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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 operators follow their operands, in contrast to prefix or Polish notation (PN), in which operators precede their operands. The notation does not need any parentheses as long as each operator has a fixed number of operands.

Explanation
In reverse Polish notation, the operators follow their operands. For example, to add 3 and 4 together, the expression is rather than . The conventional notation expression becomes in reverse Polish notation: 4 is first subtracted from 3, then 5 is added to it. The concept of a stack, a last-in/first-out construct, is integral to the left-to-right evaluation of RPN. In the example , first the 3 is put onto the stack, then the 4; the 4 is now on top and the 3 below it. The subtraction operator removes the top two items from the stack, performs , and puts the result of −1 onto the stack. Common language in this context refers to items being pushed onto the stack when added and popped or removed from the stack when taken off. The advantage of reverse Polish notation is that it removes the need for order of operations and parentheses that are required by infix notation and can be evaluated linearly, left-to-right. For example, the infix expression becomes in reverse Polish notation. == Practical implications ==
Practical implications
Reverse Polish notation has been compared to how one had to work through problems with a slide rule. 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 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. == Converting from infix notation ==
Converting from infix notation
Edsger W. Dijkstra invented the shunting-yard algorithm to convert infix expressions to postfix expressions (reverse Polish notation), so named because its operation resembles that of a railroad shunting yard. There are other ways of producing postfix expressions from infix expressions. Most operator-precedence parsers can be modified to produce postfix expressions; in particular, once an abstract syntax tree has been constructed, the corresponding postfix expression is given by a simple post-order traversal of that tree. == Implementations ==
Implementations
Hardware calculators 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. Software calculators Software calculators: • Atari CalculatorMac OS X CalculatorUnix system calculator program dcEmacs lisp library package calc • Xorg calculator (xcalc) • F-Correlatives in MultiValue dictionary items • RRDtool, a widely used tabulating and graphing software • , a program for algebraic operations on NetCDF grids, part of Generic Mapping Tools (GMT) suite • Qalculate!, a powerful and versatile cross-platform desktop calculator • WRPN Calculator Programming languages Existing implementations using reverse Polish notation include: • Stack-oriented programming languages such as: • ForthdcSTOICFactorPostScript page description language • BefungeJoyIPTSCRAELotus 1-2-3 and Lotus Symphony formulas • RPL (aka Reverse Polish Language), a programming language for the Commodore PET around 1979/1981 • RPL (aka Reverse Polish Lisp), a programming language for Hewlett-Packard calculators between 1986 and 2015 • RPNL (Reverse Polish Notation Language) • Class libraries • TRURL, a class library for the construction of RPN calculators in Object Pascal == See also ==
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