computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...

, a Boolean expression is an

expression Expression may refer to: Linguistics * Expression (linguistics), a word, phrase, or sentence * Fixed expression, a form of words with a specific meaning * Idiom, a type of fixed expression * Metaphorical expression, a particular word, phrase, o ...

used in

programming language A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language. The description of a programming ...

s that produces a

Boolean value In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in ...

when evaluated. A Boolean value is either true or false. A Boolean expression may be composed of a combination of the Boolean constants true or false, Boolean-typed variables, Boolean-valued operators, and

Boolean-valued function A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B = ), whose elements are in ...

s. Boolean expressions correspond to

propositional formula In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional fo ...

s in logic and are a

special case In logic, especially as applied in mathematics, concept is a special case or specialization of concept precisely if every instance of is also an instance of but not vice versa, or equivalently, if is a generalization of . A limiting case is ...

Boolean circuit In computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal language can be decided by a family of Boolean circuits, one circuit for each possible input ...

Boolean operators

Most

s have the Boolean operators OR,

AND or AND may refer to: Logic, grammar, and computing * Conjunction (grammar), connecting two words, phrases, or clauses * Logical conjunction in mathematical logic, notated as "∧", "⋅", "&", or simple juxtaposition * Bitwise AND, a boole ...

and NOT; in C and some languages inspired by it, these are represented by ", , " (double pipe character), "&&" (double

ampersand The ampersand, also known as the and sign, is the logogram , representing the conjunction "and". It originated as a ligature of the letters ''et''—Latin for "and". Etymology Traditionally in English, when spelling aloud, any letter that ...

) and "!" (

exclamation point The exclamation mark, , or exclamation point (American English), is a punctuation mark usually used after an interjection or exclamation to indicate strong feelings or to show emphasis. The exclamation mark often marks the end of a sentence, f ...

) respectively, while the corresponding

bitwise operation In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. It is a fast and simple action, basic to the higher-level arithmetic operati ...

s are represented by ", ", "&" and "~" (tilde).E.g. for

Java Java (; id, Jawa, ; jv, ꦗꦮ; su, ) is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea to the north. With a population of 151.6 million people, Java is the world's List ...

see . In the mathematical literature the symbols used are often "+" (

plus Plus may refer to: Mathematics * Addition * +, the mathematical sign Music * ''+'' (Ed Sheeran album), (pronounced "plus"), 2011 * ''Plus'' (Cannonball Adderley Quintet album), 1961 * ''Plus'' (Matt Nathanson EP), 2003 * ''Plus'' (Martin Ga ...

), "·" ( dot) and

overbar An overline, overscore, or overbar, is a typographical feature of a horizontal line drawn immediately above the text. In old mathematical notation, an overline was called a '' vinculum'', a notation for grouping symbols which is expressed in m ...

, or "∨" (

vel Vel ( ta, வேல், lit=Vēl) is a divine javelin or spear associated with Murugan, the Hindu god of war. Significance According to Shaiva tradition, the goddess Parvati presented the Vel to her son Murugan, as an embodiment of her shakti, ...

), "∧" ( et) and "¬" ( not) or "′" (prime). Some languages, e.g.,

Perl Perl is a family of two high-level, general-purpose, interpreted, dynamic programming languages. "Perl" refers to Perl 5, but from 2000 to 2019 it also referred to its redesigned "sister language", Perl 6, before the latter's name was offici ...

and

Ruby A ruby is a pinkish red to blood-red colored gemstone, a variety of the mineral corundum ( aluminium oxide). Ruby is one of the most popular traditional jewelry gems and is very durable. Other varieties of gem-quality corundum are called sa ...

, 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 PL/I (Programming Language One, pronounced and sometimes written PL/1) is a procedural, imperative computer programming language developed and published by IBM. It is designed for scientific, engineering, business and system programming. 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

Some programming languages, e.g.,

Ada Ada may refer to: Places Africa * Ada Foah, a town in Ghana * Ada (Ghana parliament constituency) * Ada, Osun, a town in Nigeria Asia * Ada, Urmia, a village in West Azerbaijan Province, Iran * Ada, Karaman, a village in Karaman Province, Tur ...

, have

short-circuit A short circuit (sometimes abbreviated to short or s/c) is an electrical circuit that allows a current to travel along an unintended path with no or very low electrical impedance. This results in an excessive current flowing through the circuit. ...

Boolean operators. These operators use a

lazy evaluation In programming language theory, lazy evaluation, or call-by-need, is an evaluation strategy which delays the evaluation of an expression until its value is needed (non-strict evaluation) and which also avoids repeated evaluations (sharing). The b ...

, 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 effects In medicine, a side effect is an effect, whether therapeutic or adverse, that is secondary to the one intended; although the term is predominantly employed to describe adverse effects, it can also apply to beneficial, but unintended, consequence ...

that only occur for one value of the left hand operand.

Examples

*The expression is evaluated as . *The expression is evaluated as . * and are equivalent Boolean expressions, both of which are evaluated as . *

typeof 
typeof, alternately also typeOf, and TypeOf, is an  operator provided by several programming languages to determine the data type of a variable. This is useful when constructing programs that must accept multiple types of data without explicitly sp ...
 true

and typeof false return *Of course, most Boolean expressions will contain at least one variable (), and often more ().

References

External links

The Calculus of Logic
by George Boole, Cambridge and Dublin Mathematical Journal Vol. III (1848), pp. 183–98. {{DEFAULTSORT:Boolean Expression Boolean algebra Operators (programming)

Boolean operators

Short-circuit operators

Examples

See also

References

External links