Expanding arguments before macro call

Question

I've been banging my head against this for days. I have a macro which takes a macro name and its arguments. It then re-arranges the arguments a bit and then calls the passed macro with the re-arranged arguments and so ends like this:

#1{\arga}{\argb}{\argc}

where arga ... \argc are the processed arguments. However. I need to have \arga ... \argc fully expanded before the macro stored in #1 is called. I cannot for the life of me work this out after days of playing with \expandafter, \noexpand, etextools etc. I can't use expl3 and I'd really prefer not to use etextools but etoolbox is available. Here is a MWE:

\documentclass{article}
\begin{document}

\def\x#1#2#3#4{%
  \def\arga{#2}%
  \def\argb{#3}%
  \def\argc{#4}%
  #1{\arga}{\argb}{\argc}}

\def\y#1#2#3{\detokenize{#1#2#3}}

\x\y{arg1}{arg2}{arg3}

\end{document}

This results in "\arga \argb \argc" but I want "arg1arg2arg3". \expandafter will do this in \x but not for three arguments in a row. etextools has some macros to do this but I really want to avoid it (it clashes with etoolbox in some ways and I must have etoolbox). I couldn't get the etextools macros to work even when I tried (\ExpandNextTwo etc.)

UPDATE: I realised that in my case, the args can contain robust macros like:

\documentclass{article}
\usepackage{etoolbox}
\begin{document}

\def\x#1#2#3#4{%
  \def\arga{#2}%
  \edef\argb{\ifstrequal{#3}{arg2}{arg2}{}}%
  \def\argc{#4}%
  {\protected@edef\z{\noexpand#1{\arga}{\argb}{\argc}}\z}}

\def\y#1#2#3{\detokenize{#1#2#3}}

\x\y{arg1}{arg2}{arg3}

\end{document}

In which case (using egreg's answer as an example), it isn't fully expanded. As Joseph and egreg mention below, this isn't doable, you just have to use non-robust macros in such cases, for example. I'll let the question stand as it because it is informative.

Answer 1

The 'classical' approach is to use \expandafter

\documentclass{article}
\begin{document}

\def\x#1#2#3#4{%
  \def\arga{#2}%
  \def\argb{#3}%
  \def\argc{#4}%
  \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter#1%
    \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter
      {\expandafter\expandafter\expandafter\arga\expandafter\expandafter\expandafter}%
        \expandafter\expandafter\expandafter{\expandafter\argb\expandafter}\expandafter
          {\argc}}

\def\y#1#2#3{\detokenize{#1#2#3}}

\x\y{arg1}{arg2}{arg3}

\end{document}

where we need so many of them to expand arg3 then arg2 and finally arg1. (This is what is effectively wrapped up in expl3's \exp_args:Nooo).

The rule of the number of \expandafters we need is 2ⁿ – 1, where n is how many tokens we want to expand. So for one token somewhere ahead, we need just one \expandafter in each place to be 'skipped', to expand two tokens (second one then the first one) we need three \expandafters, for three tokens (as in the current case) we need seven \expandafters, and so one. This is easiest to see if you write/print out a short second and cross off the commands as TeX would read them: you'll find everything works out.

With e-TeX available, we can use an \edef and \unexpanded:

\documentclass{article}
\begin{document}

\def\x#1#2#3#4{%
  \def\arga{#2}%
  \def\argb{#3}%
  \def\argc{#4}%
  \begingroup
    \edef\x{%
      \endgroup
      \noexpand#1
        {\unexpanded\expandafter{\arga}}%
        {\unexpanded\expandafter{\argb}}%
        {\unexpanded\expandafter{\argc}}%
    }%
  \x
}    

\def\y#1#2#3{\detokenize{#1#2#3}}

\x\y{arg1}{arg2}{arg3}

\end{document}

(You can do the same without e-TeX using a series of toks, but that gets a bit confusing so I'd not normally do it.)

---

The question says no expl3, but for contrast the approach using a minimium of the functions it provides would read

\documentclass{article}
\usepackage{expl3}
\begin{document}
\ExplSyntaxOn
\def\x#1#2#3#4{
  \def\arga{#2}
  \def\argb{#3}
  \def\argc{#4}
  \exp_args:Nooo#1\arga\argb\argc
}    
\ExplSyntaxOff
\def\y#1#2#3{\detokenize{#1#2#3}}

\x\y{arg1}{arg2}{arg3}

\end{document}

which is I hope a lot more readable. (I'd probably want to use \exp_args:NVVV as we are using 'value stored in a variable', but that function is not pre-defined so I've avoided it here.)

Answer 2

If you really want the arguments to be fully expanded, then

\documentclass{article}
\begin{document}

\def\x#1#2#3#4{%
  \begingroup\edef\z{\endgroup\noexpand#1{#2}{#3}{#4}}\z
}

\def\y#1#2#3{\detokenize{#1#2#3}}

\def\foo{This is foo}

\texttt{\x\y{arg1}{arg2}{arg3\foo}}

\end{document}

will result in printing

arg1arg2arg3This is foo

whereas the \expandafter based solutions would print

arg1arg2arg\foo

Answer 3

With functional package, tricky argument expansion can be replaced by intuitive function composition, which is similar to other programmming languages such as Lua.

The evaluation of composite functions is from inside to outside. And \Expand is a predefined function.

