Expandable test for an empty token list—methods, performance, and robustness

General

There are a few considerations when it comes to performance of TeX code:

argument grabbing costs time, don't grab arguments unnecessarily
\expandafter is slow, if you can work around it with the same amount of expansions it's faster, so instead of
```
\if...
  \expandafter\@firstoftwo
\else
  \expandafter\@secondoftwo
\fi
```
we'd use (this uses an aspect of the first point, too, namely if false only the contents of the true branch will be gobbled)
```
\long\def\my@fi@firstoftwo\fi#1#2#3{\fi#2}
\if...
  \my@fi@firstoftwo
\fi
\@secondoftwo
```
gobbling tokens explicitly as delimiters for arguments is faster than gobbling them as an argument which is delimited, so the above example can further be optimized:
```
\long\def\my@fi@firstoftwo\fi\@secondoftwo#1#2{\fi#1}
\if...
  \my@fi@firstoftwo
\fi
\@secondoftwo
```
But be aware that this way code becomes less readable, less reusable, and less maintainable, so the small performance gain comes at a cost.

\if... can represent any if test that results in a TeX-syntax if, such as \ifx AB, \iftrue, etc.

Also \if tests can be slow (depending on the used test) and so is \detokenize, if we can get around those, we should. Another thing to consider is that \if tests are not robust if their arguments contains other \if tests, \else or \fi. To overcome this the standard test for an empty argument does \detokenize the argument with:

\long\def\ifemptyStandard#1%
  {%
    \if\relax\detokenize{#1}\relax
      \expandafter\@firstoftwo
    \else
      \expandafter\@secondoftwo
    \fi
  }

This yields an unbeatable robustness, as the only possible argument that might fail this test would be an unbalanced input, which needs to be actively created, such as \expandafter\ifemptyStandard\expandafter{\iffalse{\fi}}{true}{false} (but who would do that anyway).

Of all the if tests built into TeX, \ifx is probably the fastest. So a naive test \ifx <some-token>#1<some-token> would be pretty fast, unfortunately this would not be robust. Cases for which it'd fail would be if \if..., \else, or \fi would be part of the argument or if #1 starts with <some-token> (though we can make <some-token> pretty unlikely).

Fast `\ifempty`

The following is a fast test, that considers some of the above mentioned aspects. We don't use any \if... test, but instead do the branching through TeX's argument grabbing logic:

\long\def\ifempty@true\ifempty@A\ifempty@B\@secondoftwo#1#2{#1}
\long\def\ifempty@#1\ifempty@A\ifempty@B{}
\long\def\ifempty#1%
  {%
    \ifempty@\ifempty@A#1\ifempty@B\ifempty@true
      \ifempty@A\ifempty@B\@secondoftwo
  }

So if #1 is empty \ifempty@ will gobble only the first \ifempty@A and \ifempty@B and \ifempty@true will be executed, gobbling the following \ifempty@A\ifempty@B\@secondoftwo and the false-branch. On the other hand, if #1 is not empty everything up to \@secondoftwo (non-inclusive) will be gobbled and \@secondoftwo will execute the false-branch.

This way we get a fast testing macro (taking about 70% the time of the \if\relax\detokenize{#1}\relax test during my benchmarks), that's fairly robust (only input which contains \ifempty@A\ifempty@B will fail the test, and that should be rare).

And of course, we can use tokens which are even more unlikely than \ifempty@A and \ifempty@B, e.g., why not use a <DEL> characters for both but with different category codes (that should be pretty very very unlikely to ever be part of a valid argument):

\begingroup
\lccode`\&=127
\lccode`\$=127
\catcode`\&=12
\catcode`\$=11
\lowercase{\endgroup
\long\def\ifempty@true&$\@secondoftwo#1#2{#1}
\long\def\ifempty@#1&${}
\long\def\ifempty#1{\ifempty@&#1$\ifempty@true&$\@secondoftwo}
}

Fast `\ifblank`

As a small addition, we can also create a fast \ifblank test based on the aforementioned thoughts. The standard \ifblank looks something like the following:

\long\def\ifblankStandard#1%
  {%
    \if\relax\detokenize\expandafter{\@gobble #1.}\relax
      \expandafter\@firstoftwo
    \else
      \expandafter\@secondoftwo
    \fi
  }

So essentially the same as \ifemptyStandard but with an \expandafter and a \@gobble #1. added. But we could do the same as for our fast \ifempty test with just some small additions (I'll just add this to the slightly obfuscated variant using the <DEL> tokens). And we don't want to use some \expandafters (remember they are slow) so we use \ifblank@ to gobble one token and insert the necessary tests of \ifempty.

