How to create a command that automatically escapes curly braces?

Question

How could I create a command that will automatically escape all curly braces within the current environment?

For instance, I would like a command (or environment, I suppose) that allows me to write something like this:

Kuratowski identified the ordered pair $\langle x,y \rangle$ with the set $\{\{x \},\{x,y\}\}$ whereas Wiener identified it with the set $\{\{x,\emptyset\},\{y\}\}$.

Without having to put in all of the obnoxious \'s to escape the curly braces.

Is there an easy (and, hopefully, versatile) fix to this? I want something that will let me auto-escape the curly braces when I know I'm going to be using a lot of set-theoretic notation in the next few lines (or current environment).

Answer 1

Rather than mess with the interpretation of { it is probably better to define a command that takes a comma separated list of arguments and encloses each in braces. Some variants below depending on whether you want a brace around the outer list, and whether you want a comma separator. (Beware the space after #1 is needed otherwise the case with as single argument brace group {a,b,c} does not work as TeX drops the brace.

\documentclass{article}

\makeatletter
\def\sets#1{\@for\tmp:=#1 \do{\{\tmp\}}}

\def\setsb#1{\{\@for\tmp:=#1 \do{\{\tmp\}}\}}


\def\setsc#1{\def\sep{\def\sep{,}}\@for\tmp:=#1 \do{\sep\{\tmp\}}}

\def\setsd#1{\{\def\sep{\def\sep{,}}\@for\tmp:=#1 \do{\sep\{\tmp\}}\}}


\makeatother

\begin{document}


$\sets{a,b,c}$ $\sets{a,{b,c}}$ $\sets{{a,b,c}}$

$\setsb{a,b,c}$ $\setsb{a,{b,c}}$ $\setsb{{a,b,c}}$

$\setsc{a,b,c}$ $\setsc{a,{b,c}}$ $\setsc{{a,b,c}}$

$\setsd{a,b,c}$ $\setsd{a,{b,c}}$ $\setsd{{a,b,c}}$


\end{document}

Answer 2

Rather than changing the meaning of { and } (which is potentially dangerous) you might like to use DeclarePairedDelimeter from the mathtools package as follows:

\DeclarePairedDelimiter\myset{\{}{\}}

which can then be used as $\myset{x}$ or, as below, $\myset{\myset{x},y}$

\documentclass{article}
\usepackage{mathtools}
\DeclarePairedDelimiter\myset{\{}{\}}


\begin{document}

\subsection{Original}
Kuratowski identified the ordered pair $\langle x,y \rangle$ 
with the set $\{\{x \},\{x,y\}\}$ whereas Wiener identified 
it with the set $\{\{x,\emptyset\},\{y\}\}$.

\subsection{New}
Kuratowski identified the ordered pair $\langle x,y \rangle$ 
with the set $\myset{\myset{x},\myset{x,y}}$ whereas Wiener identified 
it with the set $\myset{\myset{x,\emptyset},\myset{y}}$.

\end{document}

If you find that you need to use this command for fractions, or other content that needs \left and \right, then simply use (for example) \myset*{\frac{a}{b}}

Answer 3

LuaTeX to the rescue. No catcode trickery, and you can understand the code when you read it :)

I have written the example in ConTeXt because I am more familiar with it, but a similar approach will also work in LaTeX.

\unprotected\unexpanded\def\escapebraces#1%
    {\ctxlua{thirddata.escapebraces(\!!bs\detokenize{#1}\!!es)}}


\startluacode
  thirddata = thirddata or {}

  thirddata.escapebraces = function (data)
      context(data:gsub("([{}])", "\\%1"))
  end
\stopluacode

\starttext

The power set of $\escapebraces{ {x, y} }$ is $\escapebraces{ {\emptyset, {x}, {y}, {x,y} } }$

\stoptext

gives

Answer 4

Let me preface the proposed solution by providing a warning and disclaimer:

I do not recommend anyone actually use this code! If you use any macros after the category codes of } and { have been changed to 12 ("other") and if these macros take arguments that might be encased in curly braces, exceedingly bad things are almost certainly going to happen to your document. You've been warned!

OK, here goes:

\documentclass{article}
\usepackage[T1]{fontenc}
\begin{document}\pagestyle{empty}

{hello world}

   \catcode123=12 % change cat code of "{" to "other"
   \catcode125=12 % change cat code of "}" to "other"

{hello world}

   \catcode123=1  % restore the cat codes of "{" and "}"
   \catcode125=2

{hello world}
\end{document}

Answer 5

This is more of a proof of concept than a recommendable way to do what you're looking for. I'd stay with the \DeclarePairedDelimiter road outlined by cmhughes. However, here it is:

\documentclass{article}
\usepackage{xparse,l3regex}
\ExplSyntaxOn
\NewDocumentCommand{\escapebraces}{m}
 {
  \tl_set:Nn \l_tmpa_tl { #1 }
  \regex_replace_all:nnN { \cB. } { \c{lbrace} \c{use:n} \cB\{ } \l_tmpa_tl
  \regex_replace_all:nnN { \cE. } { \cE\} \c{rbrace} } \l_tmpa_tl
  \l_tmpa_tl
 }
\ExplSyntaxOff

\begin{document}

Kuratowski identified the ordered pair $\langle x,y \rangle$ with the set
$\escapebraces{ {{x},{x,y}} }$ whereas Wiener  identified it with the set
$\escapebraces{ {{x,\emptyset},{y}} }$.

