How extend command defined using SplitArgument so as to allow 4 arguments not just 2?

Question

I have a command \cont used mainly in the form \cont{X, Y} and defined using \SplitArgument, as shown in the source below. How can I redefine (that is, extend the definition of)\cont so as to allow 4 arguments rather than 2, which get grouped in pairs as shown in the outout equation (2)?

Notice that I want to continue using a comma as separator when there are only 2 arguments, as in \cont{X, Y}. But I want to change the (main) separator to a semicolon when there are 4 arguments, while retaining commas as subsidiary separators, as in \cont{X, x; Y, y}.

\documentclass[fleqn]{memoir}
\usepackage{xparse}
\NewDocumentCommand{\cont}{ >{\SplitArgument{1}{,}} m }{\printcont#1}
\NewDocumentCommand{\printcont}{mm}{{\mathcal{C}}({#1}\IfValueT{#2}{, {#2}})}
\begin{document}
\noindent Equation~(\ref{one}) shows use of \verb!\cont! with 2 arguments, as in \verb!\cont{X, Y}!, with comma as separator:
\begin{equation}\label{one}
\cont{X, Y}
\end{equation}
\noindent How can we \emph{extend} the definition of \verb!\cont! so that\dots\[6pt]
\mbox{}\qquad\verb!\cont{X, x; Y, y}! \[6pt]
---with commas and a single semicolon as separators----gives the same result as equation~(\ref{two}), below?
\begin{equation}\label{two}
\mathcal{C}[(X, x), (Y, y)]
\end{equation}
\end{document}

Answer 1

The macro \cont defined only using TeX primitives:

\def\cont#1{\contA#1;\end}
\def\contA#1;#2\end{\ifx;#2;{\cal C}(#1)\else\contB#1;#2\fi}
\def\contB#1;#2;{{\cal C}\bigl[(#1),(#2)\bigr]}
%% test:
$$\displaylines{
  \cont{X} \cr
  \cont{X, Y} \cr
  \cont{X;Y} \cr
  \cont{X,x;Y} \cr
  \cont{X, x;Y, y}
}$$
\bye

Answer 2

The following approach uses etoolbox's list processing capabilities to set the argument supplied by \cont, separating the argument (a list) by ; and then setting the list conditionally: A single item is set differently from a list of items.

\documentclass{article}
\usepackage{etoolbox}
\DeclareListParser{\contlist}{;}% Processes a list using ; as separator
\newcounter{contcount}
\newcommand{\cont}[1]{%
  \setcounter{contcount}{0}% Reset counter
  \renewcommand{\do}[1]{\stepcounter{contcount}}% Count items in list
  \contlist{#1}% Count elements in list
  \ifnum\value{contcount}<2
    \mathcal{C}(#1)% Singular element
  \else % \value{contcount}>1
    \mathcal{C}[
      % https://tex.stackexchange.com/a/89187/5764
      \newcommand{\contitemsep}{\renewcommand{\contitemsep}{,}}% Delayed definition of \contitemsep
      \renewcommand{\do}[1]{\contitemsep(##1)}% How each item in list should be printed
      \contlist{#1}% Print entire list
    ]
  \fi
}
\begin{document}
\noindent Equation~(\ref{one}) shows use of \verb!\cont! with 2 arguments, as in \verb!\cont{X, Y}!, with comma as separator:
\begin{equation}\label{one}
  \cont{X, Y}
\end{equation}
\noindent How can we \emph{extend} the definition of \verb!\cont! so that\dots
\qquad\verb!\cont{X, x; Y, y}!
---with commas and a single semicolon as separators----gives the same result as equation~(\ref{two}), below?
\begin{equation}\label{two}
  \cont{X, x; Y, y}
\end{equation}
\end{document}

Answer 3

I'd issue the \mathcal{C} immediately and then pass control to another command that checks for a semicolon and takes the appropriate action.

\documentclass[fleqn]{memoir}
\usepackage{amsmath}
\NewDocumentCommand{\cont}{>{\SplitArgument{1}{;}}m}{%
  \mathcal{C}%
  \printcont#1%
}
\NewDocumentCommand{\printcont}{mm}{%
  \IfNoValueTF{#2}{%
    \conttwo{#1}%
  }{%
    [\conttwo{#1},\conttwo{#2}]%
  }%
}
\NewDocumentCommand{\conttwo}{>{\SplitArgument{1}{,}}m}{%
  \printconttwo#1%
}
\NewDocumentCommand{\printconttwo}{mm}{%
  (#1\IfValueT{#2}{,#2})%
}
\begin{document}
\begin{gather}
\cont{X} \
\cont{X, Y} \
\cont{X;Y} \
\cont{X,x;Y} \
\cont{X, x;Y, y}
\end{gather}
\end{document}

If you want to add \bigl and \bigr to the brackets with \cont*, then pass the argument throughout.

