How can I see the "implementation" of protected commands such as \LaTeX?

Some macros are defined to be robust by expanding to \protect followed by a macro with almost the same name but ending with a space! Special care must be taken to define and use such macros because spaces are normally not allowed in macro names. If such a macro is written into external files (.aux, .toc, ...) the space is not taken as part of the macro name any longer, so that the original macro is called again.

To see the definitions of such macros you need to use the following code:

\expandafter\show\csname LaTeX \endcsname

The \csname <text>\endcsname can be used to build a macro called \<text> which can include non-letters like numbers or spaces. The \expandafter is required to expand \csname LaTeX \endcsname (note the space after the X) to \LaTeX  (also note the space here) before \show is executed.

I also programmed a command line tool called texdef to display such definitions:

 texdef -t latex LaTeX

(Instead of texdef -t latex you can also write latexdef if that name was installed)

This will display the definition of \LaTeX and detect that it calls \LaTeX  and also shows the definition of it.

$ texdef -t latex LaTeX

\LaTeX:
macro:->\protect \LaTeX  


\LaTeX :
\long macro:->L\kern -.36em{\sbox \z@ T\vbox to\ht \z@ {\hbox {\check@mathfonts \fontsize \sf@size \z@ \math@fontsfalse \selectfont A}\vss }}\kern -.15em\TeX 

Alternatively use quotes to add the space explicitly:

 texdef -t latex 'LaTeX '

An alternative to Martin's answer to to redefine \protect:

\begingroup
  \let\protect\show
  \LaTeX
\endgroup

(The group is not compulsory, but means that you can keep going with a document and not have everything go wrong. If you are just making a short 'test' document, you can miss it out.)

Besides Martin's solution, there is a show2e package that I often use:

% \usepackage{show2e}
\showcmd\LaTeX

When compiling, it first gets

> \LaTeX=macro:
->\protect \LaTeX  .

And then

> \LaTeX =\long macro:
->L\kern -.36em{\sbox \z@ T\vbox to\ht \z@ {\hbox {\check@mathfonts \fontsize
\sf@size \z@ \math@fontsfalse \selectfont A}\vss }}\kern -.15em\TeX .
<argument> \LaTeX