RPN 3D Touch [iPhone]

A calculator using rpn (reverse polish notation)

Wikipedia:

[https://en.wikipedia.org/wiki/Reverse_Polish_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 in the prefix position. It is also known as postfix notation and is parenthesis-free as long as operator arities are fixed. The description "Polish" refers to the nationality of logician Jan Łukasiewicz,[1] who invented (prefix) Polish notation in the 1920s.[2][3]

The reverse Polish scheme was proposed in 1954 by Burks, Warren, and Wright[4] 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.[5][6]

During the 1970s and 1980s, RPN was well-known to many calculator users, as Hewlett-Packard used it in their pioneering 9100A[7] and HP-35 scientific calculators, the succeeding Voyager series - and also the "cult" HP-12C financial calculator.[8]

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. A unary operator for which the reverse Polish notation is the general convention is the factorial.