Why do we need prefix, postfix notation

algorithm compiler-construction programming-languages formal-languages
Chander Shivdasani picture Chander Shivdasani · Sep 27, 2011 · Viewed 33.6k times · Source

I know how each of them can be converted to one another but never really understood what their applications are. The usual infix operation is quite readable, but where does it fail which led to inception of prefix and postfix notation

Answer

Jan Krüger picture Jan Krüger · Sep 27, 2011

Infix notation is easy to read for humans, whereas pre-/postfix notation is easier to parse for a machine. The big advantage in pre-/postfix notation is that there never arise any questions like operator precedence.

For example, consider the infix expression 1 # 2 $ 3. Now, we don't know what those operators mean, so there are two possible corresponding postfix expressions: 1 2 # 3 $ and 1 2 3 $ #. Without knowing the rules governing the use of these operators, the infix expression is essentially worthless.

Or, to put it in more general terms: it is possible to restore the original (parse) tree from a pre-/postfix expression without any additional knowledge, but the same isn't true for infix expressions.

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