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).