% \iffalse meta-comment
% SPDX-FileCopyrightText: Copyright (c) 2021-2025 Yegor Bugayenko
% SPDX-License-Identifier: MIT
% \fi

% \CheckSum{0}
%
% \CharacterTable
%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%   Digits        \0\1\2\3\4\5\6\7\8\9
%   Exclamation   \!     Double quote  \"     Hash (number) \#
%   Dollar        \$     Percent       \%     Ampersand     \&
%   Acute accent  \'     Left paren    \(     Right paren   \)
%   Asterisk      \*     Plus          \+     Comma         \,
%   Minus         \-     Point         \.     Solidus       \/
%   Colon         \:     Semicolon     \;     Less than     \<
%   Equals        \=     Greater than  \>     Question mark \?
%   Commercial at \@     Left bracket  \[     Backslash     \\
%   Right bracket \]     Circumflex    \^     Underscore    \_
%   Grave accent  \`     Left brace    \{     Vertical bar  \|
%   Right brace   \}     Tilde         \~}

% \GetFileInfo{eolang.dtx}
% \DoNotIndex{\endgroup,\begingroup,\let,\else,\s,\n,\r,\\,\1,\fi}

% \iffalse
%<*driver>
\ProvidesFile{eolang.dtx}
%</driver>
%<package>\NeedsTeXFormat{LaTeX2e}
%<package>\ProvidesPackage{eolang}
%<*package>
[2025/03/26 0.18.3 Formulas and Graphs for EO Programming Language]
%</package>
%<*driver>
\documentclass{ltxdoc}
\usepackage[T1]{fontenc}
\usepackage[maxnames=1,minnames=1,maxbibnames=1,natbib=true,citestyle=authoryear,bibstyle=authoryear,doi=false,url=false,isbn=false,isbn=false]{biblatex}
\addbibresource{eolang.bib}
\usepackage[tt=false, type1=true]{libertine}
\usepackage{microtype}
\AddToHook{env/verbatim/begin}{\microtypesetup{protrusion=false}}
\usepackage{graphicx}
\usepackage{xcolor}
\usepackage[runs=2,dtx]{docshots}
\usepackage[nocomments]{eolang}
\usepackage{href-ul}
\PageIndex
\EnableCrossrefs
\CodelineIndex
\RecordChanges
\begin{document}
  \DocInput{eolang.dtx}
  \PrintChanges
  \PrintIndex
\end{document}
%</driver>
% \fi

% \title{\includegraphics[height=1in]{cactus.pdf} \\ |eolang|: \LaTeX{} Package \\ for Formulas and Graphs \\ of EO Programming Language \\ and $\varphi$-calculus\thanks{The sources are in GitHub at \href{https://github.com/objectionary/eolang.sty}{objectionary/eolang.sty}}}
% \author{Yegor Bugayenko \\ \texttt{yegor256@gmail.com}}
% \date{\filedate, \fileversion}
%
% \maketitle
%
% \textbf{\color{red}NB!}
% You must run \TeX{} processor with |-shell-escape| option
% and you must have \href{https://www.perl.org}{Perl} installed.
% If you omit the |-shell-escape| option, the package will try
% to use cached files, if they exist. If they don't, compilation will
% fail. Thus, when you must prepare your document for a compilation
% without the |-shell-escape| option, run it locally with the option provided
% and then package all files (including the files in the |_eolang-*| directories)
% into a single ZIP archive. It is advised to use |tmpdir| package option
% in this case, in order to make the directory name not depend on the
% \LaTeX{} engine.
%
% If |-shell-escape| is set, this package won't work on Windows, because
% it uses POSIX command line interface.

% \section{Introduction}
%
% This package helps you print formulas of $\varphi$-calculus,
% which is a formal foundation of \href{https://www.eolang.org}{EO}
% programming language. The calculus was introduced by \citet{bugayenko2021eolang}
% and later formalized by \citet{kudasov2021}. Here is how you render
% a simple expression:
% \begin{docshot}
% \documentclass{minimal}
% \usepackage{eolang}
% \begin{document}
% \begin{phiquation*}
% app -> [[ % it's abstract!
%   ^ !-> $.b.^{^2}, 0/t~> TRUE,
%   b -> [[ *-> Q.fn(56),
%     @ -> QQ.string.trim($),
%     D> 01-FE-C3 ]]]],\\
% x -> [[ \lambda ..> ? ]].
% \end{phiquation*}
% \end{document}
% \end{docshot}

% \DescribeEnv{phiquation}
% The environment |phiquation| lets you write a $\varphi$-calculus expressions
% using simple plain-text notation, where:
% \begin{itemize}\setlength\itemsep{0em}
%   \item ``|@|'' maps to ``$\varphi$''
%     (|\varphi|),
%   \item ``|^|'' maps to ``$\rho$''
%     (|\rho|),
%   \item ``|$|'' maps to ``$\xi$''
%     (|\xi|),
%   \item ``|&|'' maps to ``$\sigma$''
%     (|\sigma|),
%   \item ``|?|'' maps to ``$\varnothing$''
%     (|\varnothing|),
%   \item ``|Q|'' maps to ``$\Phi$''
%     (|\Phi|),
%   \item ``|QQ|'' maps to ``$\dot{\Phi}$''
%     (|\dot{\Phi}|),
%   \item ``|->|'' maps to ``$\mapsto$''
%     (|\mapsto|),
%   \item ``|~>|'' maps to ``$\phiWave$''
%     (|\phiWave|),
%   \item ``|!->|'' maps to ``$\phiConst$''
%     (|\phiConst|),
%   \item ``|..>|'' maps to ``$\phiDotted$''
%     (|\phiDotted|),
%   \item ``|D>|'' maps to ``$\Delta\phiDotted$''
%     (|\Delta ..>|),
%   \item ``|L>|'' maps to ``$\lambda\phiDotted$''
%     (|\lambda ..>|),
%   \item ``|[[|'' maps to ``$\llbracket$''
%     (|\llbracket|),
%   \item ``|]]|'' maps to ``$\rrbracket$''
%     (|\rrbracket|),
%   \item ``|==|'' maps to ``$\equiv$''
%     (|\equiv|),
%   \item ``\texttt{\textbar{abc}\textbar}'' maps to ``\texttt{abc}''
%     (|\texttt{abc}|).
% \end{itemize}
% Also, a few symbols are supported for $\varphi$PU architecture:
% \begin{itemize}\setlength\itemsep{0em}
%   \item ``|<<|'' maps to ``$\langle$''
%     (|\langle|),
%   \item ``|>>|'' maps to ``$\rangle$''
%     (|\rangle|),
%   \item ``|-abc>|'' maps to ``$\phiSlot{abc}$''
%     (|\phiSlot{abc}|),
%   \item ``|:=|'' maps to ``$\vDash$''
%     (|\vDash|).
% \end{itemize}

% Before any arrow you can put a number, which will be rendered as |\alpha| with an index, for example
% |\phiq{0->x}| will render ``\phiq{0->x}''.
% Instead of a number you can use asterisk too.

% You can append a slash and a title to the number of an attribute, such as |0/g->x|.
% This will render as \phiq{0/g->x}. You can use fixed-width words too, for example
% \verb=\phiq{0/|f|->x}= will render as ``\phiq{0/|f|->x}''. It's also possible
% to use an asterisk instead of a number, such that |\phiq{*/g->x}| renders as ``\phiq{*/g->x}''

% Numbers are automatically converted to fixed-width font, no need to always decorate them with vertical bars.

% |TRUE| and |FALSE| are automatically converted to fixed-width font too.

% Object names are automatically converted to fixed-width font too, if they have more than one letter.

% Texts in double quotes are automatically converted to fixed-width font too.

% \DescribeMacro{\phiq}
% The command |\phiq| lets you inline a $\varphi$-calculus expressions
% using the same simple plain-text notation. You can use dollar sign directly too:
% \docshotOptions{firstline=4,lastline=10}
% \begin{docshot}
% \documentclass{article}
% \pagestyle{empty}
% \usepackage{eolang}
% \begin{document}
% A simple object
% \phiq{x -> [[@ -> y]]} \\
% is a decorator of
% the data object \\
% $y -> [[\Delta ..> 42]]$.
% \end{document}
% \end{docshot}

% \DescribeEnv{sodg}
% The environment |sodg| allows you to draw a \href{https://github.com/objectionary/sodg}{SODG} graph:
% \begin{docshot}
% \documentclass{standalone}
% \usepackage{eolang}
% \begin{document}
% \begin{sodg}
% v0 \\ v0===> \\ v0!!A
% v1 xy:v0,-.8,2.8 data:42 tag:d_1
% v0->v1 a:x rho \\ =>v1
% v2 xy:v0,+1,+1 atom:\xi.x+1
% v1->v2 a:|hi| bend:-15
% v2->v0 pi bend:10 % a comment
% \end{sodg}
% \end{document}
% \end{docshot}
% The content of the environment is parsed line by line. Markers in each line are
% separated by a single space. The first marker is either a unique name of a
% vertex, like ``|v1|'' in the example above, or an edge, like ``|v0->v1|.'' All other markers are either
% unary like ``|rho|'' or binary like ``|atom:$\xi.x+1$|.'' Binary markers have two
% parts, separated by colon.

