Reverse Polish NotationDate: 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 appreciative. 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 http://mathforum.org/library/drmath/view/52300.html 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? http://www.calculator.org/rpn.html 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: http://www-history.mcs.st-and.ac.uk/Mathematicians/Lukasiewicz.html Here is a nice discussion of the benefits of RPN: RPN or DAL? http://www.dotpoint.com/xnumber/rpn_or_adl.htm - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ 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: http://www.csc.liv.ac.uk/~peter/hamblin.html 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. Faculty Department of Computer Science University of Liverpool, UK |
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