adtrees (20jan16)

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+The adtrees package provides a package to write adpositional trees, a
+formalism devoted to represent natural language expressions.
+
+The package is composed by the filed
+- adtree.sty: containing the LaTeX engine to adpositional trees;
+- adtreedoc.pdf: the human readable documentation for the package;
+- adtreedoc.tex: the source code for the documentation.
+
+The package is distributed under the GNU General Public License.
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+\documentclass{amsart}
+\usepackage{amssymb}
+\usepackage{color}
+\usepackage{graphics}
+\usepackage{adtrees}
+\usepackage{url}
+
+\begin{document}
+\title{Adpositional Trees in \LaTeX}
+\date{}
+\author[Marco Benini]{Marco Benini}
+\address[Marco Benini]{Dipartimento di Scienza e Alta Tecnologia\\ 
+  Universit\`a degli Studi dell'Insubria\\
+  via Valleggio 11, I-22100 Como, Italy}
+\email{marco.benini@uninsubria.it}
+\urladdr{http://marcobenini.wordpress.com}
+\author[Federico Gobbo]{Federico Gobbo}
+\address[Federico Gobbo]{Faculty of Humanities\\
+  University of Amsterdam\\ 
+  Spuistraat 210,NL-1012VT Amsterdam, The Netherlands}
+\email{F.Gobbo@uva.nl}
+\urladdr{http://federicogobbo.name}
+\maketitle
+
+% --------------------------
+\section{Introduction}\label{sec:introduction}
+Adpositional trees (adtrees, for short) are a formal way to represent
+expressions in natural language. They have been defined, used, and
+discussed in F.~Gobbo and M.~Benini, \textit{Constructive Adpositional
+  Grammars: Foundations of Constructive Linguistics}, Cambridge
+Scholar Press (2011). Since then, they have been used without
+theoretical modifications in a number of applications.
+
+This document describes the \LaTeX\/ package to draw adtrees. This
+package is an improvement over the original one used to typeset all
+the examples in the previously cited book. The present package
+maintains the same graphical presentation with a number of
+improvements, and an incompatible syntax. Also, the original package,
+although never distributed, is no longer maintained.
+
+This document describes all the features of the package. It is written
+so that a user may start typesetting adtrees as soon as possible: all
+the fundamental commands and macros are presented in
+Section~\ref{sec:simple}. At the first reading, the subsequent
+sections may be freely skipped.
+
+Section~\ref{sec:centring} describes the next obvious step: how to put
+an adtree inside your document, controlling the way to align it with
+other objects. Section~\ref{sec:complex} explains how to control the
+length of branches via the \verb|\unitlength| value. It also
+introduces the variants of the fundamental commands to modify the
+lengths of the branches in the adtree, the angle between them, or
+both, either globally, locally, or recursively.
+
+Section~\ref{sec:internal} describes the low-level definitions that
+affect the construction of the various pieces composing
+adtrees. Changing these definitions is intended for advanced users,
+who want to modify the standard appearance of
+adtrees. Section~\ref{sec:hints} concludes the description of the
+graphical package, showing some special techniques to deal with
+adtrees, and a couple of very low-level primitives of the package.
+
+The final Section~\ref{sec:linear} describes the way to render adtrees
+in a linear format. This is a minor feature which we discourage to
+use, except for very special purposes.
+
+% --------------------------
+\section{Simple Adtrees}\label{sec:simple}
+The installation of the package is standard: see the documentation on
+your particular \TeX\/ system for the details. Using the package in a
+document requires it to be invoked with
+\verb|\usepackage{adtrees}|.\vspace{1.5ex}
+
+The simplest adtree is composed by a single morpheme:
+\begin{equation*}
+  \ATm{Liza}{O}
+\end{equation*}
+which has been typeset by the command 
+\begin{verbatim}
+    \ATm{Liza}{O}
+\end{verbatim}
+
+Sometimes, a morpheme requires to specify attributes:
+\begin{equation*}
+  \ATm{Liza}{O}[proper noun][animated]
+\end{equation*}
+this behaviour is accomplished by the command
+\begin{verbatim}
+    \ATm{Liza}{O}[proper noun][animated]
+\end{verbatim}
+
+The general form of the \verb|\ATm| command is 
+\begin{equation*}
+  \verb|\ATm{| m \verb|}{| g \verb|}[| a_1 \verb|]| \cdots \verb|[|
+    a_n \verb|]|
+\end{equation*}
+with $m$ the morpheme, $g$ its grammar character, and $a_1, \dots,
+a_n$ its attributes, if any.  The attributes are optional, and there
+can be any number of them. Also, notice how all the commands in the
+package start with \verb|\AT|: the final \verb|m| stands for
+\emph{morpheme}. This is a general naming rule: all the fundamental
+command have the form \verb|\AT| followed by a single letter which
+reminds its function. Variants of the fundamental commands use a
+two-letter code, the first letter being the same as the fundamental
+command, and the second letter reminding the variant.
+
+% --------------------------
+\subsection{Complex Adtrees}\label{subsec:complex}
+A complex adtree is made by two adtrees, composed via an
+\emph{adposition}, which is described by a morpheme together with the
+grammar character of the resulting adtree, and the
+\emph{trajectory}. The trajectory is an arrow, and it can be
+$\leftarrow$, $\rightarrow$, or $\leftrightarrow$. The following three
+examples are very similar to the ones in Figure 2.11 of Gobbo and
+Benini (2011:24):
+\begin{equation*}
+  \ATr{to}{I_2^2}
+  {\ATm{Kim}{O_2}}
+  {\ATs{The box belongs}{I_1^2}}
+  \qquad
+  \ATl{$\epsilon$}{I_2^2}
+  {\ATs{the box}{O_2}}
+  {\ATs{Kim owns}{I_1^2}}
+  \qquad 
+  \ATb{on}{E>I_1^1}
+  {\ATs{the box}{O}}
+  {\ATs{Kim jumps}{I_1^1}}
+\end{equation*}
+
+These adtrees are typeset, respectively, by the commands
+\begin{verbatim}
+    \ATr{to}{I_2^2}
+    {\ATm{Kim}{O_2}}
+    {\ATs{The box belongs}{I_1^2}}
+
+    \ATl{$\epsilon$}{I_2^2}
+    {\ATm{the box}{O_2}}
+    {\ATs{Kim owns}{I_1^2}}
+
+    \ATb{on}{E>I_1^1}
+    {\ATs{the box}{O_2}}
+    {\ATs{Kim jumps}{I_1^1}}
+\end{verbatim}\vspace{1.5ex}
+
+The general format of these commands is
+\begin{equation*}
+  c \verb|{| a \verb|}{| g \verb|}[| x_1 \verb|]| \dots \verb|[| x_n 
+  \verb|]{| L \verb|}{| R \verb|}|
+\end{equation*}
+with $c$ among \verb|\ATl|, \verb|ATr|, \verb|\ATb|; $a$ the
+adposition: $g$ the grammar character of the whole construction; $x_1,
+\dots, x_n$ the optional attributes of the construction; $L$ the left
+adtree; and $R$ the right adtree. The adposition is typeset as normal
+text, the grammar character in math mode with the roman typeface, so
+that super- and sub-scripts can be freely used, and the trajectory is
+defined by the command: \verb|\ATl| for the \emph{left} arrow,
+\verb|\ATr| for the \emph{right} arrow, and \verb|\ATb| for the arrow
+in \emph{both} direction, following the general naming rule.  The
+attributes are optional and they are typeset as in the morpheme
+construction.\vspace{1.5ex}
+
+Actually, the \verb|\ATm| command is used to typeset proper morphemes,
+while the \verb|\ATs| command is designed to typeset expressions which
+can be expanded into an adtree. In fact, the \verb|s| letter stands
+for \emph{summary}, following the general naming rule. The \verb|\ATs|
+command has the same syntax as the \verb|\ATm| command, and it differs
+just in the graphical appearance. So, it may take an arbitrary number
+of attributes, and whatever applies to \verb|\ATm| holds for
+\verb|\ATs|, too.