% The following markers are supported for a vertex:
% \begin{itemize}\setlength\itemsep{0em}
%   \item ``|tag:<math>|'' puts a custom label |<math>| into the circle;
%   \item ``|data:[<box>]|'' makes it a data vertex with an optional attached ``|<box>|''
%     (the content of the box may only be numeric data);
%   \item ``|atom:[<box>]|'' makes it an atom with an optional attached ``|<box>|''
%     (the content of the box is a math formula);
%   \item ``|box:<txt>|'' attaches a ``|<box>|'' to it;
%   \item ``|xy:<v>,<r>,<d>|'' places this vertex in a position relative to the vertex ``|<v>|,''
%     shifting it right by ``|<r>|'' and down by ``|<d>|'' centimetres;
%   \item ``|+:<v>|'' makes a copy of an existing vertex and all its kids;
%   \item ``|edgeless|'' removes the border from the vertex;
%   \item ``|style:{...}|'' adds this TikZ style to the vertex |\node|.
% \end{itemize}

% The following markers are supported for an edge:
% \begin{itemize}\setlength\itemsep{0em}
%   \item ``|rho|'' places a backward snake arrow to the edge,
%   \item ``|bend:<angle>|'' bend it right by the amount of ``|<angle>|,''
%   \item ``|a:<txt>|'' attaches label ``|<txt>|'' to it,
%   \item ``|pi|'' makes it dotted, with $\pi$ label;
%   \item ``|style:{...}|'' adds this TikZ style to the edge |\path|.
% \end{itemize}

% It is also possible to put transformation arrows to the graph, with the help of ``|v0=>v1|'' syntax. The arrow
% will be placed exactly between two vertices. You can also put an arrow from a vertex to the right,
% saying for example ``|v3=>|'', or from the left to the vertex, by saying for example ``|=>v5|.'' If you
% want the arrow to stay further away from the vertex than usual, use a few ``|=|'' symbols, for example ``|===>v0|.''

% You can also put a marker at the left side of a vertex, using ``|v5!A|'' syntax, where ``|v5|'' is the vertex
% and ``|A|'' is the text in the marker. They are useful when you put a few graphs on a picture
% explaining how one graph is transformed to another one and so forth. You can make the distance between the vertex
% and the marker a bit larger by using a few exclamation marks,
% for example ``|v5!!!A|'' will make a distance three times bigger.

% You can make a clone of an existing vertex together with all its dependants, by using this syntax: ``|v0+a|.''
% Here, we make a copy of ``|v0|'' and call it ``|v0a|.'' See the example below.

% Be aware, unrecognized markers are simply ignored, without any error reporting.

% \DescribeMacro{\eolang}
% \DescribeMacro{\phic}
% \DescribeMacro{\xmir}
% There is also a no-argument command |\eolang| to help you print the name of
% \eolang{} language. It understands the |anonymous| package option and prints itself
% differently, to double-blind your paper. There is also |\phic| command to print
% the name of \phic{}, also sensitive to |anonymous| mode. The macro |\xmir| prints "XMIR".
% \docshotOptions{firstline=3,lastline=10}
% \begin{docshot}
% \documentclass{acmart}
% \thispagestyle{empty}
% \usepackage[anonymous]{eolang}
% \begin{document}
% In our research we use \eolang{}, \\
% an experimental object-oriented \\
% dataflow language, \phic{}, as its \\
% formal foundation, and \xmir{} --- \\
% its XML-based representation.
% \end{document}
% \end{docshot}
% Without the |anonymous| option there will be no orange color:
% \docshotOptions{firstline=3,lastline=10}
% \begin{docshot}
% \documentclass[anonymous]{acmart}
% \thispagestyle{empty}
% \usepackage{eolang}
% \begin{document}
% In our research we use \eolang{}, \\
% an experimental object-oriented \\
% dataflow language, \phic{}, as its \\
% formal foundation, and \xmir{} --- \\
% its XML-based representation.
% \end{document}
% \end{docshot}

% \DescribeMacro{\phiConst}
% \DescribeMacro{\phiWave}
% \DescribeMacro{\phiDotted}
% A few simple commands are defined to help you render arrows.
% It is recommended not to use them directly, but use |!->| instead. However, if you
% want to use |\phiConst|, wrap it in |\mathrel| for better display:
% \docshotOptions{firstline=6,lastline=12}
% \begin{docshot}
% \documentclass{article}
% \pagestyle{empty}
% \usepackage[paperwidth=3in]{geometry}
% \usepackage{eolang}
% \begin{document}\noindent
% If $x$ is an identifier and $y$ is
% an object, then $x \phiConst y$
% makes $y$ a constant,
% $x \phiWave y$ makes it a decoratee
% of an arbitrary number of objects,
% while $x \phiDotted y$ makes it
% a special attribute.
% \end{document}
% \end{docshot}

% \DescribeMacro{\phiOset}
% \DescribeMacro{\phiUset}
% If you want to put a text over an arrow or under it, use |\phiOset| and |\phiUset| respectively:
% \docshotOptions{firstline=6,lastline=11}
% \begin{docshot}
% \documentclass{article}
% \pagestyle{empty}
% \usepackage[paperwidth=3in]{geometry}
% \usepackage{eolang}
% \begin{document}\noindent
% When the names of attributes and their
% values don't matter, we use an arrow
% with a star, for example:
% \begin{phiquation*}
% [[ \phiOset{*}{->} ]].
% \end{phiquation*}
% \end{document}
% \end{docshot}

% \DescribeMacro{\phiMany}
% Sometimes you may need to simplify the way you describe an object (the typesetting is a bit off, but this is not because of us, but rather because of \href{https://tex.stackexchange.com/questions/664772}{this}):
% \docshotOptions{firstline=6,lastline=14}
% \begin{docshot}
% \documentclass{article}
% \pagestyle{empty}
% \usepackage[paperwidth=3in]{geometry}
% \usepackage{eolang}
% \begin{document}\noindent
% The expression
% \phiq{[[ 1-> x_1,
%   2-> x_2, \dots,
%   \alpha_n -> x_n ]]}
% and expression
% \phiq{[[ \alpha_i
%   \phiMany{->}{i=1}{n} x_i ]]}
% are syntactically different but
% semantically equivalent.
% \end{document}
% \end{docshot}

% \DescribeMacro{\phiSaveTo}
% \DescribeMacro{\sodgSaveTo}
% If you want to use |phiquation| or |sodg| environments inside |tabular| or any other environment or command, you won't be able to do this, because |phiquation| and |sodg| are ``verbatim'' environments. |\phiSaveTo| and |\sodgSaveTo| commands will help you in this situation. You use them right before |\begin{phiquation}| or |\begin{sodg}| respectively --- the content of the equation or the graph won't be rendered, but instead saved to the file. Later, inside |tabular|, you can use it through the |\input| macro (don't forget the |\parbox|):
% \docshotOptions{firstline=5,lastline=12}
% \begin{docshot}
% \documentclass{article}
% \usepackage{eolang}
% \pagestyle{empty}
% \begin{document}
% \phiSaveTo{a}
% \begin{phiquation*}
% [[ x -> [[D>42]] ]]
% \end{phiquation*}
% \begin{tabular}{p{.5in}l}
% Free: & $[[x -> ?]]$ \\
% Bound: & \parbox{1in}{\input{a}} \\
% \end{tabular}
% \end{document}
% \end{docshot}

% \DescribeMacro{\eoAnon}
% You may want to hide some of the content with the help of the |anonymous| package option. The command |\eoAnon| may help you with this. It has two parameters: one mandatory and one optional. The mandatory one is the content you want to show and the optional one is the substituion we will render if the |anonymous| package option is set.

% \section{Package Options}

% \DescribeMacro{tmpdir}
% The default location of temp files is |_eolang|. You can change this with the help of the |tmpdir| package option:
%\iffalse
%<*verb>
%\fi
\begin{verbatim}
\usepackage[tmpdir=/tmp/foo]{eolang}
\end{verbatim}
%\iffalse
%</verb>
%\fi

% \DescribeMacro{nodollar}
% You may disable the special treatment of the dollar sign by using the |nodollar| package option:
%\iffalse
%<*verb>
%\fi
\begin{verbatim}
\usepackage[nodollar]{eolang}
\end{verbatim}
%\iffalse
%</verb>
%\fi

% \DescribeMacro{anonymous}
% You may anonymize |\eolang|, |\xmir|, and |\phic| commands by using |anonymous| package option (they all use the |\eoAnon| command mentioned earlier):
%\iffalse
%<*verb>
%\fi
\begin{verbatim}
\usepackage[anonymous]{eolang}
\end{verbatim}
%\iffalse
%</verb>
%\fi

% \DescribeMacro{noshell}
% You may prohibit any interactions with the shell by using the |noshell| option. This may be helpful when you send your document
% for outside processing and want to make sure the compilation won't break due to shell errors:
%\iffalse
%<*verb>
%\fi
\begin{verbatim}
\usepackage[noshell]{eolang}
\end{verbatim}
%\iffalse
%</verb>
%\fi

% \section{More Examples}

% The |phiquation| environment treats ends of line as signals to start
% new lines in the formula. If you don't want this to happen and want to parse
% the next line as a continuation of the current line, you can use a single
% backslash as it's done here:
% \docshotOptions{firstline=6,lastline=11}
% \begin{docshot}
% \documentclass{article}
% \usepackage{amsmath}
% \usepackage{eolang}
% \pagestyle{empty}
% \begin{document}
% \begin{phiquation*}
% \dfrac \
%  {x->[[@->y]] \quad y->[[z->42]]} \
%  {x.z -> 42} \
%  \text{\sffamily R1}
% \end{phiquation*}
% \end{document}
% \end{docshot}

% This is how you can use |\dfrac| from \href{https://ctan.org/pkg/amsmath}{amsmath} for large inference rules,
% with the help of |\begin{split}| and |\end{split}|:
% \docshotOptions{firstline=6,lastline=15}
% \begin{docshot}
% \documentclass{article}
% \usepackage{amsmath}
% \usepackage{eolang}
% \pagestyle{empty}
% \begin{document}
% \begin{phiquation*}
% \dfrac{\begin{split}
% x->[[@->y, z->42,
%   0/g->?, 1/foo->42]]
% \end{split}}{\begin{split}
% x->[[@->y, z->?, f ~> |pi|(
%   0->[[ \psi !-> |hello|(12) ]],
%     1->42)]]
% \end{split}}\text{R2}.
% \end{phiquation*}
% \end{document}
% \end{docshot}

