Polish notation

This article is about a prefix notation in mathematics and computer sciences. For the similarly named logic, see Łukasiewicz logic.

Polish notation (PN), also known as normal Polish notation (NPN), Łukasiewicz notation, Warsaw notation, Polish prefix notation, Eastern Notation, or simply prefix notation, is a mathematical notation in which operators precede their operands, in contrast to the more common infix notation, in which operators are placed between operands, as well as reverse Polish notation (RPN), in which operators follow their operands. It does not need any parentheses as long as each operator has a fixed number of operands. The description "Polish" refers to the nationality of logician Jan Łukasiewicz, who invented Polish notation in 1924.

Sometimes the term Polish notation refers collectively to normal Polish notation and reverse Polish notation (prefix notation and postfix notation, the two alternatives to infix notation).

When Polish notation is used as a syntax for mathematical expressions by programming language interpreters it is readily parsed into abstract syntax trees and can, in fact, define a one-to-one representation for the same. Because of this, Lisp (see Implementations, below) and related programming languages define their entire syntax in prefix notation (and others use postfix notation).

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