Defining characters as macros

Single characters can act as macros (defined commands), and both Plain TeX and LaTeX define the character ~ as a “non-breakable space”. A character is made definable, or “active”, by setting its category code (catcode) to be \active (13):

\catcode`\_=\active

Any character could, in principle, be activated this way and defined as a macro:

\def//{\//}

which could be characterised as an over-simple answer to using underscores. However, you must be wary: whereas people expect an active tilde, other active characters may be unexpected and interact badly with other macros. Furthermore, by defining an active character, you preclude the character's use for other purposes, and there are few characters “free” to be subverted in this way.

To define the character z as a command, one would say something like:

\catcode`\z=\active
\def z{Yawn, I'm tired}%

and each subsequent z in the text would become a yawn. This would be an astoundingly bad idea for most documents, but might have special applications. (Note that, in \def z, z is no longer interpreted as a letter; the space is therefore not necessary — \defz would do; we choose to retain the space, for what little clarity we can manage.) Some LaTeX packages facilitate such definitions. For example, the shortvrb package with its \MakeShortVerb command.

TeX uses category codes to interpret characters as they are read from the input. Changing a catcode value will not affect characters that have already been read. Therefore, it is best if characters have fixed category codes for the duration of a document. If catcodes are changed for particular purposes (the \verb command does this), then the altered characters will not be interpreted properly when they appear in the argument to another command (as, for example, in ““\verb” in command arguments”). An exemplary case is the doc package, which processes .dtx files using the shortvrb package to define |…| as a shorthand for \verb|…|. But | is also used in the preambles of tabular environments, so that tables in .dtx files can only have vertical line separation between columns by employing special measures of some sort.

Another consequence is that catcode assignments made in macros often don't work as expected (see “Active characters in command arguments”). For example, the definition

\def\mistake{%
\catcode`_=\active
\def_{\textunderscore\-}%
}

does not work because it attempts to define an ordinary _ character: When the macro is used, the category change does not apply to the underscore character already in the macro definition. Instead, one may use:

\begingroup
\catcode`_=\active
\gdef\works{%    note the global \gdef
  \catcode`_=\active
  \def_{\textunderscore\-}%
}
\endgroup

The alternative (“tricksy”) way of creating such an isolated definition depends on the curious properties of \lowercase, which changes characters without altering their catcodes. Since there is always one active character (~), we can fool \lowercase into patching up a definition without ever explicitly changing a catcode:

\begingroup
  \lccode''\~=''\_
  \lowercase{\endgroup
    \def~{\textunderscore\-}%
  }%

The two definitions have the same overall effect (the character is defined as a command, but the character does not remain active), except that the first defines a \global command.

For active characters to be used only in maths mode, it is much better to leave the character having its ordinary catcode, but assign it a special active maths code, as with

\begingroup
  \lccode''~=''x
  \lowercase{\endgroup
    \def~{\times}%
  }%
\mathcode`x="8000

The special character does not need to be redefined whenever it is made active — the definition of the command persists even if the character's catcode reverts to its original value; the definition becomes accessible again if the character once again becomes active.

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Source: Defining characters as macros