clistmap.dtx

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-----------------------------------------------------------------
##### Comma separated list partition, differentiated mapping
- Source repository: https://github.com/rogard/clistmap
- Released under the LaTeX Project Public License v1.3c or later
- See http://www.latex-project.org/lppl.txt
-----------------------------------------------------------------
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\preamble
----------------------------------------------------------------------------
clistmap ---  Partition a comma separated list, map differentiatedly across
components
Released under the LaTeX Project Public License v1.3c or later
See http://www.latex-project.org/lppl.txt
----------------------------------------------------------------------------

\endpreamble
\postamble

Copyright (C) 2022 by Erwann Rogard

This work may be distributed and/or modified under the
conditions of the LaTeX Project Public License (LPPL), either
version 1.3c of this license or (at your option) any later
version.  The latest version of this license is in the file:

http://www.latex-project.org/lppl.txt

This work is "maintained" (as per LPPL maintenance status) by
Erwann Rogard.

This work consists of the file clistmap.dtx and the derived files:
clistmap.sty, and clistmap.pdf.

\endpostamble
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}
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%</internal> 
%<package> \NeedsTeXFormat{LaTeX2e}[2021-06-01]
%<package> \RequirePackage{xparse, xtemplate, l3keys2e}[2021-06-01]
%<package> \RequirePackage{erw-l3}[2022-01-28]
%<package> \ProvidesExplPackage
%<package> {clistmap}                                  %^^A Package name
%<package> {2022-01-29}                                %^^A Release date
%<package> {1.2}                                       %^^A Release version
%<package> {Partition a comma separated list,          %^^A Description
%<package> map differentiatedly across components}
%<*driver> 
\documentclass{l3doc}
\EnableCrossrefs
\CodelineIndex
\RecordChanges
% ^^A\documentclass[full, show-notes]{l3doc}
% ^^A \listfiles
\usepackage{amsmath, amssymb, bookmark, enumitem, mathtools, microtype, tcolorbox, xparse, clistmap}
\usepackage[bibencoding=auto, backend=biber, sorting=ynt]{biblatex}
\begin{filecontents*}{\jobname.bib}
@manual{interface3,
  title        = {The \LaTeX3 interfaces},
  author       = {The \LaTeX3 Project Team},
  year         = {2019},
  note         = {\url{https://ctan.math.washington.edu/tex-archive/macros/latex/contrib/l3kernel/expl3.pdf}},
  annote       = {} }
\end{filecontents*}
\addbibresource{\jobname.bib}
\usepackage[french, german, english]{babel}
\usepackage[T1]{fontenc}
\newlist{descr}{description}{3}
\setlist[descr]{nosep, align=left, itemindent=0pt, font=\sffamily\tiny}
\ProvideDocumentCommand{\docfillblank}{}{\begin{minipage}[t]{\linewidth}\end{minipage}}
\ProvideDocumentCommand{\docpipe}{}{\textbar}
\ProvideDocumentCommand{\docexp}{}{\texttt{e}\docpipe{}\texttt{f}\docpipe{}\texttt{x}}
\ExplSyntaxOn
% ^^A *** Kernel
\cs_generate_variant:Nn\tl_map_inline:nn{e}
% ^^A *** Sectioning
\tl_gset:Nn \partname {Part}%^^A allows to test w/o babel
\ExplSyntaxOff
% ^^A *** Listing
\tcbuselibrary{listings, breakable}
\newtcblisting[auto counter]
{listing}[2][]{
  noparskip,
  breakable,
  colback=white,
  colframe=black,
  opacitybacktitle=.8,%
  fonttitle=\bfseries,
  title={Listing~\thetcbcounter. #1},
  arc=0pt,
  outer arc=0pt,
  boxrule=1pt,
  listing and text,
  #2}
\usepackage{hyperref} %^^A comes last
\begin{document}
\DocInput{\jobname.dtx}
\end{document}
%</driver> 
% \fi
% 
% \GetFileInfo{\jobname.sty}
% \title{The \pkg{clistmap}~package\thanks{^^A
% This file describes version \fileversion, last revised \filedate.^^A
% }^^A
% }
%   \author{Erwann Rogard\thanks{first.lastname at gmail.com}}
%   
%   \date{Released \filedate}
%   \begin{documentation}
%     \maketitle
%     \begin{abstract}
%       Let \meta{clist}$\doteq$\meta{e_1}|,...,|\meta{e_n}\cite[l3clist]{interface3}.
%       This package provides a key-based interface for defining templates whose job is to
%       partition \meta{clist}, and map differentiatedly across its components.
%       \cs{clistmap:nnn}\Arg{clist}|{...,|\meta{instance_i}|,...}|\meta{args} iterates over the $i$'s.
%       Implicit in \meta{instance_i} is \meta{rule sequence_i} (the template), \meta{cs name_i},
%       and \meta{signature_i}$=$\meta{args}' signature.
% A sequence of instances can be made into a new instance: 
% |serial_math_and:N|$\doteq$|{first_math:N,serial_rest_math_and:N}|, and likewise for the second component.
% |$\clistmap_inline:nnn{Z,C,Q,R}{serial_math_and:N}|\\|{\mathbb{#1}}$| expands to
% \ExplSyntaxOn$\clistmap_inline:nnn{Z,C,Q,R}{serial_math_and:N}{\mathbb{#1}}$\ExplSyntaxOff.
%       \cs{clistmap:nnnn} takes an additional argument, \meta{chain}$\sim$|end|\docpipe|append|\docpipe|nest|\docpipe|join|,
%       narrowing the set of instances needed to obtain a particular behaviour. 
%     \end{abstract}
%     
%     \tableofcontents
%     
%     \part{Usage}\label{part:usage}
%     \section{Overview}
%     Let \meta{clist}$\equiv$\meta{head}|,|\meta{rest}.
%     The lifecycle has four stages.
%     First, one provides templates called \emph{rule}s, parameterized by
%     \meta{rule sequence}, \meta{cs name}, and \meta{signature}. 
%     Typically, a rule checks for the recursion tail\cite[l3quark]{interface3} in some combination of \meta{head} and \meta{rest},
%     based on which it does either of: stop, recurse, forward to \meta{rule sequence},
%     and in each case optionally expands \cs[no-index]{\meta{cs name}:\meta{signature}n}\Arg{args}\Arg{head}.
%     Second, one associates keys to sequences of rules, \emph{rule sequence}.
%     Those preset are |first|, |middle|, |last|, |serial_second|, and |serial_last|,
%     for which the stated expression is evaluated for each \meta{e_i} in their respective subsets.
%     Brace groups are preserved.
%     Third, one declares \emph{instance}s of combinations of
%     \meta{rule sequence},  \meta{cs name}, and \meta{signature}. For example,
%     |middle_comma:N| and |serial_middle:|
%     bind together |middle| and |,#1{#2}|, and |,~#1|, respectively.
%     Fourth, define sequences of instances under the constraint that \meta{signature} is identical across them,
%     \emph{instance sequence}s. Among presets,
%     |comma:N| and |serial:| comprise in their natural order the matches for |(?:first_apply|\docpipe|comma_middle|\docpipe|comma_last):N|,
%     and |(?:first_apply|\docpipe|serial_middle|\docpipe|serial_second|\docpipe|serial_last):|, respectively.
%     They expand to |#1{|\meta{e_1}|},...,#1{|\meta{e_n}|}|, and \meta{e_1}|,~...,~and~|\meta{e_n}, respectively.
%     \cs{clistmap:nnn} works the same with an instance sequence or the list of its constituents.
