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In
computer programming Computer programming is the process of performing a particular computation (or more generally, accomplishing a specific computing result), usually by designing and building an executable computer program. Programming involves tasks such as anal ...
, operators are constructs defined within
programming languages 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 ...
which behave generally like functions, but which differ
syntactically In linguistics, syntax () is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure (constituency) ...
or semantically. Common simple examples include arithmetic (e.g. addition with ), comparison (e.g. " greater than" with >), and logical operations (e.g. AND, also written && in some languages). More involved examples include assignment (usually = or :=), field access in a record or
object Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Object (abstract), an object which does not exist at any particular time or place ** Physical object, an identifiable collection of matter * Goal, an ...
(usually .), and the scope resolution operator (often :: or .). Languages usually define a set of built-in operators, and in some cases allow users to add new meanings to existing operators or even define completely new operators.


Syntax

Syntactically In linguistics, syntax () is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure (constituency) ...
operators usually contrast to functions. In most languages, functions may be seen as a special form of prefix operator with fixed
precedence Precedence may refer to: * Message precedence of military communications traffic * Order of precedence, the ceremonial hierarchy within a nation or state * Order of operations, in mathematics and computer programming * Precedence Entertainment, ...
level and associativity, often with compulsory parentheses e.g. Func(a) (or (Func a) in
Lisp A lisp is a speech impairment in which a person misarticulates sibilants (, , , , , , , ). These misarticulations often result in unclear speech. Types * A frontal lisp occurs when the tongue is placed anterior to the target. Interdental lispin ...
). Most languages support programmer-defined functions, but cannot really claim to support programmer-defined operators, unless they have more than prefix notation and more than a single precedence level. Semantically operators can be seen as special form of function with different calling notation and a limited number of parameters (usually 1 or 2). The position of the operator with respect to its operands may be
prefix A prefix is an affix which is placed before the stem of a word. Adding it to the beginning of one word changes it into another word. For example, when the prefix ''un-'' is added to the word ''happy'', it creates the word ''unhappy''. Particul ...
,
infix An infix is an affix inserted inside a word stem (an existing word or the core of a family of words). It contrasts with '' adfix,'' a rare term for an affix attached to the outside of a stem, such as a prefix or suffix. When marking text for i ...
or postfix, and the syntax of an expression involving an operator depends on its
arity Arity () is the number of arguments or operands taken by a function, operation or relation in logic, mathematics, and computer science. In mathematics, arity may also be named ''rank'', but this word can have many other meanings in mathematics. ...
(number of
operand In mathematics, an operand is the object of a mathematical operation, i.e., it is the object or quantity that is operated on. Example The following arithmetic expression shows an example of operators and operands: :3 + 6 = 9 In the above exam ...
s), precedence, and (if applicable),
associativity In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement ...
. Most programming languages support
binary operators In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two. More specifically, an internal binary op ...
and a few unary operators, with a few supporting more operands, such as the ?: operator in C, which is ternary. There are prefix unary operators, such as unary minus -x, and postfix unary operators, such as post-increment x++; and binary operations are infix, such as x + y or x = y. Infix operations of higher arity require additional symbols, such as the ternary operator ?: in C, written as a ? b : c – indeed, since this is the only common example, it is often referred to as ''the'' ternary operator. Prefix and postfix operations can support any desired arity, however, such as 1 2 3 4 +. Occasionally parts of a language may be described as "matchfix" or "circumfix" operators, either to simplify the language's description or implementation. A circumfix operator consists of two or more parts which enclose its operands. Circumfix operators have the highest precedence, with their contents being evaluated and the resulting value used in the surrounding expression. The most familiar circumfix operator are the parentheses mentioned above, used to indicate which parts of an expression are to be evaluated before others. Another example from physics is the
inner product In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a scalar, often ...
notation of Dirac's
bra–ket notation In quantum mechanics, bra–ket notation, or Dirac notation, is used ubiquitously to denote quantum states. The notation uses angle brackets, and , and a vertical bar , to construct "bras" and "kets". A ket is of the form , v \rangle. Mathem ...
. Circumfix operators are especially useful to denote operations that involve many or varying numbers of operands. The specification of a language will specify the syntax the operators it supports, while languages such as Prolog that support programmer-defined operators require that the syntax be defined by the programmer.