% You can use the |matrix| environment too, in order to group a few lines:
% \docshotOptions{firstline=5,lastline=11}
% \begin{docshot}
% \documentclass{article}
% \usepackage{eolang}
% \pagestyle{empty}
% \begin{document}
% \begin{phiquation*}
% foo -> \left\{\begin{matrix} \
% ? \\
% [[ L> ^ \times $.\alpha_0 ]] \\
% [[ D> 42 ]] \
% \end{matrix}\right\}
% \end{phiquation*}
% \end{document}
% \end{docshot}

% The |cases| environment works too:
% \docshotOptions{firstline=5,lastline=11}
% \begin{docshot}
% \documentclass{article}
% \usepackage{eolang}
% \pagestyle{empty}
% \begin{document}
% \begin{phiquation*}
% \beta := \begin{cases} \
% [ v_2, @ -dtzd> 42 ] \\
% [ v_{33} ] \
% \end{cases}
% \end{phiquation*}
% \end{document}
% \end{docshot}

% The |phiquation| environment may be used together with the \href{https://ctan.org/pkg/acmart}{acmart} package:
% \begin{docshot}
% \documentclass{acmart}
% \usepackage{eolang}
% \thispagestyle{empty}
% \begin{document}
% \begin{phiquation*}
% x -> [[
%   y -> [[
%     z !-> $, f ..> ? ]]]],\\
% \beta_1 := [ \psi -wait> ? ].
% \end{phiquation*}
% \end{document}
% \end{docshot}

% It's possible to use |\label| inside the |phiquation| environment (pay attention to how you can disable our custom parsing of math formulas by means of curled brackets around the ``|4|'' number):
% \docshotOptions{firstline=6,lastline=13}
% \begin{docshot}
% \documentclass{article}
% \usepackage[paperwidth=3in]{geometry}
% \usepackage{eolang}
% \pagestyle{empty}
% \begin{document}\noindent
% Discriminant can be calculated using
% the following simple formula:
% \begin{phiquation}
% D = b{^2} - {4}ac.
% \label{d}
% \end{phiquation}
% Eq.~\ref{d} is also widely used in
% number theory and polynomial factoring.
% \end{document}
% \end{docshot}

% You can add comments to your equations, using the |&&| command (pay attention, the text inside |\text{}| is not processed and treated like a plain text):
% \docshotOptions{firstline=6,lastline=10}
% \begin{docshot}
% \documentclass{article}
% \usepackage[paperwidth=4in]{geometry}
% \usepackage{eolang}
% \pagestyle{empty}
% \begin{document}
% \begin{phiquation*}
% [[ 0->x ]] && \text{This is formation}
% [[ 0->? ]] && \text{Abstraction}
% x(D>42) && \text{Application}
% \end{phiquation*}
% \end{document}
% \end{docshot}

% If you don't use |nodollar| package option, you can still use normal parsing of the dollar sign, by means of |\(...\)| syntax:
% \docshotOptions{firstline=6,lastline=8}
% \begin{docshot}
% \documentclass{article}
% \usepackage[paperwidth=3in]{geometry}
% \usepackage{eolang}
% \pagestyle{empty}
% \begin{document}\noindent
% The object formation $[[0->x]]$
% may be replaced with a formula
% \( Q \times a^2 \).
% \end{document}
% \end{docshot}

% The |phiquation| environment will automatically align formulas by the first
% arrow, if there are only left-aligned formulas:
% \docshotOptions{firstline=5,lastline=11}
% \begin{docshot}
% \documentclass{acmart}
% \usepackage{eolang}
% \thispagestyle{empty}
% \begin{document}
% \begin{phiquation*}
% x(\pi) -> [[\lambda ..> f_1]], \\
% x(a,b,c) -> [[ \alpha_0 -> ?, \
%   @ -> |hello|($), x -> |FALSE| ]], \\
% \Delta = |43-09|,
% x(y) == x(0-> y).
% \end{phiquation*}
% \end{document}
% \end{docshot}

% If not a single line is indented in |phiquation|, all formulas will be centered:
% \docshotOptions{firstline=5,lastline=9}
% \begin{docshot}
% \documentclass{acmart}
% \usepackage{eolang}
% \thispagestyle{empty}
% \begin{document}
% \begin{phiquation*}
% [[ b -> ? ]],
% [[ @ -> TRUE, \Delta ..> 42 ]], \\
% \psi = << \pi, 42 >>.
% \end{phiquation*}
% \end{document}
% \end{docshot}

% It is possible to use ``manual splitting'' mode in the |phiquation| environment by starting the body with |\begin{split}|:
% \docshotOptions{firstline=5,lastline=10}
% \begin{docshot}
% \documentclass{article}
% \usepackage{eolang}
% \thispagestyle{empty}
% \begin{document}
% \begin{phiquation*}
% \begin{split}
% x(\pi) & -> 4 \\
% x(a,b,c) & -> [[ \alpha_0 -> ? ]] \\
% \end{split}
% \end{phiquation*}
% \end{document}
% \end{docshot}

% When necessary to use a percentage sign, prepend it with a backward slash:
% \docshotOptions{firstline=5,lastline=10}
% \begin{docshot}
% \documentclass{article}
% \usepackage{eolang}
% \thispagestyle{empty}
% \begin{document}
% \begin{phiquation*}
% x -> sprintf("Hello, \%s!", name)
% \end{phiquation*}
% \end{document}
% \end{docshot}

% You can make a copy of a vertex together with its kids:
% \docshotOptions{firstline=5,lastline=15}
% \begin{docshot}
% \documentclass{article}
% \pagestyle{empty}
% \usepackage{eolang}
% \begin{document}
% \begin{sodg}
% v0 \\ v0!!A
% v1 xy:v0,.7,1
% v0->v1 a:x bend:-10
% v2 xy:v1,-1.3,.8
% v1->v2 a:|foo| bend:-20
% v0+a xy:v0,3,0
% v3a xy:v0a,-.7,1
% v0a->v3a a:e bend:-15
% v0=>v0a \\ v0a!B
% \end{sodg}
% \end{document}
% \end{docshot}

% You can make a copy from a copy:
% \docshotOptions{firstline=5,lastline=15}
% \begin{docshot}
% \documentclass{article}
% \pagestyle{empty}
% \usepackage{eolang}
% \begin{document}
% \begin{sodg}
% v0
% v1 xy:v0,.7,1
% v0->v1 a:x bend:-10 rho
% v0+a xy:v0,3,0 \\ v0=>v0a
% v2a xy:v1a,-.8,1.3
% v1a->v2a a:e
% v0a+b xy:v0a,3,0 \\ v0a=>v0b
% v3b xy:v2b,-1,-1
% v2b->v3b a:\psi{} rho
% \end{sodg}
% \end{document}
% \end{docshot}

% You can have ``broken'' edges, using ``|break|'' attribute of an edge.
% The attribute must have a value, which is the percentage of the path
% between vertices that the arrow should take (can't be more than 80 and less than 20).
% This may be convenient when you can't fit all edges into the graph,
% for example:
% \docshotOptions{firstline=5,lastline=14}
% \begin{docshot}
% \documentclass{article}
% \pagestyle{empty}
% \usepackage{eolang}
% \begin{document}
% \begin{sodg}
% v0
% v1 xy:v0,-1,1
% v0->v1 a:x
% v2 xy:v0,0,1
% v0->v2 a:y
% v3 xy:v0,1,1
% v0->v3 a:\psi{}
% v3->v1 a:f bend:-75 break:30
% \end{sodg}
% \end{document}
% \end{docshot}

% You can add \href{https://en.wikipedia.org/wiki/PGF/TikZ}{TikZ} commands to |sodg| graph, for example:
% \docshotOptions{firstline=6,lastline=13}
% \begin{docshot}
% \documentclass{article}
% \pagestyle{empty}
% \usepackage{eolang}
% \usetikzlibrary{fit}
% \begin{document}
% \begin{sodg}
% v0 edgeless
% v11 xy:v0,-1,1 \\ v0->v11
% v12 xy:v0,0,1 \\ v0->v12
% v13 xy:v0,1,1 \\ v0->v13
% \node[draw=red,rounded corners,\
%  dotted,fit=(v11) (v12)] {};
% \end{sodg}
% \end{document}
% \end{docshot}

% You can modify TikZ style yourself (make sure |style:| stays at the end of the line!), for example:
% \docshotOptions{firstline=6,lastline=12}
% \begin{docshot}
% \documentclass{article}
% \pagestyle{empty}
% \usepackage{eolang}
% \usetikzlibrary{fit}
% \begin{document}
% \begin{sodg}
% v0
% v1 xy:v0,-2,1 style:font=\color{red}
% v2 xy:v0,2,1
% v0->v1 style:line width=2pt
% v0->v2 style:draw=orange
% \end{sodg}
% \end{document}
% \end{docshot}

