There's this-command-keys and this-command-keys-vector. Is there
a command that returns using the syntax of keyboard macro like
“M-‹key›” or “C-‹key›”? Or, how to convert the above to the macro
syntax string?

also when i do M-x narrow-to-region, emacs will tell me that it is
bound to C-x n n. Similar for other command that has a binding but
called with M-x. How to find out programatically the keys of a given
command? I looked at the source but didn't see any mechanism that
reminds user of a existence of a binding.

here's some detail of what i want to do:

Basically, i want to write a function like this:

(global-set-key (kbd "C-a") 'binding-changed-notify)

Xah wrote:

,----[ C-h f key-description RET ]
| key-description is a built-in function in `C source code'.
| (key-description keys &optional prefix)
|
| Return a pretty description of key-sequence keys.
| Optional arg prefix is the sequence of keys leading up to keys.
| Control characters turn into "C-foo" sequences, meta into "M-foo",
| spaces are put between sequence elements, etc.
|
| [back]
`----