Polish notation

Polish notation, also known as prefix notation, is a method of mathematical expression. It was created by Jan ?ukasiewicz, mostly to simplify certain mathematical proofs. Its distinguishing feature is that it places operators before operands.

Related Topics:
Jan ?ukasiewicz - Operator - Operand

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For example, this expression:

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+ 1 2

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evaluates to 3.

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Polish notation is not limited to only two values, nor to just addition. For example, this expression:

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(× (+ 0 1) (+ 2 3))

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evaluates to 5.

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While the examples above use parentheses, one of the benefits of Polish notation is that, assuming the arity of each operator is known, parentheses are unnecessary: the order of operations is unique and easy to determine, provided that the expression is well-formed. For example, assuming × and + are binary, then this expression:

Related Topics:
Arity - Order of operations

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× + 0 1 + 2 3

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can mean only this:

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(× (+ 0 1) (+ 2 3))

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Polish notation is used in some computer programming languages, including Lisp and its dialect Scheme. It is also used in Tcl.

Related Topics:
Computer programming language - Lisp - Scheme - Tcl

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