Semantics

The semantics of operators particularly depends on value, evaluation strategy, and argument passing mode (such as boolean short-circuiting). Simply, an expression involving an operator is evaluated in some way, and the resulting
value Value or values may refer to: Ethics and social * Value (ethics) wherein said concept may be construed as treating actions themselves as abstract objects, associating value to them ** Values (Western philosophy) expands the notion of value beyo ...
may be just a value (an r-value), or may be an object allowing assignment (an l-value). In simple cases this is identical to usual function calls; for example, addition x + y is generally equivalent to a function call add(x, y) and less-than comparison x < y to lt(x, y), meaning that the arguments are evaluated in their usual way, then some function is evaluated and the result is returned as a value. However, the semantics can be significantly different. For example, in assignment a = b the target a is not evaluated, but instead its ''location'' (address) is used to store the value of b – corresponding to
call-by-reference In a programming language, an evaluation strategy is a set of rules for evaluating expressions. The term is often used to refer to the more specific notion of a ''parameter-passing strategy'' that defines the kind of value that is passed to the f ...
semantics. Further, an assignment may be a statement (no value), or may be an expression (value), with the value itself either an r-value (just a value) or an l-value (able to be assigned to). As another example, the scope resolution operator :: and the element access operator . (as in Foo::Bar or a.b) operate not on values, but on ''names'', essentially
call-by-name In a programming language, an evaluation strategy is a set of rules for evaluating expressions. The term is often used to refer to the more specific notion of a ''parameter-passing strategy'' that defines the kind of value that is passed to the f ...
semantics, and their value is a name. Use of l-values as operator operands is particularly notable in unary
increment and decrement operators Increment and decrement operators are unary operators that ''add'' or ''subtract'' one, to or from their operand, respectively. They are commonly implemented in imperative programming languages. C-like languages feature two versions (pre- an ...
. In C, for instance, the following statement is legal and well-defined, and depends on the fact that array indexing returns an l-value: x = ++a An important use is when a left-associative binary operator modifies its left argument (or produces a side effect) and then evaluates to that argument as an l-value. This allows a sequence of operators all affecting the original argument, allowing a fluent interface, similar to
method cascading In object-oriented programming, method cascading is syntax which allows multiple methods to be called on the same object. This is particularly applied in fluent interfaces. For example, in Dart, the cascade: a..b() ..c(); is equivalent to the i ...
. A common example is the << operator in the C++ iostream library, which allows fluent output, as follows: cout << "Hello" << " " << "world!" << endl;


User-defined operators

A language may contain a fixed number of built-in operators (e.g. , etc. in C and C++, PHP), or it may allow the creation of programmer-defined operators (e.g. Prolog,
Seed7 Seed7 is an extensible general-purpose programming language designed by Thomas Mertes. It is syntactically similar to Pascal and Ada. Along with many other features, it provides an extension mechanism. Daniel Zingaro"Modern Extensible Languages" ...
, F#,
OCaml OCaml ( , formerly Objective Caml) is a general-purpose, multi-paradigm programming language Programming paradigms are a way to classify programming languages based on their features. Languages can be classified into multiple paradigms. ...
, Haskell). Some programming languages restrict operator symbols to special characters like or while others allow also names like div (e.g.
Pascal Pascal, Pascal's or PASCAL may refer to: People and fictional characters * Pascal (given name), including a list of people with the name * Pascal (surname), including a list of people and fictional characters with the name ** Blaise Pascal, Frenc ...
). Most languages have a built-in set of operators, but do not allow user-defined operators, as this significantly complicates parsing. Many languages only allow operators to be used for built-in types, but others allow existing operators to be used for user-defined types; this is known as operator overloading. Some languages allow new operators to be defined, however, either at compile time or at run time. This may involve meta-programming (specifying the operators in a separate language), or within the language itself. Definition of new operators, particularly runtime definition, often makes correct static analysis of programs impossible, since the syntax of the language may be Turing-complete, so even constructing the syntax tree may require solving the halting problem, which is impossible. This occurs for
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 offic ...
, for example, and some dialects of
Lisp A lisp is a speech impairment in which a person misarticulates sibilants (, , , , , , , ). These misarticulations often result in unclear speech. Types * A frontal lisp occurs when the tongue is placed anterior to the target. Interdental lispin ...
.


