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Reverse Polish Notation

Date: 06/26/2002 at 20:06:37
From: Dr. Graham Williams
Subject: Reverse Polish Notation

I've been teaching my Year 6 students about the rules/grammar of 
maths, and we've been using many different real and virtual
calculators. The kids are fascinated, and some of them have read about
Reverse Polish Notation (RPN). Could you please explain where the name
comes from?  If you can offer any enlightenment I'd be most

Graham Williams  
Glen Waverley  
Victoria Australia 

Date: 06/26/2002 at 23:27:16
From: Doctor Peterson
Subject: Re: Reverse Polish Notation

Hi, Dr. Williams.

Here are a few of many sites that discuss this bit of history:

    Reverse Polish Notation 

    Polish Notation was created by the Polish mathematician
    Jan Lukasiewicz (Wu-ka-SHAVE-itch).  It was first used
    for Logic to eliminate the need for parentheses within
    expressions like ((A and B) or C).  There is an obvious
    parallel with numerical expressions like ((A + B) - C).
    The original(prefix) Polish Notation for this is -+ABC
    and it is AB+C- in (postfix) Reverse Polish Notation.

    What is Reverse Polish Notation? 

    In the early days of electronic calculators these rules
    proved fiendishly difficult to implement in calculator
    hardware. But calculator designers at Hewlett-Packard
    realised that a radically different method of defining
    the arithmetic, invented in the 1920's by Polish
    mathematician Jan Lukasiewicz (1878-1956) for symbolic
    logic, could be used to simplify the electronics at the
    expense of a little learning by the user. In the 1960's
    that would be regarded as a reasonable trade-off. For
    most calculator users of the time, the alternative was
    the error prone practice of writing down intermediate
    results. The Hewlett-Packard engineers called their
    calculator logic Reverse Polish Notation (or RPN) in
    recognition of its inventor.

Here is a biography of the inventor: 

Here is a nice discussion of the benefits of RPN:

    RPN or DAL? 

- Doctor Peterson, The Math Forum 

Date: 02/17/2003 at 14:56:08
From: Peter McBurney
Subject: Reverse Polish Notation

Hi -

Jan Lukasiewicz was not the inventor of Reverse Polish Notation. He 
invented (Forward) Polish Notation, where the operator (+, *, etc) is 
placed to the left of the operands. In Reverse Polish Notation, the
operator is placed on the right of the operands. The inventor of 
Reverse Polish Notation was the Australian philosopher, Charles 
Hamblin (1922-1985), who implemented it in the computer language 
GEORGE in 1957.  

For full citation details, see my page about Hamblin at:

Hamblin published his invention in papers in 1957 and 1962, well
before the first Hewlett-Packard calculator using RPN was launched in
1968. The first computer to enable RPN was the English Electric
Company's KDF9, released in 1963.Similarly, the Burroughs B5000,
released the same year, also enabled RPN. Both machines used Hamblin's 
idea of a zero-address LIFO stack.  

If you check the Hewlett-Packard pages closely, you will see they are
careful not to claim credit for RPN, since they did not invent it.  
All they claim credit for is being the first to apply it to pocket
calculator design. 

With regards,

- Peter McBurney, Ph.D.
Department of Computer Science
University of Liverpool, UK
Associated Topics:
High School Calculators, Computers
High School History/Biography

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