+
+% --------------------------
+\subsection{Epsilon Adpositions}\label{subsec:epsilon}
+Since writing adtrees with the empty adposition, represented by the
+$\epsilon$ symbol, is very common, the following commands are
+provided: \verb|\ATle|, \verb|\ATre|, and \verb|\ATbe|, with \verb|e|
+standing for \emph{empty} in the general naming convention. They
+behave as the command without the trailing \verb|e|, but the
+adposition is automatically typeset. Also, they share the same
+syntax. So, the previous example
+\begin{equation*}
+  \ATle{I_2^2}
+  {\ATs{the box}{O}}
+  {\ATs{Kim owns}{I_1^2}}
+\end{equation*}
+can be typeset in a simplified way as
+\begin{verbatim}
+    \ATle{I_2^2}
+    {\ATs{the box}{O}}
+    {\ATs{Kim owns}{I_1^2}}
+\end{verbatim}\vspace{1.5ex}
+
+Similarly, because the so-called epsilon-transformations are common,
+and they require to forget about adpositions and morphemes, which is
+graphically marked by cancelling them with a stroke, the package
+automatically includes the \verb|cancel| package by Donald Arseneau,
+(available in CTAN, at
+\url{http://mirror.ctan.org/macros/latex/contrib/cancel}). In
+addition, to simplify the cancellation of empty adpositions, the
+commands \verb|\ATrc| \verb|\ATlc| \verb|\ATbc| are provided, with
+\verb|c| standing for \emph{cancel ed}. They work as their
+counterparts with the trailing \verb|e|, sharing the same syntax. For
+example,
+\begin{equation*}
+  \ATlc{I_2^2}
+  {\ATs{\cancel{the apple}}{O}}
+  {\ATs{Kim eats}{I_1^2}}
+\end{equation*}
+has been typeset by
+\begin{verbatim}
+    \ATlc{I_2^2}
+    {\ATs{\cancel{the apple}}{O}}
+    {\ATs{Kim eats}{I_1^2}}
+\end{verbatim}
+
+% --------------------------
+\subsection{Overlapping subtrees}\label{subsec:overlapping}
+When one has to write complex adtrees, it is often the case that there
+are overlapping subtrees. To cope with these situations, the simplest
+way is to prolong the left or the right branch of a node. This
+behaviour can be accomplished with the \verb|\ATxl| and \verb|\ATxr|
+commands, where \verb|x| stands for \emph{extends} and \verb|l| and
+\verb|r| for \emph{left} and \emph{right}, respectively. They both
+take a single argument which is the adtree being appended at the end
+of the extended branch.  For example, the following adtree, similar to
+the one in Figure~2.16 (Gobbo and Benini 2011:29):
+\begin{equation*} 
+  \unitlength.23ex
+  \ATl{with}{I^3_3}[phrase]
+  {\ATs{the key}{O}}
+  {\ATre{I^3_2}
+    {\ATxl{\ATs{the door}{O_2}}}
+    {\ATs{will be opened}{I^3}}}
+\end{equation*}
+has been typeset by the following \LaTeX\/ code
+\begin{verbatim}
+    \ATl{with}{I^3_3}[phrase]
+    {\ATs{the key}{O_3}}
+    {\ATre{I^3_2}
+      {\ATxl{\ATs{the door}{O_2}}}
+      {\ATs{will be opened}{I^3}}}
+\end{verbatim}
+
+The example also shows how to put an attribute in the top adposition.
+Normally, for reasons of space, adtrees use extensively summaries to
+put in evidence only the linguistic phenomenon needed in that
+moment. For example, the following adtree:
+\begin{equation*} 
+  \ATl{with}{I^3_3}
+  {\ATs{the key}{O_3}}
+  {\ATxr{\ATs{the door will be opened}{I^3_2}}}
+\end{equation*}
+has been typeset by the following \LaTeX\/ code
+\begin{verbatim}
+    \ATl{with}{I^3_3}
+      {\ATs{the key}{O_3}}
+      {\ATxr{\ATs{the door will be opened}{I^3_2}}}
+\end{verbatim}
+The example also shows a right-branch extension. Overlapping can be
+also avoided in complex adtrees using advanced commands. See Section
+\ref{sec:complex} for details.
+
+% --------------------------
+\subsection{Morphological adpositions}\label{subsec:mu}
+Sometimes, for the sake of clarity, morphological relations should be
+stated explicitly. For example, the following adtree:
+\begin{equation*} 
+  \unitlength.2ex
+  \ATr{-ly}{E>I^3_2}
+  {\ATm{quick-}{A}}
+  {\ATre{I^3_2}
+    {\ATxl{\ATs{the door}{O_2}}}
+    {\ATs{will be opened}{I^3}}}
+\end{equation*}
+which has been typeset by the following \LaTeX\/ code
+\begin{verbatim}
+    \ATr{-ly}{E>I^3_2}
+    {\ATm{quick-}{A}}
+    {\ATre{I^3_2}
+      {\ATxl{\ATs{the door}{O_2}}}
+      {\ATs{will be opened}{I^3}}}
+\end{verbatim}
+could be made explicit, where the $\mu$ adposition indicates a
+morphological relation. For example, the following adtree is
+linguistically equivalent to the previous one:
+\begin{equation*} 
+  \unitlength.2ex
+  \ATle{I^3_2}
+  {\ATxl{\ATxl{\ATrmu{E}
+        {\ATm{-ly}{E}}
+        {\ATm{quick-}{A}}}}}
+  {\ATre{I^3_2}
+    {\ATxl{\ATs{the door}{O_2}}}
+    {\ATs{will be opened}{I^3}}}
+\end{equation*}
+and it has been typeset by the following \LaTeX\/ code
+\begin{verbatim}
+    \ATle{I^3_2}
+    {\ATxl{\ATxl{\ATrmu{E}
+          {\ATm{-ly}{E}}
+          {\ATm{quick-}{A}}}}}
+    {\ATre{I^3_2}
+      {\ATxl{\ATs{the door}{O_2}}}
+      {\ATs{will be opened}{I^3}}}
+\end{verbatim}
+The package provides the commands \verb|\ATlmu|, \verb|\ATrmu|, and
+\verb|\ATbmu|, analogous to the $\epsilon$ variants, to simplify the
+typesetting of adtrees using the $\mu$ adposition.