% \StopEventually{}

% \section{Implementation}
% \changes{0.0.1}{2022/10/15}{First draft.}

% First, we include a few packages.
% We need \href{https://ctan.org/pkg/stmaryrd}{stmaryrd} for |\llbracket| and |\rrbracket| commands:
%    \begin{macrocode}
\RequirePackage{stmaryrd}
%    \end{macrocode}
% We need \href{https://ctan.org/pkg/amsmath}{amsmath} for |equation*| environment:
%    \begin{macrocode}
\RequirePackage{amsmath}
%    \end{macrocode}
% We need \href{https://ctan.org/pkg/amssymb}{amssymb} for |\varnothing| command. We disable |\Bbbk|
% because it may conflict with some packages from \href{https://ctan.org/pkg/acmart}{acmart}:
%    \begin{macrocode}
\let\Bbbk\relax\RequirePackage{amssymb}
%    \end{macrocode}
% We need \href{https://ctan.org/pkg/fancyvrb}{fancyvrb} for |\VerbatimEnvironment| command:
%    \begin{macrocode}
\RequirePackage{fancyvrb}
%    \end{macrocode}
% We need \href{https://ctan.org/pkg/iexec}{iexec} for executing Perl scripts:
%    \begin{macrocode}
\ifdefined\eolang@noshell\else\RequirePackage{iexec}\fi
%    \end{macrocode}

% Then, we process package options:
% \changes{0.1.0}{2022/10/26}{Parsing of package options introduced.}
% \changes{0.6.0}{2022/11/14}{Package option \texttt{nocomments} added in order to enable comments suppression in temporary \texttt{.tex} files (may be pretty important for \texttt{.dtx} documents).}
% \changes{0.8.0}{2022/11/29}{The \texttt{anonymous} package option added.}
%    \begin{macrocode}
\RequirePackage{pgfopts}
\RequirePackage{ifluatex}
\RequirePackage{ifxetex}
\pgfkeys{
  /eolang/.cd,
  tmpdir/.store in=\eolang@tmpdir,
  tmpdir/.default=_eolang\ifxetex-xe\else\ifluatex-lua\fi\fi,
  nocomments/.store in=\eolang@nocomments,
  anonymous/.store in=\eolang@anonymous,
  noshell/.store in=\eolang@noshell,
  tmpdir
}
\ProcessPgfPackageOptions{/eolang}
%    \end{macrocode}

% Then, we make a directory where all temporary files will be kept:
%    \begin{macrocode}
\makeatletter
\ifdefined\eolang@noshell\else\RequirePackage{shellesc}\fi
\IfFileExists
  {\eolang@tmpdir/\jobname}
  {\message{eolang: Temporary directory "\eolang@tmpdir/\jobname"
    already exists^^J}}
  {
    \ifdefined\eolang@noshell
      \message{eolang: Temporary directory "\eolang@tmpdir/\jobname"
        is not created, because of the "noshell" package option,
        most probably the compilation will fail later^^J}
    \else
      \ifnum\ShellEscapeStatus=1
        \iexec[null]{mkdir -p "\eolang@tmpdir/\jobname"}
      \else
        \message{eolang: Temporary directory "\eolang@tmpdir/\jobname"
          is not created, because -shell-escape is not set, and
          it doesn't exist, most probably the compilation
          will fail later^^J}
      \fi
    \fi
  }
\makeatother
%    \end{macrocode}

% \begin{macro}{\eolang@lineno}
% \changes{0.3.0}{2022/10/30}{New counter for protecting lineno.}
% Then, we define an internal counter to protect line number from changing:
%    \begin{macrocode}
\makeatletter\newcounter{eolang@lineno}\makeatother
%    \end{macrocode}
% \end{macro}

% \begin{macro}{\eolang@mdfive}
% \changes{0.1.0}{2022/10/26}{New supplementary command added to calculate MD5 sum of a file.}
% Then, we define a command for MD5 hash calculating of a file:
%    \begin{macrocode}
\RequirePackage{pdftexcmds}
\makeatletter
\newcommand\eolang@mdfive[1]{\pdf@filemdfivesum{#1}}
\makeatother
%    \end{macrocode}
% \end{macro}

% \begin{macro}{-phi.pl}
% \changes{0.0.2}{2022/10/21}{The symbols ``\texttt{[}'' and ``\texttt{]}'' replaced with ``\texttt{[[}'' and ``\texttt{]]}'' for abstract object brackets, because they conflicted with normal square brackets}
% \changes{0.0.2}{2022/10/21}{New symbol added for basket slots}
% \changes{0.0.2}{2022/10/21}{Parsing of the symbols ``\texttt{@},'' ``\texttt{\^{}},'' and ``\texttt{\&}'' enabled (\texttt{\char`\\varphi}, \texttt{\char`\\rho}, and \texttt{\char`\\sigma})}
% \changes{0.1.0}{2022/10/26}{A new Perl script "\texttt{eolang-phi.pl}" added for parsing of phi expressions.}
% \changes{0.2.0}{2022/10/29}{Numbers automatically render as \texttt{\char`\\texttt}. No need to use vertical bars around them anymore.}
% \changes{0.3.0}{2022/10/30}{New arrow added, that looks like \texttt{\char`\\leadsto}.}
% \changes{0.5.0}{2022/11/11}{Automated formatting of \texttt{TRUE} and \texttt{FALSE} added.}
% \changes{0.5.0}{2022/11/13}{A new syntax introduced for the \texttt{\char`\\alpha} attributes: \texttt{0->}.}
% \changes{0.5.0}{2022/11/14}{It's possible to use double names for attributes, such as \texttt{0/g->}.}
% \changes{0.7.0}{2022/11/17}{Object names are automatically converted to \texttt{\char`\\texttt}, provided their names include two or more symbols.}
% \changes{0.7.0}{2022/11/17}{Text in quotes is automatically converted to \texttt{\char`\\texttt}.}
% \changes{0.7.0}{2022/11/17}{New syntax sugar constructs added: \texttt{D>} and \texttt{L>} for \texttt{\char`\\Delta} and \texttt{\char`\\lambda} with a dotted arrow respectively.}
% \changes{0.7.0}{2022/11/18}{New syntax sugar for $\Phi$, just using capital ``\texttt{Q}'' is enough.}
% \changes{0.8.0}{2022/11/21}{Inside \texttt{phiquation} any text inside the \texttt{\char`\\text} macro is not processed.}
% \changes{0.9.0}{2022/12/15}{Proper handling of the \texttt{matrix} environment.}
% \changes{0.9.0}{2022/12/15}{Parsing of \texttt{<<} and \texttt{>>} implemented.}
% \changes{0.10.0}{2023/01/22}{Parsing of \texttt{==} into \texttt{\char`\\equiv} implemented.}
% \changes{0.13.0}{2023/06/28}{Parsing of \texttt{QQ} into \texttt{\char`\\dot\{\char`\\Phi\}} implemented.}
% Then, we create a Perl script for |phiquation| processing using |VerbatimOut| environment from
% \href{https://ctan.org/pkg/fancyvrb}{fancyvrb}:
%    \begin{macrocode}
\makeatletter
\ifdefined\eolang@noshell
  \message{eolang: Perl script is not going to be created,
  at "\eolang@tmpdir/\jobname-phi.pl" because of the "noshell"
  package option^^J}
\else
\openin 15=\eolang@tmpdir/\jobname-phi.pl
\ifeof 15
\message{eolang: Perl script is going to be created,
  because it is absent at "\eolang@tmpdir/\jobname-phi.pl",
  but if -shell-escape is not set, the compilation will
  most likely fail now^^J}
\begin{VerbatimOut}{\eolang@tmpdir/\jobname-phi.pl}
$macro = $ARGV[0];
open(my $fh, '<', $ARGV[1]);
my $tex; { local $/; $tex = <$fh>; }
print "% This file is auto-generated by eolang.sty 0.18.3\n";
print '% There are ', length($tex),
  ' chars in the input: ', $ARGV[1], "\n";
print '% ---', "\n";
if (index($tex, "\t") > 0) {
  print "TABS are prohibited!";
  exit 1;
}
my @lines = split (/\n/g, $tex);
foreach my $t (@lines) {
  print '% ', $t, "\n";
}
print '% ---', "\n";
$tex =~ s/(?<!\\)%.*\n/\n/g;
$tex =~ s/^\s+|\s+$//g;
my $splitting = $tex =~ /^\\begin\{split\}/;
if ($splitting) {
  print '% The manual splitting mode is ON since \begin{split} started the text' . "\n";
}
my $indents = $tex =~ /\n +/g;
my $gathered = (0 == $indents);
if ($gathered) {
  if ($splitting) {
    print '% The "gathered" is NOT used because of manual splitting' . "\n";
    $gathered = 0;
  } else {
    print '% The "gathered" is used since all lines are left-aligned' . "\n";
  }
} else {
  print '% The "gathered" is NOT used because ' .
    $indents . " lines are indented\n";
}
my $align = 0;
print '% The "align" is NOT used by default' . "\n";
if (index($tex, '&&') >= 0) {
  $macro =~ s/equation/align/g;
  $align = 1;
  print '% The "align" is used because of && seen in the text' . "\n";
}
if ($macro ne 'phiq') {
  if (not $splitting) {
    $tex =~ s/\\\\\n/\n\n/g;
    $tex =~ s/\\\n\s*//g;
  }
  $tex =~ s/\n*(\\label\{[^\}]+\})\n*/\1/g;
  $tex =~ s/\n{3,}/\n\n/g;
}
my @texts = ();
sub trep {
  my ($s) = @_;
  my $open = 0;
  my $p = 0;
  for (; $p < length($s); $p++) {
    $c = substr($s, $p, 1);
    if ($c eq '}') {
      if ($open eq 0) {
        last;
      }
      $open--;
    }
    if ($c eq '{') {
      $open++;
    }
  }
  push(@texts, substr($s, 0, $p));
  return '{TEXT' . (0+@texts - 1) . '}' . substr($s, $p + 1);
}
$tex =~ s/\\text\{(.+)/trep("$1")/ge;
if (not $splitting) {
  $tex =~ s/(?<![{&])&(?![&}])/\\sigma{}/g;
}
$tex =~ s/([^\\{a-z0-9]|^)QQ(?![a-z0-9])/\1\\dot{\\Phi{}}/g;
$tex =~ s/([^\\{a-z0-9]|^)Q(?![a-z0-9])/\1\\Phi{}/g;
$tex =~ s/([^\\{a-z0-9]|^)D>/\1\\Delta{}..>/g;
$tex =~ s/([^\\{a-z0-9]|^)L>/\1\\lambda{}..>/g;
$tex =~ s/"([^"]+)"/|"\1"|/g;
$tex =~ s/(^|(?<=[\s)(\]\[,.>\/]))([a-zA-Z][a-z0-9]+)(?=[\s)(\]\[,.-]|$)/|\2|/g;
$tex =~ s/([^_^]|^)([0-9]+|\*)\/(\\?[a-z]+|\|[a-z]+\|)
  (->|\.\.>|~>|:=|!->)/\1\\alpha_{\2}\\vert{}\3\\space{}\4/xg;
$tex =~ s/([^_^]|^)([0-9]+|\*)
  (->|\.\.>|~>|:=|!->)/\1\\alpha_{\2}\\space{}\3/xg;
if ($macro ne 'phiq') {
  if (not $splitting) {
    $tex =~ s/\\begin\{split\}\n/\\begin{split}&/g;
    $tex =~ s/\n\s*\\end\{split\}/\\end{split}/g;
    $tex =~ s/\n\n/\\\\&/g;
    $tex =~ s/\n/\\phiEOL{}\n&/g;
    $tex =~ s/\\\\$//g;
    $tex =~ s/\\\\/\\\\\n/g;
    $tex =~ s/([^&\s])\s{2}([^\s])/\1 \2/g;
    $tex =~ s/\s{2}/ \\quad{}/g;
    $tex = '&' . $tex;
  }
  my $lead = '[^\s]+\s(?:->|:=|=|==)\s';
  my @leads = $tex =~ /&${lead}/g;
  my @eols = $tex =~ /&/g;
  if (0+@leads == 0+@eols && 0+@eols > 1) {
    $tex =~ s/&(${lead})/\1&~/g;
    $gathered = 0;
    print '% The "gathered" is NOT used because all ' .
      (0+@eols) . ' lines are ' . (0+@leads) . " leads\n";
  }
}
if ($macro ne 'phiq') {
  sub strip_tabs {
    my ($env, $tex) = @_;
    $tex =~ s/&//g;
    return "\\begin{$env}" . $tex . "\\end{$env}";
  }
  foreach my $e (('matrix', 'cases')) {
    $tex =~ s/\\begin\{(\Q$e\E\*?)\}(.+)\\end\{\Q$e\E\*?\}/strip_tabs($1, $2)/sge;
  }
}
$tex =~ s/\$/\\xi{}/g;
$tex =~ s/(?<!\{)\^(?!\{)/\\rho{}/g;
$tex =~ s/\[\[/\\llbracket\\mathbin{}/g;
$tex =~ s/\]\]/\\mathbin{}\\rrbracket{}/g;
$tex =~ s/([\s,>(])([0-9A-F]{2}(?:-[0-9A-F]{2})+|
  [0-9]+(?:\.[0-9]+)?)(?!\{)/\1|\2|/xg;
$tex =~ s/TRUE/|TRUE|/g;
$tex =~ s/FALSE/|FALSE|/g;
$tex =~ s/\?/\\varnothing{}/g;
$tex =~ s/@/\\varphi{}/g;
$tex =~ s/-([a-z]+)>/\\mathrel{\\phiSlot{\1}}/g;
$tex =~ s/!->/\\mathbin{\\phiConst}/g;
$tex =~ s/->/\\mathbin{\\mapsto}/g;
$tex =~ s/~>/\\mathbin{\\phiWave}/g;
$tex =~ s/:=/\\mathrel{\\vDash}/g;
$tex =~ s/==/\\mathrel{\\equiv}/g;
$tex =~ s/\.\.>/\\mathbin{\\phiDotted}/g;
$tex =~ s/<</\\langle/g;
$tex =~ s/>>/\\rangle/g;
$tex =~ s/\|{2,}/|/g;
$tex =~ s/\|([^\|]+)\|/\\textnormal{\\texttt{\1}}{}/g;
$tex =~ s/\{TEXT(\d+)\}/'\\text{' . @texts[$1] . '}';/ge;
if ($macro eq 'phiq') {
  print '\(' if ($tex ne '');
} else {
  print '\begin{', $macro, "}\n";
  if (not($align)) {
    if ($gathered) {
      print '\begin{gathered}' . "\n";
    } elsif (not $splitting) {
      print '\begin{split}' . "\n";
    }
  }
}
if ($gathered and not($align)) {
  $tex =~ s/^&//g;
  $tex =~ s/\n&/\n/g;
}
print $tex;
if ($macro eq 'phiq') {
  print '\)' if ($tex ne '');
} else {
  if (not($align)) {
    if ($gathered) {
      print "\n" . '\end{gathered}';
    } elsif (not $splitting) {
      print "\n" . '\end{split}';
    }
  }
  print "\n" . '\end{' . $macro . '}';
}
print '\endinput';
\end{VerbatimOut}
\message{eolang: File with Perl script
  '\eolang@tmpdir/\jobname-phi.pl' saved^^J}
\else
  \message{eolang: Perl script already exists at
    "\eolang@tmpdir/\jobname-phi.pl"^^J}
\fi
\closein 15
\fi
\makeatother
%    \end{macrocode}
% \end{macro}

