Reverse Polish notation

Early history

The first computer implementing a form of reverse Polish notation (but without the name and also without a stack), was Konrad Zuse's Z3, which he started to construct in 1938 and demonstrated publicly on 12 May 1941.^{[22][23][24][25]} In dialog mode, it allowed operators to enter two operands followed by the desired operation.^{[z3 1]} It was destroyed on 21 December 1943 in a bombing raid.^[23] With Zuse's help a first replica was built in 1961.^[23] The 1945 Z4 also added a 2-level stack.^[31][32]

Other early computers to implement architectures enabling reverse Polish notation were the English Electric Company's KDF9 machine, which was announced in 1960 and commercially available in 1963,^[33] and the Burroughs B5000, announced in 1961 and also delivered in 1963:

The KDF9 designers drew ideas from Hamblin's GEORGE (General Order Generator),^{[10][11][13][34][35][32]} a high-level programming language written for a DEUCE computer installed at The New South Wales University of Technology, Kensington, Australia, in 1957.^{[10][11][13][33]}

One of the designers of the B5000, Robert S. Barton, later wrote that he developed reverse Polish notation independently of Hamblin sometime in 1958 after reading a 1954 textbook on symbolic logic by Irving Copi,^[36][37][38] where he found a reference to Polish notation,^[38] which made him read the works of Jan Łukasiewicz as well,^[38] and before he was aware of Hamblin's work.

Friden introduced reverse Polish notation to the desktop calculator market with the EC-130, designed by Robert "Bob" Appleby Ragen,^[39] supporting a four-level stack^[5] in June 1963.^[40] The successor EC-132 added a square root function in April 1965.^[41] Around 1966, the Monroe Epic calculator supported an unnamed input scheme resembling RPN as well.^[5]

Hewlett-Packard

Hewlett-Packard engineers designed the 9100A Desktop Calculator in 1968 with reverse Polish notation^[16] with only three stack levels with working registers X ("keyboard"), Y ("accumulate") and visible storage register Z ("temporary"),^[42][43] a reverse Polish notation variant later referred to as three-level RPN.^[44] This calculator popularized reverse Polish notation among the scientific and engineering communities. The HP-35, the world's first handheld scientific calculator,^[16] introduced the classical four-level RPN with its specific ruleset of the so-called operational (memory) stack^{[45][nb 1]} (later also called automatic memory stack^{[46][47][nb 1]}) in 1972.^[48] In this scheme, the Enter ↑ key duplicates values into Y under certain conditions (automatic stack lift with temporary stack lift disable), and the top register T ("top") gets duplicated on drops (top copy on pop aka top stack level repetition) in order to ease some calculations and to save keystrokes.^[47] HP used reverse Polish notation on every handheld calculator it sold, whether scientific, financial, or programmable, until it introduced the HP-10 adding machine calculator in 1977. By this time, HP was the leading manufacturer of calculators for professionals, including engineers and accountants.

Later calculators with LCDs in the early 1980s, such as the HP-10C, HP-11C, HP-15C, HP-16C, and the financial HP-12C calculator also used reverse Polish notation. In 1988, Hewlett-Packard introduced a business calculator, the HP-19B, without reverse Polish notation, but its 1990 successor, the HP-19BII, gave users the option of using algebraic or reverse Polish notation again.

In 1986,^[49][50] HP introduced RPL, 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.^[51] 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 Enter ↑ 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 automatic memory stack. From 1990 to 2003, HP manufactured the HP-48 series of graphing RPL calculators, followed by the HP-49 series between 1999 and 2008. The last RPL calculator was named HP 50g, introduced in 2006 and discontinued in 2015. However, there are several community efforts like newRPL or DB48X to recreate RPL on modern calculators.

