And one last refinement: beginning-of-buffer is able to take a prefix
argument with several different meanings. While beginning-of-line
can also take such an argument, it is more or less a safe bet that
you would rarely do so in interactive use, and you still could with a
combination of cursor-up with argument and the Pos1 key, anyhow.
So if we get a prefix-argument, we may assume
a) the beginning-of-buffer functionality is wanted
b) it is wanted with the given argument.
So you would want to make something like
(defun beginning-of-line-or-buffer (&optional arg)
"Send point to beginning of line or buffer.
If point is not yet at the beginning of the current line, it is
placed there. If already there, it is sent to the beginning of
the buffer using `beginning-of-buffer'. If a prefix argument ARG
is given, it is passed to `beginning-of-buffer' which gets then
called regardless of whether point is at the beginning of a line."
(interactive "P")
(if (or arg (bolp))
(beginning-of-buffer arg)
(beginning-of-line)))
Notice that I also changed the incorrect documentation string. You
can check those sort of strings by using
M-x checkdoc RET