% \begin{macro}{\phiSaveTo}
% \changes{0.8.0}{2022/11/20}{The output of the \texttt{phiquation} environment can be redirected to a file.}
% Then, we define the |\phiSaveTo| command to instruct the |phiquation| environment that the output should not be sent to the document but saved to the file instead:
%    \begin{macrocode}
\makeatletter
\newcommand\phiSaveTo[1]{\def\eolang@phiSaveTo{#1}}
\makeatother
%    \end{macrocode}
% \end{macro}

% \begin{macro}{\eolang@tmp}
% \changes{0.18.3}{2025/03/26}{A new supplementary \texttt{eolang@tmp} command added, to generate temporary file names.}
% Then, we define the |\eolang@tmp| command, which generates temporary file names:
%    \begin{macrocode}
\makeatletter
\newcommand\eolang@tmp[1]{#1\ifxetex-xe\else\ifluatex-lua\fi\fi.tex}
\makeatother
%    \end{macrocode}
% \end{macro}

% \begin{macro}{\eolang@ifabsent}
% \changes{0.17.0}{2023/12/28}{A new supplementary \texttt{eolang@ifabsent} command added}
% \changes{0.18.0}{2024/01/09}{The \texttt{noshell} package option added in order to enable complete prohibition of shell interactions.}
% Then, we define the |\eolang@ifabsent| command, which if a given file is absent, runs a processing command, otherwise just inputs it:
%    \begin{macrocode}
\makeatletter
\newcommand\eolang@ifabsent[2]{%
  \IfFileExists
    {#1}
    {%
      \message{eolang: File "#1" already exists ^^J}%
      \input{#1}}
    {%
      \ifdefined\eolang@noshell%
        \message{eolang: Shell processing is disabled^^J}%
      \else%
        \ifnum\ShellEscapeStatus=1\else%
          \message{eolang: The -shell-escape command line
          option is not provided, most probably compilation
          will fail now:^^J}%
        \fi%
        #2%
      \fi%
    }%
}
\makeatother
%    \end{macrocode}
% \end{macro}

% \begin{macro}{phiquation}
% \changes{0.16.0}{2023/12/27}{The processing of \texttt{phiquation} data is done only if it's the first time processing, otherwise cache is used, thus making processing faster.}
% Then, we define the |phiquation| and the |phiquation*| environments through a supplementary
% |\eolang@process| command:
%    \begin{macrocode}
\makeatletter\newcommand\eolang@process[1]{
  \def\hash{\eolang@mdfive
    {\eolang@tmpdir/\jobname/\eolang@tmp{phiquation}}-\the\inputlineno}%
  \eolang@ifabsent
    {\eolang@tmpdir/\jobname/\eolang@tmp{\hash-phiquation-post}}
    {%
      \iexec[null]{cp "\eolang@tmpdir/\jobname/\eolang@tmp{phiquation}"
        "\eolang@tmpdir/\jobname/\eolang@tmp{\hash-phiquation}"}%
      \message{Start parsing 'phi' at line no. \the\inputlineno^^J}
      \iexec[trace,stdout=\eolang@tmpdir/\jobname/\eolang@tmp{\hash-phiquation-post}]{
        perl "\eolang@tmpdir/\jobname-phi.pl"
        '#1'
        "\eolang@tmpdir/\jobname/\eolang@tmp{\hash-phiquation}"
        \ifdefined\eolang@nocomments | perl -pe 's/\%.*(\\n|$)//g'\fi
        \ifdefined\eolang@phiSaveTo > \eolang@phiSaveTo\fi}%
    }%
  \setcounter{FancyVerbLine}{\value{eolang@lineno}}%
  \def\eolang@phiSaveTo{\relax}%
}
%
\newenvironment{phiquation*}%
{\catcode`\|=12 \VerbatimEnvironment%
\setcounter{eolang@lineno}{\value{FancyVerbLine}}%
\begin{VerbatimOut}
  {\eolang@tmpdir/\jobname/\eolang@tmp{phiquation}}}
{\end{VerbatimOut}\eolang@process{equation*}}
%
\newenvironment{phiquation}%
{\catcode`\|=12 \VerbatimEnvironment%
\setcounter{eolang@lineno}{\value{FancyVerbLine}}%
\begin{VerbatimOut}
  {\eolang@tmpdir/\jobname/\eolang@tmp{phiquation}}}
{\end{VerbatimOut}\eolang@process{equation}}
\makeatother
%    \end{macrocode}
% \end{macro}

