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Reverse Polish notation

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1625: 1652: 2971: 3024: 664:, an object-oriented successor to reverse Polish notation. It deviates from classical reverse Polish notation by using a dynamic stack only limited by the amount of available memory (instead of three or four fixed levels) and which could hold all kinds of data objects (including symbols, strings, lists, matrices, graphics, programs, etc.) instead of just numbers. The system would display an error message when running out of memory instead of just dropping values off the stack on overflow as with fixed-sized stacks. It also changed the behaviour of the stack to no longer duplicate the top register on drops (since in an unlimited stack there is no longer a top register) and the behaviour of the 1833:. To perform an operation on two numbers, commands would first be given to recall the numbers from appropriate locations in the memory, followed by the command for the operation. Numbers were automatically positioned in registers in the Arithmetic Unit of the machine so that operations like division and subtraction would proceed in the right order. Results were left in a register in the AU so that long sequences of operations could be carried out. Thus, the Z-3 used a version of RPN that was nearly identical to that used by HP! I have obtained copies of early programs that Zuse had written for the evaluation of a 5 × 5 determinant, and it is possible to run these programs on an 98: 382:
typical calculations. Additionally, users of reverse Polish calculators made fewer mistakes than for other types of calculators. Later research clarified that the increased speed from reverse Polish notation may be attributed to the smaller number of keystrokes needed to enter this notation, rather than to a smaller cognitive load on its users. However, anecdotal evidence suggests that reverse Polish notation is more difficult for users who previously learned algebraic notation.
542: 2110:'s Polish notation, which enables a writer of mathematical notation to instruct a reader the order in which to execute the operations (e.g. addition, multiplication, etc) without using brackets. Polish notation achieves this by having an operator (+, ×, etc) precede the operands to which it applies, e.g., +ab, instead of the usual, a+b. Hamblin, with his training in formal logic, knew of Lukasiewicz's work. 1838:
AU was through the "f" register. This is sort of like the display register of the 41C, which is distinct from the stack. Arithmetic operations were performed on numbers in the a and b registers, so these may be thought of as corresponding to the x and y registers of HP's. Unlike modern computer practice, the actual numbers themselves were moved around the registers, not just a pointer.
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with almost no modification whatsoever (once the numbers have been placed in the storage registers beforehand). The AU of the Z-3 contained 3 registers, although Zuse never referred to them as a stack, of course. These registers were labelled "f", "a", and "b". All entrance and exit to and from the
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In comparison testing of reverse Polish notation with algebraic notation, reverse Polish has been found to lead to faster calculations, for two reasons. The first reason is that reverse Polish calculators do not need expressions to be parenthesized, so fewer operations need to be entered to perform
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in America. Like many modern pocket calculators, a zero-address machine allows the use of Reverse Polish arithmetic; this offers certain advantages to compiler writers. It is believed that the attention of the English Electric team was first drawn to the zero-address concept through contact with
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desktop electronic calculator, circa 1964. The EC-130 has RPN with a push-down stack of four registers, all visible simultaneously on a cathode ray tube display. Furthermore, they are shown upside down, that is, the last-in-first-out register is at the bottom. Around 1966, the
2756:â€č weiterentwickelt und daraus die â€șumgekehrte polnische Notationâ€č (UPN) ersonnen, da diese in seinen Rechnern verwendet wird: zunĂ€chst werden die Werte eingegeben, danach die gewĂŒnschte Rechenoperation ausgelöst. Klammern werden auf diese Weise vermieden. 751:. In contrast to RPL with its dynamic stack, it just drops values off the stack on overflow like other fixed-sized stacks do. However, like RPL, it does not emulate the behaviour of a classical operational RPN stack to duplicate the top register on drops. 1139:
version 3 can be enabled to support a dynamic RPN stack only limited by the amount of available memory instead of the classical 4-level stack. This feature was incorporated as a selectable function into the DM42 since firmware DMCP-3.21 / DM42-3.18.
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The computer can be used as a simple hand-held calculator. In this mode besides entering the numeric values the user must enter the instructions and the addresses by pressing their keys. He has to enter the numbers and operators in the reverse Polish
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is remarkable because it is the believed to be the first zero-address instruction format computer to have been announced (in 1960). It was first delivered at about the same time (early 1963) as the other famous zero-address computer, the
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als reine Rechenmaschine einsetzen, Operationen nimmt sie dann in der praktischen – wenn auch gewöhnungsbedĂŒrftigen – umgekehrten polnischen Notation entgegen. Werte im Speicher ablegen (oder von dort laden) kann man so allerdings
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soon became aware of the problems of (a) computing mathematical formulae containing brackets, and (b) the memory overhead in having dealing with memory stores each of which had its own name. One solution to the first problem was
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DATA STORAGE: 2 Auxiliary Storage Registers plus up to 7 push-up Stack Registers. 7400A 3 Registers Kit $ 299.95 Assembled $ 379.95 7400B 5 Registers Kit $ 319.95 Assembled $ 399.95 7400C 7 Registers Kit $ 339.95 Assembled $
1720:(1878–1956), and that RPN was invented and is patented by HP. Aside from the apparent contradiction in these two statements, I do not think that either of them is quite true. My first experience with RPN involved a nice old 2543:
Zum Eingeben der Zahlen stand eine Tastatur bereit (Dezimalzahlen, Gleitkommadarstellung). Anweisungen gaben Nutzer in umgekehrter polnischer Notation: zuerst die Argumente, um Register zu befĂŒllen, dann der auszufĂŒhrende
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I changed the architecture to use RPN (Reverse Polish Notation), which is the ideal notation for programming environment in which coding efficiency is critical. In the beginning, that change was not well received...
1109:(2023) derivatives support data types for stack objects (real numbers, infinite integers, finite integers, complex numbers, strings, matrices, dates and times). The latter three variants can also be switched between 102: 2633:. INFORMATIK 2005 Informatik LIVE! Band 1, BeitrĂ€ge der 35. Jahrestagung der Gesellschaft fĂŒr Informatik e.V. (GI), 19. bis 22. September 2005 in Bonn. Lecture Notes in Informatics (in German). Bonn, Germany: 2653:
Dazu stehen die beiden Register R1 und R2 als Kurzspeicher fĂŒr die Operanden der arithmetischen Operationen zur VerfĂŒgung. Gerechnet wird in der umgekehrten polnischen Notation, wie z.B. beim Taschenrechner
619:) in order to ease some calculations and to save keystrokes. HP used reverse Polish notation on every handheld calculator it sold, whether scientific, financial, or programmable, until it introduced the 754:
In late 2017, the list of active models supporting reverse Polish notation included only the 12C, 12C Platinum, 17bii+, 35s, and Prime. By July 2023, only the 12C, 12C Platinum, the freshly released
3102:. Marina Del Ray Hotel, Marina Del Ray, California, USA: Charles Babbage Institute, The Center for the History of Information Processing, University of Minnesota, Minneapolis, USA. Archived from 2477:
Die Z3 konnte in zwei Betriebsmodi betrieben werden, und zwar in dem Programm- und Dialogmodus. Das Rechnen im Dialog erfolgt wie mit einem Taschenrechner in der umgekehrten polnischen Notation.
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While calculators emulating classical models continued to support classical reverse Polish notation, new reverse Polish notation models feature a variant of reverse Polish notation, where the
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or stack - the basic mechanism of a zero-address computer - the KDF9 had other groups of central registers for improving performance which gave it an interesting internal structure.
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LaForest, Charles Eric (April 2007). "2.1 Lukasiewicz and the First Generation: 2.1.2 Germany: Konrad Zuse (1910–1995); 2.2 The First Generation of Stack Computers: 2.2.1 Zuse Z4".
4007:"Everything you've always wanted to know about RPN but were afraid to pursue – Comprehensive manual for scientific calculators – Corvus 500 – APF Mark 55 – OMRON 12-SR and others" 3729: 3434:
The operational stack and reverse Polish (Ɓukasiewicz) notation used in the HP-35 are the most efficient way known to computer science for evaluating mathematical expressions.