+
+% --------------------------
+\section{Alignments and Centring}\label{sec:centring}
+Drawing an adtree in a display is the simplest and most common way:
+\begin{equation*}
+  \ATl{with}{I^3_3}
+  {\ATs{the key}{O_3}}
+  {\ATre{I^3_2}
+    {\ATxl{\ATs{the door}{O_2}}}
+    {\ATs{will be opened}{I^3}}}
+\end{equation*}
+is generated by the following code
+\begin{verbatim}
+    \begin{equation*}
+      \ATl{with}{I^3_3}
+        {\ATs{the key}{O_3}}
+        {\ATre{I^3_2}
+          {\ATxl{\ATs{the door}{O_2}}}} 
+          {\ATs{will be opened}{I^3}}}
+    \end{equation*}
+\end{verbatim}\vspace{1.5ex}
+
+Putting an adtree in a figure environment reduces to write the
+corresponding \LaTeX\/ display inside the content of the \verb|figure|
+environment.
+
+In general, we strongly encourages the user to use a robust display
+environment, like \verb|equation*| or \verb|displaymath|, and to avoid
+the \verb|center| environment. Advanced displays to align mathematical
+material, as in AMS-\TeX\/, are another good and reliable option to
+place adtrees in a page.\vspace{1.5ex}
+
+An adtree fits exactly its enclosing box, that is
+\begin{equation*}
+  \fboxsep0pt
+  \unitlength.3ex
+    \fbox{\ATl{with}{I^3_3}
+    {\ATs{the key}{O_3}}
+    {\ATre{I^3_2}
+      {\ATxl{\ATbe{O_2}{\ATm{the}{A}}{\ATm{door}{O}}}}
+      {\ATs{will be opened}{I^3}}}}
+\end{equation*}
+If one looks closely (and that is why the adtree is so big), there is
+half of the point in the root which lies outside the box. This is done
+on purpose, to make easier to collate together adtrees.\vspace{1.5ex}
+
+Writing a morpheme or a summary directly inside the text, like
+\ATm{Gargoyle}{O}, produces a box whose baseline is exactly the
+baseline of the morpheme. This makes the behaviour predictable, even
+if the graphical appearance is quite terrible (like in this
+paragraph). An adtree, like \ATre{I_2^2} {\ATm{the box}{O_2}}
+{\ATbe{I_1^2}{\ATm{Kim}{O_1}}{\ATs{owns}{I^2}}}, behaves similarly,
+because the baseline of the box is the baseline of the lowest morpheme
+or summary in the whole tree, the one corresponding to the \emph{owns}
+morpheme in the example.
+
+So, at least in principle, since the user can rely on the size of the
+enclosing box, and on the position of the baseline, it is possible to
+align an adtree in whatever way one may desire. In our experience, the
+only really common way one requires to move adtrees in the surrounding
+text is to centre them: the package provides three commands to centre
+an adtree horizontally, vertically, or both. These are
+\verb|\ATvcentre|, \verb|\AThcentre|, and \verb|\ATcentre|,
+respectively. For example
+\begin{equation*}
+  \ATvcentre{\ATl{with}{I^3_3}
+    {\ATs{the key}{O_3}}
+    {\ATre{I^3_2}
+      {\ATxl{\ATs{the door}{O_2}}}
+      {\ATs{will be opened}{I^3}}}} 
+  \mathbin{\equiv}
+  \ATvcentre{\ATl{with}{I^3_3}
+    {\ATs{the key}{O_3}}
+    {\ATre{I^3_2}
+      {\ATs{the door}{O_2}}
+      {\ATxr{\ATs{will be opened}{I^3}}}}}
+\end{equation*}
+has been generated by
+\begin{verbatim}
+    \ATvcentre{\ATl{with}{I^3_3}
+      {\ATs{the key}{O_3}}
+      {\ATre{I^3_2}
+        {\ATxl{\ATs{the door}{O_2}}}
+        {\ATs{will be opened}{I^3}}}} 
+    \mathbin{\equiv}
+    \ATvcentre{\ATl{with}{I^3_3}
+      {\ATs{the key}{O_3}}
+      {\ATre{I^3_2}
+        {\ATs{the door}{O_2}}
+      {\ATxr{\ATs{will be opened}{I^3}}}}}
+\end{verbatim}
+
+More sophisticated ways to place an adtree in the page are discussed
+in Section~\ref{sec:hints}.
+
+% --------------------------
+\section{Dealing with Complex Adtrees}\label{sec:complex}
+Simple adtrees are easily typeset using the previously described
+commands. But, sooner or later, one has to typeset a complex adtree,
+which does not fit into the page, or whose branches overlap, no matter
+how we extend branches, or which looks awful because of a poor choice
+of dimensions. In all these cases, there are a number of strategies
+one may adopt.\vspace{1.5ex}
+
+The simplest and crudest one is to change the length of branches. In
+this respect, branches are drawn using the \LaTeX\/ \verb|picture|
+environment, so the length of each branch is
+$25\verb|\unitlength|$. The value of \verb|\unitlength| may be changed
+globally, affecting the way all subsequent adtrees in a document are
+typeset. Also, the value may be changed inside a surrounding group,
+which affects only the adtree to be typeset, but not the rest of the
+document. Finally, the value of \verb|\unitlength| can be changed
+within the adtree, to affect the point where the change appears and
+all the subtrees. Notice how there is no way to directly change the
+value of \verb|\unitlength| in a single node: we will return on this
+point later.
+
+For example,
+\begin{equation*}
+  {\unitlength.3ex
+    \ATl{with}{I^3_3}
+    {\ATs{the key}{O_3}}
+    {\ATre{I^3_2}
+      {\ATs{the door}{O_2}}
+      {\ATs{will be opened}{I^3}}} }
+\end{equation*}
+has been typeset by
+\begin{verbatim}
+      {\unitlength.3ex
+        \ATl{with}{I^3_3}
+        {\ATs{the key}{O_3}}
+        {\ATre{I^3_2}
+          {\ATs{the door}{O_2}}
+          {\ATs{will be opened}{I^3}}} }
+\end{verbatim}
+adopting the strategy to affect all the branches in the adtree. Notice
+how the outermost braces limit the scope of the change to the value of
+\verb|\unitlength|.