% \begin{macro}{\phiq}
% \changes{0.0.2}{2022/10/21}{Parsing of additional symbols enabled.}
% Then, we define |\phiq| command:
%    \begin{macrocode}
\RequirePackage{xstring}
\makeatletter\newcommand\phiq[1]{%
  \StrSubstitute{\detokenize{#1}}{'}{'"'"'}[\clean]%
  \def\hash{\pdf@mdfivesum{\clean}-\the\inputlineno}%
  \ifdefined\eolang@nodollar\else\catcode`\$=3 \fi%
  \eolang@ifabsent
    {\eolang@tmpdir/\jobname/\eolang@tmp{\hash-phiq-post}}
    {%
      \iexec[log,trace,quiet,stdout=\eolang@tmpdir/\jobname/\eolang@tmp{phiq}]{
        printf '\%s' '\clean'}%
      \iexec[quiet,null]{cp "\eolang@tmpdir/\jobname/\eolang@tmp{phiq}"
        "\eolang@tmpdir/\jobname/\eolang@tmp{\hash-phiq}"}%
      \iexec[trace,stdout=\eolang@tmpdir/\jobname/\eolang@tmp{\hash-phiq-post}]{
        perl \eolang@tmpdir/\jobname-phi.pl 'phiq'
        "\eolang@tmpdir/\jobname/\eolang@tmp{\hash-phiq}"
        \ifdefined\eolang@nocomments | perl -pe 's/\%.*(\\n|$)//g' \fi}%
      \message{eolang: Parsed `phiq' at line no. \the\inputlineno^^J}%
    }%
  \ifdefined\eolang@nodollar\else\catcode`\$\active\fi%
}\makeatother
%    \end{macrocode}
% \end{macro}

% \begin{macro}{nodollar}
% \changes{0.7.0}{2022/11/18}{Now it is possible to use dollar sign instead of the \texttt{\char`\\phiq} command.}
% Then, we redefine dollar sign:
%    \begin{macrocode}
\ifdefined\eolang@nodollar\else
  \begingroup
  \catcode`\$=\active
  \protected\gdef$#1${\phiq{#1}}
  \endgroup
  \AtBeginDocument{\catcode`\$=\active}
\fi
%    \end{macrocode}
% \end{macro}

% \begin{macro}{-sodg.pl}
% \changes{0.0.2}{2022/10/24}{The Perl file now has a fixed name, which doesn't depend on the name of the TeX job. This file may be shared among jobs, no need to make it uniquely named.}
% \changes{0.1.0}{2022/10/26}{There are two Perl scripts now: one for \texttt{phiquation}, another one for \texttt{sodg}.}
% \changes{0.2.0}{2022/10/28}{The content of the \texttt{atom} and the \texttt{data} boxes is parsed automatically as formulas and numbers, respectively.}
% \changes{0.4.0}{2022/10/31}{Labels on the edges are automatically printed as math formulas. Also, boxes are prefixed with the \texttt{\char`\\Delta} and the \texttt{\char`\\lambda} commands.}
% \changes{0.4.0}{2022/10/31}{Relative positioning of vertices fixed.}
% \changes{0.4.0}{2022/10/31}{Transforming arrows added with the \texttt{=>} syntax, also markers with exclamation mark syntax.}
% \changes{0.5.0}{2022/11/09}{New syntax introduced that allows to make clones of vertices and all their dependants.}
% \changes{0.5.0}{2022/11/09}{Now edges may have the \texttt{break} attribute, to make them shorter.}
% \changes{0.5.0}{2022/11/10}{It is possible to use multiple the ``equaltion sign'' symbols for transition arrows \texttt{=>}.}
% \changes{0.5.0}{2022/11/12}{It is possible to use TikZ commands inside the \texttt{sodg} environment.}
% \changes{0.6.0}{2022/11/13}{The \texttt{rrho} attribute is retired, now \texttt{rho} works just fine in all situations.}
% \changes{0.8.0}{2022/11/20}{The \texttt{tag} attribute is introduced for changing labels inside a vertex circle.}
% \changes{0.12.1}{2023/03/01}{The bug is fixed related to the formatting of indexes of vertices.}
% \changes{0.14.0}{2023/07/26}{The \texttt{edgeless} tag of a vertex removes the border of it.}
% \changes{0.15.0}{2023/08/210}{The \texttt{style} tag of vertices and edges.}
% Then, we create a Perl script for |sodg| graphs processing using |VerbatimOut| from
% \href{https://ctan.org/pkg/fancyvrb}{fancyvrb}:
%    \begin{macrocode}
\makeatletter
\ifdefined\eolang@noshell
\message{eolang: Perl script is not going to be created
  at "\eolang@tmpdir/\jobname-sodg.pl", because of the
  "noshell" package option^^J}
\else
\openin 15=\eolang@tmpdir/\jobname-sodg.pl
\ifeof 15
\message{eolang: Perl script is going to be created,
  because it is absent at "\eolang@tmpdir/\jobname-sodg.pl",
  but if -shell-escape is not set, the compilation will
  most likely fail now^^J}
\begin{VerbatimOut}{\eolang@tmpdir/\jobname-sodg.pl}
sub num {
  my ($i) = @_;
  $i =~ s/(\+|-)\./\10./g;
  return $i;
}
sub fmt {
  my ($tex) = @_;
  $tex =~ s/\|([^\|]+)\|/\\textnormal{\\texttt{\1}}/g;
  return $tex;
}
sub toem {
  my ($cm) = @_;
  return $cm * 2.8;
}
sub vertex {
  my ($v) = @_;
  if (index($v, 'v0') == 0) {
    return '\Phi';
  } else {
    $v =~ s/^v/v_{/g;
    $v =~ s/[^0-9]$//g;
    return $v . '}';
  }
}
sub tailor {
  my ($t, $m) = @_;
  $t =~ s/<([A-Z]?${m}[A-Z]?):([^>]+)>/\2/g;
  $t =~ s/<[A-Z]+:[^>]+>//g;
  return $t;
}
open(my $fh, '<', $ARGV[0]);
my $tex; { local $/; $tex = <$fh>; }
if (index($tex, "\t") > 0) {
  print "TABS are prohibited!";
  exit 1;
}
print '% This file is auto-generated', "\n%\n";
print '% --- there are ', length($tex),
  ' chars in the input (', $ARGV[0], "):\n";
foreach my $t (split (/\n/g, $tex)) {
  print '% ', $t, "\n";
}
print "% ---\n";
$tex =~ s/\\\\/\n/g;
$tex =~ s/\\\n//g;
$tex =~ s/(\\[a-zA-Z]+)\s+/\1/g;
$tex =~ s/\n{2,}/\n/g;
my @cmds = split(/\n/g, $tex);
print '% --- before processing:' . "\n";
foreach my $t (split (/\n/g, $tex)) {
  print '% ', $t, "\n";
}
print '% ---';
print ' (' . (0+@cmds) . " lines)\n";
print '\begin{phicture}', "\n";
for (my $c = 0; $c < 0+@cmds; $c++) {
  my $cmd = $cmds[$c];
  $cmd =~ s/^\s+//g;
  $cmd =~ s/(?<!\\)%.*//g;
  my ($head, $tail) = split(/ /, $cmd, 2);
  my %opts = {};
  my ($body, $style) = split(/style:/, $tail, 2);
  $opts{'style'} = $style;
  $tail = $body;
  foreach my $p (split(/ /, $tail)) {
    my ($q, $t) = split(/:/, $p);
    $opts{$q} = $t;
  }
  if (index($head, '\\') == 0) {
    print $cmd;
  } elsif (index($head, '->') >= 0) {
    my $draw = '\draw[';
    if (exists $opts{'pi'}) {
      $draw = $draw . '<MB:phi-pi><F:draw=none>';
      if (not exists $opts{'a'}) {
        $opts{'a'} = '\pi';
      }
    }
    if (exists $opts{'rho'} and not(exists $opts{'bend'})) {
      $draw = $draw . '<MB:,phi-rho>';
    }
    $draw = $draw . ',' . $opts{'style'} . ']';
    my ($from, $to) = split (/->/, $head);
    $draw = $draw . " (${from}) ";
    if (exists $opts{'bend'}) {
      $draw = $draw . 'edge [<F:draw=none><MF:,bend right=' .
        num($opts{'bend'}) . '>';
      if (exists $opts{'rho'}) {
        $draw = $draw . '<MB:,phi-rho>';
      }
      $draw = $draw . ']';
    } else {
      $draw = $draw . '--';
    }
    if (exists $opts{'a'}) {
      my $a = $opts{'a'};
      if (index($a, '$') == -1) {
        $a = '$' . fmt($a) . '$';
      } else {
        $a = fmt($a);
      }
      $draw = $draw . '<MB: node [phi-attr] {' . $a . '}>';
    }
    if (exists $opts{'break'}) {
      $draw = $draw . '<F: coordinate [pos=' .
        ($opts{'break'} / 100) . '] (break)>';
    }
    $draw = $draw . " (<MF:${to}><B:break-v>)";
    if (exists $opts{'break'}) {
      print tailor($draw, 'F') . ";\n";
      print '  \node[outer sep=' . toem(0.1) . 'em,inner sep=0em] ' .
        'at (break) (break-v) {$' . vertex($to) .
        '$};' . "\n";
      print '  ' . tailor($draw, 'B');
    } else {
      print tailor($draw, 'M');
    }
  } elsif (index($head, '=>') >= 0) {
    my ($from, $to) = split (/=+>/, $head);
    my $size = () = $head =~ /=/g;
    if ($from eq '') {
      print '\node [phi-arrow, left=' . toem($size * 0.6) . 'em of ' .
        $to . '.center]';
    } elsif ($to eq '') {
      print '\node [phi-arrow, right=' . toem($size * 0.6) . 'em of ' .
        $from . '.center]';
    } else {
      print '\node [phi-arrow] at ($(' .
        $from . ')!0.5!(' . $to . ')$)';
    }
    print '{}';
  } elsif (index($head, '!') >= 0) {
    my ($v, $marker) = split (/!+/, $head);
    my $size = () = $head =~ /!/g;
    print '\node [phi-marker, left=' .
      toem($size * 0.6) . 'em of ' .
      $v . '.center]{' . fmt($marker) . '}';
  } elsif (index($head, '+') >= 0) {
    my ($v, $suffix) = split (/\+/, $head);
    my @friends = ($v);
    foreach my $c (@cmds) {
      $e = $c;
      $e =~ s/^\s+//g;
      my $h = $e;
      $h = substr($e, 0, index($e, ' ')) if index($e, ' ') >= 0;
      foreach my $f (@friends) {
        my $add = '';
        if (index($h, $f . '->') >= 0) {
          $add = substr($h, index($h, '->') + 2);
        }
        if ($h =~ /->\Q${f}\E$/) {
          $add = substr($h, 0, index($h, '->'));
        }
        if (index($e, ' xy:' . $f . ',') >= 0) {
          $add = $h;
        }
        if (index($add, '+') == -1
          and $add ne ''
          and not(grep(/^\Q${add}\E$/, @friends))) {
          push(@friends, $add);
        }
      }
    }
    my @extra = ();
    foreach my $e (@cmds) {
      $m = $e;
      if ($m =~ /^\s*\Q${v}\E\s/) {
        next;
      }
      if ($m =~ /^\s*[^\s]+\+/ and not($m =~ /^\s*\Q${head}\E\s/)) {
        next;
      }
      foreach my $f (@friends) {
        my $h = $f;
        $h =~ s/[a-z]$//g;
        if ($m =~ s/^(\s*)\Q${f}\E\+\Q${suffix}\E\s?/\1${h}${suffix} /g) {
          last;
        }
        $m =~ s/^(\s*)\Q${f}\E\s/\1${h}${suffix} /g;
        $m =~ s/^(\s*)\Q${f}\E->/\1${h}${suffix}->/g;
        $m =~ s/\sxy:\Q${f}\E,/ xy:${h}${suffix},/g;
        $m =~ s/->\Q${f}\E\s/->${h}${suffix} /g;
      }
      if ($m ne $e) {
        push(@extra, ' ' . $m);
      }
    }
    splice(@extra, 0, 0, @extra[-1]);
    splice(@extra, -1, 1);
    splice(@extra, 0, 0, '% clone of ' . $v . ' (' . $head .
      '), friends: [' . join(', ', @friends) . '] in ' .
      (0+@cmds) . ' lines');
    splice(@cmds, $c, 1, @extra);
    print '% cloned ' . $v . ' at line no.' . $c .
      ' (+' . (0+@extra) . ' lines -> ' .
      (0+@cmds) . ' lines total)';
  } elsif ($head =~ /^v[0-9]+[a-z]?$/) {
    print '\node[';
    if (exists $opts{'xy'}) {
      my ($v, $right, $down) = split(/,/, $opts{'xy'});
      my $loc = '';
      if ($down > 0) {
        $loc = 'below ';
      } elsif ($down < 0) {
        $loc = 'above ';
      }
      if ($right > 0) {
        $loc = $loc . 'right';
      } elsif ($right < 0) {
        $loc = $loc . 'left';
      }
      print ',' . $loc . '=';
      print toem(abs(num($down))) . 'em and ' .
        toem(abs(num($right))) . 'em of ' . $v . '.center';
    }
    if (exists $opts{'data'}) {
      print ',phi-data';
      if ($opts{'data'} ne '') {
        my $d = $opts{'data'};
        if (index($d, '|') == -1) {
          $d = '$\Delta\phiDotted\text{' .
            '\textnormal{\texttt{' . fmt($d) . '}}}$';
        } else {
          $d = fmt($d);
        }
        $opts{'box'} = $d;
      }
    } elsif (exists $opts{'atom'}) {
      print ',phi-atom';
      if ($opts{'atom'} ne '') {
        my $a = $opts{'atom'};
        if (index($a, '$') == -1) {
          $a = '$\lambda\phiDotted{}' . fmt($a) . '$';
        } else {
          $a = fmt($a);
        }
        $opts{'box'} = $a;
      }
    } else {
      print ',phi-object';
    }
    if (exists $opts{'edgeless'}) {
      print ',draw=none';
    }
    print ',' . $opts{'style'} . ']';
    print ' (' . $head . ')';
    print ' {';
    if (exists $opts{'tag'}) {
      my $t = $opts{'tag'};
      if (index($t, '$') == -1) {
        $t = '$' . $t . '$';
      } else {
        $t = fmt($t);
      }
      print $t;
    } else {
      print '$' . vertex($head) . '$';
    }
    print '}';
    if (exists $opts{'box'}) {
      print ' node[phi-box] at (';
      print $head, '.south east) {';
      print $opts{'box'}, '}';
    }
  }
  print ";\n";
}
print '\end{phicture}%', "\n";
print "% --- after processing:\n%";
foreach my $c (@cmds) {
  print '% ', $c, "\n";
}
print '% --- (' . (0+@cmds) . " lines)\n";
print '\endinput';
\end{VerbatimOut}
\message{eolang: File with Perl script
  '\eolang@tmpdir/\jobname-sodg.pl' saved^^J}
\else
  \message{eolang: Perl script already exists at
    "\eolang@tmpdir/\jobname-sodg.pl"^^J}
\fi
\closein 15
\fi
\makeatother
%    \end{macrocode}
% \end{macro}