Examples

Common examples that differ syntactically are mathematical arithmetic operations, e.g. ">" for " greater than", with names often outside the language's set of identifiers for functions, and called with a syntax different from the language's syntax for calling functions. As a function, "greater than" would generally be named by an identifier, such as gt or greater_than and called as a function, as gt(x, y). Instead, the operation uses the special character > (which is tokenized separately during lexical analysis), and infix notation, as x > y. Common examples that differ semantically (by argument passing mode) are boolean operations, which frequently feature short-circuit evaluation: e.g. a short-circuiting conjunction (X AND Y) that only evaluates later arguments if earlier ones are not false, in a language with strict call-by-value functions. This behaves instead similarly to if/then/else. Less common operators include: * Comma operator: e, f * Dereference operator: *p and address-of operator: &x * ?: or ternary operator: number = spell_out_numbers ? "forty-two" : 42 **
Elvis operator In certain computer programming languages, the Elvis operator, often written ?:, is a binary operator that returns its first operand if that operand evaluates to a true value, and otherwise evaluates and returns its second operand. This is identic ...
: x ?: y *
Null coalescing operator The null coalescing operator (called the Logical Defined-Or operator in Perl) is a binary operator that is part of the syntax for a basic conditional expression in several programming languages, including C#, PowerShell as of version 7.0.0, Perl ...
: x ?? y * Spaceship operator (for three-way comparison): x <=> y


Compilation

A compiler can implement operators and functions with subroutine calls or with inline code. Some built-in operators supported by a language have a direct mapping to a small number of instructions commonly found on
central processing units A central processing unit (CPU), also called a central processor, main processor or just processor, is the electronic circuitry that executes instructions comprising a computer program. The CPU performs basic arithmetic, logic, controlling, an ...
, though others (''e.g.'' '+' used to express string concatenation) may have complicated implementations.


Operator overloading

In some programming languages an operator may be ''ad hoc polymorphic'', that is, have definitions for more than one kind of data, (such as in
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 mo ...
where the operator is used both for the addition of numbers and for the concatenation of strings). Such an operator is said to be ''overloaded''. In languages that support operator overloading by the programmer (such as C++) but have a limited set of operators, operator overloading is often used to define customized uses for operators. In the example IF ORDER_DATE > "12/31/2011" AND ORDER_DATE < "01/01/2013" THEN CONTINUE ELSE STOP, the operators are: ">" (greater than), "AND" and "<" (less than).


Operand coercion

Some languages also allow for the operands of an operator to be implicitly converted, or '' coerced'', to suitable data types for the operation to occur. For example, in
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 offic ...
coercion rules lead into 12 + "3.14" producing the result of 15.14. The text "3.14" is converted to the number 3.14 before addition can take place. Further, 12 is an integer and 3.14 is either a floating or fixed-point number (a number that has a decimal place in it) so the integer is then converted to a floating point or fixed-point number respectively.
JavaScript JavaScript (), often abbreviated as JS, is a programming language that is one of the core technologies of the World Wide Web, alongside HTML and CSS. As of 2022, 98% of websites use JavaScript on the client side for webpage behavior, of ...
follows opposite rules—finding the same expression above, it will convert the integer 12 into a string "12", then concatenate the two operands to form "123.14". In the presence of coercions in a language, the programmer must be aware of the specific rules regarding operand types and the operation result type to avoid subtle programming mistakes.


Operator features in programming languages

The following table shows the operator features in several programming languages:


See also

* Relational operator


Notes


References

{{reflist Programming constructs