Boolean expression: Difference between revisions

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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 a [[programming language]]s that produces a [[Boolean value]] when evaluated, i.e. oneA ofBoolean value is either '''true''' or '''false'''. A Boolean expression may be composed of a combination of the Boolean constants '''trueTrue/False''' or '''falseYes/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

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| series = Monographs in Computer Science

| title = A Logical Approach to Discrete Math

| url = httphttps://books.google.com/books?id=ZWTDQ6H6gsUC&pg=PA25

| year = 1993}}.</ref>

Boolean expressions correspond to [[propositional formula]]s in logic and are aassociated special case ofto [[Boolean circuit]]s.<ref>{{citation

| last = van Melkebeek | first = Dieter

| isbn = 9783540414926

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| series = [[Lecture Notes in Computer Science]]

| title = Randomness and Completeness in Computational Complexity

| url = httphttps://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''NOT]]; in [[C (programming language)|C]] and some newer[[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

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| publisher = Que Publishing

| title = Java 2 Programmer

| url = httphttps://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 "∨" (cup[[Descending_wedge|vel]]), "∧" (cap[[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.

==Examples==

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).

*The expression "5 > 3" is evaluated as '''true'''.

===Short-circuit operators===

*"5>=3" and "3<=5" are equivalent Boolean expressions, both of which are evaluated as '''true'''.

{{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'''}}.

*Of course, most Boolean expressions will contain at least one variable (X > 3), and often more (X > Y).

*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 (programmingcomputer 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.&nbsp;183–98.