% \begin{macro}{FancyVerbLine}
% Then, we reset the counter for \href{https://ctan.org/pkg/fancyvrb}{fancyvrb}, so that
% it starts counting lines from zero when the document starts rendering:
%    \begin{macrocode}
\setcounter{FancyVerbLine}{0}
%    \end{macrocode}
% \end{macro}

% \begin{macro}{tikz}
% Then, we include \href{https://ctan.org/pkg/tikz}{tikz} package and its libraries:
%    \begin{macrocode}
\RequirePackage{tikz}
  \usetikzlibrary{arrows}
  \usetikzlibrary{shapes}
  \usetikzlibrary{decorations}
  \usetikzlibrary{decorations.pathmorphing}
  \usetikzlibrary{decorations.pathreplacing}
  \usetikzlibrary{positioning}
  \usetikzlibrary{calc}
  \usetikzlibrary{math}
  \usetikzlibrary{arrows.meta}
%    \end{macrocode}
% \end{macro}

% \begin{macro}{phicture}
% Then, we define internal environment |phicture|:
%    \begin{macrocode}
\newenvironment{phicture}%
  {\noindent\begin{tikzpicture}[
    ->,>=stealth',node distance=0,line width=.08em,
    pics/parallel arrow/.style={
      code={\draw[-latex,phi-rho] (##1) -- (-##1);}}]}%
  {\end{tikzpicture}}
\tikzstyle{phi-arrow} = [fill=white!80!black, single arrow,
  minimum height=0.05em, minimum width=0.05em,
  single arrow head extend=2mm]
\tikzstyle{phi-marker} = [inner sep=0pt, minimum height=1.4em,
  minimum width=1.4em, font={\small\color{white}\ttfamily},
  fill=gray]
\tikzstyle{phi-thing} = [inner sep=0pt,minimum height=2.4em,
  draw,font={\small}]
\tikzstyle{phi-object} = [phi-thing,circle]
\tikzstyle{phi-data} = [phi-thing,regular polygon,
  regular polygon sides=8]
\tikzstyle{phi-empty} = [phi-object]
\tikzset{%
  phi-rho/.style={
    postaction={%
      decoration={
        show path construction,
        curveto code={
          \tikzmath{
            coordinate \I, \F, \v;
            \I = (\tikzinputsegmentfirst);
            \F = (\tikzinputsegmentlast);
            \v = ($(\I) -(\F)$);
            real \d, \a, \r, \t;
            \d = 0.8;
            \t = atan2(\vy, \vx);
            if \vx<0 then { \a = 90; } else { \a = -90; };
            {
              \draw[arrows={-latex}, decorate,
              decoration={%
                snake, amplitude=.4mm,
                segment length=2mm,
                post length=1mm
              }]
              ($(\F)!.5!(\I) +(\t: -\d em) +(\t +\a: 1ex)$)
              -- ++(\t: 2*\d em);
            };
          }
        },
        lineto code={
          \tikzmath{
            coordinate \I, \F, \v;
            \I = (\tikzinputsegmentfirst);
            \F = (\tikzinputsegmentlast);
            \v = ($(\I) -(\F)$);
            real \d, \a, \r, \t;
            \d = 0.8;
            \t = atan2(\vy, \vx);
            if \vx<0 then { \a = 90; } else { \a = -90; };
            {
              \draw[arrows={-latex}, decorate,
              decoration={%
                snake, amplitude=.4mm,
                segment length=2mm,
                post length=1mm}]
              ($(\F)!.5!(\I) +(\t: -\d em) +(\t +\a: 1ex)$)
              -- ++(\t: 2*\d em);
            };
          }
        }
      },
      decorate
    }
  }
}
\tikzstyle{phi-pi} = [draw,dotted]
\tikzstyle{phi-atom} = [phi-object,double]
\tikzstyle{phi-box} = [xshift=-5pt,yshift=3pt,draw,fill=white,
  rectangle,line width=.04em,minimum width=1.2em,anchor=north west,
  font={\scriptsize}]
\tikzstyle{phi-attr} = [midway,sloped,inner sep=0pt,
  above=2pt,sloped/.append style={transform shape},
  font={\scriptsize},color=black]
%    \end{macrocode}
% \end{macro}