%     
%     \section{Programming}
%     \subsection{\textsf{key}}
%     \begin{function}{rule}
%       \begin{syntax}
%         \cs{clistmap_keys_set:n}|{ rule = |\Arg{key}\Arg{code}| }|
%       \end{syntax}
%       \begin{descr}
%       \item[Parameter semantics]\docfillblank
%         \begin{descr}
%         \item[\#1] \meta{rule sequence}
%         \item[\#2] \meta{cs name}
%         \item[\#3] \meta{signature}
%         \item[\#4] \meta{head is group}
%         \item[\#5] \meta{arguments}
%         \item[\#6] \meta{clist head}
%         \item[\#7] \meta{clist rest}
%         \end{descr}
%       \item[Requirement] \meta{code} is in terms of \texttt{\#1-\#7}
%       \end{descr}
%     \end{function}
%     \begin{function}{rule_if_rest_is_tail_eval_else, rule_if_empty_stop_else}
%       \begin{syntax}
%         \cs{clistmap_keys_set:n}|{ rule_if_rest_is_tail_eval_else = |\Arg{name}\Arg{code}| }|
%       \end{syntax}
%       \begin{descr}
%       \item[Semantics] Specialization of |rule|
%       \end{descr}
%     \end{function}
%     \begin{function}{rule_sequence}
%       \begin{syntax}
%         \cs{clistmap_keys_set:n}|{ rule_sequence = {...,|\meta{key_j} = |{ ...|\Arg{rule_i}|...},...} }|
%       \end{syntax}
%     \end{function}
%     \begin{function}{instance}
%       \begin{syntax}
%         \cs{clistmap_keys_set:n}|{ instance = { |\meta{key prefix}| = |\Arg{rule sequence}\Arg{cs name}\Arg{signature}| } }|
%       \end{syntax}
%       \begin{descr}
%       \item[Semantics] Associates \cs{clistmap_instance_key:nn}\Arg{key prefix}\Arg{signature} with the RHS of \meta{key prefix}| = |
%       \end{descr}
%     \end{function}
%     \begin{function}{instance_sequence}
%       \begin{syntax}
%         \cs{clistmap_keys_set:n}|{ instance_sequence = { |\meta{key} = |{ ...,|\meta{instance_i}|,...},... } }|
%       \end{syntax}
%     \end{function}
%     \subsection{\textsf{cs}}
%     \begin{function}{clistmap_keys_set:n}
%       \begin{syntax}
%         \cs{clistmap_keys_set:n}\Arg{keyval list}
%       \end{syntax}
%     \end{function}
%     \begin{function}[EXP]{\clistmap_info_clist:nn, \clistmap_info_prop:nn}
%       \begin{syntax}
%         \cs{clistmap_info_clist:nn}\Arg{key}\Arg{code}
%       \end{syntax}
%       \begin{descr}
%       \item[Note] Used for generating this doc
%       \end{descr}
%     \end{function}
%     \begin{function}[EXP]
%       {\clistmap_signature:n,
%       \clistmap_instance_key:nn}
%       \begin{syntax}
%         \cs{clistmap_instance_key:n}\Arg{key prefix}\Arg{signature}
%       \end{syntax}
%       \begin{descr}
%       \item[Expands to] \meta{key prefix}|:|\meta{signature}
%       \end{descr}
%     \end{function}
%     \begin{function}[EXP]
%       { \clistmap_instance_sequence_p:n,
%       \clistmap_instance_p:n }
%       \begin{syntax}
%         \cs{clistmap_instance_p:n}\Arg{key}
%       \end{syntax}
%       \begin{descr}
%       \item[Semantics] Whether the instance has been registered 
%       \end{descr}
%     \end{function}
%     \begin{function}[EXP]
%       {\clistmap_use_w:nnnn,
%       \clistmap_use_w:nnnnn,
%       \clistmap_use_w_group:nnnnnn }
%       \begin{syntax}
%         \cs{clistmap_use_w:nnnnn}
%         \Arg{rule}
%         \Arg{rule sequence (internal) }
%         \Arg{cs name}
%         \Arg{signature}
%         \Arg{head is group}\meta{more}\cs[no-index]{q_recursion_stop}
%       \end{syntax}
%       \begin{descr}
%       \item[Semantics] Evaluates \meta{code} associated with \meta{rule}
%       \item[Note] For use inside \meta{code} on the RHS of | rule = |\meta{rule bis}\meta{code}
%       \end{descr}
%     \end{function}
%     \begin{function}[EXP]
%       {\clistmap_bound_cs_group:nnnnn}
%       \begin{syntax}
%         \cs{clistmap_bound_cs_group:nnnnn}
%         \Arg{cs name}
%         \Arg{signature}
%         \Arg{group}
%         \Arg{args}
%         \Arg{elem}
%       \end{syntax}
%       \begin{descr}
%       \item[Definition] \meta{new elem}$=$|\bool_if:nTF|\Arg{group}|{|\Arg{elem}|}{|\meta{elem}|}|
%       \item[Semantics] \cs{\meta{cs name}:\meta{signature}}\meta{args}\Arg{new elem}
%       \item[Note] For use in conjunction with \cs{clistmap_use_w:nnnnn} and variants
%       \end{descr}
%     \end{function}
%     \begin{function}[EXP]
%       {\clistmap:nnn}
%       \begin{syntax}
%         \cs{clistmap:nnn}\Arg{clist}|{ ...,|\meta{instance_i}|,... }|\Arg{args}
%         \cs{clistmap:nnn}\Arg{clist}|{ ...,|\meta{instance sequence_i}|,... }|\Arg{args}
%       \end{syntax}
%       \begin{descr}
%       \item[Requirement]\docfillblank
%         \begin{description}
%         \item \meta{clist} has no trailing |,|
%         \item \meta{args} has signature \cs{clistmap_signature:n}\Arg{instance_i}
%         \end{description}
%       \item[Expands to]\docfillblank
%         \begin{descr}
%         \item[First version] For each $i$, the \meta{code} associated with \meta{rule_i}.
%         \item[Second version] Iterates over the constituents of \meta{rule sequence_i}
%         \end{descr}
%       \end{descr}
%     \end{function}
%     \begin{function}{\clistmap_inline:nnn}
%       \begin{syntax}
%         \cs{clistmap_inline:nnn}|{ ...,|\meta{instance_i}|,... }|\Arg{code}
%         \begin{descr}
%         \item[Requirement] \cs{clistmap_signature:n}\Arg{instance_i}$=$|N|
%         \end{descr}
%       \end{syntax}
%     \end{function}
%     \begin{function}[EXP]
%       {\clistmap:nnnn}
%       \begin{syntax}
%         \cs{clistmap:nnnn}\Arg{clist}\Arg{instances}\Arg{args}\Arg{end}
%         \cs{clistmap:nnnn}\Arg{clist}\Arg{instances}\Arg{args}\Arg{append}
%         \cs{clistmap:nnnn}\Arg{clist}\Arg{instances}\Arg{args}\Arg{nest}
%         \cs{clistmap:nnnn}\Arg{clist_1}\Arg{instances}\Arg{args}\Arg{join}\Arg{clist_2}
%       \end{syntax}
%       \begin{descr}
%       \item[Semantics]\docfillblank
%         \begin{descr}
%         \item[end] \cs{clistmap:nnn}\Arg{clist}\Arg{instances}\Arg{args}
%         \item[append] \meta{end}\cs{clistmap:nnnn}\Arg{clist}
%         \item[nest] \cs{clistmap:nnnn}\Arg{end}
%         \item[join] \cs{clistmap:nnnn}|{|\meta{end},\meta{clist_2}|}|
%         \end{descr}
