# Definition:Polish Notation/Reverse Polish Notation

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## Contents

## 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:

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

## Also see

## 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.

## Sources

- 1955: John L. Kelley:
*General Topology*... (previous) ... (next): Chapter $0$: Subsets and Complements; Union and Intersection: Theorem $3 \ \text{(b)}$ - 1993: M. Ben-Ari:
*Mathematical Logic for Computer Science*... (previous) ... (next): Chapter $2$: Propositional Calculus: $\S 2.2$: Propositional formulas - 1996: H. Jerome Keisler and Joel Robbin:
*Mathematical Logic and Computability*... (previous) ... (next): Appendix $\text{A}.8$: Cartesian Product - 2009: Kenneth Kunen:
*The Foundations of Mathematics*... (previous) ... (next): $\mathrm{II}.4$ Polish Notation - 2012: M. Ben-Ari:
*Mathematical Logic for Computer Science*(3rd ed.) ... (previous) ... (next): $\S 2.1.3$