% \begin{macro}{\sodgSaveTo}
% \changes{0.8.0}{2022/11/20}{The output of the \texttt{sodg} environment can be redirected to a file.}
% Then, we define the |\sodgSaveTo| command to instruct the |sodg| environment that the output should not be sent to the document but saved to the file instead:
%    \begin{macrocode}
\makeatletter
\newcommand\sodgSaveTo[1]{\def\eolang@sodgSaveTo{#1}}
\makeatother
%    \end{macrocode}
% \end{macro}

% \begin{macro}{sodg}
% \changes{0.0.2}{2022/10/20}{The environment \texttt{phigure} renamed to \texttt{sodg} for the sake of better semantic. The graph in the picture is solely a SODG graph, that's why the name \texttt{sodg} is better.}
% \changes{0.16.0}{2023/12/27}{The processing of \texttt{sodg} data is done only if it's the first time processing, otherwise cache is used, thus making processing faster.}
% Then, we create a new environment |sodg|, as suggested
% \href{https://tex.stackexchange.com/questions/661056}{here}:
%    \begin{macrocode}
\makeatletter\newenvironment{sodg}%
{\catcode`\|=12 \VerbatimEnvironment%
\setcounter{eolang@lineno}{\value{FancyVerbLine}}%
\begin{VerbatimOut}
  {\eolang@tmpdir/\jobname/\eolang@tmp{sodg}}}
{\end{VerbatimOut}%
  \def\hash{\eolang@mdfive
    {\eolang@tmpdir/\jobname/\eolang@tmp{sodg}}-\the\inputlineno}%
  \catcode`\$=3 %
  \eolang@ifabsent
    {\eolang@tmpdir/\jobname/\eolang@tmp{\hash-sodg-post}}
    {%
      \iexec[null]{cp "\eolang@tmpdir/\jobname/\eolang@tmp{sodg}"
        "\eolang@tmpdir/\jobname/\eolang@tmp{\hash-sodg}"}%
      \message{eolang: Start parsing `sodg' at line no. \the\inputlineno^^J}
      \iexec[trace,stdout=\eolang@tmpdir/\jobname/\eolang@tmp{\hash-sodg-post}]{
        perl "\eolang@tmpdir/\jobname-sodg.pl"
        "\eolang@tmpdir/\jobname/\eolang@tmp{\hash-sodg}"
        \ifdefined\eolang@nocomments | perl -pe 's/\%.*(\\n|$)//g'\fi
        \ifdefined\eolang@sodgSaveTo > \eolang@sodgSaveTo\fi}%
    }
  \catcode`\$\active%
  \setcounter{FancyVerbLine}{\value{eolang@lineno}}%
  \def\eolang@sodgSaveTo{\relax}%
}\makeatother
%    \end{macrocode}
% \end{macro}

% \begin{macro}{\eoAnon}
% Then, we define a supplementary command to help us anonymize some content.
% \changes{0.9.0}{2022/11/29}{New command \texttt{\char`\\eoAnon} added.}
%    \begin{macrocode}
\RequirePackage{hyperref}
\pdfstringdefDisableCommands{
  \def\({}%
  \def\){}%
  \def\alpha{alpha}%
  \def\varphi{phi}%
}
\makeatletter
\NewExpandableDocumentCommand{\eoAnon}{O{ANONYMIZED}m}{%
  \ifdefined\eolang@anonymous%
    \textcolor{orange}{#1}%
  \else%
    #2%
  \fi%
}\makeatother
%    \end{macrocode}
% \end{macro}

% \begin{macro}{\eolang}
% Then, we define a simple supplementary command to help you print \eolang{}, the name of our language.
% \changes{0.1.0}{2022/10/25}{New command \texttt{\char`\\eolang} added to print the name of the language in both
% normal and the anonymous mode of \texttt{acmart}.}
%    \begin{macrocode}
\newcommand\eolang{%
  \eoAnon[XYZ]{{\sffamily EO}}}
%    \end{macrocode}
% \end{macro}

% \begin{macro}{\phic}
% Then, we define a simple supplementary command to help you print \phic{}, the name of our formal apparatus.
% \changes{0.1.0}{2022/10/25}{New command \texttt{\char`\\phic} prints the name of $\varphi$-calculus in both
% normal and the anonymous mode of \texttt{acmart}.}
%    \begin{macrocode}
\newcommand\phic{%
  \eoAnon[\(\alpha\)-cal\-cu\-lus]{\(\varphi\)-cal\-cu\-lus}}
%    \end{macrocode}
% \end{macro}

% \begin{macro}{\xmir}
% Then, we define a simple supplementary command to help you print \xmir{}, the name of our XML-based format of program representation.
% \changes{0.2.0}{2022/10/28}{New command \texttt{\char`\\xmir} prints XMIR in both normal and the anonymous mode of \texttt{acmart}.}
%    \begin{macrocode}
\newcommand\xmir{%
  \eoAnon[XML\(^+\)]{XMIR}}
%    \end{macrocode}
% \end{macro}

% \begin{macro}{\phiConst}
% \changes{0.1.0}{2022/10/26}{New command \texttt{\char`\\phiConst} added to denote a link to a constant attribute.}
% Then, we define a command to render an arrow for a constant attribute,
% as suggested \href{https://tex.stackexchange.com/questions/663121}{here}:
%    \begin{macrocode}
\newcommand\phiConst{%
  \mathrel{\hspace{.15em}}%
  \mapstochar\mathrel{\hspace{-.15em}}\mapsto}
%    \end{macrocode}
% \end{macro}

% \begin{macro}{\phiWave}
% \changes{0.3.0}{2022/10/30}{New command \texttt{\char`\\phiWave} added to denote a link to a multi-layer attribute.}
% Then, we define a command to render an arrow for a multi-layer attribute,
% as suggested \href{https://tex.stackexchange.com/questions/198755}{here}:
%    \begin{macrocode}
\newcommand\phiWave{%
  \mapstochar\mathrel{\mspace{0.45mu}}\leadsto}
%    \end{macrocode}
% \end{macro}

% \begin{macro}{\phiSlot}
% \changes{0.5.0}{2022/11/10}{New command \texttt{\char`\\phiSlot} added to denote a link to a slot in a basket.}
% Then, we define a command to render an arrow for a slot in a basket:
%    \begin{macrocode}
\newcommand\phiSlot[1]{%
  \xrightarrow{\text{\sffamily\scshape #1}}}
%    \end{macrocode}
% \end{macro}

% \begin{macro}{\phiOset}
% \changes{0.8.0}{2022/11/20}{New commands \texttt{\char`\\phiOset} and \texttt{\char`\\phiUset} help position text over and under an arrow.}
% Then, we define two commands to position a text over and under an arrow, as suggested \href{https://tex.stackexchange.com/a/194805/1449}{here}:
%    \begin{macrocode}
\makeatletter
\newcommand{\phiOset}[2]{%
  \mathrel{\mathop{#2}\limits^{
    \vbox to 0ex{\kern-2\ex@
    \hbox{$\scriptscriptstyle#1$}\vss}}}}
\newcommand{\phiUset}[2]{%
  \mathrel{\mathop{#2}\limits_{
    \vbox to 0ex{\kern-6.3\ex@
    \hbox{$\scriptscriptstyle#1$}\vss}}}}
\makeatother
%    \end{macrocode}
% \end{macro}

% \begin{macro}{\phiMany}
% \changes{0.5.0}{2022/11/10}{New command \texttt{\char`\\phiMany} enables iterating over an arrow.}
% Then, we define a command for an arrow with iterating indecies:
%    \begin{macrocode}
\newcommand\phiMany[3]{%
  \phiOset{#3}{\phiUset{#2}{#1}}}
%    \end{macrocode}
% \end{macro}

% \begin{macro}{\phiEOL}
% \changes{0.9.0}{2022/11/24}{New command \texttt{\char`\\phiEOL} added, instead of \texttt{\char`\\\char`\\[-4pt]}.}
% Then, we define a command for line breaks in formulas:
%    \begin{macrocode}
\newcommand\phiEOL{\\[-4pt]}
%    \end{macrocode}
% \end{macro}

% \begin{macro}{\phiDotted}
% \changes{0.1.0}{2022/10/27}{New command \texttt{\char`\\phiDotted} added to denote a link to a special attribute.}
% Then, we define a command to render an arrow for a special attribute,
% as suggested \href{https://tex.stackexchange.com/questions/663176}{here}:
%    \begin{macrocode}
\RequirePackage{trimclip}
\RequirePackage{amsfonts}
\makeatletter
\newcommand{\phiDotted}{%
  \mapstochar\mathrel{\mathpalette\phiDotted@\relax}}
\newcommand{\phiDotted@}[2]{%
  \begingroup%
  \settowidth{\dimen\z@}{$\m@th#1\rightarrow$}%
  \settoheight{\dimen\tw@}{$\m@th#1\rightarrow$}%
  \sbox\z@{%
    \makebox[\dimen\z@][s]{%
      \clipbox{0 0 {0.4\width} 0}%
        {\resizebox{\dimen\z@}{\height}%
          {$\m@th#1\dashrightarrow$}}%
      \hss%
      \clipbox{{0.69\width} {-0.1\height} 0
        {-\height}}{$\m@th#1\rightarrow$}%
    }%
  }%
  \ht\z@=\dimen\tw@ \dp\z@=\z@%
  \box\z@%
  \endgroup%
}
\makeatother
%    \end{macrocode}
% \end{macro}

% \Finale

% \clearpage
% \printbibliography
% \clearpage

% \PrintChanges
% \clearpage
% \PrintIndex
