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Video: Keys pressed for calculating eight times six on a HP-32SII (employing RPN) from 1991. 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.
In computer science, the shunting yard algorithm is a method for parsing arithmetical or logical expressions, or a combination of both, specified in infix notation.It can produce either a postfix notation string, also known as reverse Polish notation (RPN), or an abstract syntax tree (AST). [1]
For example, postfix notation would be written 2, 3, multiply instead of multiply, 2, 3 (prefix or Polish notation), or 2 multiply 3 (infix notation). The programming languages Forth, Factor, RPL, PostScript, BibTeX style design language [2] and many assembly languages fit this paradigm.
Polish notation (PN), also known as normal Polish notation (NPN), [1] Łukasiewicz notation, Warsaw notation, Polish prefix notation or simply prefix notation, is a mathematical notation in which operators precede their operands, in contrast to the more common infix notation, in which operators are placed between operands, as well as reverse Polish notation (RPN), in which operators follow ...
The instruction set carries out most ALU actions with postfix (reverse Polish notation) operations that work only on the expression stack, not on data registers or main memory cells. This can be very convenient for executing high-level languages because most arithmetic expressions can be easily translated into postfix notation.
The instruction set carries out most ALU actions with postfix (reverse Polish notation) operations that work only on the expression stack, not on data registers or arbitrary main memory cells. This can be very convenient for compiling high-level languages, because most arithmetic expressions can be easily translated into postfix notation. [8]
A binary expression tree is a specific kind of a binary tree used to represent expressions.Two common types of expressions that a binary expression tree can represent are algebraic [1] and boolean.
Postfix notation makes the language easier to parse and extend; Forth's flexibility makes a static BNF grammar inappropriate, and it does not have a monolithic compiler. Extending the compiler only requires writing a new word, instead of modifying a grammar and changing the underlying implementation.