+
+On the contrary,
+\begin{equation*}
+  \ATl{with}{I^3_3}
+  {\unitlength.12ex\ATxl{\ATbe{O_3}
+    {\ATm{the}{A}}
+    {\ATm{key}{O}}}}
+  {\unitlength.33ex\ATre{I^3_2}
+    {\ATs{the door}{O_2}}
+    {\ATs{will be opened}{I^3}}}
+\end{equation*}
+modifies the length of all the branches in the left subtree to
+\verb|3ex| (since $3 = 25 \cdot 0.12$), and to \verb|8.25ex| in the
+right subtree
+\begin{verbatim}
+    \ATl{with}{I^3_3}
+    {\unitlength.12ex\ATxl{\ATbe{O_3}
+      {\ATm{the}{A}}
+      {\ATm{key}{O}}}}
+    {\unitlength.33ex\ATre{I^3_2}
+      {\ATs{the door}{O_2}}
+      {\ATs{will be opened}{I^3}}}
+\end{verbatim}
+
+The adposition, and the related arrow and grammar character are moved
+accordingly, which is not pleasant in this example, although it is
+what one usually wants when changing the value of \verb|\unitlength|
+in the whole adtree. 
+
+The right way to have the adposition always in the same place with
+respect to the branches in a node, is to fix a suitable
+\verb|\unitlength| for the whole adtree, and to extend locally, just
+in the single node, its value. The exact technique is a bit complex,
+and it will be explained by an example later. Usually, there is no
+need to cope with these minor details, except for maniacs or for high
+precision works.\vspace{1.5ex}
+
+The length of branches can be changed locally to a single node,
+without recursively affecting the subtrees, as it happens when we
+change the value of \verb|\unitlength| inside a node, like in the
+latest example. This can be achieved using the length variant of the
+adtree drawing commands. There are also an angle variant, and a
+variant affecting both the length and the angle.
+
+The complete list of complex adtree drawing commands, with all the
+variants is:
+\begin{center}
+  \begin{tabular}{cccc}\renewcommand{\arraystretch}{1.3}
+    \textbf{base command} & \textbf{length variant} & \textbf{angle
+      variant} & \textbf{combined variant}\\ 
+    \hline\hline
+    \multicolumn{4}{c}{{\huge\strut}\emph{plain adtrees}}\\
+    \verb|\ATl| & \verb|\ATlL| & \verb|\ATlA| & \verb|\ATlLA|\\
+    \verb|\ATr| & \verb|\ATrL| & \verb|\ATrA| & \verb|\ATrLA|\\
+    \verb|\ATb| & \verb|\ATbL| & \verb|\ATbA| & \verb|\ATbLA|\\
+    \hline
+    \multicolumn{4}{c}{{\huge\strut}\emph{extensions}}\\
+    \verb|\ATxl| & \verb|\ATxlL| & \verb|\ATxlA| & \verb|\ATxlLA|\\
+    \verb|\ATxr| & \verb|\ATxrL| & \verb|\ATxrA| & \verb|\ATxrLA|\\
+    \hline
+    \multicolumn{4}{c}{{\huge\strut}\emph{adtrees with special
+        adpositions}}\\ 
+    \verb|\ATle| & \verb|\ATleL| & \verb|\ATleA| & \verb|\ATleLA|\\
+    \verb|\ATlc| & \verb|\ATlcL| & \verb|\ATlcA| & \verb|\ATlcLA|\\
+    \verb|\ATlmu| & \verb|\ATlmuL| & \verb|\ATlmuA| & \verb|\ATlmuLA|\\ 
+    \verb|\ATre| & \verb|\ATreL| & \verb|\ATreA| & \verb|\ATreLA|\\
+    \verb|\ATrc| & \verb|\ATrcL| & \verb|\ATrcA| & \verb|\ATrcLA|\\
+    \verb|\ATrmu| & \verb|\ATrmuL| & \verb|\ATrmuA| & \verb|\ATrmuLA|\\ 
+    \verb|\ATbe| & \verb|\ATbeL| & \verb|\ATbeA| & \verb|\ATbeLA|\\
+    \verb|\ATbc| & \verb|\ATbcL| & \verb|\ATbcA| & \verb|\ATbcLA|\\
+    \verb|\ATbmu| & \verb|\ATbmuL| & \verb|\ATbmuA| & \verb|\ATbmuLA|\\ 
+    \hline
+  \end{tabular}
+\end{center}
+The names of these commands are easy to remember: the length variant
+has a trailing \verb|L|, the angle variant a trailing \verb|A|, and
+the combined variant a trailing \verb|LA|.  
+
+The syntax of the length variant is the same as the base command
+except that there is an additional argument, the first one, which
+contains the value for the local \verb|\unitlength|. In fact, the
+length we specify has exactly the same effect of changing
+\verb|\unitlength| just before the command, but the change does not
+apply recursively.
+
+It is worth remarking that, e.g., \verb|\ATlL{\unitlength}| is
+equivalent to \verb|\ATl|, so to reduce the length of branches to
+$90\%$ of their current value, it suffices the write something like
+\verb|\ATrL{.9\unitlength}|.
+
+Similarly, the syntax of the angle variant requires an additional
+first argument which can be $60$, $90$, or $120$, representing the
+angle between the branches: the default is $60$ degrees. Specifying
+any other values resorts to the default.  
+
+The combined variant requires two additional arguments, the length and
+the angle, in this order, before any other parameter.
+
+A hidden, very technical, feature of the package is that, whatever
+follows the length in the \verb|L| argument gets evaluated inside the
+group which generates the branches in the node. So, for those well
+inside \LaTeX\/ mysteries, this feature can be used to tweak the
+behaviour of the graphical engine.\vspace{1.5ex}
+
+For example,
+\begin{equation*}
+  \ATlL{.4ex}{with}{I^3_3}
+  {\ATbe{O_3}
+    {\ATm{the}{A}}
+    {\ATm{key}{O}}}
+  {\ATreL{.25ex}{I^3_2}
+    {\ATs{the door}{O_2}}
+    {\ATs{will be opened}{I^3}}}
+\end{equation*}
+has been typeset by
+\begin{verbatim}
+    \ATlL{.4ex}{with}{I^3_3}
+    {\ATbe{O_3}
+      {\ATm{the}{A}}
+      {\ATm{key}{O}}}
+    {\ATreL{.25ex}{I^3_2}
+      {\ATs{the door}{O_2}}
+      {\ATs{will be opened}{I^3}}}
+\end{verbatim}\vspace{1.5ex}
+
+The \emph{trick} to have the adposition always in the same place we
+speak before, is now easy to write, although slightly
+cumbersome. Specifically, the trick is to choose a reasonable global
+value for \verb|\unitlength| which affects all the adtree, and then to
+locally extend the branches with the \verb|\ATxlL| and \verb|\ATxrL|
+commands whenever there is a need. The sensible choice for
+\verb|\unitlength| minimises the number of extensions, and nicely
+place the adpositions. For example
+\begin{verbatim}
+    {\unitlength.32ex
+      \ATl{with}{I^3_3}
+      {\ATxlL{.1ex}
+        {\ATbe{O_3}
+          {\ATm{the}{A}}
+          {\ATm{key}{O}}}}
+      {\ATxrL{.2ex}
+        {\ATre{I^3_2}
+          {\ATs{the door}{O_2}}
+          {\ATs{will be opened}{I^3}}}}}
+\end{verbatim}
+generates
+\begin{equation*}
+  {\unitlength.3ex
+    \ATl{with}{I^3_3}
+    {\ATxlL{.1ex}{\ATbe{O_3}
+        {\ATm{the}{A}}
+        {\ATm{key}{O}}}}
+    {\ATxrL{.2ex}{\ATre{I^3_2}
+        {\ATs{the door}{O_2}}
+        {\ATs{will be opened}{I^3}}}}}
+\end{equation*}\vspace{1.5ex}
+
+Another possibility to change the geometry of adtrees is to modify the
+angle between the branches. The commands to change the angle in the
+whole document, or within any group, affecting just the content of the
+group, are \verb|\ATnormalangle|, which sets the angle to $60$
+degrees, the default, \verb|\ATwideangle|, which sets the angle to
+$90$ degrees, and \verb|\ATextrawideangle|, which sets the angle to
+$120$ degrees. These values are the only possible ones, also in the
+angle variant of the commands, as said before. Moreover, the value
+$60$, $90$, or $120$ passed to the angle variant of a command (or to
+the combined variant) affect the node locally, as in the length
+variants' case.
