Re: Then how to replace all my $$ ... $$ to \[ \] through search and replace?

[harven]

> David Kastrup once mention this (or a similar example with
> `replace-regexp') on some newsgroup or mailing list.  I don't remember
> if it is possible to use this with M-x replace-... or
> query-replace... as well.

M-:(replace-regexp "\\$\\$" '("\\\[" "\\\]"))
It is in fact a feature of the perform-replace function.
Quoting the elisp manual section dealing with this function:

> The argument REPLACEMENTS specifies what to replace occurrences >  with.  If 
> it is a string, that string is used.  It can also be a
>  list of strings, to be used in cyclic order.

>  If REPLACEMENTS is a cons cell, `(FUNCTION . DATA)', this means to
> call FUNCTION after each match to get the replacement text.  This
> function is called with two arguments: DATA, and the number of
> replacements already made.