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calculator offered RPN with a stack of four, a printer, and either 14 or 42 step programmability. The instruction booklets with these two calculators make no mention of RPN or
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In reference to "In dialog mode, it allowed operators to enter two operands followed by the desired operation" for the Z3 computer, the following citations are relevant :
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stores, and became part of DSG International. A variety of calculator models was sold in the 1970s under the Prinztronic brand, all made for them by other companies.
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Kasprzyk, Dennis Michael; Drury, Colin G.; Bialas, Wayne F. (1979) . "Human behaviour and performance in calculator use with Algebraic and Reverse Polish Notation".
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key (for "entry"). In contrast to Hewlett-Packard's reverse Polish notation implementation, W filled with 0 instead of its contents being duplicated on stack drops.
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Hoffman, Errol; Ma, Patrick; See, Jason; Yong, Chee Kee; Brand, Jason; Poulton, Matthew (1994). "Calculator logic: when and why is RPN superior to algebraic?".
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key so that it no longer duplicated values into Y, which had shown to sometimes cause confusion among users not familiar with the specific properties of the
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In terms of practical choice between calculators, it would appear that RPN is faster and more accurate overall but particularly for more complex problems.
2784: 2680: 2638: 2531: 4644: 2960:(NB. This is an edited version of a talk given to North West Group of the Society at the Museum of Science and Industry, Manchester, UK on 1996-10-01.) 4878: 3663: 2624:. "2. DialogfÀhigkeit der Maschine Z3". Written at Berlin, Germany. In Cremers, Armin B.; Manthey, Rainer; Martini, Peter; Steinhage, Volker (eds.). 2161: 505:, where he found a reference to Polish notation, which made him read the works of Jan Ɓukasiewicz as well, and before he was aware of Hamblin's work. 3682: 501:, later wrote that he developed reverse Polish notation independently of Hamblin sometime in 1958 after reading a 1954 textbook on symbolic logic by 3496: 1958: 4770: 3699: 2049: 4622:
Kreifeldt, John G.; McCarthy, Mary E. (1981-10-15) . Written at Department of Engineering Design, Tufts University, Medford, Massachusetts, USA.
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typically refers specifically to the method used to enter calculations into hardware or software calculators, which often have additional
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calculator in 1977. By this time, HP was the leading manufacturer of calculators for professionals, including engineers and accountants.
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hardware platform, support classical Hewlett-Packard-style reverse Polish notation supporting automatic stack lift behaviour of the
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ARPCalc, a powerful scientific/engineering RPN calculator for Windows, Linux and Android that also has a web-browser based version
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to convert infix expressions to postfix expressions (reverse Polish notation), so named because its operation resembles that of a
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The advantage of reverse Polish notation is that it removes the need for order of operations and parentheses that are required by
4883: 3882: 3762: 2428: 1589: 781: 3294: 3265: 2600: 3964: 3337: 1882: 4631:. Proceedings of the Seventeenth Annual Conference on Manual Control. University of California, Los Angeles, California, USA: 4013: 4873: 4107: 4077: 4047: 3563: 3237:. He retired from Xerox RD in 1990. He is responsible for the development of the first commercial electronic calculator, the 2135: 1985: 1746: 176: 4789: 2634: 4720: 4592: 4468: 4412: 4354:
Dagnat, Fabien; Keryell, Ronan; Aoun, Youssef; Sastre, Laura Barrero; de RosiĂšre, Emmanuel Donin; Torneri, Nicolas (2003),
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used RPN in all of their desktop and hand-held calculators, and has continued to use it in some models into the 2020s. In
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Novus 650 Mathbox, 3500 Sliderule, 4510 Mathematician, 4515 Mathematician PRO/RG, 4520 Scientist and 4525 Scientist PR
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The first computer to use postfix notation, though it long remained essentially unknown outside of Germany, was
4636: 3652: 2936: 1910:; Warren, Don W.; Wright, Jesse B. (1954). "An Analysis of a Logical Machine Using Parenthesis-Free Notation". 1603: 1412: 1392: 479: 464: 230: 2770: 2676: 2625: 2517: 649:
calculator also used reverse Polish notation. In 1988, Hewlett-Packard introduced a business calculator, the
4623: 4383:(December 2000). "Kapitel 1. LOTUS 1-2-3-Format (WKS/WK1)" [Chapter 1. Lotus 1-2-3 WKS/WK1 format]. 3821: 3324: 2892: 2166: 2127: 2102: 2036: 2009: 1999: 1977: 1950: 1621: 1558: 926:, are backwards compatible with them. Their extended architecture is also based on reverse Polish notation. 572:. This calculator popularized reverse Polish notation among the scientific and engineering communities. The 400: 391: 300: 245: 138: 3809: 2172: 620: 440:
The first computer implementing a form of reverse Polish notation (but without the name and also without a
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key and top register copies on pops, but switchable between a four- and an eight-level operational stack.
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models) used reverse Polish notation for both automatic mode and programming. Modern Russian calculators
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Reckoners - The prehistory of the digital computer, from relays to the stored program concept, 1935–1945
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Company (HP), the best known manufacturer of RPN calculators, says that RPN is based on a suggestion by
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Among these was the PROGRAM Programmable Scientific Calculator which featured reverse Polish notation.
2097: 1476: 4868: 2944: 2306:(1). Department of Industrial Engineering, University at Buffalo, State University of New York, USA: 2226: 2195: 1340: 1128:
mode, which had already been available as a compile-time option for the WP 34S and WP 31S.
952: 491: 419: 415: 4439:(December 2000). "Kapitel 2. LOTUS 1-2-3-Format (WK3)" [Chapter 2. Lotus 1-2-3 WK3 format]. 808: 332:, a last-in/first-out construct, is integral to the left-to-right evaluation of RPN. In the example 160:
their operands. The notation does not need any parentheses for as long as each operator has a fixed
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GEORGE IA and II: A semi-translation programming scheme for DEUCE: Programming and Operation Manual
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A promotional Hewlett-Packard "No Equals" hat from the 1980s – both a boast and a reference to RPN
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Dateiformate – Eine Referenz – Tabellenkalkulation, Text, Grafik, Multimedia, Sound und Internet
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Dateiformate – Eine Referenz – Tabellenkalkulation, Text, Grafik, Multimedia, Sound und Internet
2705: 2107: 1730: 1717: 1595: 1581: 1550: 1532: 541: 191: 4763: 4673:(1). Department of Engineering Design, Tufts University, Medford, Massachusetts, USA: 329–332. 4665:
Kreifeldt, John G. (October 1981). "Hand Calculator Performance Under Interrupted Operation".
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Other early computers to implement architectures enabling reverse Polish notation were the
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File formats – a reference – spreadsheets, text, graphics, multimedia, sound and internet
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File formats – a reference – spreadsheets, text, graphics, multimedia, sound and internet
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in 1968 with reverse Polish notation with only three stack levels with working registers
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Reverse Polish notation has been compared to how one had to work through problems with a
19:"Operational stack" redirects here. For the English Channel lorry parking procedure, see 4717:"RPN or DAL? A brief analysis of Reverse Polish Notation against Direct Algebraic Logic" 1799: 2775: 2432: 1679: 1455: 854: 773: 623: 536: 355: 50: 3786: 3750: 1245:
Mouseless Stack-Calculator scientific/engineering calculator including complex numbers
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Wickes, William C. (January–February 1987). "The HP-28C: An Insider's Perspective".
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describes the general scheme in mathematics and computer sciences, whereas the term
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Implementation of RPN with custom functions support and flexible list of operators.
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There are other ways of producing postfix expressions from infix expressions. Most
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As of 2011, Hewlett-Packard was offering the calculator models 12C, 12C Platinum,
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key, a feature often requested by the community. They also support a rarely seen
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machine, which was announced in 1960 and commercially available in 1963, and the
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in reverse Polish notation: 4 is first subtracted from 3, then 5 is added to it.
