How to extend the \romannumeral-based \fullyexpand to handle empty/all-space arguments?

Question

In Expandable full expansion of tokens that preserves catcodes, Joseph Wright presents the following code:

\long\def\fullyexpand#1{%
  \csname donothing\fullyexpandauxi{#1}{}%
}
\long\def\fullyexpandauxi#1{%
  \expandafter\fullyexpandauxii\romannumeral -`0#1\fullyexpandend
}
\long\def\fullyexpandauxii#1#2\fullyexpandend#3{%
  \ifx\donothing#2\donothing
    \expandafter\fullyexpandend
  \else
    \expandafter\fullyexpandloop
  \fi
  {#1}{#2}{#3}%
}
\long\def\fullyexpandend#1#2#3{\endcsname#3#1}
\long\def\fullyexpandloop#1#2#3{%
  \fullyexpandauxi{#2}{#3#1}%
}
\def\donothing{}

Of which he says:

I'd also note that the above code needs some guards adding for a blank (empty or all space) argument, as currently things fail in these cases.

And this is true enough, if not exactly grammatical. Unfortunately, I'm not up to scratch on my TeX, so I'm not sure how to add such guards. Any takers?

(For my application, anything that will work in pdfTeX is fine.)

Answer 1

This version needs exactly two expansions to work, and avoids needing the \csname construction by using two \romannumeral applications instead. The outer one makes sure we need exactly two expansions, the inner one does the expanding:

\long\def\fullyexpand#1{%
  \romannumeral-`0%
    \fullyexpandauxi{#1}{}%
}
\long\def\fullyexpandauxi#1{%
  % The space in the following line is deliberate: it will always finish the
  % \romannumeral before \fullyexpandauxii expands
  \expandafter\fullyexpandauxii\romannumeral-`0#1 \fullyexpandend
}
\long\def\fullyexpandauxii#1{%
  \ifx\fullyexpandend#1%
    \expandafter\fullyexpandend
  \else
    \expandafter\fullyexpandauxiii
  \fi
    {#1}%
}
\long\def\fullyexpandauxiii#1#2\fullyexpandend#3{%
  \expandafter\fullyexpandauxii\romannumeral-`0#2 \fullyexpandend{#3#1}%
}
% Here, #1 will be "\fullyexpandend", as we have reached the end of the loop
\long\def\fullyexpandend#1#2{ #2}

The previous version coded in a test for an entirely blank argument, but this fails if the argument is not blank but expands to something which is:

\long\def\fullyexpand#1{%
  \romannumeral-`0%
    \expandafter\ifx\expandafter\relax\detokenize\expandafter
      {\gobble#1 ?}\relax
      \expandafter\fullyexpandblank
    \else
      \expandafter\fullyexpandauxi
    \fi
      {#1}{}%
}
\long\def\gobble#1{}
\long\def\fullyexpandauxi#1{%
  \expandafter\fullyexpandauxii\romannumeral -`0#1\fullyexpandend
}
\long\def\fullyexpandauxii#1#2\fullyexpandend#3{%
  \expandafter\ifx\expandafter\relax\detokenize{#2}\relax
    \expandafter\fullyexpandend
  \else
    \expandafter\fullyexpandloop
  \fi
  {#1}{#2}{#3}%
}
\long\def\fullyexpandend#1#2#3{ #3#1}
\long\def\fullyexpandloop#1#2#3{%
  \fullyexpandauxi{#2}{#3#1}%
}
\long\def\fullyexpandblank#1#2{ }