+
+For example
+\begin{equation*}
+  {\ATwideangle\unitlength.3ex
+    \ATl{with}{I^3_3}
+    {\ATbe{O_3}
+      {\ATm{the}{A}}
+      {\ATm{key}{O}}}
+    {\ATxrL{.2ex}{\ATre{I^3_2}
+      {\ATs{the door}{O_2}}
+      {\ATs{will be opened}{I^3}}}} }
+\end{equation*}
+has been typeset by
+\begin{verbatim}
+    {\ATwideangle\unitlength.3ex
+      \ATl{with}{I^3_3}
+      {\ATbe{O_3}
+        {\ATm{the}{A}}
+        {\ATm{key}{O}}}
+      {\ATxrL{.2ex}{\ATre{I^3_2}
+        {\ATs{the door}{O_2}}
+        {\ATs{will be opened}{I^3}}}} }
+\end{verbatim}
+
+However, the following adtree
+\begin{equation*}
+  \ATlLA{.5ex}{120}{with}{I^3_3}
+  {\ATbe{O_3}
+    {\ATm{the}{A}}
+    {\ATm{key}{O}}}
+  {\ATreL{.25ex}{I^3_2}
+    {\ATs{the door}{O_2}}
+    {\ATs{will be opened}{I^3}}}
+\end{equation*}
+has been generated by
+\begin{verbatim}
+    \ATlLA{.5ex}{120}{with}{I^3_3}
+    {\ATbe{O_3}
+      {\ATm{the}{A}}
+      {\ATm{key}{O}}}
+    {\ATreL{.25ex}{I^3_2}
+      {\ATs{the door}{O_2}}
+      {\ATs{will be opened}{I^3}}}
+\end{verbatim}
+
+The placement of the adposition varies when the angle is changed: this
+has been done on purpose to cope with the reduction in height which is
+induced by a larger angle between the branches. Notice how the
+reduction in height may cause the adposition part of the adtree to
+fall beyond the base of the branches.
+
+% --------------------------
+\section{Internal Constructions}\label{sec:internal}
+All the major parts of an adtree can be customised. This section
+describes a number of definitions which are used to control the
+spacing between the various parts of morpheme blocks, summaries, and
+adposition blocks. Also, the boxes which are deputed to provide a
+format to a single morpheme, a grammar character, or an attribute, are
+described.\vspace{1.5ex}
+
+The shape of the adposition block, which lies just below the root of a
+node in the adtree, is synthetically described as:
+\begin{equation*}
+  {\unitlength2ex
+    \begin{picture}(14,14)
+      \thinlines
+      \put( 0, 2){\line(1,0){14}}
+      \put( 0, 4){\line(1,0){14}}
+      \put( 0, 6){\line(1,0){14}}
+      \put( 0, 8){\line(1,0){14}}
+      \put( 0,10){\line(1,0){14}}
+      \put( 0,12){\line(1,0){14}}
+      \put( 7,13){\makebox(0,0){pre skip}}
+      \put( 7,11){\makebox(0,0){$t$}}
+      \put( 7, 9){\makebox(0,0){first intermediate skip}}
+      \put( 7, 7){\makebox(0,0){$a$}}
+      \put( 7, 5){\makebox(0,0){second intermediate skip}}
+      \put( 7, 3){\makebox(0,0){$g + x$}}
+      \put( 7, 1){\makebox(0,0){post skip}}
+      \thicklines
+      \put( 0, 0){\line(1,0){14}}
+      \put( 0,14){\line(1,0){14}}
+      \put( 0, 0){\line(0,1){14}}
+      \put(14, 0){\line(0,1){14}}
+    \end{picture}}
+  \qquad\qquad\qquad
+  \raisebox{6ex}{\ATb{$a$}{g}[x]{\ATm{}{}}{\ATm{}{}}}
+\end{equation*}
+Here, $t$ stands for the trajectory, one of $\leftarrow$,
+$\rightarrow$, or $\leftrightarrow$, as in the exemplifying adtree
+above; $a$ is the adposition; $g$ is the grammar character; $x$ is an
+attribute. The various skips are \LaTeX\/ commands deputed to add
+vertical space between the components.
+
+These commands, together with their definition, are:
+\begin{verbatim}
+    \def\ATpreadpositionskip{\relax}
+    \def\ATfirstinteradpositionskip{\vskip.3ex}
+    \def\ATsecondinteradpositionskip{\vskip.3ex}
+    \def\ATpostadpositionskip{\relax}
+\end{verbatim}
+They can be redefined globally, to affect all the adtrees following
+the redefinition, or locally, within a group which limits the
+scope. For example, the following adtree
+\begin{equation*}
+  {\def\ATpreadpositionskip{\vskip-2ex}
+    \ATrL{.3ex}{to}{I_2^2}
+    {\ATm{Kim}{O_2}}
+    {\ATs{The box belongs}{I^2_1}}}
+\end{equation*}
+has been obtained by the code
+\begin{verbatim}
+    {\def\ATpreadpositionskip{\vskip-2ex}
+      \ATrL{.3ex}{to}{I_2^2}
+      {\ATm{Kim}{O_2}}
+      {\ATs{The box belongs}{I^2_1}}}
+\end{verbatim}
+
+The \verb|L| hidden feature of the package, already introduces, allows
+to redefine these commands within the scope of a single node, as in
+the root of
+\begin{equation*}
+  \ATrL{\unitlength\def\ATpreadpositionskip{\vskip-2ex}}
+  {to}{I_2^2}{\ATm{Kim}{O}}
+  {\ATbe{I_1^2}{\ATs{The box}{O_1}}{\ATm{belongs}{I^2_1}}}
+\end{equation*}
+This effect is obtained by the following code
+\begin{verbatim}
+    \ATrL{\unitlength\def\ATpreadpositionskip{\vskip-2ex}}
+    {to}{I_2^2}
+    {\ATm{Kim}{O_2}}
+    {\ATbe{I_1^2}{\ATs{The box}{O_1}}{\ATm{belongs}{I^2}}}
+\end{verbatim}\vspace{1.5ex}
+
+Attributes are managed so to form a unique block together with the
+grammar character. This block is constructed by the \verb|\ATm| and
+\verb|\ATs| commands, and inside the previously described adposition
+block.