\begingroup
\lccode`\&=127
\lccode`\$=127
\catcode`\&=12
\catcode`\$=11
\lowercase{\endgroup
\long\def\ifempty@true&$\@secondoftwo#1#2{#1}
\long\def\ifempty@#1&${}
\long\def\ifempty#1{\ifempty@&#1$\ifempty@true&$\@secondoftwo}
\long\def\ifblank@#1{\ifempty@&}
\long\def\ifblank#1{\ifblank@#1.$\ifempty@true&$\@secondoftwo}
}

In case you need an expandable empty-test which does without e-TeX-extensions and without forbidden tokens, I can offer this one:

%%-----------------------------------------------------------------------------
%% Check whether argument is empty:
%%.............................................................................
%% \CheckWhetherEmpty{<Argument which is to be checked>}%
%%                   {<Tokens to be delivered in case that argument
%%                     which is to be checked is empty>}%
%%                   {<Tokens to be delivered in case that argument
%%                     which is to be checked is not empty>}%
%%
%% The gist of this macro comes from Robert R. Schneck's \ifempty-macro:
%% <https://groups.google.com/forum/#!original/comp.text.tex/kuOEIQIrElc/lUg37FmhA74J>
%%
%% Due to \romannumeral0-expansion the result is delivered after two
%% expansion-steps/after two "hits" by \expandafter.
\long\def\firstoftwo#1#2{#1}%
\long\def\secondoftwo#1#2{#2}%
\long\def\CheckWhetherEmpty#1{%
  \romannumeral0\expandafter\secondoftwo\string{\expandafter
  \secondoftwo\expandafter{\expandafter{\string#1}\expandafter
  \secondoftwo\string}\expandafter\firstoftwo\expandafter{\expandafter
  \secondoftwo\string}\firstoftwo\expandafter{} \secondoftwo}%
  {\firstoftwo\expandafter{} \firstoftwo}%
}%

Like anything else that works in terms of macros, this does not work with arguments that contain \outer-tokens.

Deviating from the requirements formulated in the question, \CheckWhetherEmpty is rather slow.

I take \CheckWhetherEmpty for a moot thing/for a slow workaround in situations where one can't take for granted that e-TeX's \detokenize is available/is allowed by the terms of the macro-writing-challenge.

I emphasize that the gist/the basic idea of "hitting" either the first token of the non-empty argument or the closing brace behind the empty argument with \string and cranking out the brace-cases by removing a brace-balanced argument does not come from me but does come from Robert R. Schneck's \ifempty-macro.

I just added \romannumeral0-expansion and stringification and removal of superfluous curly braces via \secondoftwo in favor of removing superfluous curly braces via \iffalse..\fi.
I did so for ensuring that things won't break half-way through the expansion-chain due to unbalanced \if..\else..\fi at some stage popping up that might be contained in the argument or might come into being due to "hitting" the first token of the argument with \string...

In order to explain how the test works, let's rewrite this with different line-breaking:

\long\def\CheckWhetherEmpty#1{%
  \romannumeral0%
  \expandafter\secondoftwo\string{%
  \expandafter\secondoftwo % <- The interesting \secondoftwo
  \expandafter{% <- Opening brace of interesting \secondoftwo's first argument.
  \expandafter{%
  \string#1} % <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is an opening brace (Scenario 1).
  \expandafter
  \secondoftwo\string}% <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is not an opening brace (Scenario 2).
  \expandafter\firstoftwo\expandafter{\expandafter
  \secondoftwo\string}%
  \firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
  {\firstoftwo\expandafter{} \firstoftwo}%
}%

Let's look at the three scenarios:

Scenario 1: #1 is not empty and #1's first token is an opening brace—e.g., #1={foo}bar:

\CheckWhetherEmpty{{foo}bar}{empty}{not empty}%

Step 1:

