Reverse Polish Notation

E232845

expression notation mathematical notation postfix notation

Reverse Polish Notation is a mathematical expression format that places operators after their operands, eliminating the need for parentheses and simplifying stack-based computation.

Try in SPARQL Jump to: Surface forms Disambiguation Statements Elicitation Referenced by

All labels observed (2)

Label	Occurrences
Reverse Polish Notation canonical	2
Reverse Polish notation	2

How this entity was disambiguated

This entity first appeared as the object of triple T2074845 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Reverse Polish Notation
Context triple: [HP calculators, notableFor, Reverse Polish Notation]

A. shunting-yard algorithm
The shunting-yard algorithm is a method for parsing mathematical expressions and converting infix notation to postfix (or prefix) form using a stack-based procedure.
B. Knuth’s up-arrow notation
Knuth’s up-arrow notation is a mathematical notation introduced by Donald Knuth to concisely represent very large integers using iterated exponentiation and its higher-order generalizations.
C. Peano notation
Peano notation is a formal symbolic system for representing natural numbers and arithmetic operations using axioms and successor functions, developed by Giuseppe Peano.
D. Mathematike Syntaxis
Mathematike Syntaxis, better known by its later Arabic-derived title Almagest, is Ptolemy’s foundational astronomical treatise that systematically presents the geocentric model of the cosmos and dominated Western and Islamic astronomy for over a millennium.
E. Backus–Naur Form
Backus–Naur Form is a formal notation used to define the syntax of programming languages and other formal grammars in a precise, structured way.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Reverse Polish Notation
Target entity description: Reverse Polish Notation is a mathematical expression format that places operators after their operands, eliminating the need for parentheses and simplifying stack-based computation.

A. shunting-yard algorithm
The shunting-yard algorithm is a method for parsing mathematical expressions and converting infix notation to postfix (or prefix) form using a stack-based procedure.
B. Knuth’s up-arrow notation
Knuth’s up-arrow notation is a mathematical notation introduced by Donald Knuth to concisely represent very large integers using iterated exponentiation and its higher-order generalizations.
C. Peano notation
Peano notation is a formal symbolic system for representing natural numbers and arithmetic operations using axioms and successor functions, developed by Giuseppe Peano.
D. Mathematike Syntaxis
Mathematike Syntaxis, better known by its later Arabic-derived title Almagest, is Ptolemy’s foundational astronomical treatise that systematically presents the geocentric model of the cosmos and dominated Western and Islamic astronomy for over a millennium.
E. Backus–Naur Form
Backus–Naur Form is a formal notation used to define the syntax of programming languages and other formal grammars in a precise, structured way.
F. None of above. chosen

Statements (47)

Predicate	Object
instanceOf	expression notation ⓘ mathematical notation ⓘ postfix notation ⓘ
avoids	associativity rules in parsing ⓘ operator precedence rules in parsing ⓘ
canBeConvertedFrom	infix notation ⓘ
canBeConvertedTo	infix notation ⓘ
eliminatesNeedFor	parentheses in many expressions ⓘ
hasAbbreviation	RPN ⓘ
hasAlternativeName	Polish postfix notation ⓘ postfix notation ⓘ
hasKeyProperty	evaluation can proceed left to right using a stack ⓘ every valid expression is unambiguous ⓘ order of operations is encoded by position rather than precedence rules ⓘ
hasTypicalExample	"3 4 +" for the infix expression "3 + 4" ⓘ "3 4 5 * +" for the infix expression "3 + 4 * 5" ⓘ
isAdvantage	enables simple one-pass evaluation ⓘ maps directly to stack machine instructions ⓘ reduces need for parentheses ⓘ
isBasedOn	Polish notation ⓘ
isCommonlyUsedBy	HP calculators ⓘ some scientific calculators ⓘ
isConvertedUsing	shunting-yard algorithm ⓘ
isDefinedAs	a mathematical notation in which every operator follows all of its operands ⓘ
isDisadvantage	can be harder to read for complex expressions ⓘ less familiar to many users than infix notation ⓘ
isEvaluatedNaturallyWith	stack data structure ⓘ
isRelatedTo	Polish notation ⓘ infix notation ⓘ prefix notation ⓘ
isUsedFor	representing arithmetic expressions ⓘ representing logical expressions ⓘ stack-based computation ⓘ
isUsedIn	Forth programming language ⓘ linked to: Forth PostScript language ⓘ linked to: PostScript calculator design ⓘ compiler design ⓘ computer science ⓘ expression evaluation algorithms ⓘ stack-based virtual machines ⓘ
simplifies	expression parsing ⓘ implementation of expression evaluators ⓘ
supports	left-associative operators without parentheses ⓘ right-associative operators without parentheses ⓘ
usesOperatorPosition	after operands ⓘ
wasIntroducedBy	Charles L. Hamblin NERFINISHED ⓘ
wasIntroducedInYear	1957 ⓘ

How these facts were elicited

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

HP calculators → notableFor → Reverse Polish Notation ⓘ

HP calculators → hasInputMethod → Reverse Polish Notation ⓘ

shunting-yard algorithm → produces → Reverse Polish notation ⓘ

linked to: Reverse Polish Notation

shunting-yard algorithm → relatedTo → Reverse Polish notation ⓘ