How do I format a regular expression in math mode?

Question

I want to display some regular expression, like the following, in LaTeX math mode.

\[
(F+(A+I*)*)|(F*(A+I*)+)E
\]

However, the spacing is all wrong, because TeX formats + and * as binary operators, rather than as postfix ones. I would expect that the postfix operators would appear close to the preceding operand, and, in cases where the successor element is an operand, they would introduce some additional space to prevent the appearance's ambiguity.

An example formatted in the way I'd like it to be appears below. I have marked with red the places where additional spacing is unwanted and with green places where additional spacing is required. However, I'd be open to other formatting suggestions from typography experts.

Is there a way to handle this without adding manual spacing commands?

Answer 1

It would be possible to set up +*? to act automatically as postfix, but how easy it is depends a bit if they also need their normal definitions within the same document or same expression.

Probably simplest is to set up simple commands for the postfix versions for example:

\documentclass{article}

\makeatletter

\def\+{\@postfix+}
\def\*{\@postfix*}
\def\?{\@postfix?}



\def\@postfix#1{{#1}\@ifnextchar){}{\;}}

\makeatother
\begin{document}

\[
(F+(A+I*)*)|(F*(A+I*)+)E
\]


\[
(F\+(A\+I\*)\*)|(F\*(A\+I\*)\+)E
\]


\end{document}

Answer 2

I suggest to mark up regular expressions, so that you can do whatever change you want with them. Here's a possibility:

\documentclass{article}

\newcommand{\regex}[1]{\ensuremath{
  \begingroup
  \makeord{+}
  \makeord{*}
  \makeord{?}
  #1
  \endgroup
}}

\makeatletter
\newcommand{\makeord}[1]{
  \@tempcnta=\mathcode`#1
  \divide\@tempcnta by "1000
  \multiply\@tempcnta by "1000
  \mathcode`#1=\numexpr\the\mathcode`#1-\@tempcnta\relax
}
\makeatother

\begin{document}
\[
\regex{(F+(A+I*)*)|(F*(A+I*)+)E}
\]
\end{document}

You can also use \regex directly in text mode.

The "magic" \makeord macro strips off from a character its type as math atom: a mathcode is a 15 bit number; the three most significant digits tell TeX what kind of atom and 0 corresponds to "ordinary". So we do

n - (n mod 4096)

where n is the mathcode of the character and assign this as the mathcode: the character which is printed is the same, but treated as an ordinary symbol as far as spacing is concerned.

---

An alternative way that adds the desired spacing is with

\newcommand{\makeord}[1]{
  \edef\@tempa{\the\mathcode`#1 }
  \begingroup\lccode`~=`#1
  \lowercase{\endgroup\edef~}{\mathpunct{\mathchar\@tempa}}
  \mathcode`#1="8000
}

which, with the same regex as before, produces

However this won't work for things such as

A*?

because a space would be inserted between * and ?.

The trick here is to consider +, * and ? as punctuation symbols.