If you do both (use flipped parentheses around the operators), it makes even more sense, and makes the parsing trivial to boot: just surround the entire expression with parentheses and parse normally. For instance: 1 + 2 )( 3 Becomes (1 + 2 )( 3) Which is actually just what the author wants. You might even want multiple, or an arbitrary numbers of external parentheses. Say we want to give the divide the least precedence, the multiply the middle, and the add the most. We could do that like: 1 + 2 )/( 3 ))(( 4 Surround it with two sets of parens and you have: ((1 + 2 )/( 3 ))(( 4)) I haven't just proved to myself this always does what you expect, though...