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has been constructed, the corresponding postfix expression is given by a simple
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and can be evaluated linearly, left-to-right. For example, the infix expression
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RPNL. Eine FORTH Ă€hnliche Sprache mit strukturunterstĂŒtzenden Sprachkonstrukten
3696:"Reversing Sinclair's amazing 1974 calculator hack – half the ROM of the HP-35" 2078: 1982:
Proceedings of the First Australian Conference on Computing and Data Processing
4070:"Bit's WP 34S and 31S patches and custom binaries (version: r3802 20150805-1)" 3993: 3989: 3985: 3208: 2621: 2453: 2247: 1309: 1262: 1259:
orpie, RPN calculator for the terminal for real or complex numbers or matrices
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introduced reverse Polish notation to the desktop calculator market with the
3981: 3977: 3581: 1980:(June 1957). "An addressless coding scheme based on mathematical notation". 516: 234: 4815: 4568: 3050: 2988: 2339: 4150: 853:
photographic and electronic goods stores retail chain, later rebranded as
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Bob holds over 80 patents awarded during his work as Director of RD for
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In addition to the optional support for an eight-level stack, the newer
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can be modified to produce postfix expressions; in particular, once an
304: 145: 3396: 1878: 568:("temporary"), a reverse Polish notation variant later referred to as 4512:(NB. According to this book, a 4 KB compiler was available from 4344:(NB. This book is informally called "red book" due to its red cover.) 3883:"A new standard!... The 7400 scientific & engineering calculator" 3835:"Elektronika MK-61/52 and 152/161: small tech review (En) - ĐšĐŸĐœ-йОĐșĐž" 1834: 1315: 1232: 1163: 1136: 1132: 1098: 1094: 1076: 1072: 1068: 1064: 1060: 715: 711: 707: 703: 688: 684: 650: 646: 642: 638: 634: 630: 527:
calculator supported an unnamed input scheme resembling RPN as well.
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and implications depending on the actual implementation involving a
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SR4921 RPN Reverse Notation Scientific Calculator Instruction Manual
2706:"Die Computerwelt von Konrad Zuse - Auf den Spuren eines EDV-Genies" 1923: 4213: 3486:"Section 3: The Automatic Memory Stack, LAST X, and Data Storage". 1212: 762: 213:, Don Warren, and Jesse Wright and was independently reinvented by 4100:"[34S & 31S] Unique display mode: significant figures" 3834: 3234: 3163: 2659: 2655: 1830: 1555:
Aristotle's Syllogistic from the Standpoint of Modern Formal Logic
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Aristotle's Syllogistic from the Standpoint of Modern Formal Logic
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TRURL, a class library for the construction of RPN calculators in
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key behaves as in RPL. This latter variant is sometimes known as
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in 1945. The reverse Polish scheme was again proposed in 1954 by
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providing many implementations in several programming languages.
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Existing implementations using reverse Polish notation include:
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rpCalc, a simple reverse polish notation calculator written in
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grpn scientific/engineering calculator using the GIMP Toolkit (
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with stack levels named X, Y, Z, and W (rather than T) and an
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added a square root function in April 1965. Around 1966, the
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and notation for this scheme were extended by the Australian
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Er hat wohl auch als erster die vom polnischen Mathematiker
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An eight-level stack was suggested by John A. Ball in 1978.
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Later calculators with LCDs in the early 1980s, such as the
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https://forum.swissmicros.com/viewtopic.php?f=15&t=2845
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https://forum.swissmicros.com/viewtopic.php?f=16&t=2939
3895:(Advertisement). Vol. 43, no. 12. New York, USA: 1955:
An Addressless Coding Scheme based on Mathematical Notation
1462:, the inventors of the stack principle, called their stack 961:(originally firming as RPN-Calc) calculators including the 722:(RPL) and 50g (RPL) which support reverse Polish notation. 307:. For example, to add 3 and 4 together, the expression is 110:
Video: Keys pressed for calculating eight times six on a
3980:, but the text erroneously refers to the later algebraic 3147:
Galler, Bernard A.; Rosin, Robert F., eds. (1985-09-06).
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A New Approach to the Design of a Digital Computer (1961)
1858:"Konrad Zuse's Legacy: The Architecture of the Z1 and Z3" 683:
between 1999 and 2008. The last RPL calculator was named
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Presumably, the KDF9 designers drew ideas from Hamblin's
3526:"The slide rule killer: a milestone in computer history" 2573:, Congressional Information Service, Inc. p. 0010. 1829:
was that this code was very similar to that of, say, an
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Proceedings of the Human Factors Society Annual Meeting
3858: 2291:"Electronic calculators: which notation is the better?" 599:
key duplicates values into Y under certain conditions (
2518:"Zum 75. Geburtstag von Konrad Zuses Z3: Ratterkasten" 1359:(aka Reverse Polish Lisp), a programming language for 1166:
applications e.g. "reverse polish notation calculator"
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Interruption as a test of the user-computer interface