%       \end{descr}
%     \end{function}
%     \begin{function}[EXP]
%       {\clistmap_inline:nnnn}
%       \begin{syntax}
%         \cs{clistmap_inline:nnnn}\Arg{clist}\Arg{instances}\Arg{code}\Arg{chain}
%       \end{syntax}
%       \begin{descr}
%       \item[Requirement] \cs{clistmap_signature:n}\Arg{instance_i}$=$|empty| or |N|
%       \end{descr}
%     \end{function}
%     \clearpage
%     \part{Listing}\label{part:listing}
%     
%     \section{Using keys}
%     \addcontentsline{toc}{subsection}{\texttt{rule}}
%     \iffalse
%<*guardlisting>     
%     \fi
\begin{listing}[\texttt{rule}]
  {label=lst:opt:rule,listing only}
  \clistmap_keys_set:n
  {%
    rule = {if_rest_is_tail_stop_else_forward_rest}
    {%    
      \quark_if_recursion_tail_stop:n{#7}
      \clistmap_use_w:nnne
      {#1}{#2}{#3}
      {\tl_if_head_is_group_p:n{#7}}#5#7\q_recursion_stop
    }
  }
\end{listing}
% \iffalse
%</guardlisting> 
% \fi
% 
% \addcontentsline{toc}{subsection}{\texttt{rule_sequence}}
% \iffalse
%<*guardlisting> 
% \fi
\begin{listing}[\texttt{rule_sequence}]
  {label=lst:opt:ruleseq, listing only}
  \clistmap_keys_set:n
  {
    rule_sequence =
    {
      first =
      {
        {if_empty_stop_else_forward_head}
        {if_rest_is_tail_eval_else_error}
      }
    }
  }
\end{listing}
% \iffalse
%</guardlisting> 
% \fi
% 
% \addcontentsline{toc}{subsection}{\texttt{instance}}
% \iffalse
%<*guardlisting> 
% \fi
\begin{listing}[\texttt{instance}]
  {label=lst:opt:inst, listing only}
  \clistmap_keys_set:n
  {
    instance =
    {
      {N}{first_apply}{first}{@@_apply},
      {}{first_apply}{first}{@@_apply}
    }
  }
\end{listing}
% \iffalse
%</guardlisting> 
% \fi
% 
% \addcontentsline{toc}{subsection}{\texttt{instance_sequence}}
% \iffalse
%<*guardlisting> 
% \fi
\begin{listing}[\texttt{instance_sequence}]
  {label=lst:opt:inst_seq, listing only}
  \clistmap_keys_set:n
  {%
    instance_sequence =
    {
      {N}{comma:}{first_apply:, rest_comma:},
      {}{serial_and:}{first_apply:, serial_rest_and:},
    }
  }
\end{listing}
% \iffalse
%</guardlisting> 
% \fi
% \section{Preset keys}
% \addcontentsline{toc}{subsection}{\texttt{rule}}
% \iffalse
%<*guardlisting> 
% \fi
\begin{listing}[\texttt{rule}]{label=lst:preset:rule, text only}
  \ExplSyntaxOn
  \begin{descr}
    \clistmap_info_clist:nn{rule}{\item[#1]}
  \end{descr}
  \ExplSyntaxOff
\end{listing}
% \iffalse
%</guardlisting> 
% \fi
% 
% \addcontentsline{toc}{subsection}{\texttt{rule_sequence}}
% \iffalse
%<*guardlisting> 
% \fi
% \begin{listing}[\texttt{rule_sequence}]{label=lst:preset:rule_sequence, text only}
\ExplSyntaxOn
\begin{descr}
  \tl_map_inline:en
  { \clistmap_info_prop:n{rule_sequence}}{\item[\use_i:nn#1]}
\end{descr}
\ExplSyntaxOff
\end{listing}
% \iffalse
%</guardlisting> 
% \fi
% 
% \addcontentsline{toc}{subsection}{\texttt{instance}}
% \iffalse
%<*guardlisting> 
% \fi
\begin{listing}[\texttt{instance}]{label=lst:preset:instance, text only}
  \ExplSyntaxOn
  \begin{descr}
    \tl_map_inline:en
    { \clistmap_info_prop:n{instance} }
    { \item[\use_i:nn#1]\docfillblank }
  \end{descr}
  \ExplSyntaxOff
\end{listing}
% \iffalse
%</guardlisting> 
% \fi
% 
% \addcontentsline{toc}{subsection}{\texttt{instance_sequence}}
% \iffalse
%<*guardlisting> 
% \fi
\begin{listing}[\texttt{instance_sequence}]{label=lst:preset:instance_sequence, text only}
  \ExplSyntaxOn
  \begin{descr}
    \tl_map_inline:en
    { \clistmap_info_prop:n{instance_sequence} }
    { \item[\use_i:nn#1]\docfillblank }
  \end{descr}
  \ExplSyntaxOff
\end{listing}
% \iffalse
%</guardlisting> 
% \fi
% 
% \section{\textsf{cs}}
% \subsection{\textsf{plain}}
% \addcontentsline{toc}{subsection}{\texttt{math}}
% \iffalse
%<*guardlisting> 
% \fi
\begin{listing}[\texttt{math}]{label=lst:cs:math}
  \ExplSyntaxOn
  \clistmap:nnn{Z, C, Q, R}
  { first_math:N, serial_rest_math_and:N }
  {\mathbb}
  \ExplSyntaxOff
\end{listing}
% \iffalse
%</guardlisting> 
% \fi
%
% \subsection{\textsf{chain}}
% \addcontentsline{toc}{subsection}{\texttt{append}}
% \iffalse
%<*guardlisting> 
% \fi
\begin{listing}[\texttt{append}]{label=lst:cs:append}
  \ExplSyntaxOn
  \clistmap_inline:nnnn
  {{J,u,l,e,s},Jim,Catherine}
  {first_map:N}
  {#1}
  {append}
  {middle_comma:N}
  {~#1}
  {append}
  {%^^A
    serial_second:N,%^^A ignored in this case
    serial_last:N
  }
  {~et~#1}
  {end}
  \ExplSyntaxOff
\end{listing}
% \iffalse
%</guardlisting> 
% \fi
% 
% \addcontentsline{toc}{subsection}{\texttt{nest}}
% \iffalse
%<*guardlisting> 
% \fi
\begin{listing}[\texttt{nest}]{label=lst:cs:nest}
  \ExplSyntaxOn
  \noindent
  \clistmap_inline:nnnn
  {{foo},{bar,baz},{qux}}
  {comma_unbrace:}
  {}
  {nest}
  {newline:}
  {}
  {end}
  \ExplSyntaxOff
\end{listing}
% \iffalse
%</guardlisting> 
% \fi
% 
% \addcontentsline{toc}{subsection}{\texttt{join}}
% \iffalse
%<*guardlisting> 
% \fi
\begin{listing}[\texttt{join}]{label=lst:cs:join}
  \ExplSyntaxOn
  \clistmap_inline:nnnn
  {foo,bar}
  {comma:}
  {}
  {join}
  {baz}
  {comma:}
  {}
  {end}
  \ExplSyntaxOff
\end{listing}
% \iffalse
%</guardlisting> 
% \fi
% 
% 
% \part{Other}
% \section{Bibliograhy}
% \printbibliography[heading=none]
% \section{To do}\label{other:bug}
% \begin{enumerate}
% \item ``Warning: A control sequence of the form ...__clistmap''
%   That's because of the way \cs[no-index]{__clist_instance_name:nn} is set up,
%  and passing to it an internal control sequence. So?
%  Modify \cs[no-index]{__clist_instance_name:nn}.
% \end{enumerate}
% \section{Support}\label{other:support}
% 
% This package is available from \url{https://github.com/rogard/clistmap}.
% 
% \changes{v1.0}
% {2022/01/27}
% {Initial version}
% \changes{v1.1}
% {2022/01/28}
% {Updated dependency to erw-l3 (from 4.1 to 4.2)}
% \changes{v1.2}
% {2022/01/29}
% {Pkg name change}
%
%   \StopEventually{
%    \clearpage
%     \PrintChanges
%     \PrintIndex %^^A https://tex.stackexchange.com/q/610349/112708
%   }
%
% \end{documentation}
% \begin{implementation}
%   \part{Implementation}\label{part:implem}
%    \begin{macrocode}
%<*package>      
%<@@=clistmap>      
%      \ExplSyntaxOn
%    \end{macrocode}
% \section{\textsf{boilerplate}}
