# Definition:Polish Notation/Reverse Polish Notation

## Definition

For stack-based programming languages, reverse Polish language is a useful variant of Polish notation, because it naturally coincides with how the input is to be structured for the language.

As the name suggests, a string $\mathsf P$ is in reverse Polish language if and only if reversing it gives a string $\tilde {\mathsf P}$ in Polish notation.

Thus the reverse Polish language equivalents of these examples of Polish notation:

$\Box p q \ldots$
$\Box {\diamond} p {\diamond} q \ldots$

are:

$\ldots q p \Box$
$\ldots q {\diamond} p {\diamond} \Box$

## Historical Note

Polish notation, along with its variant reverse Polish notation, was developed by a group of Polish mathematicians, led by Jan Łukasiewicz who invented it in the $1920$s.