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Galler, Bernard A.; Rosin, Robert F., eds. (1986) .
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In their advertisements and also in a letter to me,
16:
Mathematics notation where operators follow operands
3204:"1928–2012 Obituary Condolences Robert (Bob) Ragen" 2895:- The Bulletin of the Computer Conservation Society 4265: 2511: 2509: 2171: 1678: 4855:Free online Algebraic expression to RPN Converter 4816:"RPN Tutorial, incl. some things HP did not tell" 4151:"CGTK - ARPCalc - Al's Reverse Polish Calculator" 3448:HP-42S RPN Scientific Calculator – Owner's Manual 2425:Alumni-Magazin der Technischen UniversitĂ€t Berlin 1972: 1970: 1968: 1945: 1943: 1941: 1912:Mathematical Tables and Other Aids to Computation 1825:The interesting aspect of the programming of the 1252:for Linux and MS Windows and published under the 2836: 2834: 2627:Die ergonomischen Erfindungen der Zuse-Maschinen 1228:, a widely used tabulating and graphing software 935:A seven-level stack had been implemented in the 475:, announced in 1961 and also delivered in 1963: 4853:https://xrjunque.nom.es/ConvertAlg2RPN_RPL.aspx 3602: 3600: 2122: 2120: 2118: 2031: 2029: 2027: 1231:grdmath, a program for algebraic operations on 343:The common terminology is that added items are 3548: 3546: 1790: 1788: 1046:Community-developed hardware-based calculators 3961:"MITS 7400 Scientific/Engineering Calculator" 3499:September 2011. pp. 32–46. 00015-90001. 3481: 3479: 2878: 2876: 2844:Second-Generation Stack Computer Architecture 2822:Computer architecture: Concepts and evolution 2289:Agate, Seb J.; Drury, Colin G. (March 1980). 2284: 2282: 1685:(1 ed.). Cambridge, Massachusetts, USA: 679:of graphing RPL calculators, followed by the 78: 8: 4276:(27th printing, August 1998, 1st ed.). 3607:Wessman, Timothy "Tim" James (2016-06-21) . 2448: 2446: 2444: 2442: 1848: 1846: 1487: 1463: 784:(1975) models used reverse Polish notation. 564:("accumulate") and visible storage register 340:, and puts the result of −1 onto the stack. 4496:(in German) (2 ed.). Munich, Germany: 2826:Addison-Wesley Longman Publishing Co., Inc. 2677:"Fast Calculators: Konrad Zuse's Z1 and Z3" 2234:(9). Department of Industrial Engineering, 1672: 1670: 1668: 1666: 584:with its specific ruleset of the so-called 3149:"Oral History: Burroughs B5000 Conference" 2498:(German Historical Museum). Archived from 1588:(in Polish) (1 ed.). Warsaw, Poland: 849:were own-brand trade names of the British 763:HP-related community-developed calculators 85: 71: 27: 4356:"BibTeX++: Toward Higher-order BibTeXing" 4268:PostScript Language Tutorial and Cookbook 4165:"Katharina & Paul Wilkins' Home Page" 3664:Hewlett-Packard Development Company, L.P. 3572: 3570: 2526:(in German). Vol. 2016, no. 6. 1764: 1646: 1626:"Translation to and from Polish notation" 1563:(Reprinted by Garland Publishing in 1987 675:. From 1990 to 2003, HP manufactured the 183:. The description "Polish" refers to the 4699:. The Museum of HP Calculators (MoHPC). 3497:Hewlett-Packard Development Company, LP. 3162:, University of Minnesota, Minneapolis: 2162:"Wall Street's Cult Calculator Turns 30" 1959:New South Wales University of Technology 1118: 1080: 831: 812: 801: 726: 665: 593: 576:, the world's first handheld scientific 194:, who invented Polish notation in 1924. 4764:"Good Ideas, Through the Looking Glass" 4534:(in German). Wolf-Detlef Luther, Gens. 3489:Hewlett-Packard HP-15C Owner's Handbook 3129:"The Burroughs B5000 Conference (1985)" 3096:The Burroughs B 5000 Conference - OH 98 2771:"Computergeschichte: Zuse Z3 "im Test"" 2236:State University of New York at Buffalo 2012:(November 1985). "Computer Languages". 1866:IEEE Annals of the History of Computing 1524: 1504: 1433: 695:to recreate RPL on modern calculators. 315:. The conventional notation expression 3454:(1 ed.). Corvallis, Oregon, USA: 3315:Monnier, Richard E. (September 1968). 2427:(in German). Vol. 2, no. 3. 2132:"Tom Osborne's Story in His Own Words" 2094:"Charles L. Hamblin: Computer Pioneer" 137:, is a mathematical notation in which 3287:"Friden EC-132 Electronic Calculator" 3258:"Friden EC-130 Electronic Calculator" 2196:"In Praise Of RPN (with Python Or C)" 939:scientific desktop calculator in 1972 259:, reverse Polish notation is used in 7: 4555:Dietrich, Johannes W. (2019-07-24). 4308:PostScript Language Reference Manual 4104:MoHPC - The Museum of HP Calculators 4074:MoHPC - The Museum of HP Calculators 4044:MoHPC - The Museum of HP Calculators 3613:MoHPC - The Museum of HP Calculators 3401:MoHPC - The Museum of HP Calculators 2970:Duncan, Fraser George (1977-05-01). 2462:Professor Dr.-Ing. habil. Horst Zuse 1284:Stack-oriented programming languages 1242:galculator, a GTK desktop calculator 1059:The community-developed calculators 1051: 261:stack-oriented programming languages 4214:"Home - mouseless Stack-Calculator" 3893:- For men with ideas in electronics 3458:June 1988. p. 3. 00042-90001. 2711:. Die Welt der technischen Museen. 955:calculators like the Mark 55 (1976) 497:One of the designers of the B5000, 347:on the stack and removed items are 3241:, which has been displayed at the 3233:and as Senior Project Engineer at 2796:Über die I/O-Einheit kann man die 1369:(Reverse Polish Notation Language) 611:("top") gets duplicated on drops ( 14: 4530:Wostrack, Gustav (January 1989). 4316:Addison-Wesley Publishing Company 4278:Addison Wesley Publishing Company 4038:Paul, Matthias R. (2015-02-18) . 3760:Commodore Business Machines, Inc. 3651:Nelson, Richard J. (April 2012). 3332:(1). Palo Alto, California, USA: 3065:Australian Computer Society, Inc. 2885:"The KDF9 Computer — 30 Years On" 2769:Tremmel, Sylvester (2021-11-21). 2160:Peterson, Kristina (2011-05-04). 2075:"Charles L. Hamblin and his work" 2004:The Australian Journal of Science 1363:calculators between 1986 and 2015 818:key, both implementing a form of 486:programming system written for a 4879:Science and technology in Poland 2675:Bonten, Jo H. M. (2009-05-28) . 