Metacommand for commands that dynamically select a parameter?

Question

Original question

I would like to create a metacommand for creating new projection commands. Specifically, \newproj{\cmd}{<n>}{<m>} should create \cmd as a new command of <n> (mandatory) arguments that always expands to the <m>th argument.

For example, if we have \newproj{\fst}{2}{1} and \newproj{\snd}{2}{2}, then \fst{x}{y} should expand to x whereas \snd{x}{y} should expand to y.

Here is my attempt at this:

\documentclass{article}

\newcommand*{\newproj}[3]{%
  \newcommand*#1[#2]{%
    \expandafter#\expandafter##3%
  }%
}

\newproj{\fst}{2}{1}
\newproj{\snd}{2}{2}

\begin{document}
\begin{tabular}{ll}
\verb^\fst{x}{y}^:& \fst{x}{y} \\
\verb^\snd{x}{y}^:& \snd{x}{y}
\end{tabular}
\end{document}

Unfortunately, this gives the error "Illegal parameter number in definition of \newproj. <to be read again> \expandafter" How can I use a parameter as a function of some integer or metaparameter?

Extended question: indirection via a macro

A.Ellett and Hendrik Vogt suggest using \newcommand*#1[#2]{###3} because ## expands to #. This works perfectly if a positive integer is passed as #3 to \newproj! However, suppose that I pass a macro to \newproj as #3. How can I use expansion of a macro to dynamically select a parameter?

For example, the following should produce the correct results. However, it gives the error "Illegal parameter number in definition of \fst. <to be read again> \i".

\documentclass{article}

\newcommand*{\newproj}[3]{%
  \newcommand*#1[#2]{%
    \expandafter###3%
  }%
}

\def\i{1}
\newproj{\fst}{2}{\i}
\newproj{\snd}{2}{2}

\begin{document}
\begin{tabular}{ll}
\verb^\fst{x}{y}^:& \fst{x}{y} \\
\verb^\snd{x}{y}^:& \snd{x}{y}
\end{tabular}
\end{document}

Answer 1

You just want to fully expand both arguments using \number to get their decimal expansion, while avoiding expanding everything else (for which a toks register is useful)

\documentclass{article}

\newcommand*{\newproj}[3]{%
  \toks0{\newcommand*#1}%
  \edef\tmp{\the\toks0[\number#2]{####\number#3}}%
\tmp
  }

\def\i{1}
\newproj{\fst}{2}{\i}
\newproj{\snd}{2}{2}

\begin{document}
\begin{tabular}{ll}
\verb^\fst{x}{y}^:& \fst{x}{y} \\
\verb^\snd{x}{y}^:& \snd{x}{y}
\end{tabular}
\end{document}

Answer 2

Here's a start at something

\documentclass{article}
\newcommand{\newproj}[3]{%
    \expandafter\newcommand\csname #1\expandafter\endcsname[#2]{###3}
}
\pagestyle{empty}
\begin{document}

Hello

\newproj{helloworldapplesauce}{4}{3}

\helloworldapplesauce{a}{b}{c}{d}
\end{document}

Alternatively you might try to do (following the advice of @HendrikVogt )

\newcommand{\newproj}[3]{\newcommand{#1}[#2]{###3}}

should also do the trick

Regardless of the approach, you'll probably want to make sure that the values passed in the parameters are numbers and that whatever is passed in the third argument defining the function is no larger than the second.

Answer 3

\documentclass[12pt]{article}
\usepackage{catoptions}
\makeatletter
% \generateparams is not any costlier than using \newcommand:
\new@def*\generateparams#1#2{%
  \ifnum#1<\numexpr#2+1####\number#1%
    \expandafter\generateparams
    \expandafter{\number\numexpr#1+1\expandafter}%
    \expandafter{\number#2\expandafter}%
  \fi
}
\robust@def*\newproj#1#2#3{%
  \@ifdefinable#1\relax
  \cptexpanded{\def\noexpand#1\generateparams1{#2}{#####3}}%
}

% Examples of \newproj:
\def\one{1}
\newproj{\fst}{2}{\one}
\newproj{\snd}{2}{2}

% Using a loop to avoid repeating \newproj for every new definition:
\robust@def*\NewProj#1{%
  \cptforeach \x/\y/\z \in#1\do{%
    \cptexpandsecond\newproj{\noexpandcsn{\x}{\y}{\z}}%
  }%
}

% Examples of \NewProj:
\NewProj{fstb/2/\one, sndb/2/2}

\makeatother

% Let us print the examples:
\begin{document}
\begin{tabular}{ll}
\verb^\fst{x}{y}^:& \fst{x}{y} \\
\verb^\snd{x}{y}^:& \snd{x}{y} \\
\verb^\fstb{x}{y}^:& \fstb{x}{y} \\
\verb^\sndb{x}{y}^:& \sndb{x}{y}
\end{tabular}
\end{document}

Answer 4

With expl3 one can define a temporary macro and set the desired one to be equal to it. Nothing is left behind, because we are doing it in a group and exploit that \cs_new_eq:NN (here in the \cs_new_eq:Nc variant) does a global definition.

I use \prg_replicate:nn to build the desired number of arguments.

Possible variation: if a non-long macro is desired, use \cs_set_nopar:cx instead of \cs_set:cx.

Both arguments can be macros or integer variables.

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\newproj}{mmm}
 {% #1 is the name of a command
  % #2 is the number of arguments
  % #3 is the argument to choose
  \group_begin:
  \tl_set:Nx \l_tmpa_tl { __deyoung_temp: \prg_replicate:nn { #2 } { n } }
  \cs_set:cx { \l_tmpa_tl } { ## \int_eval:n { #3 } }
  \cs_new_eq:Nc #1 { \l_tmpa_tl }
  \group_end:
}
\ExplSyntaxOff

\newcommand\idx{1} \newcounter{baz} \setcounter{baz}{2}
\newproj{\fst}{2}{\idx}
\newproj{\snd}{2}{\value{baz}}

\begin{document}

\verb^\fst{x}{y}^: \fst{x}{y}

\verb^\snd{x}{y}^: \snd{x}{y}

Is it expandable? \edef\test{\fst{x}{y}}
\texttt{\meaning\test}

\newproj{\foo}{9}{4}\texttt{\meaning\foo}

\end{document}