Active characters let to a (non-active) character

Question

It seems that if I \let\amp&, the alignment tab & can be replaced by \amp everywhere (e.g., in the preamble and in the body of an \halign). It is also possible to make the character & active, and give it the same meaning by \catcode`\&=13 \let&\amp. It seems that that active & which has been let to the alignment tab & can be used wherever an alignment tab & was used.

This idea is quite general: we can define macro which takes a character as its argument, lets its active version to itself (with its current catcode), and finally makes the character active. This uses an \lccode trick, described by Phillipe Goutet.

\def\activate#1{\begingroup
  \lccode`\~=`#1%
  \lowercase{\endgroup \let~#1}%
  \catcode`#1=13\relax}

Here is an example to show that this operation does not break most uses I can think of for $, &, etc. In particular, $$...$$ is still recognized, and macro parameters too.

\activate &
\halign{#&#\cr a&b\cr}

\activate $    \activate ^    \activate _
$$ x^2_2 + y^2_2 $$

\activate #
\def\myshow#1{\show#1}
\myshow #    
\bye

So my question is: "what are the drawbacks of this approach?" It allows a fix for peeking ahead with \futurelet in alignments.

Answer 1

One drawback of this approach is that earlier defined macros which have these special characters in their parameter text will stop working. Good written packages will change the catcode to this characters to a pre-defined value before calling such macros, but you never know. Also sometimes this isn't doable like when the macro should be fully expandable.

In general your redefinition should work identical to the original in every context where TeX is executing the found tokens, e.g. inside normal boxing mode, but will result in different results in scanning mode.

Answer 2

Such active characters let to the original character work exactly the same as the original character, except in delimited arguments from macros defined prior to the category code change, and within \csname...\endcsname constructions.

\def\delimited#1&{}
\let\amp&
\catcode`&=\active
\let&\amp
{\delimited...&} % BOOM: & is not seen
\csname &\endcsname % BOOM
\bye

The second case comes up when trying to add \let\amp& etc to the beginning of a LaTeX file which uses amsmath. That's due to \newhelp using a \csname...\endcsname construction to store help messages, one of which contains &. That could be avoided by redefining & locally inside \newhelp:

\let\amp&
\catcode`&=\active
\let&\amp
\RequirePackage{amsgen}
\def\newhelp#1#2{\edef&{\string&}%
  \newtoks#1#1\expandafter{\csname #2\endcsname}% old def of \newhelp
  \let&\amp}
\RequirePackage{amsmath}
\relax

or by letting it be active but only equal to an alignment tab after \begin{document} since alignment tabs are only useful inside tables, none of which typically appear outside the document:

\def\alignmenttab{&}
\catcode`&=\active
\let&\alignmenttab % macro!
\AtBeginDocument{\expandafter\let\expandafter&\alignmenttab}
%
\documentclass{article}
\usepackage{amsmath}
% ...
\begin{document}