299:In reverse Polish notation, the 31: 4822:from the original on 2023-09-23 4802:from the original on 2020-06-14 4776:from the original on 2017-06-24 4747:from the original on 2017-06-24 4737:"Postfix Notation Mini-Lecture" 4723:from the original on 2017-06-24 4703:from the original on 2017-06-24 4650:from the original on 2022-01-30 4609:from the original on 2022-12-26 4474:from the original on 2016-11-29 4418:from the original on 2016-11-29 4361:, Proceedings of EuroTeX 2003, 4335:from the original on 2017-02-18 4110:from the original on 2023-09-24 4080:from the original on 2023-09-24 4050:from the original on 2023-09-23 4019:from the original on 2017-06-24 3967:from the original on 2017-04-30 3906:from the original on 2022-12-28 3768:from the original on 2017-06-25 3732:from the original on 2022-10-20 3702:from the original on 2022-08-26 3673:from the original on 2022-10-20 3619:from the original on 2023-09-24 3524:Laporte, Jacques (2014-05-22). 3506:from the original on 2017-09-17 3465:from the original on 2017-09-17 3407:from the original on 2023-09-23 3378:from the original on 2021-10-22 3343:from the original on 2022-10-20 3297:from the original on 2022-10-20 3268:from the original on 2022-10-20 3216:from the original on 2017-12-18 3185:from the original on 2023-09-23 3049:Allen, Murray W. (1985-11-01). 2916:from the original on 2020-07-27 2861:from the original on 2022-01-20 2818:Brooks, Jr., Frederick Phillips 2787:from the original on 2022-03-01 2739:from the original on 2019-10-17 2683:from the original on 2022-07-01 2644:from the original on 2022-07-01 2603:from the original on 2022-07-01 2534:from the original on 2022-07-01 2468:from the original on 2022-07-01 2431:. December 2000. Archived from 2349:from the original on 2023-09-23 2206:from the original on 2023-09-23 2138:from the original on 2022-04-04 2055:from the original on 2020-04-04 2014:The Australian Computer Journal 1888:from the original on 2022-07-03 1816:from the original on 2022-07-01 1773:from the original on 2022-07-01 1071:(2015), which are based on the 1052:Hewlett-Packard RPN calculators 918:, designed and manufactured in 592:) in 1972. In this scheme, the 4788:Vanderbeek, Greg (July 2007). 4314:(1st printing, 3rd ed.). 3758:. Palo Alto, California, USA: 3720:Sharwood, Simon (2013-09-02). 3063:(4). Darlinghurst, Australia: 2824:. Boston, Massachusetts, USA: 2092:McBurney, Peter (2008-07-27). 2073:McBurney, Peter (2008-12-06). 2002:(1957). "Computer Languages". 1986:Weapons Research Establishment 1984:. Salisbury, South Australia: 1681:Algorithms for RPN calculators 1600:Elements of mathematical logic 482:(General Order Generator), an 386:Converting from infix notation 1: 3051:"Charles Hamblin (1922–1985)" 2899:Computer Conservation Society 2516:Bundesmann, Jan (June 2016). 2496:Deutsches Historisches Museum 2429:Technische UniversitĂ€t Berlin 1745:Kennedy, John (August 1982). 1590:PaƄstwowe Wydawnictwo Naukowe 1586:Elementy logiki matematycznej 1408:Head-directionality parameter 221:in the early 1960s to reduce 4814:Klaver, Hans (2023-08-14) . 4715:Redin, James (2005-02-12) . 4492:Feichtinger, Herwig (1987). 4453:(in German). Bonn, Germany: 4397:(in German). Bonn, Germany: 3897:Gernsback Publications, Inc. 3582:"RPLMan from Goodies Disk 4" 2850:(thesis). Waterloo, Canada: 2421:"Rechenhilfe fĂŒr Ingenieure" 2391:10.1016/0003-6870(94)90048-5 2316:10.1016/0003-6870(80)90114-3 1604:Wojtasiewicz, Olgierd Adrian 1173:applications e.g. "RealCalc" 870:Aircraft Navigation Computer 605:temporary stack lift disable 366:in reverse Polish notation. 251:During the 1970s and 1980s, 127:reverse Ɓukasiewicz notation 4791:Order of Operations and RPN 4600:Hewlett-Packard Corporation 4012:. T. K. Enterprises. 1976. 3899:December 1972. p. 17. 3291:www.oldcalculatormuseum.com 3262:www.oldcalculatormuseum.com 3056:Australian Computer Journal 2883:Beard, Bob (Autumn 1997) . 2635:Gesellschaft fĂŒr Informatik 2342:. 0003-6870/80/01 0002-05. 2194:Williams, Al (2023-06-21). 1691:John Wiley & Sons, Inc. 1398:FOCAL keystroke programming 580:, introduced the classical 412:operator-precedence parsers 4900: 4735:Brown, Bob (2015-06-05) . 4679:10.1177/107118138102500187 4598:. Corvallis, Oregon, USA: 4303:Adobe Systems Incorporated 4274:Adobe Systems Incorporated 3976:(NB. Shows a photo of the 3791:www.vintagecalculators.com 3156:Marina del Rey, California 2238:, Amherst, New York, USA: 1448:operational (memory) stack 1049: 922:since 2007 and offered by 894:programmable calculators ( 760: 756:HP 15C Collector's Edition 617:top stack level repetition 586:operational (memory) stack 534: 517:Robert "Bob" Appleby Ragen 490:computer installed at the 389: 18: 4741:Kennesaw State University 4695:Hicks, David G. (2013) . 4633:Jet Propulsion Laboratory 4494:Arbeitsbuch Mikrocomputer 3928:Berger, Ivan (May 1973). 3160:Charles Babbage Institute 3131:. 2023-06-17. p. 49. 2637:(GI). pp. 200–204 . 2561:"2. Computers in Germany" 2460:[Z3 in details]. 2248:10.1080/00140137908924675 1539:(1 ed.). p. 78. 1486:called his stack concept 1312:page description language 1195:lisp library package calc 1003:DM10L Collector's Edition 747:form of entry RPN called 156:(PN), in which operators 114:(employing RPN) from 1991 4847:http://rpn.codeplex.com/ 4637:Office of Naval Research 4218:www.stack-calculator.com 3432:. p. i. p. i: 2679:. Geldrop, Netherlands. 2037:Hamblin, Charles Leonard 2010:Hamblin, Charles Leonard 2000:Hamblin, Charles Leonard 1978:Hamblin, Charles Leonard 1951:Hamblin, Charles Leonard 1622:Hamblin, Charles Leonard 1489:Automatisches GedĂ€chtnis 1413:Scrambling (linguistics) 1393:Calculator input methods 1180:applications e.g. "RPN9" 607:), and the top register 554:9100A Desktop Calculator 465:English Electric Company 4884:Operators (programming) 4769:. ZĂŒrich, Switzerland. 3371:. 1968. pp. 8–10. 3325:Hewlett-Packard Journal 3158:, USA, archived by the 2167:The Wall Street Journal 1559:Oxford University Press 826:came with a variant of 782:Scientific Programmable 660:In 1986, HP introduced 552:engineers designed the 401:shunting-yard algorithm 392:Shunting-yard algorithm 205:in 1941 as well as his 173:reverse Polish notation 131:Polish postfix notation 119:Reverse Polish notation 4796:University of Nebraska 4569:10.5281/zenodo.3257689 3367:(marketing brochure). 