\end{document}

Limitations: you can't use macros with arguments in the argument of \escapebraces, nor subscripts or superscripts enclosed in braces. For these you might use \bgroup and \egroup, so

$\escapebraces{ {x_\bgroup11\egroup,x_\bgroup12\egroup} }$

would work. Don't try using \sqrt\bgroup12\egroup, please.

Answer 6

If one wants to use braces directly also in math mode, the mathcodes and delcodes must be correctly set. This is done here:

\documentclass{article}
\usepackage[T1]{fontenc}

\def\displaybrace<{\bgroup\catcode`\>=2 \delcode123="266308
    \delcode125="267309 \mathcode123="4266 \mathcode125="5267
    \catcode123=12 \catcode125=12 }

\begin{document}\pagestyle{empty}

 \[\displaybrace<{{x},{x,y}}>\]

\end{document}

Any use of a > will close the macro. Within the \displaybrace<..stuff...> we have a substitute only for the closing group delimiter with >.

So if one wants to do other things than just display some collection of braces and letters, the following slight extension is needed, which just additionally makes < also serve as opening group character:

\documentclass{article}
\usepackage[T1]{fontenc}

\def\displaybrace<{\bgroup\catcode`\<=1 \catcode`\>=2 
    \delcode123="266308
    \delcode125="267309 
    \mathcode123="4266 \mathcode125="5267
    \catcode123=12 \catcode125=12 }

\begin{document}\pagestyle{empty}


 \[\displaybrace<{{x},{x,y}}>\]


 \[\omega < \displaybrace<\left{\int_a^b e^<-x^2>\,dx\right}> <z^2 \]

\end{document}

Please ntake note how I used < and > inside \displaybrace to code the superscript.

More generally any code (be it in text or math mode) where one would have used traditionnally { and } must be written with < and >. And it will work perfectly fine if this constraint is obeyed (except if some macro is used which really requires that { and } are in their traditional habits, or and this is more probable, some macro which would be completely surprised to learn that < and > are now the opening and closing group characters).

Obviously using < and > this way makes writing inequalities impossible... But we could let + and - play the rôle here played by < and >. Again + and - are used for many things so one would have to find something better...

...for example ^^A and ^^B (which have character codes 1 and 2) could play the rôle here attributed to < and > and this would allow complete freedom to set-up arbitrary math formulas (perhaps your sets are defined mathematically?). But then the input would not be so readable.

Let me explicitely points out that the above code is designed to work well with arbitrary \left or \big.. like constructions.

\[\displaybrace<\Biggl{\biggl{x\biggr},{x,y}\Biggr}>\]

Answer 7

The following was motivated by the answer by David Carlisle. Note that \sets{{a,{b,c},{{c,d},e}}} does not work with this (accepted) answer (neither would \setsb, \setsc, nor setsd).

CAVEAT: any input mistake (non matching braces) makes the TeX run end in an error!

CAVEAT2: only accepted elements here are letters (lowercase and uppercase) and \emptyset.

Please note how {} are converted into \emptyset (and how spaces in the input are ignored, as is expected anyhow in math mode).

The macro has to be used in math mode because of its use of \emptyset.

Edit1: improvement to allow spaces in the input ... (particularly, a space just before a closing brace was a disaster before the edit).

Nota Bene : this code is a bit to play with TeX's mechanism of grouping and local scope and recursive macros. It could be made more general. In a way, it's like telling TeX to show us it understands sets!

Edit2: one last update, just to fix the problem of { } giving {\emptyset} rather than just \emptyset.

\documentclass{article}

\def\printset #1{\ifx\relax#1\relax\emptyset\else
                 \screensp #1\relax\emptyset
                 {\{\setaux #1\relax,\}}\fi}

\makeatletter
\def\screensp #1\relax{\ifx#1\@sptoken\relax\expandafter\@firstoftwo\else
                       \expandafter\@secondoftwo\fi}
\makeatother

\def\setaux #1#2,#3{\ifx\relax#1\relax\emptyset\else
                  \ifx#1\emptyset\emptyset\else
                  \ifcat#1a#1\else
                  {\printset {#1}}\fi\fi\fi
                  \ifx\relax#3\relax,\expandafter\setaux\else
                  \ifx#3\}\else,\expandafter\expandafter\expandafter
                  \setaux\fi\fi {#3}}


\begin{document}\pagestyle{empty}

\[\printset{}\]

\[\printset{{}}\]

\[\printset{{},{{}}}\]

\[\printset{{},{{}},{{},{{}}}}\]

\[\printset{{a,{b,c},\emptyset},{{c,d},e}}\]

\[\printset{{{a,b},{\emptyset,U,{}, {V,W}, {}},{{}},{d,{e,{U,{V,W}},\emptyset,f}}}}\]

\[\printset{a , b , { c , { d , { u , { v , w } } }} , { e } }\]

\[\printset{    }\]

\[\printset{   {  }   }\]

\end{document}