+
+It is important to remark that, although the size of text is normal in
+the case of the morpheme and summary blocks, and while it is small in
+the case of the adposition block, the values of skips are not affected
+by the size. Thus, we strongly suggest, if you want to change them, to
+express these values in the \verb|ex| unit, which is the right unit to
+measure vertical space in terms of the \emph{current} font size.
+
+The structure of the attribute block is
+\begin{equation*}
+  {\unitlength2ex
+    \begin{picture}(14,14)
+      \thinlines
+      \put( 0, 2){\line(1,0){14}}
+      \put( 0, 4){\line(1,0){14}}
+      \put( 0, 6){\line(1,0){14}}
+      \put( 0, 8){\line(1,0){14}}
+      \put( 0,10){\line(1,0){14}}
+      \put( 0,12){\line(1,0){14}}
+      \put( 7,13){\makebox(0,0){$g$}}
+      \put( 7,11){\makebox(0,0){first skip}}
+      \put( 7, 9){\makebox(0,0){$a_1$}}
+      \put( 7, 7){\makebox(0,0){intermediate skip}}
+      \put( 7, 5){\makebox(0,0){$\vdots$}}
+      \put( 7, 3){\makebox(0,0){intermediate skip}}
+      \put( 7, 1){\makebox(0,0){$a_n$}}
+      \thicklines
+      \put( 0, 0){\line(1,0){14}}
+      \put( 0,14){\line(1,0){14}}
+      \put( 0, 0){\line(0,1){14}}
+      \put(14, 0){\line(0,1){14}}
+    \end{picture}}
+  \qquad\qquad\qquad
+  {\def\ATAttributeBox#1{\strut\textsf{#1}}
+    \raisebox{20ex}{\ATm{}{g}[\lbrack$a_1$\rbrack]
+      [\vdots]
+      [\lbrack$a_n$\rbrack]} }
+\end{equation*}
+Here, $g$ is the grammar character, while $a_1, \dots, a_n$ are the
+various attributes. The commands defining the skips in this block are
+\begin{verbatim}
+    \def\ATfirstattrskip{\vskip.7ex}
+    \def\ATinterattrskip{\vskip.5ex}
+\end{verbatim}
+These definitions can be changed globally or locally, within the scope
+of a group. Also, in the case of attributes in the adposition block,
+they can be redefined within the single node, with the same technique
+as before.
+
+It is worth remarking that any kind of material can be generated by
+these commands, not only vertical space. For example
+\begin{equation*}
+  {\makeatletter
+    \def\ATfirstattrskip{\vskip.5ex
+      \hbox to\@ATlen{\hfil\tiny * * *\hfil}\nointerlineskip
+      \vskip.3ex}
+    \makeatother
+    \ATbe{O}[determ]
+    {\ATm{the}{A}}
+    {\ATm{box}{O}}}
+\end{equation*}
+has been generated by
+\begin{verbatim}
+    {\makeatletter
+      \def\ATfirstattrskip{\vskip.5ex
+        \hbox to\@ATlen{\hfil\tiny * * *\hfil}\nointerlineskip
+        \vskip.3ex}
+      \makeatother
+      \ATbe{O}[determ]
+      {\ATm{the}{A}}
+      {\ATm{box}{O}}}
+\end{verbatim}\vspace{1.5ex}
+
+Finally, morpheme and summary blocks are as follows:
+\begin{equation*}
+  {\unitlength2ex
+    \begin{picture}(14,12)
+      \thinlines
+      \put( 0, 2){\line(1,0){14}}
+      \put( 0, 4){\line(1,0){14}}
+      \put( 0, 6){\line(1,0){14}}
+      \put( 0, 8){\line(1,0){14}}
+      \put( 0,10){\line(1,0){14}}
+      \put( 7,11){\makebox(0,0){$\triangle$, if a summary}}
+      \put( 7, 9){\makebox(0,0){pre skip}}
+      \put( 7, 7){\makebox(0,0){$m$}}
+      \put( 7, 5){\makebox(0,0){intermediate skip}}
+      \put( 7, 3){\makebox(0,0){$g + x$}}
+      \put( 7, 1){\makebox(0,0){post skip}}
+      \thicklines
+      \put( 0, 0){\line(1,0){14}}
+      \put( 0,12){\line(1,0){14}}
+      \put( 0, 0){\line(0,1){12}}
+      \put(14, 0){\line(0,1){12}}
+    \end{picture}}
+  \qquad\qquad
+  \raisebox{15ex}{\ATm{m}{g}[x]}
+  \qquad
+  \raisebox{14ex}{\ATs{m}{g}[x]}
+\end{equation*}
+Here, $m$ is the morpheme or expression, and $g$ is the grammar
+character together with its attributes $x$. The commands defining the
+skips in this block are
+\begin{verbatim}
+    \def\ATpremorphemeskip{\vskip.5ex}
+    \def\ATintermorphemeskip{\vskip1ex}
+    \def\ATpostmorphemeskip{\relax}
+\end{verbatim}
+Again, these definitions can be modified globally, or locally, within
+a group that limits the scope of the change. It is worth remarking
+that nesting an \verb|\ATm| or \verb|\ATs| command inside a complex
+adtree provides a natural group. For example
+\begin{equation*}
+  \ATbe{O}
+  {\def\ATpremorphemeskip{\vskip0ex}
+    \def\ATintermorphemeskip{\vskip.2ex}
+    \ATm{the}{A}}
+  {\ATm{box}{O}}
+\end{equation*}
+has been typeset by
+\begin{verbatim}
+    \ATbe{O}
+    {\def\ATpremorphemeskip{\vskip0ex}
+      \def\ATintermorphemeskip{\vskip.2ex}
+      \ATm{the}{A}}
+    {\ATm{box}{O}}
+\end{verbatim}\vspace{1.5ex}
+
+Actually, the face of morphemes, adpositions, and expressions in
+summaries is controlled by the following command:
+\begin{verbatim}
+    \def\ATMorphemeBox#1{#1\strut}
+\end{verbatim}
+The \verb|\strut| forces all the instances to have the same minimal
+height and depth. So, to typeset all the morphemes and summaries in
+italic, as in
+\begin{equation*}
+  {\def\ATMorphemeBox#1{\textit{#1}\strut}
+    \ATb{in}{E>I_2^2}