\documentclass{article}
\usepackage{functional}
\begin{document}

\PrgNewFunction \x {Nmmm} {%
  #1{\Expand{#2}}{\Expand{#3}}{\Expand{#4}}%
}

\PrgNewFunction \xx {Nmmm} {%
  #1{\Expand{#2}}{\Expand{\StrIfEqTF{#3}{arg2}{\Result{arg2}}{}}}{\Expand{#4}}%
}

\PrgNewFunction \y {mmm} {\detokenize{#1,#2,#3}}

\x\y{arg1}{arg2}{arg3}

\xx\y{arg1}{arg2}{arg3}

\end{document}

Answer 4

Only traditional (La)TeX:

\documentclass{article}

\newcommand\Exchange[2]{#2#1}

\makeatletter
\DeclareRobustCommand\x[4]{%
  \begingroup
  \let\protect=\@unexpandable@protect
  \edef\scratchmacro{{#2}{#3}{#4}}%
  % #1 can easily consist of more than a single token when using
  % \Exchange instead of doing "\expandafter-hopping"
  \expandafter\Exchange\expandafter{\scratchmacro}{\endgroup#1}%
}%
\makeatother

% \detokenize doubles hashes.
% Thus expanding \scratchmacro first halves the amount of 8 hashes of catcode 6 and you
% have 4 hashes of catcode 6.
% Then \detokenize doubles the amount of 4 hashes hashes of catcode 6 and you have 8 
% hashes of catcode 12.

\newcommand\y[3]{\detokenize{\y{#1}{#2}{#3}}}

\begin{document}

\def\arga{arg1}%
\def\argb{arg2}%
\def\argc{arg3}%

\texttt{\x\y{\arga}{\argb}{\argc ########}}

\end{document}

Caveats:

• \x is not fully expandable as assignments are performed and grouping/scoping is used.
• A scratch-macro is defined from the arguments of \x and afterwards expanded. Expanding the scratch-macro leads to amounts of consecutive hashes provided as components of arguments of \x being halved.

---

If e-TeX-extensions are available, you can use \unexpanded:

\documentclass{article}

\makeatletter
\DeclareRobustCommand\x[4]{%
  \begingroup
  \let\protect=\@unexpandable@protect
  \edef\scratchmacro{\endgroup\unexpanded{#1}{#2}{#3}{#4}}%
  \scratchmacro
}%
\makeatother

% \detokenize doubles hashes.
% Thus expanding \scratchmacro first halves the amount of 8 hashes of catcode 6 and you
% have 4 hashes of catcode 6.
% Then \detokenize doubles the amount of 4 hashes hashes of catcode 6 and you have 8 
% hashes of catcode 12.

\newcommand\y[3]{\detokenize{\y{#1}{#2}{#3}}}

\begin{document}

\def\arga{arg1}%
\def\argb{arg2}%
\def\argc{arg3}%

\texttt{\x\y{\arga}{\argb}{\argc ########}}

\end{document}

Caveats:

• \x is not fully expandable as assignments are performed and grouping/scoping is used.
• A scratch-macro is defined from the arguments of \x and afterwards expanded. Expanding the scratch-macro leads to amounts of consecutive hashes provided as components of arguments of \x being halved.

---

If you work with an engine where \expanded is available:

\documentclass{article}

\newcommand\Exchange[2]{#2#1}
\makeatletter
\DeclareRobustCommand\x[4]{%
  \begingroup
  \let\protect=\@unexpandable@protect
  \expanded{\endgroup\unexpanded{#1}{#2}{#3}{#4}}%
}%
\makeatother

% \detokenize doubles hashes.
% \detokenize doubles the amount of 8 hashes hashes of catcode 6 and you have 16 
% hashes of catcode 12.

\newcommand\y[3]{\detokenize{\y{#1}{#2}{#3}}}

\begin{document}

\def\arga{arg1}%
\def\argb{arg2}%
\def\argc{arg3}%

\texttt{\x\y{\arga}{\argb}{\argc ########}}

\end{document}

Caveat:

• \x is not fully expandable as assignments are performed and grouping/scoping is used.

Benefit:

• No temporary macro is defined from the arguments of \x whose expanding would lead to halving amounts of consecutive hashes provided as components of arguments of \x.

---

The following variant is fully expandable as it does neither define a scratch-macro nor perform a \let-assignment for taking LaTeX's \protect-mechanism into account nor use grouping/scoping:

\documentclass{article}

\newcommand\x[4]{%
  \expanded{\unexpanded{#1}{#2}{#3}{#4}}%
}%

% \detokenize doubles hashes.
% \detokenize doubles the amount of 8 hashes hashes of catcode 6 and you have 16 
% hashes of catcode 12.

\newcommand\y[3]{\detokenize{\y{#1}{#2}{#3}}}

\begin{document}

\def\arga{arg1}%
\def\argb{arg2}%
\def\argc{arg3}%

\texttt{\x\y{\arga}{\argb}{\argc ########}}

\end{document}

Caveat: This variant does not take the oldschool \protect-mechanism of the LaTeX 2ε-kernel into account and fails with fragile commands.

Benefits:

• This variant of \x is fully expandable.
• No temporary macro is defined from the arguments of \x whose expanding would lead to halving amounts of consecutive hashes provided as components of arguments of \x.