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+\documentclass{article}
+\begin{document}
+\title{From math lists to MathML}
+\subtitle{The algorithm in luamml}
+\author{Marcel}
+\maketitle
+\section{General concepts}
+In the following I assume basic familiarity with both Lua\TeX's representation of math noads and MathML.
+
+\subsection{Representation of XML elements}
+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.
+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.
+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
+\begin{verbatim}
+<math block="display">
+  <mn>0</mn>
+  <mo> &lt; </mo>
+  <mi mathvariant="normal">x</mi>
+</math>
+\end{verbatim}
+would be represented by the Lua table
+\begin{verbatim}
+{[0] = "math", block="display",
+  {[0] = "mn", "0"},
+  {[0] = "mo", "<"},
+  {[0] = "mi", mathvariant="normal", "x"}
+}
+\end{verbatim}
+
+\subsection{Expression cores}
+MathML knows the concept of \enquote{embellished operators}:
+\begin{blockquote}
+  The precise definition of an \enquote{embellished operator} is:
+  \begin{itemize}
+    \item an \tag{mo} element;
+    \item or one of the elements \tag{msub}, \tag{msup}, \tag{msubsup}, \tag{munder}, \tag{mover}, \tag{munderover}, \tag{mmultiscripts}, \tag{mfrac}, or \tag{semantics} (§ 5.1 Annotation Framework), whose first argument exists and is an embellished operator;
+    \item or one of the elements \tag{mstyle}, \tag{mphantom}, or \tag{mpadded}, such that an mrow containing the same arguments would be an embellished operator;
+    \item or an \tag{maction} element whose selected sub-expression exists and is an embellished operator;
+    \item or an \tag{mrow} whose arguments consist (in any order) of one embellished operator and zero or more space-like elements.
+  \end{itemize}
+\end{blockquote}
+For every embellished operator, MathML calls the \tag{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.
+The core is always a \tag{mo}, \tag{mi}, or \tag{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 \tag{mo} element representing the core of the embellished operator.
+The core is a \tag{mi} or a \tag{mn} element if and only if the element would be an embellished operator with this core if this element where a \tag{mo} element.
+The core is the special space like marker for space like elements. Otherwise the core is \texttt{nil}.
+
+\section{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}
+
+\subsection{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.
+
+\subsubsection{\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}.
+(For \textt{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 \tag{mn} elements, everything else becomes a \tag{mi} element with \texttt{mathvariant} set to \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}.
+
+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}
+{[0] = 'mi',
+  mathvariant = 'normal',
+  ["tex:family"] = 3,
+  "a"
+}
+\end{verbatim}
+
+\subsection{\texttt{sub_box} kernel noads}
+I am open to suggestions how to convert them properly.
+
+\subsection{\texttt{sub_mlist} kernel noads}
+The inner list is converted as a \tag{mrow} element, with the core being the core of the \tag{mrow} element. See the rules for this later.
+
+\subsection{\texttt{delim} kernel noads}
+If the \texttt{small_char} is zero, these get converted as space like elements of the form
+\begin{verbatim}
+{[0] = 'mspace',
+  width = '1.196pt',
+}
+\end{verbatim}
+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,
+except that instead of \texttt{mi} or \tag{mn} elements,
+\texttt{mo} elements are generated,
+\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 
+nd \texttt{lspace} and \texttt{rspace} attributes are set to zero.
+
+\subsection{\texttt{acc} kernel noads}
+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.
+Otherwise the \textt{stretchy} attribute is set to false if the operator is on the list of default stretchy operators.
+
+\end{document}