\documentclass[fleqn]{memoir}
\usepackage{amsmath}
\NewDocumentCommand{\cont}{s>{\SplitArgument{1}{;}}m}{%
  \mathcal{C}%
  \printcont{#1}#2%
}
\NewDocumentCommand{\printcont}{mmm}{%
  \IfNoValueTF{#3}{%
    \conttwo{#2}%
  }{%
    \IfBooleanT{#1}{\bigl}[%
    \conttwo{#2},\conttwo{#3}
    \IfBooleanT{#1}{\bigr}]%
  }%
}
\NewDocumentCommand{\conttwo}{>{\SplitArgument{1}{,}}m}{%
  \printconttwo#1%
}
\NewDocumentCommand{\printconttwo}{mm}{%
  ({#1}\IfValueT{#2}{, {#2}})
}
\begin{document}
\begin{gather}
\cont{X} \
\cont{X, Y} \
\cont{X;Y} \
\cont{X,x;Y} \
\cont{X, x;Y, y} \
\cont{X,x;Y} \
\cont{X, x;Y, y}
\end{gather}
\end{document}

Answer 4

This variant is reluctant with adding parentheses and with this variant \cont{X,Y} is the same as \cont{X;Y} and \cont*{X,Y} is the same as \cont*{X;Y}, i.e., you get square brackets only if both comma and semicolon occurs in \cont's non-star-argument.

\documentclass[fleqn]{memoir}
\usepackage{amsmath}
\NewDocumentCommand{\cont}{s>{\SplitArgument{1}{;}}m}{%
  % #1  - \BooleanTrue/\BooleanFalse - flag / control-word-token
  %       denoting the presence/non-presence of star.
  % #2  - user-provided argument, split in two brace-nested arguments, one holding
  %       "things before first semicolon", the other holding "things behind first semicolon".
  \conttwo#2{#1}%
}
\NewDocumentCommand{\conttwo}{>{\SplitArgument{1}{,}}mm}{%
  % #1 - things before first semicolon, split in two brace-nested arguments at first comma.
  % #2 - things behind first semicolon
  % You need to check if #2 is the NoValue-marker as 
  % xparse-argument-processors like \SplitArgument do not work on
  % the NoValue-Marker
  \IfNoValueTF{#2}{\printcont{#2}}{\contthree}{#2}#1%
}
\NewDocumentCommand{\contthree}{>{\SplitArgument{1}{,}}m}{%
  % #1 - things behind first semicolon, split in two brace-nested arguments at first comma.
  \printcont#1%
}
\NewDocumentCommand\printcont{mmmmm}{%
  % #1 - first component of things behind first semicolon after splitting these things at first comma.
  % #2 - second component of things behind first semicolon after splitting these things at first comma.
  % #3 - first component of things before first semicolon after splitting these things at first comma.
  % #4 - second component of things before first semicolon after splitting these things at first comma.
  % #5 - \BooleanTrue/\BooleanFalse - flag denoting presence of star.
  \mathcal{C}%
  \IfNoValueTF{#1}{%
    (#3\IfNoValueF{#4}{,#4})% <-only commas
  }{%
    \IfNoValueTF{#4}{%
                      \IfNoValueTF{#2}{(#3,#1)}% <-only semicolons
                                      {\IfBooleanT{#5}{\bigl}[#3,(#1,#2)\IfBooleanT{#5}{\bigr}]}%
                    }%
                    {\IfBooleanT{#5}{\bigl}[(#3,#4),\IfNoValueTF{#2}{#1}{(#1,#2)}\IfBooleanT{#5}{\bigr}]}%
  }%
}%
\begin{document}
\Huge
\begin{tabular}{|l|l|}
\hline
(\cont{X})&(\cont{X}) \
\hline
(\cont{X, Y})&(\cont{X, Y}) \
\hline
(\cont{X;Y})&(\cont{X;Y}) \
\hline
(\cont{X,x;Y})&(\cont{X,x;Y}) \
\hline
(\cont{X;Y, y})&(\cont{X;Y, y}) \
\hline
(\cont{X, x;Y, y})&(\cont{X, x;Y, y})\
\hline
\end{tabular}
\end{document}