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Some sort of polish notation extended to all of a languages grammar?
Extreme. As already commented, human minds might be a problem in
implementing it - tho' I'd say in slow speech a human could perhaps handle
it (in response to Christophe's post: at least I occasionally embed
subclauses in such a way that parts of the main clause might linger on in
even half a minute, but this is only when showing off :-)) and I know
occasions when I've had to rush to class without having had the time to get
back to the head clause, ...)... in a way, I'd think it'd be more probably
that the mapwords would rather tend to spread out and be a few compounds
here and there, sort of like perhaps clusters of two or three parts.

>Of course, when you start using subclauses things can get seriously
>complicated.

Nah, I'd believe they'd just introduce a mapword as introduction to it -
polish notation does parentheses like that:
(1 + 5) * 3 -> * + 1 5 3

and
* + 1 5 + 3  4 => * (+ 1 5) (+ 3 4) => (1+5)*(3+4)

(only a rough sketch and I might be a bit wrong)