prefix notation
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A student writes a mathematical expression using prefix notation on a whiteboard.
Definition
Noun: A method of writing mathematical or logical expressions without parentheses, where each operator is placed before its operands. This is a type of Polish notation.
Usage
"Prefix notation" is a technical term used primarily in mathematics, computer science, and logic. It describes a specific, unambiguous way to structure expressions. It eliminates the need for parentheses to indicate the order of operations because the position and sequence of the operators inherently define it.
Examples
- In the expression , the plus operator precedes the operands 3 and 4. This is prefix notation for 3 + 4.
- The more complex infix expression is written as in prefix notation.
- Compilers often parse expressions using a form of prefix notation for internal representation.
Advanced Usage
- In Computing: Prefix notation is fundamental to the operation of stack-based languages and virtual machines (e.g., Forth, PostScript, and the Java Virtual Machine's bytecode for certain operations). It is also the structure of function calls in many programming languages (e.g., can be seen as a prefix notation where is the operator).
- In Linguistics: The term can be used analogously to describe the structure of certain compound words or phrases where a modifying element comes first.
Variants and Related Words
- Polish Notation: This is a synonym for prefix notation, named after the Polish logician Jan Łukasiewicz who invented it.
- Infix Notation: The common notation where the operator is placed operands (e.g., ). This is the contrast to prefix notation.
- Postfix Notation (Reverse Polish Notation): A notation where each operator follows its operands (e.g., ).
Synonyms
- Polish Notation
- Łukasiewicz Notation
Antonyms
- Infix Notation
- Postfix Notation (Reverse Polish Notation) — while related, it is the direct structural opposite in terms of operator placement.
A student writes a mathematical expression using prefix notation on a whiteboard.
Noun
- a parenthesis-free notation for forming mathematical expressions in which each operator precedes its operands