2989:10.1109/MC.1977.315873 2901:(CCS). pp. 7–15. 2852:University of Waterloo 1805:PPC Calculator Journal 1752:PPC Calculator Journal 1677:Ball, John A. (1978). 1648:10.1093/comjnl/5.3.210 1488: 1464: 1452:automatic memory stack 1148:Software calculators: 943:National Semiconductor 673:automatic memory stack 590:automatic memory stack 546: 494:, Australia, in 1957. 405:railroad shunting yard 370:Practical implications 115: 4874:Mathematical notation 3984:model instead of the 3787:"Prinztronic Program" 3362:"hp 9100A Calculator" 3168:Burroughs Corporation 2951:. Besides a hardware 2520:. Report / JubilĂ€um. 2383:Elsevier Science Ltd. 1608:The MacMillan Company 1275:Programming languages 1237:Generic Mapping Tools 887:Soviet Union / Semico 544: 456:also added a 2-level 109: 4500:. pp. 427–428. 2945:University of Sydney 2456:, ed. (2008-02-22). 2240:Taylor & Francis 1908:Burks, Arthur Walter 1800:"1941 RPN Computer?" 1144:Software calculators 645:, and the financial 601:automatic stack lift 492:University of Sydney 431:Hardware calculators 420:post-order traversal 416:abstract syntax tree 4602:. 1979. 5953-1930. 4498:Franzis-Verlag GmbH 4193:galculator.mnim.org 3456:Hewlett-Packard Co. 2814:Blaauw, Gerrit Anne 1856:(April–June 1997). 1474:parallel discoverer 1422:Object subject verb 1418:Subject object verb 1186:calculator program 1158:Mac OS X Calculator 1126:significant figures 778:Sinclair Scientific 588:(later also called 225:access and use the 4557:"TRURL RPN Engine" 4305:(February 1999) . 4290:. 9-780201-101799. 4264:(1986) . Preface. 4212:Schrijver, Frans. 4098:Bit (2015-02-07). 4068:Bit (2014-11-15). 3822:Elektronika MK-161 3426:HP35 User's Manual 2854:. pp. 8, 11. 2754:polnische Notation 2752:entwickelte â€ș 2746:. pp. 32–33: 2714:Welt der Fertigung 2492:"An einem 12. Mai" 2374:Applied Ergonomics 2308:IPC Business Press 2299:Applied Ergonomics 2128:Osborne, Thomas E. 1687:Wiley-Interscience 1470:operational cellar 1460:Friedrich L. Bauer 1218:F-Correlatives in 768:Sinclair Radionics 547: 397:Edsger W. Dijkstra 248:in the mid-1950s. 246:Charles L. Hamblin 243:computer scientist 219:Edsger W. Dijkstra 215:Friedrich L. Bauer 162:number of operands 116: 45:("Reverse Polish") 4661:(13 of 702 pages) 4514:Lifeboat Software 4455:Galileo Computing 4399:Galileo Computing 3935:Popular Mechanics 3891:Radio-Electronics 3824:page on RSkey.org 3812:page on RSkey.org 3810:Elektronika B3-21 2134:. Steve Leibson. 1879:10.1109/85.586067 1747:"RPN Perspective" 1606:. New York, USA: 1584:(February 1929). 1454:. Interestingly, 1178:Windows 10 Mobile 1117:behaviour of the 800:(MM6) without an 360:(3 + 4) × (5 + 6) 326:The concept of a 148:, in contrast to 125:), also known as 107: 95: 94: 4891: 4830: 4828: 4827: 4810: 4808: 4807: 4784: 4782: 4781: 4775: 4768: 4755: 4753: 4752: 4731: 4729: 4728: 4711: 4709: 4708: 4690: 4658: 4656: 4655: 4649: 4630: 4617: 4615: 4614: 4608: 4597: 4579: 4578: 4576: 4575: 4552: 4546: 4545: 4541:978-3-88707022-9 4527: 4521: 4511: 4489: 4483: 4482: 4480: 4479: 4473: 4452: 4433: 4427: 4426: 4424: 4423: 4417: 4396: 4377: 4371: 4370: 4360: 4351: 4345: 4343: 4341: 4340: 4334: 4313: 4299: 4293: 4291: 4271: 4262:Geschke, Charles 4258: 4252: 4251: 4249: 4248: 4242:rpcalc.bellz.org 4234: 4228: 4227: 4225: 4224: 4209: 4203: 4202: 4200: 4199: 4185: 4179: 4178: 4176: 4175: 4161: 4155: 4154: 4147: 4141: 4136: 4130: 4125: 4119: 4118: 4116: 4115: 4095: 4089: 4088: 4086: 4085: 4065: 4059: 4058: 4056: 4055: 4035: 4029: 4027: 4025: 4024: 4018: 4011: 4003: 3997: 3975: 3973: 3972: 3957: 3951: 3950: 3948: 3947: 3940:Hearst Magazines 3925: 3919: 3918: 3912: 3911: 3905: 3887: 3879: 3873: 3872: 3870: 3869: 3855: 3849: 3848: 3846: 3845: 3831: 3825: 3819: 3813: 3807: 3801: 3800: 3798: 3797: 3783: 3777: 3776: 3774: 3773: 3767: 3757: 3747: 3741: 3740: 3738: 3737: 3717: 3711: 3710: 3708: 3707: 3691: 3685: 3681: 3679: 3678: 3672: 3657: 3653:"HP RPN Evolves" 3648: 3642: 3641: 3638:"HP Calculators" 3634: 3628: 3627: 3625: 3624: 3604: 3595: 3594: 3592: 3591: 3586: 3574: 3565: 3562: 3550: 3541: 3540: 3538: 3537: 3528:. Archived from 3521: 3515: 3514: 3512: 3511: 3505: 3494: 3483: 3474: 3473: 3471: 3470: 3464: 3453: 3443: 3437: 3436: 3422: 3416: 3415: 3413: 3412: 3393: 3387: 3386: 3384: 3383: 3377: 3366: 3358: 3352: 3351: 3349: 3348: 3342: 3321: 3312: 3306: 3305: 3303: 3302: 3283: 3277: 3276: 3274: 3273: 3254: 3248: 3247: 3222: 3221: 3200: 3194: 3193: 3191: 3190: 3184: 3153: 3144: 3133: 3132: 3125: 3119: 3117: 3115: 3114: 3108: 3101: 3090: 3084: 3082: 3080: 3079: 3046: 3040: 3038: 3036: 3035: 3029: 3023:. Archived from 2976: 2967: 2961: 2957: 2943:computer by the 2922: 2921: 2915: 2889: 2880: 2871: 2869: 2867: 2866: 2860: 2849: 2838: 2829: 2828: 2810: 2804: 2803: 2793: 2792: 2766: 2760: 2758: 2745: 2744: 2738: 2722: 2710: 2702: 2696: 2695: 2689: 2688: 2672: 2666: 2664: 2650: 2649: 2643: 2632: 2618: 2612: 2611: 2609: 2608: 2557:Ceruzzi, Paul E. 2553: 2547: 2546: 2540: 2539: 2513: 2504: 2503: 2488: 2482: 2479: 2474: 2473: 2450: 2437: 2436: 2417: 2411: 2410: 2368: 2362: 2360: 2355: 2354: 2348: 2295: 2286: 2277: 2275: 2221: 2215: 2214: 2212: 2211: 2191: 2185: 2184: 2182: 2181: 2175: 2170:. Archived from 2157: 2151: 2150: 2144: 2143: 2124: 2113: 2112: 2096:. Archived from 2089: 2083: 2082: 2077:. Archived from 2070: 2064: 2063: 2061: 2060: 2054: 2047: 2033: 2022: 2021: 2007: 1996: 1990: 1989: 1974: 1963: 1962: 1947: 1936: 1935: 1904: 1898: 1896: 1894: 1893: 1887: 1862: 1850: 1841: 1840: 1822: 1821: 1796:Ceruzzi, Paul E. 1792: 1783: 1781: 1779: 1778: 1768: 1742: 1736: 1735: 1684: 1674: 1661: 1659: 1657: 1651:. Archived from 1650: 1634:Computer Journal 1630: 1618: 1612: 1611: 1602:. Translated by 1596:Ɓukasiewicz, Jan 1592: 1582:Ɓukasiewicz, Jan 1578: 1572: 1562: 1551:Ɓukasiewicz, Jan 1547: 1541: 1540: 1533:Ɓukasiewicz, Jan 1529: 1512: 1509: 1497: 1494:automatic memory 1491: 1485: 1477:Wilhelm KĂ€mmerer 1472:") in 1955, and 1467: 1465:Operationskeller 1441: 1374:Class libraries 1353:around 1979/1981 1222:dictionary items 1153:Atari Calculator 1131:Since 2021, the 1122: 1091:SwissMicros DM42 1084: 873:Heathkit OC-1401 816: 805: 730: 669: 597: 499:Robert S. Barton 365: 361: 339: 335: 322: 318: 314: 310: 257:computer science 169:postfix notation 135:postfix notation 108: 87: 80: 73: 60: 46: 42:Postfix notation 35: 28: 4899: 4898: 4894: 4893: 4892: 4890: 4889: 4888: 4859: 4858: 4841:Rosettacode.org 4837: 4825: 4823: 4818:. Netherlands. 