Prefix notation

Polish notation (PN), also known as normal Polish notation (NPN),Łukasiewicz notation, Warsaw notation, Polish prefix notation or simply prefix notation, is a form of notation for logic, arithmetic, and algebra. Its distinguishing feature is that it places operators to the left of their operands. If the arity of the operators is fixed, the result is a syntax lacking parentheses or other brackets that can still be parsed without ambiguity. The Polish logician Jan Łukasiewicz invented this notation in 1924 in order to simplify sentential logic.

The term Polish notation is sometimes taken (as the opposite of infix notation) to also include Polish postfix notation, or reverse Polish notation (RPN), in which the operator is placed after the operands.

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 below) and related programming languages define their entire syntax in terms of prefix notation (and others use postfix notation).

A quotation from a paper by Jan Łukasiewicz, Remarks on Nicod's Axiom and on "Generalizing Deduction", page 180, states how the notation was invented:

I came upon the idea of a parenthesis-free notation in 1924. I used that notation for the first time in my article Łukasiewicz(1), p. 610, footnote.

The reference cited by Łukasiewicz is apparently a lithographed report in Polish. The referring paper by Łukasiewicz Remarks on Nicod's Axiom and on "Generalizing Deduction" was reviewed by H. A. Pogorzelski in the Journal of Symbolic Logic in 1965.

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