Reverse Polish notation

Reverse Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation or simply postfix notation, is a mathematical notation in which <a href="/facts/Operation_(mathematics)/Yplv602Q">operators</a> follow their <a href="/facts/Operand/HSuUzrKz">operands</a>, in contrast to <a href="/facts/Prefix_notation/dUzpf2Ys">prefix</a> or <a href="/facts/Polish_notation/dUzpf2Ys">Polish notation</a> (PN), in which operators precede their operands. The notation does not need any parentheses for as long as each operator has a fixed <a href="/facts/Arity/zSVuwHvP">number of operands</a>.
The term postfix notation describes the general scheme in mathematics and computer sciences, whereas the term reverse Polish notation typically refers specifically to the method used to enter calculations into hardware or software calculators, which often have additional <a href="/facts/Side_effect_(computer_science)/AU3GlLzG">side effects</a> and implications depending on the actual implementation involving a <a href="/facts/Stack_(data_structure)/bj7l94v1">stack</a>. The description "Polish" refers to the <a href="/facts/Nationality/pK1x6rjn">nationality</a> of <a href="/facts/Logician/8JnpJLtt">logician</a> <a href="/facts/Jan_%25C5%2581ukasiewicz/1rlu9ej8">Jan Łukasiewicz</a>, who invented Polish notation in 1924.
The first computer to use postfix notation, though it long remained essentially unknown outside of Germany, was <a href="/facts/Konrad_Zuse/yrvbaEg3">Konrad Zuse</a>'s <a href="/facts/Z3_(computer)/JNPXGqDp">Z3</a> in 1941 as well as his <a href="/facts/Z4_(computer)/RNjK5G7f">Z4</a> in 1945. The reverse Polish scheme was again proposed in 1954 by <a href="/facts/Arthur_Burks/EeqQrm7d">Arthur Burks</a>, Don Warren, and Jesse Wright and was independently reinvented by <a href="/facts/Friedrich_L._Bauer/JlesFToV">Friedrich L. Bauer</a> and <a href="/facts/Edsger_W._Dijkstra/910x0MjT">Edsger W. Dijkstra</a> in the early 1960s to reduce <a href="/facts/Computer_memory/hQKVQ51J">computer memory</a> access and use the <a href="/facts/Stack_(data_structure)/bj7l94v1">stack</a> to evaluate <a href="/facts/Expression_(mathematics)/MPrMlYbE">expressions</a>. The <a href="/facts/Algorithm/fnl5NmRt">algorithms</a> and notation for this scheme were extended by the philosopher and computer scientist <a href="/facts/Charles_Leonard_Hamblin/IntQjLF7">Charles L. Hamblin</a> in the mid-1950s.[excessive citations]
During the 1970s and 1980s, <a href="/facts/Hewlett-Packard/abuNSYNu">Hewlett-Packard</a> used RPN in all of their desktop and hand-held calculators, and has continued to use it in some models into the 2020s. In <a href="/facts/Computer_science/lN3pEyPz">computer science</a>, reverse Polish notation is used in <a href="/facts/Stack-oriented_programming_languages/RFhFMhuj">stack-oriented programming languages</a> such as <a href="/facts/Forth_(programming_language)/mYtWVNhF">Forth</a>, <a href="/facts/Dc_(programming_language)/bzeN0TwH">dc</a>, <a href="/facts/Factor_(programming_language)/oSKmJ26c">Factor</a>, <a href="/facts/STOIC/Qc7yNl8Y">STOIC</a>, <a href="/facts/PostScript/4EeEtnLv">PostScript</a>, <a href="/facts/RPL_(programming_language)/JqMsmMWp">RPL</a>, and <a href="/facts/Joy_(programming_language)/R6s5dz7V">Joy</a>.

Reverse Polish notation open-in-new

Reverse Polish notation