Your last example,
"2 3 4 - +" --> 2 + 3 - 4
makes use of the fact that subtraction associates with
addition on the left. That is,
2 + (3 - 4) == (2 + 3) - 4
While this is true for addition and subtraction, it's
not necessarily true for any arbitrary operators you might
define in the hash. In trying to generalize this problem,
you're walking a fine line between overgeneralizing (so
that we need to write an entire theorem-prover to solve
it (which would be NP-complete, BTW)), and undergeneralizng
(tying yourself too closely to the familiar case of
ordinary arithmetic).
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