title: Which of the following postfix notations correctly represents infix sum 1+2+3+4?
body: <p>I am testing an infix-to-postfix-to-infix converter and found some kind of uncertainty. For example, a simple infix sum</p>
  <pre><code>1 + 2 + 3 + 4
  </code></pre>
  <p>can be converted to postfix one</p>
  <pre><code>1 2 + 3 + 4 +
  </code></pre>
  <p>assuming that operators with equal precedence are not accumulated. If they are then I get</p>
  <pre><code>1 2 3 4 + + +
  </code></pre>
  <p>On the other hand, all the following postfix expressions can be converted to the initial sum</p>
  <pre><code>1 2 + 3 + 4 +
  1 2 + 3 4 + +
  1 2 3 4 + + +
  </code></pre>
  <p>Are all these postfix expressions correct?</p>
  <h3>UPDATE1</h3>
  <p>If you would make such converter, to which form would you choose? I need to choose one for testing.</p>