+    {\ATs{the house}{O}}
+    {\ATs{Kim moves}{I^2_1}} }
+\end{equation*}
+the following code suffices
+\begin{verbatim}
+    {\def\ATMorphemeBox#1{\textit{#1}\strut}
+      \ATb{in}{E>I_2^2}
+      {\ATs{the house}{O}}
+      {\ATs{Kim moves}{I^2_1}} }
+\end{verbatim}\vspace{1.5ex}
+
+Similarly, the face of grammar characters, wherever they appear, is
+controlled by the command
+\begin{verbatim}
+    \def\ATGrammarCharacterBox#1{$\mathrm{#1}$}
+\end{verbatim}
+The same scoping rules apply as in the case of
+\verb|\ATMorphemeBox|. So, for example, we can make the grammar
+character of the left subtree to be \verb|\Huge|, as in
+\begin{equation*}
+  \ATb{in}{E>I_2^2}
+  {\def\ATGrammarCharacterBox#1{\Huge$\mathrm{#1}$}
+    \ATs{the house}{O}}
+  {\ATs{Kim move}{I_1^2}}
+\end{equation*}
+by typing the following code
+\begin{verbatim}
+    \ATb{in}{E>I_2^2}
+    {\def\ATGrammarCharacterBox#1{\Huge$\mathrm{#1}$}
+      \ATs{the house}{O}}
+    {\ATs{Kim moves}{I_1^2}}
+\end{verbatim}\vspace{1.5ex}
+
+Also attributes are typeset according to a command:
+\begin{verbatim}
+    \def\ATAttributeBox#1{\textsf{[#1]}}
+\end{verbatim}
+So, for example, the illustrating attribute block on the previous page
+has been generated by the following code
+\begin{verbatim}
+    {\def\ATAttributeBox#1{\strut\textsf{#1}}
+      \raisebox{20ex}{\ATm{}{g}[\lbrack$a_1$\rbrack]
+        [\vdots]
+        [\lbrack$a_n$\rbrack]} }
+\end{verbatim}\vspace{1.5ex}
+
+Finally, the symbol denoting a summary can be customised by changing
+\begin{verbatim}
+    \def\ATSummarySymbol{$\triangle$}
+\end{verbatim}
+It is important to remark that the top vertex of the triangle lies in
+the middle of the top of the $\triangle$ character, providing a
+natural point to join with the branches of adtrees. This fact should
+be taken in account when changing the definition.
+
+% --------------------------
+\section{Hints and Tricks}\label{sec:hints}
+There are a few last features which can be exploited in the
+\verb|adtrees| package. These are the low-level commands to draw the
+branches:
+\begin{verbatim}
+    \def\ATleftbranch#1#2{\line(#1,#2)}
+    \def\ATrightbranch#1#2{\line(#1,#2)}
+    \def\ATcircle{\circle*}
+\end{verbatim}
+
+The \verb|\ATleftbranch| and \verb|\ATrightbranch| commands draw the
+left and the right branch of an adtree, respectively. Also, they draw
+the extensions, when present. They can be redefined globally, locally
+within the scope of a group, or locally within a node, using the
+implicit scope of the length variant, as previously described by the
+trick to equalise the position of adposition blocks.
+
+For example,
+\begin{equation*}
+  \unitlength.2ex
+  {\def\ATrightbranch#1#2{\color{red}\line(#1,#2)}
+    \ATlL{\unitlength
+      \def\ATleftbranch##1##2{\color{green}\line(##1,##2)}}
+    {with}{I^3_3}
+    {\ATs{the key}{O_3}}
+    {\ATre{I^3_2}
+      {\ATxl{\ATs{the door}{O_2}}}
+      {\ATs{will be opened}{I^3}}} }
+\end{equation*}
+is obtained by making all the right branches red, and the topmost left
+branch green:
+\begin{verbatim}
+    {\def\ATrightbranch#1#2{\color{red}\line(#1,#2)}
+      \ATlL{\unitlength
+        \def\ATleftbranch##1##2{\color{green}\line(##1,##2)}}
+      {with}{I^3_3}
+      {\ATs{the key}{O_3}}
+      {\ATre{I^3_2}
+        {\ATxl{\ATs{the door}{O_2}}}
+        {\ATs{will be opened}{I^3}}} }
+\end{verbatim}
+
+Also, the following definition
+\begin{verbatim}
+    {\def\ATcircle#1{\relax}
+      \ATl{with}{I^3_3}
+      {\ATs{the key}{O_3}}
+      {\ATre{I^3_2}
+        {\ATxl{\ATs{the door}{O_2}}}
+        {\ATs{will be opened}{I^3}}} }
+\end{verbatim}
+suppresses the points in the whole adtree
+\begin{equation*}
+  \unitlength.2ex
+  {\def\ATcircle#1{\relax}
+    \ATl{with}{I^3_3}
+    {\ATs{the key}{O_3}}
+    {\ATre{I^3_2}
+      {\ATxl{\ATs{the door}{O_2}}}
+      {\ATs{will be opened}{I^3}}} }
+\end{equation*}
+
+As a rather extreme and useless example, one can typeset the previous
+adtree without showing the branches and making the points really huge
+\begin{equation*}
+  {\def\ATcircle#1{\circle*{8}}
+    \def\ATleftbranch#1#2#3{\relax}
+    \def\ATrightbranch#1#2#3{\relax}
+    \unitlength.22ex
+    \ATl{with}{I^3_3}
+    {\ATs{the key}{O_3}}
+    {\ATre{I^3_2}
+      {\ATxl{\ATs{the door}{O_2}}}
+      {\ATs{will be opened}{I^3}}} }
+\end{equation*}
+by the following code
+\begin{verbatim}
+    {\def\ATcircle#1{\circle*{8}}
+      \def\ATleftbranch#1#2#3{\relax}
+      \def\ATrightbranch#1#2#3{\relax}
+      \unitlength.22ex
+      \ATl{with}{I^3_3}
+      {\ATs{the key}{O_3}}
+      {\ATre{I^3_2}
+        {\ATxl{\ATs{the door}{O_2}}}
+        {\ATs{will be opened}{I^3}}} }
+\end{verbatim}\vspace{1.5ex}
+
+Another important aspect of the package is that every adtree lies in a
+\TeX\/ box. It means that all the standard commands to manipulate
+boxes are available.
