109.166.138.251: associated to, not special case

2025-03-13T13:52:07Z

associated to, not special case

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{{Short description|Expression in a computer program}}
In [[computer science]], a '''Boolean expression''' (also known as '''logical expression''') is an [[Expression (programming)|expression]] used in [[programming language]]s that produces a [[Boolean value]] when evaluated. A Boolean value is either '''true''' or '''false'''. A Boolean expression may be composed of a combination of the Boolean constants '''True/False''' or '''Yes/No''', [[Boolean data type|Boolean-typed]] variables, Boolean-valued operators, and [[Boolean-valued function]]s.<ref>{{citation
| last1 = Gries | first1 = David | author1-link = David Gries
| last2 = Schneider | first2 = Fred B. | author2-link = Fred B. Schneider
| contribution = Chapter 2. Boolean Expressions
| isbn = 9780387941158
| page = 25ff
| publisher = Springer
| series = Monographs in Computer Science
| title = A Logical Approach to Discrete Math
| url = https://books.google.com/books?id=ZWTDQ6H6gsUC&pg=PA25
| year = 1993}}.</ref>

Boolean expressions correspond to [[propositional formula]]s in logic and are associated to [[Boolean circuit]]s.<ref>{{citation
| last = van Melkebeek | first = Dieter
| isbn = 9783540414926
| page = 22
| publisher = Springer
| series = [[Lecture Notes in Computer Science]]
| title = Randomness and Completeness in Computational Complexity
| url = https://books.google.com/books?id=-S0zCjOAIVwC&pg=PA22
| volume = 1950
| year = 2000}}.</ref>

==Boolean operators==
Most [[programming language]]s have the Boolean operators [[Logical disjunction|OR]], [[Logical conjunction|AND]] and [[Negation|NOT]]; in [[C (programming language)|C]] and some [[List of C-family programming languages|languages inspired by it]], these are represented by "||" (double pipe character), "&&" (double [[ampersand]]) and "!" ([[Exclamation mark|exclamation point]]) respectively, while the corresponding [[bitwise operation]]s are represented by "|", "&" and "~" (tilde).<ref>E.g. for [[Java (programming language)|Java]] see {{citation
| last1 = Brogden | first1 = William B.
| last2 = Green | first2 = Marcus
| isbn = 9780789728616
| page = 45
| publisher = Que Publishing
| title = Java 2 Programmer
| url = https://books.google.com/books?id=24nPZw9Wsf4C&pg=PA45
| year = 2003}}.</ref> In the mathematical literature the symbols used are often "+" ([[Plus sign|plus]]), "'''·'''" ([[Full stop|dot]]) and [[overbar]], or "∨" ([[Descending_wedge|vel]]), "∧" ([[Wedge_(symbol)|et]]) and "¬" ([[Negation|not]]) or "′" (prime).

Some languages, e.g., [[Perl]] and [[Ruby (programming language)|Ruby]], have two sets of Boolean operators, with identical functions but different precedence. Typically these languages use '''and''', '''or''' and '''not''' for the lower precedence operators.

Some programming languages derived from [[PL/I]] have a bit string type and use BIT(1) rather than a separate Boolean type. In those languages the same operators serve for Boolean operations and bitwise operations. The languages represent OR, AND, NOT and EXCLUSIVE OR by "|", "&", "¬" (infix) and "¬" (prefix).

===Short-circuit operators===
{{Main|Short-circuit evaluation}}
Some programming languages, e.g., [[Ada (programming language)|Ada]], have [[Short-circuit evaluation|short-circuit]] Boolean operators. These operators use a [[lazy evaluation]], that is, if the value of the expression can be determined from the left hand Boolean expression then they do not evaluate the right hand Boolean expression. As a result, there may be [[Side effect (computer science)|side effects]] that only occur for one value of the left hand operand.

==Examples==

*The expression {{code|5 > 3}} is evaluated as {{samp|true}}.
*The expression {{code|3 > 5}} is evaluated as {{samp|false}}.
*{{code|1=5>=3}} and {{code|1=3<=5}} are equivalent Boolean expressions, both of which are evaluated as {{samp|true}}.
*Of course, most Boolean expressions will contain at least one variable ({{code|X > 3}}), and often more ({{code|X > Y}}).

==See also==
*[[Expression (computer science)]]
*[[Expression (mathematics)]]
*[[Boolean function]]

==References==
{{reflist}}

==External links==
*[http://www.maths.tcd.ie/pub/HistMath/People/Boole/CalcLogic/CalcLogic.html The Calculus of Logic], by George Boole, Cambridge and Dublin Mathematical Journal Vol. III (1848), pp. 183–98.

{{DEFAULTSORT:Boolean Expression}}
[[Category:Boolean algebra]]
[[Category:Operators (programming)]]

Boolean expression - Revision history

109.166.138.251: associated to, not special case