What is "reverse polish notation"

n. (context arithmetic English) an arithmetic notation in which numbers precede the operators to be applied to them.

n. a parenthesis-free notation for forming mathematical expressions in which each operator follows its operands [syn: postfix notation, suffix notation]

Reverse Polish notation (RPN) is a mathematical notation in which every operator follows all of its operands, in contrast to Polish notation (PN), which puts the operator before its operands. It is also known as postfix notation and does not need any parentheses as long as each operator has a fixed number of operands. The description "Polish" refers to the nationality of logician Jan Łukasiewicz, who invented (prefix) Polish notation in the 1920s.

The reverse Polish scheme was proposed in 1954 by Burks, Warren, and Wright and was independently reinvented by F. L. Bauer and E. W. Dijkstra in the early 1960s to reduce computer memory access and utilize the stack to evaluate expressions. The algorithms and notation for this scheme were extended by Australian philosopher and computer scientist Charles Hamblin in the mid-1950s.

During the 1970s and 1980s, RPN was well-known to many calculator users, as Hewlett-Packard used it in their pioneering 9100A and HP-35 scientific calculators, the succeeding Voyager series - and also the "cult" HP-12C financial calculator.

In computer science, postfix notation is often used in stack-based and concatenative programming languages. It is also common in dataflow and pipeline-based systems, including Unix pipelines.

Most of what follows is about binary operators. An example of a unary operator whose standard notation uses postfix is the factorial.