Delimited arguments and using a macro inside of itself

Question

I wanted to play with delimiter sizing without using the \delimiterfactor, -shortfall, etc. and made the following:

\newdimen\bigdim  \bigdim  = 1.9743ex
\newdimen\Bigdim  \Bigdim  = 2.671ex
\newdimen\biggdim \biggdim = 3.3678ex
\newdimen\Biggdim \Biggdim = 4.0646ex

\def\fence#1#2#3{
  \setbox0\hbox{$\displaystyle #3$}
  \ifdim\ht0 < .9\bigdim #1\box0 #2\else
  \ifdim\ht0 < .9\Bigdim \bigl#1\box0\bigr#2\else
  \ifdim\ht0 < .9\biggdim \Bigl#1\box0\Bigr#2\else
  \ifdim\ht0 < .9\Biggdim \biggl#1\box0\biggr#2\else
  \ifdim\ht0 < .9\Biggdim \Biggl#1\box0\Biggr#2\else
  \left#1\box0\right#2
  \fi\fi\fi\fi\fi}

\def\args(#1){\fence(){#1}}

$$
  \args(bar\args(baz))
$$

\bye

(before you push that comment-button, I know there should be \mathsurround=0pt and such in there, I just wanted to keep this simple) but this results in an error saying the argument of \args has an extra }.

I thought it would have something to do with macro argument delimiters, so made a quick test:

\def\foo(#1){(#1)}
\foo(bar\foo(baz))
\bye

but that seemed to work just fine. Now I don't know what else could be the issue. Note that if there isn't an \args inside of \args, it works.

Answer 1

You have

\args(bar\args(baz))

so the argument to the outer \args is

 bar\args(baz

as it stops at the first )

you want

 \args({bar\args(baz)})

in the \foo example, the arguments are interpreted the same way, but it accidentally works.

for the outer \foo '#1 is

bar\foo(baz

so that expands to

(bar\foo(baz)

then the inner \foo expands to

 (baz)

and finally the ) which was never used as a macro delimiter is typeset.

Answer 2

You can use \ensurebalanced macro for another types of parens by the following way:

\def\macro(#1){\ensurebalanced()\macroA{#1}}
\def\macroA#1{the "#1" is balanced here in () meaning}

\macro(abc(de(f))g(hi)) % prints: the "abc(de(f))g(hi)" is balanced here in () meaning.

Or your example:

\def\args(#1){\ensurebalanced(){\fence()}{#1}}

My macro \ensurebalanced looks like this:

\newcount\tmpnum
\def\ensurebalanced#1#2#3#4{%
   \isbalanced#1#2{#4}\iftrue #3{#4}%
   \else
      \def\ensurebalancedA##1##2#2{%
         \isbalanced#1#2{##1#2##2}\iftrue #3{##1#2##2}%
         \else \def\next{\ensurebalancedA{##1#2##2}}\expandafter\next\fi
      }%
      \def\next{\ensurebalancedA{#4}}\expandafter\next\fi
}
\def\isbalanced#1#2#3\iftrue{\tmpnum=0 \isbalancedA#1#2#3\isbalanced}
\def\isbalancedA#1#2#3{%
    \ifx\isbalanced#3\def\next{\csname ifnum\endcsname\tmpnum=0 }%
    \else \def\next{\isbalancedA#1#2}%
          \ifx#3#1\advance\tmpnum by1\fi
          \ifx#3#2\advance\tmpnum by-1\fi
    \fi \next
}