Conditionally redefine big, bigg, etc. to left or right (locally)

Question

To speed up my typesetting work I'm exploring the possibility to redefine 
some commands "locally".

In this particular case I'd like to redefine the big, Big, etc. commands to the left and right commands. The redefinition must be conditioned by the next-char (or next-regexp).

E.g. something like this "pseudo-code":

newcommand{myRedefinedBigs}{%
  COND 1 next char (or next regexp) is (or "(" "[" "{")
  renewcommand{big}{left}
  renewcommand{Big}{left}
  renewcommand{bigg}{left}
  renewcommand{Bigg}{left}
  COND 2 next char (or next regexp) is (or ")" "]" "}")
  renewcommand{big}{right}
  renewcommand{Big}{right}
  renewcommand{bigg}{right}
  renewcommand{Bigg}{right}}

The idea is to wrap an equation with this command. E.g.:

{myRedefinedBigs
begin{equation}
big(frac{1}{2}big)
end{equation}}relax

Can this be made in LaTeX? If so, what do I need to looking for?

Edit. Wermer solution seemed to work but it fails in the case on nested pair of the same kind. E.g.:

{myRedefinedBigs
begin{equation}
big(frac{1}{2}big(3)big)
end{equation}}relax

Note.

I don't write documents myself from scratch. I prepare the works of scientists to be published in physics journals. So I have to "correct" layout "errors" according to the guidelines provided.

Werner · Accepted Answer

The following assumes that you're using big and friends in a paired form, similar to left and right. Also, it assumes opening delimiters are associated with left and closing delimiters with right. Any unmatched <delim>iters revert back to big<delim>.

documentclass{article}

makeatletter
newcommand{myRedefinedBigs}{%
  letoldbigbig% Copy big into oldbig
  defbig{% Redeine big
    @ifnextchar({biglparen}{% big is followed by (
    @ifnextchar){bigrparen}{% big is followed by )
    @ifnextchar[{biglbracket}{% big is followed by [
    @ifnextchar]{bigrbracket}{% big is followed by ]
    @ifnextchar{{biglbrace}{% big is followed by {
    @ifnextchar}{bigrbrace}{% big is followed by }
    oldbig}}}}}}}% big is followed by something else, so resort to oldbig
  defbiglparen({left(}% big( is replaced by left(
  defbigrparen){right)}% big) is replaced by right)
  defbiglbracket[{left[}% big[ is replaced by left[
  defbigrbracket]{right]}% big] is replaced by left]
  defbiglbrace{{left{}% big{ is replaced by left{
  defbigrbrace}{right}}% big} is replaced by left}
  letBigbig% Handle Big just like big
  letbiggbig% Handle bigg just like big
  letBiggbig% Handle Bigg just like big
}
makeatother

begin{document}

[
  big(frac{1}{2}big)
]

{myRedefinedBigs
[
  big(frac{1}{2}big)
]}

[
  big(frac{1}{2}^{Big{frac{1}{2}Big]}big)
]

{myRedefinedBigs
[
  big(frac{1}{2}^{Big{frac{1}{2}Big]}big)
]}

[
  big(frac{1}{2}big(3big)big)
]

{myRedefinedBigs
[
  big(frac{1}{2}big(3big)big)big|
]}

end{document}

Fólkvangr · Answer

About the issue
A user is supposed to use opening and closing delimiters in its formulas. Moreover, you should not redefine a useful macro but use another macro as appropriate.
You can see different delimiters (sizes and shapes) in the following example. You can also see the opening and closing delimiters.
Exercice 17.14 (TeXbook)
pi(n)=sum_{m=2}^nleftlfloorbiggl(sum_{k=1}^{m-1}
  bigllfloor(m/k)big/lceil m/krceilbigrrfloorbiggr)^{-1}
rightrfloor

It is easy to replace opening and closing delimitors in the sample code.
Important: left or right followed by a delimiter don't always produce the expected delimiters (typographic aesthetics).
For instance, we can see two formatting of the same formula. The formula on the right corresponds to the formatting recommended in the TeXbook while the formula on the left could appear after replacing the corresponding modifiers (bigl, biggr...) by left or right in the above code snippet.

Moreover, the "modifiers" left and right must appear in the same part of the formula.
About the solution
It is necessary to replace each "modifier" preceding a delimiter with the appropriate modifier.
These modifiers may be automatically replaced by their matching modifiers. The algorithm to be used does not seem very complicated. Its implementation probably must depend on a text editor, obviously not on (La)TeX.

Conditionally redefine big, bigg, etc. to left or right (locally)

2 Answers

About the issue

Exercice 17.14 (TeXbook)

About the solution

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