% \begin{macro}{\clistmap_keys_set:n, \clistmap_info_clist:nn}
%    \begin{macrocode}
\cs_generate_variant:Nn\str_if_eq:nnTF{e}
\cs_generate_variant:Nn\tl_to_str:n{e}
\cs_generate_variant:Nn\prop_gput:Nnn{Nee}
\cs_generate_variant:Nn\erw_parameter:n{e}
\cs_generate_variant:Nn\erw_argument:nn{ne}
\cs_generate_variant:Nn\erw_parameter:nn{ne}
\cs_generate_variant:Nn\erw_clist_tl:nn{ne}
\cs_new:Npn\@@_empty:w#1\q_recursion_stop{}
\clist_new:N\@@_helper_clist
\cs_new_protected:Nn
\clistmap_keys_set:n{ \keys_set:nn{ @@ }{ #1 } }
\prop_new:N\@@_info_clist_prop
\cs_new_protected:Npn
\@@_info_clist_put:nn
#1 % <key>
#2 % <name:signature>
{\prop_gput:Nnn\@@_info_clist_prop{#1}{#2}}
\cs_new_protected:Npn
\clistmap_info_clist:nn
#1 % <key>
#2 % <code>
{\clist_map_inline:cn{\prop_item:Nn\@@_info_clist_prop{#1}}{#2}}
\prop_new:N\@@_info_prop_prop
\cs_new_protected:Npn
\@@_info_prop_put:nn
#1 % <key>
#2 % <name:signature>
{\prop_gput:Nnn\@@_info_prop_prop{#1}{#2}}
\cs_new:Nn
\@@_brace:nn{{{#1}{#2}}}
\cs_new:Npn
\clistmap_info_prop:n
#1 % <key>
{ \prop_map_function:cN
  {\prop_item:Nn\@@_info_prop_prop{#1}}\@@_brace:nn }
\cs_new:Npn
\clistmap_info_prop:nn
#1 % <key>
#2 % <code>
{ \prop_map_inline:cn
  {\prop_item:Nn\@@_info_prop_prop{#1}}{#2} }
\cs_new:Nn
\@@_group_if:nn
{\bool_if:nTF{#2}{{#1}}{#1}}
\cs_generate_variant:Nn\@@_group_if:nn{e}
\cs_new:Nn
\@@_head_clist:n
{%
  \exp_args:Ne
  \tl_head:n
  { \clist_map_function:nN{#1}\@@_head_clist_aux:n }
}
\cs_new:Nn
\@@_head_clist_aux:n{#1}
%    \end{macrocode}
% \end{macro}
% \section{\textsf{name}}
% \begin{macro}
%   {
%   \@@_rule_name:n,
%   \@@_instance_name:nnn,
%   \@@_instance_signature:n,
%   \@@_rule_sequence_name:n
% }
%    \begin{macrocode}
\cs_new:Npn
\@@_rule_name:n
#1 % <rules>
{rule_#1}
\cs_new:Npn
\@@_instance_name:nn
#1 % <rules>
#2 % <cs name>
{instance_#1_#2}
\cs_new:Npn
\@@_instance_name:nnn
#1 % <rule>
#2 % <next rules>
#3 % <cs name>
{\@@_instance_name:nn{#1_#2}{#3}}
\cs_new:Npn
\@@_instance_signature:n
#1 % <signature>
{n#1w}
%    \end{macrocode}
% \end{macro}
% \section{\textsf{c}}
%    \begin{macrocode}
\cs_new:Npn
\@@_c:n
#1 % <name>
{@@_#1}
\cs_generate_variant:Nn\@@_c:n{e}
\cs_new:Npn
\@@_c:nn
#1 % <name>
#2 % <signature>
{\@@_c:n{#1:#2}}
\cs_generate_variant:Nn\@@_c:nn{e, ee}
\cs_new:Npn
\@@_bound_cs_c:nn
#1 % <name>
#2 % <signature>
{#1:#2n}
\cs_new:Npn
\@@_rule_c:n
#1 % <rule>
{%
  \@@_c:en
  {\@@_rule_name:n{#1}}
  {nnnnnnnn}
}
\cs_new:Npn
\@@_instance_c:nn
#1 % <rules>
#2 % <cs name>
{ \@@_c:e
  { \@@_instance_name:nn{#1}{#2} } }
\cs_generate_variant:Nn\@@_instance_c:nn{e}
\cs_new:Npn
\@@_instance_c:nnn
#1 % <rules>
#2 % <cs name>
#3 % <signature>
{%
  \@@_c:ee
  { \@@_instance_name:nn{#1}{#2} }
  { \@@_instance_signature:n{#3} }
}
\cs_generate_variant:Nn\@@_instance_c:nnn{e, nne}
\cs_new:Npn
\@@_instance_c_this:nnnn
#1 % <rule>
#2 % <next rules>
#3 % <cs name>
#4 % <signature>
{ \@@_instance_c:enn
  {\@@_rule_link:nn{#1}{#2}}{#3}{#4} }
%    \end{macrocode}
% \section{\textsf{rule_link}}
%    \begin{macrocode}
\cs_new:Npn
\@@_rule_link:nn
#1 % <rule 1>
#2 % <rule 2>
{#1_#2}
\cs_new:Npn
\@@_rule_link:n
#1 % <{rule{1}}...>
{%
  \@@_rule_link:w#1\q_recursion_tail\q_recursion_stop
}
\cs_generate_variant:Nn\@@_rule_link:n{e}
\cs_new:Npn
\@@_rule_link:w
#1
\q_recursion_stop
{%
  \quark_if_recursion_tail_stop:n{#1}
  \@@_rule_link:nw #1 \q_recursion_stop}
\cs_new:Npn
\@@_rule_link:nw
#1 % <rules>
#2 % <{rule{1}}...>
\q_recursion_stop
{%
  \quark_if_recursion_tail_stop_do:nn{#2}{#1}
  \@@_rule_link:nnw{#1}#2\q_recursion_stop}
\cs_generate_variant:Nn\@@_rule_link:nw{e}
\cs_new:Npn
\@@_rule_link:nnw
#1 % <rules>
#2 % <rule{1}>
#3 % <{rule{2}}...>
\q_recursion_stop
{%
  \@@_rule_link:ew
  {%
    \@@_rule_link:nn
    {#1} % <rule 1>
    {#2} % <rule 2>
  } % <rules>
  #3 % <{rule{1}}...>
  \q_recursion_stop
}
%    \end{macrocode}
% \section{\textsf{inline}}
%    \begin{macrocode}
\cs_new_protected:Nn
\@@_inline_set_exp_nnnot:Nn
{\cs_set:Nn#1
  {\exp_not:n
    {\exp_not:n
      {\exp_not:n{#2}}}}}
\cs_generate_variant:Nn\@@_inline_set_exp_nnnot:Nn{c}
\cs_new:Nn\@@_inline_c:n{@@_#1:n}
\cs_new:Nn\@@_inline_use:n
{%^^A BUG
  \use:c{\@@_inline_c:n{#1}}}
\cs_new_protected:Nn
\@@_inline_set_exp_nnnot:nn
{\@@_inline_set_exp_nnnot:cn
  {\@@_inline_c:n{#1}}{#2}}
\msg_new:nnn{@@}
{inline-empty-N}
{instance~signature~must~be~empty~or~N;~got~'#1'}
\msg_new:nnn{@@}
{inline-empty-args}
{instance~signature=empty;~so~should~args=#1}
%    \end{macrocode}
% \section{\textsf{eval}}
% \begin{macro}
%   {\clistmap:nnn, \clistmap_inline:nnn}
%    \begin{macrocode}
\msg_new:nnn{@@}{key}
{no~match~for~#1~in~instance~or~instance~sequence}
\msg_new:nnn{@@}{signature-mismatch}
{instance~signature~must~be~#1;~instances:~#2}
\cs_new_protected:Npn
\clistmap_inline:nnn
#1 % <clist>
#2 % <instances>
#3 % <empty|code using #1>
{%^^A
  \bool_if:nTF
  { \__clistmap_instance_signature_p:nn{#2}{N} }
  {%^^A
    \__clistmap_inline_set_exp_nnnot:nn{a}{#3}
    \clistmap:nnn
    {#1} % <clist>
    {#2} % <key 1>
    {\__clistmap_a:n}
  }
  {%^^A
    \bool_if:nTF
    { \__clistmap_instance_signature_p:nn{#2}{} }
    {%^^A
      \tl_if_empty:nTF
      {#3}
      {%^^A
        \clistmap:nnn
        {#1} % <clist>
        {#2} % <key 1>
        {}
      }
      {%^^A
        \msg_error:nnnn{__clistmap}
        {inline-empty-args}
        {#3}
      }
    }
    {%^^A
      \msg_error:nnnn{__clistmap}
      {inline-empty-N}
      {#2}
    }
  }
}
\cs_new:Npn
\clistmap:nnn
% ^^A Warning: trailing ',' inside #2 => Error
#1 % <clist>
#2 % <key,...>
#3 % <arguments>
{%  
  \@@_eval:nenn
  {#2} % <instance key>,...
  {\tl_if_head_is_group_p:n{#1}} % <head is group>
  {#3} % <arguments>
  {#1} % <clist>
}
\cs_generate_variant:Nn\clistmap:nnn{e,f,x}
\cs_new:Npn
\@@_eval:nnnn
#1 % <instance key>,...
#2 % <head is group>
#3 % <arguments>
#4 % <clist>
{%
  \exp_args:Ne
  \@@_eval_aux:nnnn
  {\@@_instance_expand:n{#1}}
  {#2} % <head is group>
  {#3} % <arguments>
  {#4} % <clist>
}
\cs_new:Npn
\@@_eval_aux:nnnn
#1 % <instance key>,...
#2 % <head is group>
#3 % <arguments>
#4 % <clist>
{%
  \@@_eval:nnnw
  {#2} % <head is group>
  {#3} % <arguments>
  {#4} % <clist>
  #1 % <instance key>,...
