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I want to map
;) to Escapeand wrote the following in my .vmrc
inoremap ; <ESC>
inoremap <C-;> ;
(1) allows me to escape from the insert mode, but (2) also behaves like Escape rather than giving ;.
What am I missing here? Any help is appreciated.
It looks like <C-;> does not work in vim. Might I suggest using <A-;> (Alt) instead? That one seems to work for me.
Ctrl-; is not a valid control sequence, so vim cannot capture it. You will need to use gvim or to configure your terminal emulator to translate Ctrl-; to something vim can capture
Please look at the ascii table, which has 4 columns of code/characters - from right to left, lowercase alphabets, uppercase alphabets, symbols/numbers, and non-printable code (or called CTRL characters) - basically only these Ctrl keys are supported. And you have the Ctrl-F1 up to Ctrl-F12 as bonus. 
The keyboard has come a long way since about 40 years ago. In the good old days when the terminal was invented, these 128 code/characters were all we have and all we need. We made use of the first 32 code to control the position of cursor in terminal as well as commnunication.
The keyboard interprets what you type and sends two bytes to computer - one is character code, the other is scan code. (since about 30 years ago. I'm not clear about the beginning.) For the range of ASCII, it sends a character code of Dec in blue column, and a scan code of 0.
You get code of [a-z] when you type directly. You get code of [A-Z] when you type w/ modifier SHIFT. You get code of [0-9] when you type the upper row. You get code of symbols when you type the numbers w/ SHIFT. Finally you get the CONTROL code exactly when you type the character w/ modifier CTRL. Look! This is what the keyboard does/interprets for you (smart enough. The mapping rules were still simple.).
Soon we felt 128 code is not enough and invented Alt etc. modifiers. I think the scan code was introduced at that time. All the Alt-related key combinations require a non-zero scan code. It's also true for the arrow keys in Keypad. The mapping rule become complicated.
Because of such long-time historical progress, you'll find that those modifiers CTRL, SHIFT, ALT (and even Win, Fn) are not treated fairly...SHIFT and ALT can modify more keys, but CTRL the least. (Sorry for your Ctrl-;) (I believe it's for backward compatibility.)
Although it's not impossible or definitely difficult to add more Ctrl keys, like the Ctrl-1...Ctrl-9 available in GUI Desktop, I don't think it's a good idea for VI - VI has been designed to work both for terminal and new GUI environments. It has to be consistent for both. However, making such changes in terminal protocols is not easy.
<c-;>is the same as;in your terminal. Press Ctrl-V and then Ctrl-;, you'll likely see just;.Ctrl-Vand thenCtrl+;give;, indeed.Ctrl-Vand then;also give;. Isn'tCtrl-Vthe blockwise-visual mode?:help i_ctrl-v… Vim is a modal editor.