4813: 4805: 4803: 4787: 4779: 4777: 4773: 4766: 4762:(2005-06-15) . 4758: 4750: 4748: 4734: 4726: 4724: 4714: 4706: 4704: 4694: 4664: 4653: 4651: 4647: 4628: 4621: 4612: 4610: 4606: 4595: 4591: 4588: 4586:Further reading 4583: 4582: 4573: 4571: 4554: 4553: 4549: 4542: 4529: 4528: 4524: 4508: 4491: 4490: 4486: 4477: 4475: 4471: 4465: 4450: 4435: 4434: 4430: 4421: 4419: 4415: 4409: 4394: 4379: 4378: 4374: 4358: 4353: 4352: 4348: 4338: 4336: 4332: 4326: 4311: 4301: 4300: 4296: 4288: 4260: 4259: 4255: 4246: 4244: 4236: 4235: 4231: 4222: 4220: 4211: 4210: 4206: 4197: 4195: 4187: 4186: 4182: 4173: 4171: 4163: 4162: 4158: 4149: 4148: 4144: 4137: 4133: 4126: 4122: 4113: 4111: 4097: 4096: 4092: 4083: 4081: 4067: 4066: 4062: 4053: 4051: 4037: 4036: 4032: 4022: 4020: 4016: 4009: 4005: 4004: 4000: 3970: 3968: 3959: 3958: 3954: 3945: 3943: 3927: 3926: 3922: 3909: 3907: 3903: 3885: 3881: 3880: 3876: 3867: 3865: 3857: 3856: 3852: 3843: 3841: 3833: 3832: 3828: 3820: 3816: 3808: 3804: 3795: 3793: 3785: 3784: 3780: 3771: 3769: 3765: 3755: 3749: 3748: 3744: 3735: 3733: 3719: 3718: 3714: 3705: 3703: 3694:Shirriff, Ken. 3693: 3692: 3688: 3684:(4 of 56 pages) 3676: 3674: 3670: 3655: 3650: 3649: 3645: 3636: 3635: 3631: 3622: 3620: 3606: 3605: 3598: 3589: 3587: 3584: 3578:Hewlett-Packard 3576: 3575: 3568: 3552: 3551: 3544: 3535: 3533: 3523: 3522: 3518: 3509: 3507: 3503: 3492: 3485: 3484: 3477: 3468: 3466: 3462: 3451: 3445: 3444: 3440: 3430:Hewlett-Packard 3424: 3423: 3419: 3410: 3408: 3395: 3394: 3390: 3381: 3379: 3375: 3369:Hewlett-Packard 3364: 3360: 3359: 3355: 3346: 3344: 3340: 3334:Hewlett-Packard 3319: 3314: 3313: 3309: 3300: 3298: 3285: 3284: 3280: 3271: 3269: 3256: 3255: 3251: 3219: 3217: 3202: 3201: 3197: 3188: 3186: 3182: 3151: 3146: 3145: 3136: 3127: 3126: 3122: 3112: 3110: 3106: 3099: 3092: 3091: 3087: 3077: 3075: 3048: 3047: 3043: 3033: 3031: 3027: 2974: 2969: 2968: 2964: 2932:Burroughs B5000 2919: 2917: 2913: 2897:. No. 18. 2887: 2882: 2881: 2874: 2864: 2862: 2858: 2847: 2840: 2839: 2832: 2812: 2811: 2807: 2790: 2788: 2768: 2767: 2763: 2750:Jan Lukasiewicz 2742: 2740: 2736: 2716: 2708: 2704: 2703: 2699: 2686: 2684: 2674: 2673: 2669: 2651:. p. 201: 2647: 2645: 2641: 2630: 2620: 2619: 2615: 2606: 2604: 2581: 2571:Greenwood Press 2555: 2554: 2550: 2537: 2535: 2515: 2514: 2507: 2490: 2489: 2485: 2471: 2469: 2452: 2451: 2440: 2419: 2418: 2414: 2370: 2369: 2365: 2352: 2350: 2346: 2293: 2288: 2287: 2280: 2223: 2222: 2218: 2209: 2207: 2193: 2192: 2188: 2179: 2177: 2159: 2158: 2154: 2141: 2139: 2126: 2125: 2116: 2108:Jan Ɓukasiewicz 2100:on 2008-12-07. 2091: 2090: 2086: 2072: 2071: 2067: 2058: 2056: 2052: 2045: 2035: 2034: 2025: 2008: 2006:(20?): 135–139; 1998: 1997: 1993: 1976: 1975: 1966: 1949: 1948: 1939: 1924:10.2307/2001990 1906: 1905: 1901: 1891: 1889: 1885: 1860: 1852: 1851: 1844: 1819: 1817: 1794: 1793: 1786: 1776: 1774: 1744: 1743: 1739: 1731:Jan Ɓukasiewicz 1718:Jan Ɓukasiewicz 1714:Hewlett-Packard 1700: 1676: 1675: 1664: 1655: 1628: 1620: 1619: 1615: 1594: 1580: 1579: 1575: 1549: 1548: 1544: 1531: 1530: 1526: 1521: 1516: 1515: 1510: 1506: 1501: 1500: 1479: 1444:Hewlett-Packard 1442: 1435: 1430: 1389: 1361:Hewlett-Packard 1277: 1269:WRPN Calculator 1235:grids, part of 1146: 1123: 1120: 1097:as well as the 1085: 1082: 1054: 1048: 937:MITS 7400C 932: 889: 866: 840: 833: 817: 814: 811:(MM6X) with an 806: 803: 790: 770: 765: 731: 728: 670: 667: 613:top copy on pop 598: 595: 570:three-level RPN 550:Hewlett-Packard 539: 533: 531:Hewlett-Packard 473:Burroughs B5000 438: 433: 428: 426:Implementations 394: 388: 372: 363: 359: 337: 333: 320: 316: 312: 308: 297: 253:Hewlett-Packard 223:computer memory 192:Jan Ɓukasiewicz 154:Polish notation 97: 91: 62: 58: 57: 56:Prefix notation 48: 44: 43: 24: 21:Operation Stack 17: 12: 11: 5: 4897: 4895: 4887: 4886: 4881: 4876: 4871: 4861: 4860: 4857: 4856: 4850: 4844: 4836: 4835:External links 4833: 4832: 4831: 4811: 4785: 4760:Wirth, Niklaus 4756: 4732: 4712: 4697:"What is RPN?" 4692: 4662: 4619: 4587: 4584: 4581: 4580: 4547: 4540: 4522: 4506: 4484: 4463: 4428: 4407: 4372: 4346: 4324: 4294: 4286: 4253: 4229: 4204: 4180: 4156: 4142: 4131: 4120: 4090: 4060: 4030: 3998: 3952: 3920: 3913:. p. 17: 3874: 3850: 3826: 3814: 3802: 3778: 3742: 3712: 3686: 3643: 3629: 3596: 3566: 3542: 3516: 3475: 3438: 3417: 3388: 3353: 3307: 3293:. 2022-07-15. 3278: 3264:. 2020-08-09. 3249: 3212:. 2012-07-23. 3195: 3134: 3120: 3085: 3041: 2962: 2872: 2830: 2805: 2761: 2697: 2667: 2613: 2579: 2548: 2541:. p. 94: 2530:. p. 94. 2505: 2502:on 2013-05-30. 2483: 2458:"Z3 im Detail" 2438: 2435:on 2009-02-13. 2412: 2363: 2278: 2216: 2186: 2152: 2114: 2084: 2081:on 2008-12-06. 2065: 2023: 1991: 1964: 1957:(Typescript). 1937: 1899: 1842: 1823:. p. 25: 1798:(April 1980). 1784: 1766:10.1.1.90.6448 1737: 1698: 1662: 1658:on 2022-10-20. 1641:(3): 210–213. 1624:(1962-11-01). 1613: 1573: 1557:(2 ed.). 1542: 1523: 1522: 1520: 1517: 1514: 1513: 1503: 1502: 1499: 1498: 1456:Klaus Samelson 1432: 1431: 1429: 1426: 1425: 1424: 1415: 1410: 1405: 1400: 1395: 1388: 1385: 1384: 1383: 1382: 1381: 1372: 1371: 1370: 1364: 1354: 1344: 1341:Lotus Symphony 1334: 1329: 1324: 1319: 1313: 1307: 1302: 1297: 1292: 1276: 1273: 1272: 1271: 1266: 1260: 1257: 1246: 1243: 1240: 1229: 1223: 1216: 1209: 1206: 1196: 1190: 1181: 1174: 1167: 1162:Several Apple 1160: 1155: 1145: 1142: 1105:(2022) / 1101:(2019) / 1047: 1044: 1043: 1042: 956: 949: 946: 940: 931: 928: 888: 885: 881:five-level RPN 865: 862: 855:Currys Digital 839: 836: 828:four-level RPN 789: 786: 774:Clive Sinclair 769: 766: 624:adding machine 582:four-level RPN 560:("keyboard"), 537:HP calculators 535:Main article: 532: 529: 515:, designed by 437: 434: 432: 429: 427: 424: 422:of that tree. 390:Main article: 387: 384: 371: 368: 356:infix notation 296: 293: 93: 92: 90: 89: 82: 75: 67: 64: 63: 54: 51:Infix notation 40: 37: 36: 15: 13: 10: 9: 6: 4: 3: 2: 4896: 4885: 4882: 4880: 4877: 4875: 4872: 4870: 