  , \q_recursion_tail
  \q_recursion_stop
}
\cs_generate_variant:Nn\@@_eval:nnnn{ ne }
\cs_new:Npn
\@@_eval:nnnw
#1 % <head is group>
#2 % <arguments>
#3 % <clist>
#4 % <instance key>
\q_recursion_stop
{%
  \quark_if_recursion_tail_stop:n{#4}
  \@@_eval:nnnnw
  {#1} % <head is group>
  {#2} % <arguments>
  {#3} % <clist>
  #4 % <instance key>
  \q_recursion_stop
}
\cs_new:Npn
\@@_eval:nnnnw
#1 % <head is group>
#2 % <arguments>
#3 % <clist>
#4 % <instance key>
, #5 % <instance key,...>
\q_recursion_stop
{%
  \exp_last_unbraced:Ne
  \@@_eval:nnnnnn
  { \@@_instance_get:n{#4} }
  {#1}{#2}{#3}
  \@@_eval:nnnw
  {#1} % <head is group>
  {#2} % <arguments>
  {#3} % <clist>
  #5 % <instance key>
  \q_recursion_stop
}
\cs_new:Npn
\@@_eval:nnnnnn
#1 % <rule sequence>
#2 % <cs name>
#3 % <signature>
#4 % <head is group>
#5 % <arguments>
#6 % <clist>
{%
  \exp_args:Ne
  \clistmap_use_w:nnnn
  { \@@_rule_sequence_name:n{#1} } % <rule sequence>
  {#2}  % <cs name>
  {#3}  % <signature>
  {#4} % <head is group>
  #5
  #6, \q_recursion_tail\q_recursion_stop
}
%    \end{macrocode}
% \end{macro}
% \section{\textsf{chain}}
%    \begin{macrocode}
\msg_new:nnn{@@}
{chain}{unknown~chain~tag~#1}
\cs_new_protected:Npn
\@@_append:NNN
#1 % <new>
#2 % <\@@_append(?:_inline):nnn>
#3 % <\clistmap(?_inline):nnnn>
{%^^A
  #1
  #2  
  {%^^A
    \clistmap:nnn{##1}{##2}{##3}
    #3{##1}
  }
}
\@@_append:NNN
\cs_new:Nn
\@@_append:nnn
\clistmap:nnnn
\@@_append:NNN
\cs_new_protected:Nn
\@@_append_inline:nnn
\clistmap_inline:nnnn
\cs_new_protected:Npn
\@@_nest:NNN
#1 % <new>
#2 % <\@@_nest(?:_inline):nnn>
#3 % <\clistmap(?_inline):nnnn>
{%^^A
  #1
  #2  
  {%^^A
    \exp_args:Ne
    #3{ \clistmap:nnn{##1}{##2}{##3} }
  }
}
\@@_nest:NNN
\cs_new:Nn
\@@_nest:nnn
\clistmap:nnnn
\@@_nest:NNN
\cs_new_protected:Nn
\@@_nest_inline:nnn
\clistmap_inline:nnnn
\cs_new_protected:Npn
\@@_join:NNNN
#1 % <new>
#2 % <\@@_join(?:_inline):nnnn>
#3 % <\@@_join(?:_inline):nnn>
#4 % <\clistmap(?_inline):nnnn>
{%^^A
  #1
  #2  
  { #4{##1,##2}{##3}{##4} }
  #1
  #3
  { #2{\clistmap:nnn{##1}{##2}{##3}} }  
}
\@@_join:NNNN
\cs_new:Nn
\@@_join:nnnn
\@@_join:nnn
\clistmap:nnnn
\@@_join:NNNN
\cs_new_protected:Nn
\@@_join_inline:nnnn
\@@_join_inline:nnn
\clistmap_inline:nnnn
\cs_new_protected:Npn
\@@_chain:NNNNN
#1 % <new>
#2 % <@@_chain(?:_inline):nnnn>
#3 % <@@_append(?:_inline):nnn>
#4 % <@@_nest(?:_inline):nnn>
#5 % <@@_join(?:_inline):nnn>
{%^^A
  #1
  #2
  {%^^A
    \str_case:nnTF
    {##4}
    {%^^A
      {end}
      { \clistmap:nnn{##1}{##2}{##3} }
      {append}
      { #3{##1}{##2}{##3} }
      {nest}
      { #4{##1}{##2}{##3} }
      {join}
      { #5{##1}{##2}{##3} }
    }
    {}
    { \msg_error:nnn{@@}{chain}{##4} }
  }
}
\@@_chain:NNNNN
\cs_new:Nn
\clistmap:nnnn
\@@_append:nnn
\@@_nest:nnn
\@@_join:nnn
\@@_chain:NNNNN
\cs_new_protected:Nn
\@@_inline_aux:nnnn
\@@_append_inline:nnn
\@@_nest_inline:nnn
\@@_join_inline:nnn
\cs_new_protected:Npn
\clistmap_inline:nnnn
#1 % <clist>
#2 % <inst>
#3 % <args>
#4 % <chain>
{%^^A
  \bool_if:nTF
  { \@@_instance_signature_p:nn{#2}{N} }
  {%^^A
    \@@_inline_set_exp_nnnot:nn{a}{#3}
    \@@_inline_aux:nnnn{#1}{#2}{\@@_a:n}{#4}
  }
  { \@@_inline_aux:nnnn{#1}{#2}{}{#4} }
}
%    \end{macrocode}
% \section{\textsf{use_w}}\label{sec:code}
% \begin{macro}
%   {
%   \clistmap_use_w_group:nnnnnn,
%   \clistmap_use_w:nnnn,
%   \clistmap_use_w:nnnnn
% }
%   For use inside \meta{code} inside \nameref{sec:rule}
%    \begin{macrocode}
\cs_new:Npn
\clistmap_use_w_group:nnnnnn
#1  % <rule sequence>
#2  % <cs name>
#3  % <signature>
#4  % <head is group>
#5  % <arguments>
#6  % <clist head>
{%
  \clistmap_use_w:nnnn
  {#1}{#2}{#3}
  {#4}#5{#6}
}
\cs_new:Npn
\clistmap_use_w:nnnn
#1 % <rule sequence>
#2 % <cs name>
#3 % <signature>
#4 % <head is group>
{%
  \use:c{ \@@_instance_c:nnn{#1}{#2}{#3} }{#4}
}
\cs_generate_variant:Nn\clistmap_use_w:nnnn{nnne}
\cs_new:Npn
\clistmap_use_w:nnnnn
#1 % <rule>
#2 % <next rule sequence>
#3 % <cs name>
#4 % <signature>
#5 % <head is group>
{%
  \use:c{%
    \@@_instance_c_this:nnnn
    {#1} % <rule>
    {#2} % <next rules>
    {#3} % <cs name>
    {#4} % <signature>
  }{#5}
}
\cs_generate_variant:Nn\clistmap_use_w:nnnnn{nnnne}
%    \end{macrocode}
% \end{macro}
% \begin{macro}
%   { \clistmap_bound_cs_group:nnnnn }
%    \begin{macrocode}
\cs_new:Npn
\clistmap_bound_cs_group:nnnnn
#1 % <cs name>
#2 % <signature>
#3 % <group (bool)>
#4 % <arguments>
#5 % <clist>
{\@@_bound_cs:nnne{#1}{#2}{#4}{\bool_if:nTF{#3}{{#5}}{#5}}}
\cs_generate_variant:Nn\clistmap_bound_cs_use_group:nnnnn{nnenn}
\cs_new:Npn
\@@_bound_cs:nnnn
#1 % <cs name>
#2 % <signature>
#3 % <arguments>
#4 % <clist>
{ \use:c{\@@_bound_cs_c:nn{#1}{#2}}#3{#4} }
\cs_generate_variant:Nn\@@_bound_cs:nnnn{nnne}
%    \end{macrocode}
% \end{macro}
% \section{\textsf{rule}}\label{sec:rule}
% \begin{macro}{rule}
%    \begin{macrocode}
\keys_define:nn{ @@ }
{ rule.code:n = \@@_rule:nn#1 }
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\@@_rule:nn}
%    \begin{macrocode}
\prop_new:N\@@_rule_clist
\@@_info_clist_put:nn{rule}{@@_rule_clist}
\cs_new_protected:Npn
\@@_rule:nn
#1 % <rule>
#2 % <code>
{%
  \clist_gput_right:Nn\@@_rule_clist{#1}
  \exp_args:Nno
  \cs_new_protected:cn
  { \@@_rule_c:n{#1} } 
  {%
    \@@_rule_apply:nnnnnnnn
    {#1} % {<rule>}
    {#2} % {<code>}
    {##1} % <next rule>
    {##2} % <cs name>
    {##3} % <signature>
    {{##4}{##5}{##6}} % <head is group>
    % ^^A <arguments>
    % ^^A <clist head>
    {##7} % <clist rest>
    {##8} % <parameters}
  }
}
% ^^A  ##1 % <next rules>
% ^^A  ##2 % <cs name>
% ^^A  ##3 % <signature>
% ^^A  ##4 % <head is group>
% ^^A  ##5 % <arguments>
% ^^A  ##6 % <clist head>
% ^^A  ##7 % <clist rest>
% ^^A  ##8 % <parameters>
\cs_new_protected:Npn
\@@_rule_apply:nnnnnnnn
#1 % <rule>
#2 % <code>
#3 % <next rules>
#4 % <cs name>
#5 % <signature>
#6 % {<head is group>}{<arguments>}{<clist head>}
#7 % <clist rest>
#8 % <parameters>
{%
  \@@_rule_apply:ennnnnn
  {\@@_instance_c_this:nnnn{#1}{#3}{#4}{#5}}
  {#2}#6{#7}{#8}
}
\cs_new_protected:Npn
\@@_rule_apply:nnnnnnn
#1 % <instance>
#2 % <code>
#3 % <head is group>
#4 % <arguments>
#5 % <clist head>
#6 % <clist rest>
#7 % <parameters>
{%
  \cs_if_exist:cF{#1}
  {%^^A
    \cs_new:cpn{#1}
    #3#7#5, #6\q_recursion_stop % <parameters>
    {#2}
  }
}
\cs_generate_variant:Nn\@@_rule_apply:nnnnnnn{e}
%    \end{macrocode}
% \end{macro}
% \section{\textsf{rule template}}
%    \begin{macrocode}
\cs_new:Nn
\@@_quark_if_recursion_tail_stop:nn
{\quark_if_recursion_tail_stop:n{#1#2}}
\cs_generate_variant:Nn\@@_quark_if_recursion_tail_stop:nn{e}
%    \end{macrocode}
% \begin{macro}
%   {rule_if_rest_is_tail_eval_else}
%    \begin{macrocode}
\keys_define:nn{ @@ }
{%
  rule_if_rest_is_tail_eval_else.code:n
  = {\@@_rule_if_rest_is_tail_eval_else:nn#1}
}
\cs_new_protected:Npn
\@@_rule_if_rest_is_tail_eval_else:nn
#1 % <name>
#2 % <else code>
{%
  % ^^A  ##1 % <next rules>
  % ^^A  ##2 % <cs name>
  % ^^A  ##3 % <signature>
  % ^^A  ##4 % <head is group>
  % ^^A  ##5 % <arguments>
  % ^^A  ##6 % <clist head>
  % ^^A  ##7 % <clist rest>
  % ^^A  ##8 % <parameters>
  \clistmap_keys_set:n
  {%
