Operator (computer programming)

Short description: Construct associated with a mathematical operation in computer programs

In computer programming, operators are constructs defined within programming languages which behave generally like functions, but which differ syntactically 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 (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.

## Contents

* 1 Syntax
* 2 Semantics
* 3 User-defined operators
* 4 Examples
* 5 Compilation
* 6 Operator overloading
* 7 Operand coercion
* 8 Operator features in programming languages
* 9 See also
* 10 Notes
* 11 References

## Syntax

Syntactically operators usually contrast to functions. In most languages, functions may be seen as a special form of prefix operator with fixed precedence level and associativity, often with compulsory parentheses e.g. `Func(a)` (or `(Func a)` in Lisp). 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, infix or postfix, and the syntax of an expression involving an operator depends on its arity (number of operands), precedence, and (if applicable), associativity. Most programming languages support binary operators 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[1][2] parts of a language may be described as "matchfix" or "circumfix"[3][4] 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 notation of Dirac's bra–ket notation. 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 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 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 semantics, and their value is a name.

Use of l-values as operator operands is particularly notable in unary increment and decrement operators. 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[i];

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.[lower-alpha 1] This allows a sequence of operators all affecting the original argument, allowing a fluent interface, similar to method cascading. 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,[5] Seed7,[6] F#, OCaml, Haskell). Some programming languages restrict operator symbols to special characters like + or := while others allow also names like `div` (e.g. Pascal).

Most languages have a built-in set of operators, but do not allow user-defined operators, as this significantly complicates parsing.[lower-alpha 2] 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, for example, and some dialects of Lisp.

## Examples

See also: Category:Operators (programming)

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: `x ?: y`
* Null coalescing operator: `x ?? y`
* Spaceship operator (for three-way comparison): `x <=> y`
* Compound operators combining two or more atomic operations into one to simplify expressions, ease compiler optimizations depending on the underlying hardware implementation, or improve performance for speed or size. An example are the set of compound assignment operators (aka augmented assignments) in C/C++: `+=`, `-=`, `*=`, `/=`, `%=`, `<<=`, `>>=`, `&=`, `^=`, `|=` Similarly, some digital signal processors provide special opcodes for fused operations like multiply-accumulate (MAC/MAD) or fused multiply-add (FMA) and some high-performance software libraries support functions like cis x = cos x \+ i sin x to boost processing speed or reduce code size.

## 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, though others (e.g. '+' used to express string concatenation) may have complicated implementations.

## Operator overloading

Main article: 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 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

Further information: Type conversion

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 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 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:

Programming language  | Nonalphanumeric operator symbols  | Alphanumeric operator symbols  | Prefix  | Infix  | Postfix  | Precedence  | Associativity  | Script error: No such module "Vertical header". | Script error: No such module "Vertical header". | Script error: No such module "Vertical header".

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ALGOL 68 | +* ** * / % %* %× - + < <= >= > = /= & -:= +:= *:= /:= %:= %*:= +=: :=: :/=:

(All operators have bold Alphanumeric equivalents, c.f. next column. Some have non ASCII equivalents, c.f. below.) ¬ +× ⊥ ↑ ↓ ⌊ ⌈ × ÷ ÷× ÷* □ ≤ ≥ ≠ ∧ ∨ ×:= ÷:= ÷×:= ÷*:= %×:= :≠:

| Yes  | Yes  | No  | Yes (prefix operators always have priority 10) | Infix operators are left associative, prefix operators are right associative  | Yes  | Yes  | Yes
APL | \+ - × ÷ ⌈ ⌊ * ⍟ | ! ○ ~ ∨ ∧ ⍱ ⍲ < ≤ = ≥ > ≠ . @ ≡ ≢ ⍴ , ⍪ ⍳ ↑ ↓ ? ⍒ ⍋ ⍉ ⌽ ⊖ ∊ ⊥ ⊤ ⍎ ⍕ ⌹ ⊂ ⊃ ∪ ∩ ⍷ ⌷ ∘ → ← / ⌿ \ ⍀ ¨ ⍣ & ⍨ ⌶ ⊆ ⊣ ⊢ ⍠ ⍤ ⌸ ⌺ ⍸ | Alphanumeric symbols need a ⎕ before the keyword  | Yes (first-order functions only) | Yes  | Yes (higher-order functions only) | Higher-order functions precede first-order functions  | Higher-order functions are left associative, first-order functions are right associative  | Yes  | Yes  | Yes (alphanumeric only)
C | () [] -> . ! ~ ++ -- + - * & / % << >> < <= > >= == != ^ | && || ?: = += -= *= /= %= &= ^= | sizeof | Yes  | Yes  | Yes  | Yes  | Yes  | Yes  | No  | No
C++ (more)  | sizeof typeid new delete throw decltype static cast dynamic cast reinterpret cast const cast | Yes  | Yes  | Yes  | Yes  | Yes  | Yes  | Yes  | No
C# (more)  | Same as C/C++, along with ?. ?[] ?? ??= | sizeof nameof new stackalloc await throw checked unchecked is as delegate default true false
LINQ: from select where group...by group...by...into join...in...on...equals join...in...on...equals...into orderby orderby...descending
Roslyn-only: __makeref __refvalue __reftype | Yes  | Yes  | Yes  | Yes  | Yes  | Yes  | Yes  | No
Java | Same as C/C++  | new throw instanceof  | Yes  | Yes  | Yes  | Yes  | Yes  | Yes  | No  | No
Eiffel | [] + - * / // = /= | not and or implies "and then" "or else" | Yes  | Yes  | No  | Yes  | Yes  | No  | Yes  | Yes
Haskell | \+ - * / ^ ^^ ** == /= > < >= <= && || >>= >> $ $! . ++ !! : Many more in common libraries | The function's name must be put into backticks  | Yes  | Yes  | No  | Yes  | Yes  | Yes, using Type classes | Yes
Pascal | * / + - = < > <> <= >= := | not div mod and or in  | Yes  | Yes  | No  | Yes  | Yes  | Yes  | No  | No
Perl | print sort chmod chdir rand and or not xor lt gt le ge eq ne cmp x | Yes  | Yes  | Yes  | Yes  | Yes  | Yes  | Yes  | No
PHP | [] ** ++ -- ~ @![7] * / % + - . << >> < <= > >= == != === !== <> <=> & ^ | && || ?? ?: = += -= *= **= /= .= %= &= |= ^= <<= >>= | clone new unset print echo isset instanceof and or xor | Yes  | Yes  | Yes  | Yes  | Yes  | No  | No  | No
PL/I  | ( ) -> \+ - * / ** > ¬> >= = ¬= <= < ¬< ¬ & | || |  | Yes  | Yes  | No  | Yes  | Yes  | No  | No  | No
Prolog | :- ?- ; , . =.. = \= < =< >= > == \== - + / * | spy nospy not is mod | Yes  | Yes  | Yes  | Yes  | Yes  | No  | No  | Yes
Raku | ++ -- ** ! ~ ~~ * / + - . < > <= >= == != <=> & | ^ && || // [8] | print sort chmod chdir rand and or not xor lt gt le ge eq ne leg cmp x xx | Yes  | Yes  | Yes  | Yes  | Yes  | Yes  | Yes  | Yes[9]
Seed7 | {} [] -> ** ! + - * / << >> & >< | = <> > >= < <= <& := +:= -:= *:= /:= <<:= >>:= &:= @:= | conv varConv parse conj div rem mdiv mod times mult in not and or digits lpad rpad lpad0 | Yes  | Yes  | Yes  | Yes  | Yes  | Yes  | Yes  | Yes
Smalltalk | (yes - Up to two characters[10])  | Alphanumeric symbols need a colon after the keyword  | No  | Yes  | Yes  | No  | No  | Yes  | Yes  | Yes
Swift | Any Unicode symbol string except ., including ! ~ + - * / % =+ =- =* =/ =% &\+ &\- &* =&\+ =&\- =&* && || << >> & | ^ == != < <= > >= ?? ... ..< in standard library  | is as as? | Yes  | Yes  | Yes  | Yes (defined as partial order in precedence groups) | Yes (defined as part of precedence groups) | Yes  | Yes  | Yes
Visual Basic .NET | () . ! ?() ?. ?! + - * / \ & << >> < <= > >= ^ <> = += -= *= /= \= &= ^= <<= >>= | New Await Mod Like Is IsNot Not And AndAlso Or OrElse Xor If(...,...) If(...,...,...) GetXmlNamespace(...) GetType(...) NameOf(...) TypeOf...Is TypeOf...IsNot DirectCast(...,...) TryCast(...,...) CType(...,...) CBool(...) CByte(...) CChar(...) CDate(...) CDec(...) CDbl(...) CInt(...) CLng(...) CObj(...) CSByte(...) CShort(...) CSng(...) CStr(...) CUInt(...) CULng(...) CUShort(...)
LINQ: From Aggregate...Into Select Distinct Where <Order By>...[Ascending|Descending] Take <Take While> Skip <Skip While> Let Group...By...Into Join...On <Group Join...On...Into> | Yes  | Yes  | Yes  | Yes  | Yes  | Yes  | Yes  | No

## See also

* Relational operator

## Notes

1. ↑ Conversely a right-associative operator with its right argument, though this is rarer.
2. ↑ Introducing a new operator changes the lexical specification of the language, which changes the lexical analysis. The arity and precedence of the operator is then part of the phrase syntax of the language, which changes the phrase-level analysis. For example, adding an operator `@` requires lexing and tokenizing this character, and the phrase structure (syntax tree) depends on the arity and precedence of this operator.

## References

1. ↑ "Operator Input Forms—Wolfram Language Documentation". https://reference.wolfram.com/language/tutorial/OperatorInputForms.html.en.
2. ↑ "Maxima 5.42.0 Manual: 7. Operators". http://maxima.sourceforge.net/docs/manual/maxima_7.html.
3. ↑ "Prefix, Postfix and Circumfix Operators". https://mythryl.org/my-Prefix__Postfix_and_Circumfix_Operators.html.
4. ↑ "Operators". http://doc.perl6.org/language/operators#___top.
5. ↑ "SWI-Prolog -- op/3". https://www.swi-prolog.org/pldoc/man?predicate=op/3.
6. ↑ "Declare an operator". http://seed7.sourceforge.net/examples/operator.htm.
7. ↑ "PHP: Error Control Operators - Manual". https://php.net/manual/en/language.operators.errorcontrol.php.
8. ↑ "Operators". https://docs.perl6.org/language/operators.
9. ↑ "Functions". https://docs.perl6.org/language/functions#Defining_Operators.
10. ↑ Goldberg, Adele. "Smalltalk-80: The Language and its Implementation, p. 27, ISBN 0-201-11371-6". http://stephane.ducasse.free.fr/FreeBooks/BlueBook/Bluebook.pdf.

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