} % }
\end{verbatim} % \end{verbatim}
where 1.196 is replaced by the current value of \verb+\nulldelimiterspace+ converted to \texttt{bp}. % where 1.196 is replaced by the current value of \verb+\nulldelimiterspace+ converted to \texttt{bp}.
%
Otherwise the same rules as for \texttt{math_char} apply, % Otherwise the same rules as for \texttt{math_char} apply,
except that instead of \texttt{mi} or \xmltag{mn} elements, % except that instead of \texttt{mi} or \xmltag{mn} elements,
\texttt{mo} elements are generated, % \texttt{mo} elements are generated,
\texttt{mathvariant} is never set, % \texttt{mathvariant} is never set,
\texttt{stretchy} is set to \texttt{true} if the operator is not on the list of default stretchy operators in the MathML specification % \texttt{stretchy} is set to \texttt{true} if the operator is not on the list of default stretchy operators in the MathML specification
nd \texttt{lspace} and \texttt{rspace} attributes are set to zero. % nd \texttt{lspace} and \texttt{rspace} attributes are set to zero.
%
\subsubsection{\texttt{acc} kernel noads} % \subsubsection{\texttt{acc} kernel noads}
Depending on the surrounding element containing the \texttt{acc} kernel noad, it is either stretchy or not. % Depending on the surrounding element containing the \texttt{acc} kernel noad, it is either stretchy or not.
If it's stretchy, the same rules as for \texttt{delim} apply, except that \texttt{lspace} and \texttt{rspace} are not set. % If it's stretchy, the same rules as for \texttt{delim} apply, except that \texttt{lspace} and \texttt{rspace} are not set.
Otherwise the \texttt{stretchy} attribute is set to false if the operator is on the list of default stretchy operators. % Otherwise the \texttt{stretchy} attribute is set to false if the operator is on the list of default stretchy operators.