reverse Polish notation

Whereas operators are traditionally placed between operands, with parentheses used to override operator precedence, it is possible to place operators to the right of operands, thus eliminating ambiguity and the need for parentheses, and even the need for rules of operator precedence. This is known as reverse Polish notationMathworldPlanetmath (after the Polish mathematician Jan Łukasiewicz who came up with Polish notation, abbreviated RPN), or postfix notation. Invented by Australian philosopher Charles Hamblin, reverse Polish notation requires that the number of operands of a given operator be defined in advance.

For example, 3×16-1 probably means 47, but if the possibility exists that the author meant but neglected to put in parentheses, the expression could actually mean 3×(16-1)=45. In reverse Polish notation, we could define the basic arithmeticPlanetmathPlanetmath operators to all be binary, and write 316×1- with the confidence that it will evaluate to 47 and not 45.

Reverse Polish notation is particularly advantageous for stack-based programming languages like Forth and Adobe PostScript. Most Hewlett-Packard calculators use reverse Polish notation (though a few, such as the HP-38G, use the sort of infix notation conventional to most calculators). Some beginning programming language courses give as an exercise to the student the implementation of an RPN calculator. Instead of having to remember multiple addresses for different variables and constants, most RPN implementations use a stack and a stack pointer to keep track of data.

The factorialMathworldPlanetmath notation (e.g., n!) is a fairly common use of postfix notation in mostly infix contexts. (Most unary operators in C++ are prefix).

To convert from standard infix notation to reverse Polish notation, the Dutch computer programmer Edsger Dijkstra came up with the shunting yard algorithm.

Title reverse Polish notation
Canonical name ReversePolishNotation
Date of creation 2013-03-22 16:10:04
Last modified on 2013-03-22 16:10:04
Owner Mravinci (12996)
Last modified by Mravinci (12996)
Numerical id 6
Author Mravinci (12996)
Entry type Definition
Classification msc 68N17
Classification msc 03B70
Synonym postfix notation
Synonym RPN
Synonym Zciweisakul notation
Synonym reverse-Polish
Synonym reverse-Polish notation
Related topic PolishNotation