    rule = {if_rest_is_tail_eval_else_#1}
    {%
      \quark_if_recursion_tail_stop_do:nn{##7}
      {%
        \clistmap_bound_cs_group:nnnnn
        {##2} % <cs name>
        {##3} % <signature>
        {##4} % <head is group>
        {##5} % <arguments>
        {##6} % <clist>
      }
      #2
    }
  }
}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{rule_if_empty_stop_else}
%    \begin{macrocode}
\keys_define:nn
{ @@ }
{
  rule_if_empty_stop_else.code:n
  = {\@@_rule_if_empty_stop_else:nn#1}
}
\cs_new_protected:Npn
\@@_rule_if_empty_stop_else:nn
#1 % <name>
#2 % <else code>
{%
  % ^^A  ##1 % <next rules>
  % ^^A  ##2 % <cs name>
  % ^^A  ##3 % <signature>
  % ^^A  ##4 % <head is group>
  % ^^A  ##5 % <arguments>
  % ^^A  ##6 % <clist head>
  % ^^A  ##7 % <clist rest>
  % ^^A  ##8 % <parameters>
  \clistmap_keys_set:n
  {%
    rule = {if_empty_stop_else_#1}
    {%
      \@@_quark_if_recursion_tail_stop:en
      {\bool_if:nTF{##4}{{##6}}{##6}}{##7}
      #2
    }
  }
}
%    \end{macrocode}
% \end{macro}
% \section{\textsf{instantiate}}
% \begin{macro}{\@@_instantiate:nnnn}
%    \begin{macrocode}
\cs_new_protected:Npn
\@@_instantiate:nnnn
#1 % <rule>
#2 % <next rules>
#3 % <cs name>
#4 % <signature>
{%
  \exp_args:Ne
  \@@_instantiate:nnnnn
  {\tl_count:n{#4}} % <signature arity>
  {#1} % <rule>
  {#2} % <next rules>
  {#3} % <cs name>
  {#4} % <signature>
}
\cs_new_protected:Npn
\@@_instantiate:nnnnn
#1 % <signature arity>
#2 % <rule>
#3 % <next rules>
#4 % <cs name>
#5 % <signature>
{%^^A
  \@@_instantiate:eeeeennn
  { \erw_parameter:n{ 1 } } % <head is group>
  { \erw_parameter:ne{2}{ #1 } } % <parameters>
  { \erw_parameter:e{ \int_eval:n{#1+2} } } % <clist head>
  { \erw_parameter:e{ \int_eval:n{#1+3} } } % <clist rest>
  { \erw_argument:ne{2}{ #5 } } % <arguments>
  { #2 } % <rule>
  { #3 } % <next rules>
  { #4 } % <cs name>
  { #5 } % <signature>
}
\cs_new:Npn
\@@_instantiate:nnnnnnnn
#1 % <head is group>
#2 % <parameters>
#3 % <clist head>
#4 % <clist rest>
#5 % <arguments>
#6 % <rule>
#7 % <next rules>
#8 % <cs name>
#9 % <signature>
{%
  \use:c{ \@@_rule_c:n{#6} }
  {#7} % <next rules>
  {#8} % <cs name>
  {#9} % <signature>
  {#1} % <head is group>
  {#2} % <arguments>
  {#3} % <clist head>
  {#4} % <clist rest>
  {#2} % <parameters>
}
\cs_generate_variant:Nn\@@_instantiate:nnnnnnnn{eeeee}
%    \end{macrocode}
% \end{macro}
% \section{\textsf{property}}
% \begin{macro}{rule_sequence}
%    \begin{macrocode}
\cs_new:Npn
\@@_rule_sequence_name:n
#1 % <rule sequence>
{%
  \@@_rule_link:e
  {\@@_rule_sequence_get:n{#1}{null}}
}
\keys_define:nn{@@}
{ rule_sequence.code:n = \@@_rule_sequence_from_keyval:n{#1} }
\prop_new:N\@@_rule_sequence_prop
\@@_info_prop_put:nn{rule_sequence}{@@_rule_sequence_prop}
\cs_new_protected:Npn
\@@_rule_sequence_from_keyval:n
#1 % <key = {{rule{1}}...>
{%
  \prop_set_from_keyval:Nn
  \@@_rule_sequence_prop{#1}
}
\cs_new:Npn
\@@_rule_sequence_get:n
#1 % <key>
{%
  \exp_args:Ne
  \@@_rule_sequence_aux:n
  {%
    \prop_item:Nn
    \@@_rule_sequence_prop{#1}
  }
}
\cs_new:Npn
\@@_rule_sequence_aux:n
#1 % <value>
{%
  \prop_if_in:NnTF
  \@@_rule_sequence_prop
  {#1}
  {\@@_rule_sequence_get:n{#1}}
  {#1}
}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\clistmap_signature:n, \clistmap_instance_p:n}
%    \begin{macrocode}
\prg_new_conditional:Npnn
\clistmap_instance:n
#1
{p}
{\prop_if_in:NnTF
  \@@_instance_prop{#1}
  {\prg_return_true:}
  {\prg_return_false:}
}
\msg_new:nnn{@@}{instance-not}{#1~is~not~an~instance}
\msg_new:nnn{@@}{key-conflict}{key~#1~already~exists~in~prop~#2}
\prop_new:N\@@_instance_prop
\@@_info_prop_put:nn{instance}{@@_instance_prop}
\cs_new_protected:Npn
\@@_instance_put:nnnn
#1 % <key>
#2 % <rule sequence>
#3 % <name>
#4 % <signature>
{%
  \prop_gput:Nnn
  \@@_instance_prop{#1}
  { {#2}{#3}{#4} }
}
\cs_new:Npn
\@@_instance_get:n
#1 % <key>
{ \prop_item:Nn\@@_instance_prop{#1} }
\cs_new:Nn
\clistmap_signature:n
{%^^A
  \bool_if:nTF
  { \clistmap_instance_p:n{#1} }
  { \@@_instance_signature_get:n{#1} }
  { \msg_error:nnn{@@}{instance-not}{#1} }
}
\cs_new:Npn
\@@_instance_signature_get:n
#1 % <instance>
{\exp_last_unbraced:Ne\use_iii:nnn
  {\@@_instance_get:n{#1}}}
\cs_new:Npn
\@@_instance_expand:n
#1 %^^A <instance(?:_sequence)_1,...>
{%^^A
  \@@_instance_expand:w
  #1, \q_recursion_tail
  \q_recursion_stop
}
\cs_new:Npn
\@@_instance_expand:w
#1 %^^A <instance(?:_sequence)_1,...>
,#2
\q_recursion_stop
{
  \quark_if_recursion_tail_stop:n{#1#2}
  \@@_instance_expand:nw#1, #2\q_recursion_stop
}
\cs_new:Npn
\@@_instance_expand:nw
#1 % <head>
, #2 % <rest>
\q_recursion_stop
{
  \bool_if:nTF
  {\clistmap_instance_sequence_p:n{#1}}
  {%^^A
    \exp_args:Ne
    \@@_instance_expand:n
    { \@@_instance_sequence_get:n{#1} }
  }
  {%
    \bool_if:nTF
    {\clistmap_instance_p:n{#1}}
    {#1}
    {\msg_error:nnn{@@}{neither-inst-seq}{#1}}
  }
  \quark_if_recursion_tail_stop:n{#2},%^^A comma
  \@@_instance_expand:nw#2\q_recursion_stop
}
\msg_new:nnn{@@}{neither-inst-seq}
{#1~is~neither~an~instance~nor~a~sequence}
\prg_new_conditional:Npnn
\@@_instance_signature:nn
#1 % <instance_1,...>
#2 % <signature>
{p}
{%^^A
  \bool_if:nTF
  {
    \exp_args:Ne
    \@@_instance_signature_aux_p:nn
    {%^^A
      \exp_args:Ne
      \clist_map_function:nN
      { \@@_instance_expand:n{#1} }
      \clistmap_signature:n
    }
    {#2}
  }
  {\prg_return_true:}
  {\prg_return_false:}
}
\prg_new_conditional:Npnn
\@@_instance_signature_aux:nn
#1 % <signature_1,...>
#2 % <signature>
{p}
{%
  \tl_if_empty:nTF
  {#1}
  {%^^A
    \tl_if_empty:nTF{#2}
    {\prg_return_true:}
    {\prg_return_false:}
  }
  {%^^A
    \bool_if:nTF
    {%^^A
      \erw_and_tl_p:nn
      { \str_if_eq_p:nn{#2} }
      { #1 }
    }
    {\prg_return_true:}
    {\prg_return_false:}
  }
}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{instance_sequence, \clistmap_instance_sequence_p:n}
%    \begin{macrocode}
\keys_define:nn{ @@ }
{%^^A
  instance_sequence.code:n
  = {%^^A
    \clist_map_function:nN{#1}
    \@@_instance_sequence_put:n
  }
}
\prg_new_conditional:Npnn
\clistmap_instance_sequence:n
#1
{p}
{%
  \prop_if_in:NnTF
  \@@_instance_sequence_prop{#1}
  {\prg_return_true:}
  {\prg_return_false:}
}
\prop_new:N
\@@_instance_sequence_prop
\@@_info_prop_put:nn{instance_sequence}{@@_instance_sequence_prop}
\cs_new:Nn\@@_first_braced:nn{{#1}}
\cs_new:Nn\@@_instance_sequence_keys:
{%
  \prop_map_function:NN
  \@@_instance_sequence_prop
  \@@_first_braced:nn
}
% ^^A\cs_new_protected:Npn
% ^^A\@@_instance_sequence_put:n
% ^^A#1 % <{key}{key{1},...}>
% ^^A{ \@@_instance_sequence_put:nn#1 }
\cs_new_protected:Npn
\@@_instance_sequence_put:n
#1 % <{signature}{prefix key}{prefix key{1},...}>
{ \@@_instance_sequence_put:nnn#1 }
\cs_new:Npn
\@@_instance_sequence_value:nn
#1 % <signature>
#2 % <key prefix 1,...>
{%
  \exp_args:Nne
  \erw_clist_tl:nn{\c_false_bool}
  {%^^A
    \clist_map_tokens:nn
    {#2}
    { \@@_instance_sequence_value_aux:nn{#1} }
  }
}
\cs_new:Nn
\@@_instance_sequence_value_aux:nn
{{\clistmap_instance_key:nn{#2}{#1}}}
\cs_new_protected:Npn
\@@_instance_sequence_put:nnn
#1 % <signature>
#2 % <prefix key>
#3 % <prefix key{1}>,...