As of 2011, Hewlett-Packard was offering the calculator models 12C, 12C Platinum, 17bII+, 20b, 30b, 33s, 35s, 48gII (RPL) and 50g (RPL) which support reverse Polish notation.^[52]

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 Enter ↑ key behaves as in RPL. This latter variant is sometimes known as entry RPN.^[53]

In 2013, the HP Prime introduced a 128-level form of entry RPN called advanced RPN. In contrast to RPL with its dynamic stack, it just drops values off the stack on overflow like other fixed-sized stacks do.^[51] However, like RPL, it does not emulate the behaviour of a classical operational RPN stack to duplicate the top register on drops.

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 HP 15C Collector's Edition, and the Prime remain active models supporting RPN.

Sinclair Radionics

In Britain, Clive Sinclair's Sinclair Scientific (1974) and Scientific Programmable (1975) models used reverse Polish notation.^[54][55]

Commodore

In 1974, Commodore produced the Minuteman *6 (MM6) without an Enter ↑ key and the Minuteman *6X (MM6X) with an Enter ↑ key, both implementing a form of two-level RPN. The SR4921 RPN came with a variant of four-level RPN with stack levels named X, Y, Z, and W (rather than T) and an Ent 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.^[56]

Prinztronic

Prinz and Prinztronic were own-brand trade names of the British Dixons photographic and electronic goods stores retail chain, later rebranded as Currys Digital 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.

Among these was the PROGRAM^[57] Programmable Scientific Calculator which featured reverse Polish notation.

Heathkit

The Aircraft Navigation Computer Heathkit OC-1401/OCW-1401 used five-level RPN in 1978.

Soviet Union / Semico

Soviet programmable calculators (MK-52, MK-61, B3-34 and earlier B3-21^[58] models) used reverse Polish notation for both automatic mode and programming. Modern Russian calculators MK-161^[59] and MK-152,^[60] designed and manufactured in Novosibirsk since 2007 and offered by Semico,^[61] are backwards compatible with them. Their extended architecture is also based on reverse Polish notation.

Others

• A seven-level stack had been implemented in the MITS 7400C scientific desktop calculator in 1972^[62][63][64]
• National Semiconductor 4615 and 4640
• Novus 650 Mathbox, 3500 Sliderule, 4510 Mathematician, 4515 Mathematician PRO/RG, 4520 Scientist and 4525 Scientist PR
• Some APF calculators like the Mark 55 (1976)^[65]
• SwissMicros (originally firming as RPN-Calc) calculators including the DM-10CC (2012), DM-11CC (2012), DM-12CC (2012), DM-15CC (2012), DM-16CC (2012), DM10 (2013), DM11 (2013), DM12 (2013), DM15 (2013), DM16 (2013), DM10L Collector's Edition (2020), DM11L (2016), DM12L (2016), DM15L (2015), DM16L (2015), DM41 (2015), DM41L (2015), DM41X (2020), DM42 (2017) and DM32 (2023).
• The Tektronix 7854 Digital Oscilloscope (1980) included calculator functionality implemented using RPN, where operations could be applied to entire waveforms (arrays).Rousseau, Tom; Cox, Bill (August 1980). "Digital Waveform Processing in a High-Performance 7000-Series Oscilloscope" (PDF). TekScope. Vol. 12, no. 3. Beaverton, Oregon, US: Tektronix, Inc. Retrieved 2026-06-07.

Community-developed hardware-based calculators

An eight-level stack was suggested by John A. Ball in 1978.^[5]

The community-developed calculators WP 34S (2011), WP 31S (2014) and WP 34C (2015), which are based on the HP 20b/HP 30b hardware platform, support classical Hewlett-Packard-style reverse Polish notation supporting automatic stack lift behaviour of the Enter ↑ key and top register copies on pops, but switchable between a four- and an eight-level operational stack.

In addition to the optional support for an eight-level stack, the newer SwissMicros DM42-based WP 43S as well as the WP 43C (2019) / C43 (2022) / C47 (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 classical and entry RPN behaviour of the Enter ↑ key, a feature often requested by the community.^[66] They also support a rarely seen significant figures mode, which had already been available as a compile-time option for the WP 34S and WP 31S.^[67][68]

Since 2021, the HP-42S simulator Free42 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.^[69][70]