4867: 4866: 4864: 4854: 4851: 4848: 4845: 4842: 4839: 4838: 4834: 4821: 4817: 4812: 4801: 4797: 4793: 4792: 4786: 4772: 4765: 4761: 4757: 4746: 4742: 4738: 4733: 4722: 4718: 4713: 4702: 4698: 4693: 4688: 4684: 4680: 4676: 4672: 4668: 4663: 4660: 4646: 4642: 4638: 4634: 4627: 4626: 4620: 4605: 4601: 4594: 4590: 4589: 4585: 4570: 4566: 4562: 4558: 4551: 4548: 4543: 4537: 4533: 4526: 4523: 4519: 4515: 4509: 4507:3-7723-8022-0 4503: 4499: 4495: 4488: 4485: 4470: 4466: 4464:3-934358-83-7 4460: 4456: 4448: 4444: 4443: 4438: 4432: 4429: 4414: 4410: 4408:3-934358-83-7 4404: 4400: 4392: 4388: 4387: 4382: 4376: 4373: 4368: 4364: 4357: 4350: 4347: 4331: 4327: 4325:0-201-37922-8 4321: 4317: 4310: 4309: 4304: 4298: 4295: 4289: 4287:0-201-10179-3 4283: 4279: 4275: 4270: 4269: 4263: 4257: 4254: 4243: 4239: 4233: 4230: 4219: 4215: 4208: 4205: 4194: 4190: 4184: 4181: 4170: 4166: 4160: 4157: 4152: 4146: 4143: 4140: 4135: 4132: 4129: 4124: 4121: 4109: 4105: 4101: 4094: 4091: 4079: 4075: 4071: 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3150: 3143: 3141: 3139: 3135: 3130: 3124: 3121: 3109:on 2012-04-22 3105: 3098: 3097: 3089: 3086: 3074: 3070: 3066: 3062: 3058: 3057: 3052: 3045: 3042: 3030:on 2023-10-15 3026: 3022: 3018: 3014: 3010: 3006: 3002: 2998: 2994: 2990: 2986: 2982: 2981: 2973: 2966: 2963: 2959: 2956: 2954: 2953:nesting store 2950: 2946: 2942: 2938: 2933: 2928: 2923:. p. 8: 2912: 2908: 2904: 2900: 2896: 2894: 2886: 2879: 2877: 2873: 2857: 2853: 2846: 2845: 2837: 2835: 2831: 2827: 2823: 2819: 2815: 2809: 2806: 2802: 2799: 2786: 2782: 2778: 2777: 2772: 2765: 2762: 2757: 2755: 2751: 2735: 2731: 2727: 2723: 2720: 2715: 2707: 2701: 2698: 2694: 2682: 2678: 2671: 2668: 2663: 2661: 2657: 2640: 2636: 2629: 2628: 2623: 2617: 2614: 2602: 2598: 2594: 2590: 2586: 2582: 2580:0-313-23382-9 2576: 2572: 2568: 2567: 2562: 2558: 2552: 2549: 2545: 2533: 2529: 2525: 2524: 2519: 2512: 2510: 2506: 2501: 2497: 2494:(in German). 2493: 2487: 2484: 2481: 2478: 2467: 2464:(in German). 2463: 2459: 2455: 2449: 2447: 2445: 2443: 2439: 2434: 2430: 2426: 2422: 2416: 2413: 2408: 2404: 2400: 2396: 2392: 2388: 2384: 2380: 2376: 2375: 2367: 2364: 2359: 2356:. p. 6: 2345: 2341: 2337: 2333: 2329: 2325: 2321: 2317: 2313: 2309: 2305: 2301: 2300: 2292: 2285: 2283: 2279: 2273: 2269: 2265: 2261: 2257: 2253: 2249: 2245: 2242:: 1011–1019. 2241: 2237: 2233: 2229: 2228: 2220: 2217: 2205: 2201: 2197: 2190: 2187: 2176:on 2015-03-16 2174: 2169: 2168: 2163: 2156: 2153: 2149: 2137: 2133: 2129: 2123: 2121: 2119: 2115: 2111: 2109: 2104: 2099: 2095: 2088: 2085: 2080: 2076: 2069: 2066: 2051: 2044: 2043: 2038: 2032: 2030: 2028: 2024: 2020:(4): 195–198. 2019: 2015: 2011: 2005: 2001: 1995: 1992: 1987: 1983: 1979: 1973: 1971: 1969: 1965: 1960: 1956: 1952: 1946: 1944: 1942: 1938: 1933: 1929: 1925: 1921: 1918:(46): 53–57. 1917: 1913: 1909: 1903: 1900: 1884: 1880: 1876: 1872: 1868: 1867: 1859: 1855: 1849: 1847: 1843: 1839: 1836: 1832: 1828: 1815: 1811: 1807: 1806: 1801: 1797: 1791: 1789: 1785: 1772: 1767: 1762: 1758: 1754: 1753: 1748: 1741: 1738: 1734: 1732: 1728: 1723: 1722:Friden EC-130 1719: 1715: 1710:. p. 2: 1709: 1705: 1701: 1699:0-471-03070-8 1695: 1692: 1688: 1683: 1682: 1673: 1671: 1669: 1667: 1663: 1654: 1649: 1644: 1640: 1636: 1635: 1627: 1623: 1617: 1614: 1610:. p. 24. 1609: 1605: 1601: 1597: 1591: 1587: 1583: 1577: 1574: 1570: 1569:0-8240-6924-2 1566: 1560: 1556: 1552: 1546: 1543: 1538: 1534: 1528: 1525: 1518: 1508: 1505: 1495: 1490: 1483: 1478: 1475: 1471: 1466: 1461: 1457: 1453: 1449: 1445: 1440: 1438: 1434: 1427: 1423: 1419: 1416: 1414: 1411: 1409: 1406: 1404: 1403:Stack machine 1401: 1399: 1396: 1394: 1391: 1390: 1386: 1380: 1379:Object Pascal 1376: 1375: 1373: 1368: 1365: 1362: 1358: 1355: 1352: 1351:Commodore PET 1348: 1345: 1342: 1338: 1335: 1333: 1330: 1328: 1325: 1323: 1320: 1317: 1314: 1311: 1308: 1306: 1303: 1301: 1298: 1296: 1293: 1291: 1288: 1287: 1285: 1282: 1281: 1280: 1274: 1270: 1267: 1264: 1261: 1258: 1255: 1251: 1247: 1244: 1241: 1238: 1234: 1230: 1227: 1224: 1221: 1217: 1214: 1210: 1207: 1204: 1200: 1197: 1194: 1191: 1189: 1185: 1182: 1179: 1175: 1172: 1168: 1165: 1161: 1159: 1156: 1154: 1151: 1150: 1149: 1143: 1141: 1138: 1134: 1129: 1127: 1116: 1112: 1108: 1104: 1100: 1096: 1092: 1087: 1078: 1074: 1070: 1066: 1062: 1057: 1053: 1045: 1040: 1036: 1032: 1028: 1024: 1020: 1016: 1012: 1008: 1004: 1000: 996: 992: 988: 984: 980: 976: 972: 968: 964: 960: 957: 954: 950: 947: 945:4615 and 4640 944: 941: 938: 934: 933: 929: 927: 925: 921: 917: 913: 909: 905: 901: 897: 893: 886: 884: 882: 878: 874: 871: 863: 861: 858: 856: 852: 848: 844: 837: 835: 829: 825: 821: 820:two-level RPN 810: 809:Minuteman *6X 799: 796:produced the 795: 787: 785: 783: 779: 775: 767: 764: 759: 757: 752: 750: 746: 743:introduced a 742: 739:In 2013, the 737: 735: 723: 721: 717: 713: 709: 705: 701: 696: 694: 690: 686: 682: 678: 674: 663: 658: 656: 652: 648: 644: 640: 636: 632: 627: 625: 622: 618: 614: 610: 606: 602: 591: 587: 583: 579: 575: 571: 567: 563: 559: 555: 551: 543: 538: 530: 528: 526: 522: 518: 514: 510: 506: 504: 500: 495: 493: 489: 485: 481: 476: 474: 470: 466: 461: 459: 455: 451: 447: 443: 436:Early history 435: 430: 425: 423: 421: 417: 413: 408: 406: 402: 399:invented the 398: 393: 385: 383: 379: 377: 369: 367: 364:3 4 + 5 6 + × 357: 352: 350: 346: 341: 331: 330: 324: 306: 303:follow their 302: 294: 292: 290: 286: 282: 278: 274: 270: 266: 262: 258: 254: 249: 247: 244: 240: 236: 232: 228: 224: 220: 216: 212: 208: 204: 200: 195: 193: 190: 186: 182: 178: 174: 170: 165: 163: 159: 155: 151: 147: 143: 140: 136: 132: 128: 124: 120: 113: 88: 83: 81: 76: 74: 69: 68: 66: 65: 61: 53: 52: 47: 39: 38: 34: 30: 29: 26: 22: 4824:. 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Index

Operation Stack

Postfix notation
("Reverse Polish")

Infix notation
Prefix notation
("Polish")

v
t
e
HP-32SII
operators
operands
prefix
Polish notation
number of operands
side effects
stack
nationality
logician
Jan Ɓukasiewicz
Konrad Zuse
Z3
Z4
Arthur Burks
Friedrich L. Bauer
Edsger W. Dijkstra
computer memory
stack
expressions
algorithms
philosopher

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

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