+
+For example
+\begin{equation*}
+  \rotatebox{-30}
+  {\ATlcLA{.3ex}{90}{I_2^2}
+    {\ATs{\cancel{the apple}}{O_2}}
+    {\ATs{Kim eats}{I_1^2}}}
+\end{equation*}
+has been generated by
+\begin{verbatim}
+    \rotatebox{-30}
+    {\ATlcLA{.3ex}{90}{I_2^2}
+      {\ATs{\cancel{the apple}}{O_2}}
+      {\ATs{Kim eats}{I_1^2}}}
+\end{verbatim}
+
+Sometimes, scaling a box is required:
+\begin{equation*}
+  \scalebox{1.5}
+  {\ATlcLA{.3ex}{90}{I_2^2}
+    {\ATs{\cancel{the apple}}{O_2}}
+    {\ATs{Kim eats}{I_1^2}}}
+\end{equation*}
+has been generated by
+\begin{verbatim}
+    \scalebox{1.5}
+    {\ATlcLA{.3ex}{90}{I_2^2}
+      {\ATs{\cancel{the apple}}{O_2}}
+      {\ATs{Kim eats}{I_1^2}}}
+\end{verbatim}\vspace{1.5ex}
+
+A final point is that, when the \verb|\smaller| command is available,
+as in AMS-\TeX, changing the font size automatically makes the
+adposition blocks to be \verb|\smaller| than the size of the normal
+text, which is used to typeset the morpheme and summary blocks. For
+example,
+\begin{equation*}
+  \hbox{\huge
+    \ATlcLA{.3ex}{120}{I_2^2}
+      {\ATs{\cancel{the apple}}{O_2}}
+      {\ATs{Kim eats}{I_1^2}}}
+\end{equation*}
+which has been generated by
+\begin{verbatim}
+    {\huge
+      \ATlcLA{.3ex}{120}{I_2^2}
+        {\ATs{\cancel{the apple}}{O_2}}
+        {\ATs{Kim eats}{I_1^2}}}
+\end{verbatim}
+
+When the \verb|smaller| command is not available, the size of the
+adposition block is fixed to be \verb|\small|. This can be changed
+modifying the (internal) command \verb|\@ATsmall|:
+\begin{verbatim}
+    \makeatletter
+    \def\@ATsmall{\small}
+    \makeatother
+\end{verbatim}
+Changing \verb|\small| in the above code, modifies the size of the
+components of the adposition block. We suggest to avoid such a change,
+except in a local group which contains a complete adtree.
+
+% --------------------------
+\section{Linear Adtrees}\label{sec:linear}
+Adtrees can be rendered in a linear format. This is not graphically
+pleasant, so we discourage users to adopt it.\vspace{1.5ex}
+
+Nevertheless, it may be useful to have a very compact representation
+of adtrees. This can be automatically obtained by prepending the
+\verb|\ATlinearise| command to an adtree. For example
+\begin{equation*}
+  \ATlinearise{\ATlcL{.3ex}{I_2^2}[phrase]
+    {\ATm{\cancel{something}}{O}[object][fruit]}
+    {\ATs{Kim eats}{I_1^2}}}
+\end{equation*}
+is the same as
+\begin{equation*}
+  \ATlcL{.3ex}{I_2^2}[phrase]
+  {\ATm{\cancel{something}}{O}[object][fruit]}
+  {\ATs{Kim eats}{I_1^2}}
+\end{equation*}
+which shows how all the features of adtrees are rendered in the linear
+format. 
+
+The linear presentation has been generated by
+\begin{verbatim}
+    \ATlinearise{\ATlcL{.3ex}{I_2^2}[phrase]
+      {\ATm{\cancel{something}}{O}[object][fruit]}
+      {\ATs{Kim eats}{I_1^2}}}
+\end{verbatim}
+which differs from the code to draw the graphics presentation just for
+\verb|\ATlinearise|.\vspace{1.5ex}
+
+Declaring \verb|\ATLinear| in some point of the text makes linear all
+the adtrees from that point on. To reestablish the standard behaviour
+of graphical adtrees, one issues the command
+\verb|\ATNormal|.\vspace{1.5ex} 
+
+Linear adtrees are composed using the following commands
+\begin{verbatim}
+    \def\ATlinearadpositionblock#1#2#3{%
+       {#2}${}^{\hbox{#1}}_{\hbox{#3}}$}
+    \def\ATlinearfirstattribute#1#2{{#1}:{#2}}
+    \def\ATlinearnextattribute#1#2{{#1};{#2}}
+    \def\ATlinearsubtrees#1#2{(#1,\linebreak[0] #2)}
+    \def\ATlinearmorphemeblock#1#2{{#1}${}_{\hbox{#2}}$}
+    \def\ATlinearsummaryblock#1#2{({#1})${}_{\hbox{#2}}$}
+\end{verbatim}
+Their meaning should be intuitive after the explanations in
+Section~\ref{sec:internal}. 
+
+Also, it must be remarked that \verb|\ATMorphemeBox|,
+\verb|\ATGrammarCharacterBox|, and \verb|\ATAttributeBox| are still
+used to write the corresponding elements.\vspace{1.5ex}
+
+Linear adtrees are useful when it is required to perform some
+computation on an adtree inside \LaTeX, e.g., when trying to write a
+macro which manipulates an argument which is an adtree. 
+
+The reason is double: first, the linear format require far less
+computation than the graphical rendering; and, second, the building
+macros receive inputs which have not been heavily preprocessed to
+prepare their graphical rendering, thus closer to what the user has
+written in the source code.
+
+For example, to list all the morpheme attributes occurring inside
+\begin{equation*}
+  \ATlL{.3ex}{with}{I^2_2}[phrase]
+  {\ATs{the key}{O}[third actant]}
+  {\ATre{I^2_1}
+    {\ATxl{\ATs{the door}{O}[second actant]}}
+    {\ATs{will be opened}{I^3}[governor]}}
+\end{equation*}
+we can execute
+\begin{verbatim}
+    {\def\ATlinearadpositionblock#1#2#3{\relax}
+      \def\ATlinearfirstattribute#1#2{#2}
+      \def\ATlinearnextattribute#1#2{[{#2}]}
+      \def\ATlinearsubtrees{\relax}
+      \def\ATlinearmorphemeblock#1{\relax}
+      \def\ATlinearsummaryblock#1{\relax}
+      \ATlinearise{\ATl{with}{I^2_2}[phrase]
+        {\ATs{the key}{O}[third actant]}
+        {\ATre{I^2_1}
+          {\ATxl{\ATs{the door}{O}[second actant]}}
+          {\ATs{will be opened}{I^2}[governor]}}} }
+\end{verbatim}
+which produces
+\begin{equation*}
+  {\def\ATlinearadpositionblock#1#2#3{\relax}
+    \def\ATlinearfirstattribute#1#2{#2}
+    \def\ATlinearnextattribute#1#2{[{#2}]}
+    \def\ATlinearsubtrees{\relax}
+    \def\ATlinearmorphemeblock#1{\relax}
+    \def\ATlinearsummaryblock#1{\relax}
+    \ATlinearise{\ATl{with}{I^2_2}[phrase]
+      {\ATs{the key}{O}[third actant]}
+      {\ATre{I^2_1}
+        {\ATxl{\ATs{the door}{O}[second actant]}}
+        {\ATs{will be opened}{I^2}[governor]}}} }
+\end{equation*}
+It is needless to say that such computations require a real \TeX\/
+magician, who is able to understand (and, hopefully, improve) the code
+of the package! Nevertheless, this opens the door to \LaTeX\/ macros
+that operate on adtrees, treating them like data structures.\vfill
+
+\end{document}
\ No newline at end of file