\romannumeral0%
\expandafter\secondoftwo\string{%
\expandafter\secondoftwo % <- The interesting \secondoftwo
\expandafter{% <- Opening brace of interesting \secondoftwo's first argument.
\expandafter{%
\string{foo}bar} % <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is an opening brace (Scenario 1).
\expandafter
\secondoftwo\string}% <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is not an opening brace (Scenario 2).
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 2: \romannumeral0-expansion initiated:

%\romannumeral0-expansion in progress:
\expandafter\secondoftwo\string{%
\expandafter\secondoftwo % <- The interesting \secondoftwo
\expandafter{% <- Opening brace of interesting \secondoftwo's first argument.
\expandafter{%
\string{foo}bar} % <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is an opening brace (Scenario 1).
\expandafter
\secondoftwo\string}% <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is not an opening brace (Scenario 2).
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 3: \expandafter "hits" \string and { gets stringified:

%\romannumeral0-expansion in progress:
\secondoftwo{₁₂%
\expandafter\secondoftwo % <- The interesting \secondoftwo
\expandafter{% <- Opening brace of interesting \secondoftwo's first argument.
\expandafter{%
\string{foo}bar} % <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is an opening brace (Scenario 1).
\expandafter
\secondoftwo\string}% <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is not an opening brace (Scenario 2).
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 4: \secondoftwo removes {₁₂:

%\romannumeral0-expansion in progress:
\expandafter\secondoftwo % <- The interesting \secondoftwo
\expandafter{% <- Opening brace of interesting \secondoftwo's first argument.
\expandafter{%
\string{foo}bar} % <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is an opening brace (Scenario 1).
\expandafter
\secondoftwo\string}% <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is not an opening brace (Scenario 2).
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 5: \expandafter-chain "hits" \string which in case of the argument not being empty strigifies the argument's first token and in case of the argument being empty stringifies the closing brace:

%\romannumeral0-expansion in progress:
\secondoftwo % <- The interesting \secondoftwo
{% <- Opening brace of interesting \secondoftwo's first argument.
{%
{₁₂foo}bar} % <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is an opening brace (Scenario 1).
\expandafter
\secondoftwo\string}% <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is not an opening brace (Scenario 2).
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 6: The interesting \secondoftwo acts:

%\romannumeral0-expansion in progress:
\expandafter
\secondoftwo\string}% <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is not an opening brace (Scenario 2).
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 7: \expandafter "hits" \string and } gets stringified:

%\romannumeral0-expansion in progress:
\secondoftwo}₁₂% <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is not an opening brace (Scenario 2).
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 8: \secondoftwo removes }₁₂:

%\romannumeral0-expansion in progress:
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 9: \expandafter-chain "hits" \string and } gets stringified:

%\romannumeral0-expansion in progress:
\firstoftwo{\secondoftwo}₁₂%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 10: \firstoftwo acts:

%\romannumeral0-expansion in progress:
\secondoftwo}₁₂%
\firstoftwo\expandafter{} \secondoftwo
{empty}{not empty}%

Step 11: \secondoftwo removes }₁₂:

%\romannumeral0-expansion in progress:
\firstoftwo\expandafter{} \secondoftwo
{empty}{not empty}%

Step 12: \firstoftwo acts:

%\romannumeral0-expansion in progress:
\expandafter⟨space token⟩\secondoftwo
{empty}{not empty}%

Step 13: \expandafter "hits" \secondoftwo:

%\romannumeral0-expansion in progress:
⟨space token⟩not empty%

Step 14: \romannumeral0-expansion finds the ⟨space token⟩ and discards it and stops searching for more digits. Thus \romannumeral finds the non-positive number 0 and therefore terminates without delivering any token in return:

%\romannumeral0-expansion terminated:
not empty%

Scenario 2: #1 is not empty and #1's first token is not an opening brace—e.g., #1=foobar:

\CheckWhetherEmpty{foobar}{empty}{not empty}%

Step 1:

\romannumeral0%
\expandafter\secondoftwo\string{%
\expandafter\secondoftwo % <- The interesting \secondoftwo
\expandafter{% <- Opening brace of interesting \secondoftwo's first argument.
\expandafter{%
\string foobar} % <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is an opening brace (Scenario 1).
\expandafter
\secondoftwo\string}% <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is not an opening brace (Scenario 2).
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 2: \romannumeral0-expansion initiated:

%\romannumeral0-expansion in progress:
\expandafter\secondoftwo\string{%
\expandafter\secondoftwo % <- The interesting \secondoftwo
\expandafter{% <- Opening brace of interesting \secondoftwo's first argument.
\expandafter{%
\string foobar} % <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is an opening brace (Scenario 1).
\expandafter
\secondoftwo\string}% <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is not an opening brace (Scenario 2).
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 3: \expandafter "hits" \string and { gets stringified:

%\romannumeral0-expansion in progress:
\secondoftwo{₁₂%
\expandafter\secondoftwo % <- The interesting \secondoftwo
\expandafter{% <- Opening brace of interesting \secondoftwo's first argument.
\expandafter{%
\string foobar} % <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is an opening brace (Scenario 1).
\expandafter
\secondoftwo\string}% <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is not an opening brace (Scenario 2).
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 4: \secondoftwo removes {₁₂:

%\romannumeral0-expansion in progress:
\expandafter\secondoftwo % <- The interesting \secondoftwo
\expandafter{% <- Opening brace of interesting \secondoftwo's first argument.
\expandafter{%
\string foobar} % <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is an opening brace (Scenario 1).
\expandafter
\secondoftwo\string}% <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is not an opening brace (Scenario 2).
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

%\romannumeral0-expansion in progress:
\secondoftwo % <- The interesting \secondoftwo
{% <- Opening brace of interesting \secondoftwo's first argument.
{%
f₁₂oobar} % <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is an opening brace (Scenario 1).
\expandafter
\secondoftwo\string}% <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is not an opening brace (Scenario 2).
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 6: The interesting \secondoftwo acts:

%\romannumeral0-expansion in progress:
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 7: \expandafter-chain "hits" \string and } gets stringified::

%\romannumeral0-expansion in progress:
\firstoftwo{\secondoftwo}₁₂%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 8: \firstoftwo acts:

%\romannumeral0-expansion in progress:
\secondoftwo}₁₂%
\firstoftwo\expandafter{} \secondoftwo
{empty}{not empty}%

Step 9: \secondoftwo removes }₁₂:

%\romannumeral0-expansion in progress:
\firstoftwo\expandafter{} \secondoftwo
{empty}{not empty}%

Step 10: \firstoftwo acts:

%\romannumeral0-expansion in progress:
\expandafter⟨space token⟩\secondoftwo
{empty}{not empty}%

Step 11: \expandafter "hits" \secondoftwo:

%\romannumeral0-expansion in progress:
⟨space token⟩not empty%

Step 12: \romannumeral0-expansion finds the ⟨space token⟩ and discards it and stops searching for more digits. Thus \romannumeral finds the non-positive number 0 and therefore terminates without delivering any token in return:

%\romannumeral0-expansion terminated:
not empty%

Scenario 3: #1 is empty:

\CheckWhetherEmpty{}{empty}{not empty}%

Step 1:

\romannumeral0%
\expandafter\secondoftwo\string{%
\expandafter\secondoftwo % <- The interesting \secondoftwo
\expandafter{% <- Opening brace of interesting \secondoftwo's first argument.
\expandafter{%
\string} % <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is an opening brace (Scenario 1).
\expandafter
\secondoftwo\string}% <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is not an opening brace (Scenario 2).
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 2: \romannumeral0-expansion initiated:

%\romannumeral0-expansion in progress:
\expandafter\secondoftwo\string{%
\expandafter\secondoftwo % <- The interesting \secondoftwo
\expandafter{% <- Opening brace of interesting \secondoftwo's first argument.
\expandafter{%
\string} % <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is an opening brace (Scenario 1).
\expandafter
\secondoftwo\string}% <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is not an opening brace (Scenario 2).
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 3: \expandafter "hits" \string and { gets stringified:

%\romannumeral0-expansion in progress:
\secondoftwo{₁₂%
\expandafter\secondoftwo % <- The interesting \secondoftwo
\expandafter{% <- Opening brace of interesting \secondoftwo's first argument.
\expandafter{%
\string} % <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is an opening brace (Scenario 1).
\expandafter
\secondoftwo\string}% <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is not an opening brace (Scenario 2).
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 4: \secondoftwo removes {₁₂:

%\romannumeral0-expansion in progress:
\expandafter\secondoftwo % <- The interesting \secondoftwo
\expandafter{% <- Opening brace of interesting \secondoftwo's first argument.
\expandafter{%
\string} % <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is an opening brace (Scenario 1).
\expandafter
\secondoftwo\string}% <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is not an opening brace (Scenario 2).
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

%\romannumeral0-expansion in progress:
\secondoftwo % <- The interesting \secondoftwo
{% <- Opening brace of interesting \secondoftwo's first argument.
{%
}₁₂ % <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is an opening brace (Scenario 1).
\expandafter
\secondoftwo\string}% <- Closing brace of interesting \secondoftwo's first argument in case #1's first token is not an opening brace (Scenario 2).
\expandafter\firstoftwo\expandafter{\expandafter
\secondoftwo\string}%
\firstoftwo\expandafter{} \secondoftwo}% <- Closing brace of interesting \secondoftwo's first argument in case #1 is empty (Scenario 3).
{\firstoftwo\expandafter{} \firstoftwo}%
{empty}{not empty}%

Step 6: The interesting \secondoftwo acts:

%\romannumeral0-expansion in progress:
\firstoftwo\expandafter{} \firstoftwo
{empty}{not empty}%

Step 7: \firstoftwo acts:

%\romannumeral0-expansion in progress:
\expandafter⟨space token⟩\firstoftwo
{empty}{not empty}%

Step 8: \expandafter "hits" \firstoftwo:

%\romannumeral0-expansion in progress:
⟨space token⟩empty%

Step 9: \romannumeral0-expansion finds the ⟨space token⟩ and discards it and stops searching for more digits. Thus \romannumeral finds the non-positive number 0 and therefore terminates without delivering any token in return:

%\romannumeral0-expansion terminated:
empty%

Based on that you can implement an \ifblank-test as follows:

%%-----------------------------------------------------------------------------
%% Check whether argument is blank (empty or only spaces):
%%-----------------------------------------------------------------------------
%% -- Take advantage of the fact that TeX discards space tokens when
%%    "fetching" _un_delimited arguments: --
%% \CheckWhetherBlank{<Argument which is to be checked>}%
%%                   {<Tokens to be delivered in case that
%%                     argument which is to be checked is blank>}%
%%                   {<Tokens to be delivered in case that argument
%%                     which is to be checked is not blank}%
\long\def\CheckWhetherBlank#1{%
  \romannumeral\expandafter\expandafter\expandafter\secondoftwo
  \expandafter\CheckWhetherEmpty\expandafter{\firstoftwo#1{}.}%
}%

Based on the gist of the implementation of \CheckWhetherEmpty you can implement checking whether a non-delimited argument's first token is an explicit character token of category code 1 (begin group): Just ensure by appending a dot that the \string which gets carried out right before executing the "interesting \secondoftwo" never "hits" a closing brace (which implies elimination of scenario 3) and implement forking between scenario 1 and scenario 2:

%%-----------------------------------------------------------------------------
%% Check whether argument's first token is a catcode-1-character
%%-----------------------------------------------------------------------------
%% \CheckWhetherBrace{<Argument which is to be checked>}%
%%                   {<Tokens to be delivered in case that argument
%%                     which is to be checked has leading
%%                     catcode-1-token>}%
%%                   {<Tokens to be delivered in case that argument
%%                      which is to be checked has no leading
%%                      catcode-1-token>}%
%%
%% Due to \romannumeral0-expansion the result is delivered after two
%% expansion-steps/after two "hits" by \expandafter.
%%
\long\def\CheckWhetherBrace#1{%
  \romannumeral0\expandafter\secondoftwo\expandafter{\expandafter{%
  \string#1.}\expandafter\firstoftwo\expandafter{\expandafter
  \secondoftwo\string}\firstoftwo\expandafter{} \firstoftwo}%
  {\firstoftwo\expandafter{} \secondoftwo}%
}%

Expandable test for an empty token list—methods, performance, and robustness

General

Fast `\ifempty`

Fast `\ifblank`

Tags:

Performance

Conditionals

E Tex

Expl3

Token Lists

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Expandable test for an empty token list—methods, performance, and robustness

General

Fast \ifempty

Fast \ifblank

Tags:

Performance

Conditionals

E Tex

Expl3

Token Lists

Related

Fast `\ifempty`

Fast `\ifblank`