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, 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.
Polish notation
Polish notation (PN), also known as normal Polish notation (NPN),Łukasiewicz notation, Warsaw notation, Polish prefix notation or simply prefix notation, is a form of notation for logic, arithmetic, and algebra. Its distinguishing feature is that it places operators to the left of their operands. If the arity of the operators is fixed, the result is a syntax lacking parentheses or other brackets that can still be parsed without ambiguity. The Polish logician Jan Łukasiewicz invented this notation in 1924 in order to simplify sentential logic.
The term Polish notation is sometimes taken (as the opposite of infix notation) to also include Polish postfix notation, or reverse Polish notation (RPN), in which the operator is placed after the operands.
When Polish notation is used as a syntax for mathematical expressions by programming language interpreters, it is readily parsed into abstract syntax trees and can, in fact, define a one-to-one representation for the same. Because of this, Lisp (see below) and related programming languages define their entire syntax in terms of prefix notation (and others use postfix notation).
Forth (programming language)
Forth is an imperative stack-based computer programming language and environment originally designed by Charles "Chuck" Moore. Language features include structured programming, reflection (the ability to modify the program structure during program execution), concatenative programming (functions are composed with juxtaposition) and extensibility (the programmer can create new commands). Although not an acronym, the language's name is sometimes spelled with all capital letters as FORTH, following the customary usage during its earlier years.
A procedural programming language without type checking, Forth features both interactive execution of commands (making it suitable as a shell for systems that lack a more formal operating system) and the ability to compile sequences of commands for later execution. Some Forth implementations (usually early versions or those written to be extremely portable) compile threaded code, but many implementations today generate optimized machine code like other language compilers.