{%^^A
  \exp_args:Nee
  \@@_instance_sequence_put:nn
  { \clistmap_instance_key:nn{#2}{#1} }
  { \@@_instance_sequence_value:nn{#1}{#3} }
}
\cs_new_protected:Npn
\@@_instance_sequence_put:nn
#1 % <key>
#2 % <instance key{1}>,...
{%
  \prop_if_in:NnTF
  \@@_instance_prop{#1}
  {\msg_error:nnnn{@@}{key-conflict}{#1}{instance}}
  {%  
    \prop_gput:Nnn
    \@@_instance_sequence_prop{#1}
    { #2 }
  }
}
\cs_new:Nn
\clistmap_instance_sequence:n
{\@@_instance_sequence_get:n{#1}}
\cs_new:Npn
\@@_instance_sequence_get:n
#1 % <key>
{\prop_item:Nn\@@_instance_sequence_prop{#1}}
%    \end{macrocode}
% \end{macro}
% \section{\textsf{instance}}
% \begin{macro}{instance, \clistmap_instance_key:nn}
%    \begin{macrocode}
\keys_define:nn{@@}
{ instance.code:n = \clist_map_function:nN{#1} \@@_instance:n }
\cs_new_protected:Npn
\@@_instance:n
% ^^A#1 % {key prefix}{<rule sequence>}{<cs name>}{<signature>}
#1 % {<signature>}{key prefix}{<rule sequence>}{<cs name>}
{ \@@_instance:nnnn#1 }
\cs_new_protected:Npn
\@@_instance:nnnn
% ^^A#1 % <key prefix>
% ^^A#2 % <rule sequence>
% ^^A#3 % <cs name>
% ^^A#4 % <signature>
#1 % <signature>
#2 % <key prefix>
#3 % <rule sequence>
#4 % <cs name>
{%
  \exp_args:Ne
  \@@_instance_aux:nnnn
  { \clistmap_instance_key:nn{#2}{#1} }
  {#3}{#4}{#1}
}
\cs_new:Npn
\clistmap_instance_key:nn
#1 % <key prefix>
#2 % <signature>
{#1:#2}
\cs_new_protected:Npn
\@@_instance_aux:nnnn
#1 % <key>
#2 % <rule sequence>
#3 % <signature>
#4 % <cs name>
{%  
  \@@_instance_put:nnnn{#1}{#2}{#3}{#4}
  \@@_instance_using_key:nnn{#2}{#3}{#4}
}
\cs_new_protected:Npn
\@@_instance_using_key:nnn
#1 % <rule sequence>
#2 % <cs name>
#3 % <signature>
{%
  \@@_instance_using_list:enn
  { \@@_rule_sequence_get:n{#1}{null} } % <{rule{1}}...>
  {#2} % <cs name>
  {#3}% <signature>
}
\cs_new_protected:Npn
\@@_instance_using_list:nnn
#1 % <{rule{1}}{rule{2}}...>
#2 % <cs name>
#3 % <signature>
{%
  \exp_last_unbraced:Ne
  \@@_instance_backward:nnnnn
  {%
    { \tl_count:n{#3} } % <signature arity>
    \erw_last:n{#1}  % <rule{n}>
    { \erw_remove_first:e{\tl_reverse:n{#1}} } % <{rule{n-1}}{rule{n-2}}...>
  }
  { #2 } % <cs name>
  { #3 } % <signature>
}
\cs_generate_variant:Nn\@@_instance_using_list:nnn{enn}
\msg_new:nnn{@@}{null}
{clistmap~expects~'null'~as~the~last~rule;~got~'#1'}
\cs_new_protected:Npn
\@@_instance_backward:nnnnn
#1 % <signature arity>
#2 % <rule{n}>
#3 % <{rule{n-1}}{rule{n-2}}...>
#4 % <cs name>
#5 % <signature>
{%
  \str_case:nnTF{#2}
  { {null}{} }
  {%
    \@@_instance_backward:nnnw
    {#2} % <next rules>
    {#4} % <cs name>
    {#5} % <signature>
    #3\q_recursion_tail % <{rule{n}}{rule{n-1}}...>
    \q_recursion_stop
  }
  {%
    \msg_error:nnn{@@}
    {null}
    {#2}
  }
}
\cs_generate_variant:Nn\@@_instance_backward:nnnnn{eee}
\cs_new_protected:Npn
\@@_instance_backward:nnnw
#1 % <next rules>
#2 % <cs name>
#3 % <signature>
#4 % <{rule{n}}{rule{n-1}}...>
\q_recursion_stop
{%
  \quark_if_recursion_tail_stop:n{#4}
  \@@_instance_backward:nnnnw
  {#1} % <next rules>
  {#2} % <cs name>
  {#3} % <signature>
  #4 % <rule{n}>
  % <{rule{n-1}}...>
  \q_recursion_stop
}
\cs_generate_variant:Nn\@@_instance_backward:nnnw{e}
\cs_new_protected:Npn
\@@_instance_backward:nnnnw
#1 % <next rules>
#2 % <cs name>
#3 % <signature>
#4 % <rule{n}>
#5 % <{rule{n-1}}...>
\q_recursion_stop
{%
  \@@_instantiate:nnnn
  {#4} % <rule>
  {#1} % <next rules>
  {#2} % <cs name>
  {#3} % <signature>
  \@@_instance_backward:ennw
  {\@@_rule_link:nn{#4}{#1}} % <next rules>
  {#2} % <cs name>
  {#3} % <signature>
  #5 % <{rule{n}}...>
  \q_recursion_stop
}
%    \end{macrocode}
% \end{macro}
% \section{\textsf{preset}}
% \subsection{\textsf{rule}}
%    \begin{macrocode}
\msg_new:nnn{@@}{tail}{expects~tail;~got~'#1'}
% ^^A ##1 % <next rules>
% ^^A ##2 % <cs name>
% ^^A ##3 % <signature>
% ^^A ##4 % <head is group>
% ^^A ##5 % <arguments>
% ^^A ##6 % <clist head>
% ^^A ##7 % <clist rest>
% ^^A ##8 % <args>
\clistmap_keys_set:n
{%
  rule = {if_rest_is_tail_stop_else_eval_recurse}
  {%
    \quark_if_recursion_tail_stop:n{#7}
    \clistmap_bound_cs_group:nnnnn
    {#2} % <cs name>
    {#3} % <signature>
    {#4} % <head is group>
    {#5} % <arguments>
    {#6} % <clist>    
    \clistmap_use_w:nnnne
    {if_rest_is_tail_stop_else_eval_recurse} % <rule>
    {#1} % <next rule rule sequence>
    {#2} % <cs name>
    {#3} % <signature>
    {\tl_if_head_is_group_p:n{#7}}#5#7\q_recursion_stop % <head is group>
  },
  rule = {if_rest_is_tail_stop_else_forward_rest}
  {%    
    \quark_if_recursion_tail_stop:n{#7}
    \clistmap_use_w:nnne
    {#1}{#2}{#3}
    {\tl_if_head_is_group_p:n{#7}}#5#7\q_recursion_stop
  },
  rule_if_empty_stop_else = {error}
  {%
    \msg_error:nnn{@@}{tail}{#6#7}
    \@@_empty:w{}\q_recursion_stop
  },  
  rule_if_empty_stop_else = {forward_head}
  {%
    \bool_if:nTF{#4}
    {%
      \clistmap_use_w_group:nnnnnn{#1}{#2}{#3}{#4}{#5}{#6}
      ,\q_recursion_tail\q_recursion_stop
    }
    {%
      \clistmap_use_w:nnnn{#1}{#2}{#3}
      {#4}#5#6,\q_recursion_tail\q_recursion_stop
    }
  },
  rule_if_empty_stop_else = {forward_rest}
  {%
    \clistmap_use_w:nnne
    {#1}{#2}{#3}
    {\tl_if_head_is_group_p:n{#7}}#5#7\q_recursion_stop
  },
  rule_if_empty_stop_else = {forward_all}
  {%
    \bool_if:nTF{#4}
    {%
      \clistmap_use_w_group:nnnnnn{#1}{#2}{#3}{#4}{#5}{#6},
      #7\q_recursion_stop
    }
    {%
      \clistmap_use_w:nnnn
      {#1}{#2}{#3}{#4}#5#6, #7\q_recursion_stop
    }
  },
  rule_if_rest_is_tail_eval_else = {error}
  {%
    \msg_error:nnn{@@}{tail}{#6}
    \@@_empty:w\q_recursion_stop
  },
  rule_if_rest_is_tail_eval_else = {stop}
  {%
    \@@_empty:w{}\q_recursion_stop
  },  
  rule_if_rest_is_tail_eval_else = {recurse}
  {%
    \clistmap_use_w:nnnne
    {if_rest_is_tail_eval_else_recurse} % <rule>
    {#1} % <next rule rule sequence>
    {#2} % <cs name>
    {#3} % <signature>
    {\tl_if_head_is_group_p:n{#7}} % <head is group>
    #5 % <argument>
    #7 % <clist>
