it will be easier to reason about this "^"
if you abandon the notion of operator,
and inverse it from denoting bound vars
to UNbound vars.

say

in a written program it is allowed to denote
the requirement of a particular variable
to be unbound at the occurrence of said notation.

the machine could simply check the status before
doing the match thing
and replace a "bad-match" error with "already bound"
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