Polish notation

Polish notation, also known as prefix notation, is a method of mathematical expression. It was created by Jan Łukasiewicz. 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.

Polish notation

See also