Force LaTeX to obey spaces in math mode

Question

I have experienced a very frustrating feature of LaTeX.

I have used bnf.tex to be able to write a BNF grammar definition. As I found the notation <some text> very convenient, I decided to use it through the entire document. This might be a bad idea, but now I would rather not change the whole source.

Here are my macros:

{\catcode`\ =\active{\global\let =\ }}
\gdef<{\ensuremath{\langle}%
   \ifmmode\catcode`\ =\active\relax\fi%
   \begingroup\sf}
\gdef>{\/\endgroup\ensuremath{\rangle}%
   \ifmmode\catcode`\ =10\relax\fi%
   \relax}

It works very well, except when argument to complex math commands.

So

<cou cou>
$<cou cou>$
and $\sqrt{<cou cou>}$

will keep their inner space, but

$$\frac{<cou cou>}{E}$$
and $\Instr{<cou cou>}{E}$

will lose their's, looking like <coucou>.

In fact, any solution formatting the text between < and > as normal (\sf) text in both math and normal mode would be very useful here :-)

Here is a full file containing the examples:

\documentclass[12pt,a4paper]{article}
\usepackage[utf8x]{inputenc}
\usepackage[english]{babel}
\usepackage{amsmath}

\DeclareMathOperator{\instr}{Instr}
\newcommand{\Instr}[2]{\instr(#1,#2)}

\catcode`\>\active
\catcode`\<\active

{\catcode`\ =\active{\global\let =\ }}

\begingroup

    \gdef<{\ensuremath{\langle}%
        \ifmmode\catcode`\ =\active\relax\fi%
        \begingroup\sf}
    \gdef>{\/\endgroup\ensuremath{\rangle}%
        \ifmmode\catcode`\ =10\relax\fi%
        \relax}

\endgroup

\begin{document}

<cou cou>

$<cou cou>$

$$\frac{<cou cou>}{E}$$

$\Instr{<cou cou>}{E}$

\end{document}

Answer 1

I would simplify the definition to this one:

\catcode`\<\active
\protected\def<#1>{\ensuremath{\langle\text{\normalfont\sffamily #1\/}\rangle}}

Example:

\documentclass[12pt,a4paper]{article}
\usepackage{amsmath}

\DeclareMathOperator{\instr}{Instr}

\catcode`\<\active
\protected\def<#1>{\ensuremath{\langle\text{\normalfont\sffamily#1\/}\rangle}}

\begin{document}

<cou cou>

$<cou cou>\frac{<cou cou>}{2}$

\[\frac{<cou cou>}{E}\]

$\instr(<cou cou>,E)$

\end{document}

I don't see any advantage in using an \Instr command that hides the semantics. Never use $$...$$ in LaTeX. Also consider that two-letter commands such as \sf are obsolete and should not be used: it's best to stick with the LaTeX2e commands \sffamily and similar ones that suggest more clearly what font attribute we are selecting; \normalfont is used to avoid that the surrounding font can influence the typesetting of the syntactic object.

However, instead of activating <, I suggest you

\protected\def\<#1>{\ensuremath{\langle\text{\normalfont\sffamily#1\/}\rangle}}

and then to input the thing as

\<cou cou>

Answer 2

Generally it's a bad idea to change catcodes mid document, just use a box to switch to text mode (with an extra group in case you ever use color)

\documentclass{article}
\usepackage[utf8x]{inputenc}
\usepackage[english]{babel}
\usepackage{amsmath}

\DeclareMathOperator{\instr}{Instr}
\newcommand{\Instr}[2]{\instr(#1,#2)}

\catcode`\>\active
\catcode`\<\active


\begingroup

    \gdef<{\ensuremath{\langle}\hbox\bgroup\bgroup\sffamily}
    \gdef>{\/\egroup\egroup\ensuremath{\rangle}}

\endgroup

\begin{document}

<cou cou>

$<cou cou>$

$$\frac{<cou cou>}{E}$$

$\Instr{<cou cou>}{E}$

\end{document}