Polish notation
From Exampleproblems
Polish notation, also known as prefix notation, is a method of mathematical expression. It was created by Jan Łukasiewicz, mostly to simplify certain mathematical proofs. Its distinguishing feature is that it places operators before operands.
For example, this expression:
+ 1 2
evaluates to 3.
Polish notation is not limited to only two values, nor to just addition. For example, this expression:
(× (+ 0 1) (+ 2 3))
evaluates to 5.
While the examples above use parentheses, one of the benefits of Polish notation is that, assuming the arity of each operator is known, parentheses are unnecessary: the order of operations is unique and easy to determine, provided that the expression is well-formed. For example, assuming × and + are binary, then this expression:
× + 0 1 + 2 3
can mean only this:
(× (+ 0 1) (+ 2 3))
Polish notation is used in some computer programming languages, including Lisp and its dialect Scheme. It is also used in Tcl.