    \q_recursion_stop
  }
}
%    \end{macrocode}
% \subsection{\textsf{rule_sequence}}
%    \begin{macrocode}
\clistmap_keys_set:n
{%
  rule_sequence =
  {%
    first =
    {
      {if_empty_stop_else_forward_head}
      {if_rest_is_tail_eval_else_error}
    },
    middle =
    {
      {if_empty_stop_else_forward_all}
      {if_rest_is_tail_stop_else_forward_rest}
      {if_rest_is_tail_stop_else_eval_recurse}
    },
    last =
    {
      {if_empty_stop_else_forward_all}
      {if_rest_is_tail_stop_else_forward_rest}
      {if_rest_is_tail_eval_else_recurse}
    },   
    serial_second =
    {
      {if_empty_stop_else_forward_all}
      {if_rest_is_tail_stop_else_forward_rest}
      {if_rest_is_tail_eval_else_stop}
    },
    serial_last =
    {
      {if_empty_stop_else_forward_all}
      {if_rest_is_tail_stop_else_forward_rest}
      {if_rest_is_tail_stop_else_forward_rest}
      {if_rest_is_tail_eval_else_recurse}
    }
  }
}
%    \end{macrocode}
% \subsection{\textsf{cs}}
%    \begin{macrocode}
\msg_new:nnnn{@@}{text}{text~is~not~loaded}{amsmath}
\cs_new:Nn\@@_unbrace_aux:n{#1}
\erw_keys_set:n
{
  clist_map_inline =
  {%
    {Nn}{apply}{#1{#2}},
    {Nn}{math}{\ensuremath{#1{#2}}},
    {Nn}{comma_map}{,\clist_map_function:nN#2#1},
    {Nn}{comma}{,#1{#2}},
    {Nn}{serial_math}{\text{,~}\ensuremath{#1{#2}}},
    {Nn}{serial_math_and}{\text{,~and~}\ensuremath{#1{#2}}},
    {Nn}{map}{\clist_map_function:nN#2#1},
    {Nn}{noindent}{\noindent},
    {n}{apply}{#1},
    {n}{math}{\ensuremath{#1}},
    {n}{comma_math}{,\ensuremath{#1}},
    {n}{newline}{\\#1},
    {n}{comma_unbrace}{,\@@_unbrace_aux:n#1},
    {n}{comma}{,#1},
    {n}{noindent}{\noindent},
    {n}{serial_and}{,~and~#1},
    {n}{serial_math_and}{\text{,~and~}\ensuremath{#1}},
    {n}{serial_math}{\text{,~}\ensuremath{#1}},
    {n}{serial}{,~#1},
    {n}{unbrace}{\@@_unbrace_aux:n#1}
  }
  {nnn}
  {
    \clist_gput_right:Nn\@@_helper_clist{#2:#1}
    \cs_new:cn{@@_#2:#1}{#3}
  }
}
%    \end{macrocode}
% \subsection{\textsf{instance}}
%    \begin{macrocode}
\clistmap_keys_set:n
{
  instance =
  {
    {N}{first_apply}{first}{@@_apply},
    {N}{first_map}{first}{@@_map},
    {N}{first_math}{first}{@@_math},
    {N}{first_noindent}{first}{@@_noindent},
    {N}{last_apply}{last}{@@_apply},
    {N}{last_comma_map}{last}{@@_comma_map},
    {N}{last_comma_math}{last}{@@_comma_math},
    {N}{last_comma}{last}{@@_comma},
    {N}{serial_last}{serial_last}{@@_comma},
    {N}{serial_second}{serial_second}{@@_comma},
    {N}{middle_apply}{middle}{@@_apply},
    {N}{middle_comma_map}{middle}{@@_comma_map},
    {N}{middle_comma_math}{middle}{@@_comma_math},
    {N}{middle_comma}{middle}{@@_comma},
    {N}{serial_last_math_and}{serial_last}{@@_serial_math_and},
    {N}{serial_middle_math}{middle}{@@_serial_math},
    {N}{serial_second_math_and}{serial_second}{@@_serial_math_and},
    {}{first_apply}{first}{@@_apply},
    {}{first_math}{first}{@@_math},
    {}{first_noindent}{first}{@@_noindent},
    {}{first_unbrace}{first}{@@_unbrace},
    {}{last_apply}{last}{@@_apply},
    {}{last_comma_math}{last}{@@_comma_math},
    {}{last_comma_unbrace}{last}{@@_comma_unbrace},
    {}{last_comma}{last}{@@_comma},
    {}{last_newline}{last}{@@_newline},
    {}{last_unbrace}{last}{@@_unbrace},
    {}{middle_apply}{middle}{@@_apply},
    {}{middle_comma_math}{middle}{@@_comma_math},
    {}{middle_comma_unbrace}{middle}{@@_comma_unbrace},
    {}{middle_comma}{middle}{@@_comma},
    {}{middle_newline}{middle}{@@_newline},
    {}{middle_unbrace}{middle}{@@_unbrace},
    {}{serial_last_and}{serial_last}{@@_serial_and},
    {}{serial_last_math_and}{serial_last}{@@_serial_math_and},
    {}{serial_middle_math}{middle}{@@_serial_math},
    {}{serial_middle}{middle}{@@_serial},
    {}{serial_second_and}{serial_second}{@@_serial_and},
    {}{serial_second_math_and}{serial_second}{@@_serial_math_and},
  }
}
%    \end{macrocode}
% \subsection{\textsf{instance_sequence}}
%    \begin{macrocode}
\clistmap_keys_set:n
{%
  instance_sequence =
  {
    {N}{apply}{first_apply, rest_apply},
    {N}{comma_map}{first_map, rest_comma_map},
    {N}{comma_math}{first_math, rest_comma_math},
    {N}{comma}{first_apply, rest_comma},
    {N}{rest_apply}{middle_apply, last_apply},
    {N}{rest_comma_map}{middle_comma_map, last_comma_map},
    {N}{rest_comma_math}{middle_comma_math, last_comma_math},
    {N}{rest_comma}{middle_comma, last_comma},
    {N}{serial_and}{first_apply, serial_rest_and},
    {N}{serial_math_and}{first_math, serial_rest_math_and},
    {N}{serial_rest_and}{serial_middle, serial_second_and, serial_last_and},
    %^^A <one long entry>
    {N}
    {serial_rest_math_and}
    {serial_middle_math, serial_second_math_and, serial_last_math_and}
    %^^A </one long entry>
    ,
    {}{apply}{first_apply, rest_apply},
    {}{comma_math}{first_math, rest_comma_math},
    {}{newline}{first_apply, rest_newline},
    {}{comma_unbrace}{first_unbrace, rest_comma_unbrace},
    {}{comma}{first_apply, rest_comma},
    {}{rest_apply}{middle_apply, last_apply},
    {}{rest_comma_math}{middle_comma_math, last_comma_math},
    {}{rest_newline}{middle_newline, last_newline},
    {}{rest_comma_unbrace}{middle_comma_unbrace, last_comma_unbrace},
    {}{rest_comma}{middle_comma, last_comma},
    {}{rest_unbrace}{middle_unbrace, last_unbrace},
    {}{serial_and}{first_apply, serial_rest_and},
    {}{serial_math_and}{first_apply, serial_rest_math_and},
    {}{unbrace}{first_unbrace, rest_unbrace},
    % ^^A <one long entry>
    {}{serial_rest_and}
    {serial_middle, serial_second_and, serial_last_and}
    % ^^A </one long entry>
    ,
    % ^^A <one long entry>
    {}{serial_rest_math_and}
    {serial_middle_math, serial_second_math_and, serial_last_math_and}
    % ^^A </one long entry>
  }
}
%    \end{macrocode}
% \section{\textsf{other}}
%    \begin{macrocode}
\ProcessKeysOptions{@@}
\ExplSyntaxOff
%</package> 
%    \end{macrocode}
% \end{implementation}
% \Finale
\endinput