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Operator overloading

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</style><table class="sidebar nomobile nowraplinks" style="width:auto"><tbody><tr><th class="sidebar-title"><a href="Polymorphism_(computer_science)" title="Polymorphism (computer science)">Polymorphism</a></th></tr><tr><th class="sidebar-heading" style="background-color:#ddf;font-size:110%">

<a href="Ad_hoc_polymorphism" title="Ad hoc polymorphism">Ad hoc polymorphism</a></th></tr><tr><td class="sidebar-content plainlist">

<ul><li><a href="Function_overloading" title="Function overloading">Function overloading</a></li>

</ul></td>

</tr><tr><th class="sidebar-heading" style="background-color:#ddf;font-size:110%">

<a href="Parametric_polymorphism" title="Parametric polymorphism">Parametric polymorphism</a></th></tr><tr><td class="sidebar-content plainlist">

<ul><li><a href="Generic_function" title="Generic function">Generic function</a></li>

<li><a href="Generic_programming" title="Generic programming">Generic programming</a></li></ul></td>

</tr><tr><th class="sidebar-heading" style="background-color:#ddf;font-size:110%">

<a href="Subtyping" title="Subtyping">Subtyping</a></th></tr><tr><td class="sidebar-content plainlist">

<ul><li><a href="Virtual_function" title="Virtual function">Virtual function</a></li>

<li><a href="Dynamic_dispatch" title="Dynamic dispatch">Single and dynamic dispatch</a></li>

<li><a href="Double_dispatch" title="Double dispatch">Double dispatch</a></li>

<li><a href="Multiple_dispatch" title="Multiple dispatch">Multiple dispatch</a></li>

<li><a href="Predicate_dispatch" title="Predicate dispatch">Predicate dispatch</a></li></ul></td>

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In <a href="Computer_programming" title="Computer programming">computer programming</a>, operator overloading, sometimes termed operator <a href="Ad_hoc_polymorphism" title="Ad hoc polymorphism">ad hoc polymorphism</a>, is a specific case of <a href="Polymorphism_(computer_science)" title="Polymorphism (computer science)">polymorphism</a>, where different <a href="Operator_(computer_programming)" title="Operator (computer programming)">operators</a> have different implementations depending on their arguments. Operator overloading is generally defined by a <a href="Programming_language" title="Programming language">programming language</a>, a <a href="Programmer" title="Programmer">programmer</a>, or both.

<div class="mw-heading mw-heading2"><h2 id="Rationale">Rationale </h2></div>

Operator overloading is <a href="Syntactic_sugar" title="Syntactic sugar">syntactic sugar</a>, and is used because it allows programming using notation nearer to the target domain<a href="#cite_note-1">[1]</a> and allows user-defined types a similar level of syntactic support as types built into a language. It is common, for example, in scientific computing, where it allows computing representations of mathematical objects to be manipulated with the same syntax as on paper.

Operator overloading does not change the <a href="Expressive_power_(computer_science)" title="Expressive power (computer science)">expressive power</a> of a language (with functions), as it can be emulated using function calls. For example, consider variables <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">a</code>, <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">b</code> and <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">c</code> of some user-defined type, such as <a href="Matrix_(mathematics)" title="Matrix (mathematics)">matrices</a>:

In a language that supports operator overloading, and with the usual assumption that the <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">*</code> operator has higher <a href="Order_of_operations" title="Order of operations">precedence</a> than the <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">+</code> operator, this is a concise way of writing:

<code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">Add(a, Multiply(b, c))</code>

However, the former syntax reflects common mathematical usage.

<div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2></div>

In this case, the addition operator is overloaded to allow addition on a user-defined type <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">Time</code> in <a href="C%2B%2B" title="C++">C++</a>:

<div class="mw-highlight mw-highlight-lang-cpp mw-content-ltr" dir="ltr"><pre>Time operator+(const Time& lhs, const Time& rhs) {

temp.seconds += rhs.seconds;

temp.minutes += temp.seconds / 60;

temp.seconds %= 60;

temp.minutes += rhs.minutes;

temp.hours += temp.minutes / 60;

temp.minutes %= 60;

temp.hours += rhs.hours;

return temp;

}

</pre></div>

Addition is a <a href="Binary_operation" title="Binary operation">binary operation</a>, which means it has two <a href="Operand" title="Operand">operands</a>. In C++, the arguments being passed are the operands, and the <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">temp</code> object is the returned value.

The operation could also be defined as a class method, replacing <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">lhs</code> by the hidden <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">this</code> argument; However, this forces the left operand to be of type <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">Time</code>:

<div class="mw-highlight mw-highlight-lang-cpp mw-content-ltr" dir="ltr"><pre>// The "const" right before the opening curly brace means that |this| is not modified.

Time Time::operator+(const Time& rhs) const {

Time temp = *this; // |this| should not be modified, so make a copy.

temp.minutes += rhs.minutes;

temp.hours += rhs.hours;

return temp;

}

</pre></div>

Note that a <a href="Unary_operation" title="Unary operation">unary</a> operator defined as a class method would receive no apparent argument (it only works from <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">this</code>):

<div class="mw-highlight mw-highlight-lang-cpp mw-content-ltr" dir="ltr"><pre>bool Time::operator!() const {

return hours == 0 && minutes == 0 && seconds == 0;

}

</pre></div>

The less-than (<) operator is often overloaded to sort a structure or class:

<div class="mw-highlight mw-highlight-lang-cpp mw-content-ltr" dir="ltr"><pre>class Pair {

public:

bool operator<(const Pair& p) const {

if (x_ == p.x_) {

return y_ < p.y_;

}

return x_ < p.x_;

}

private:

int x_;

int y_;

};

</pre></div>

Like with the previous examples, in the last example operator overloading is done within the class. In C++, after overloading the less-than operator (<), <a href="Sort_(C%2B%2B)" title="Sort (C++)">standard sorting functions</a> can be used to sort some classes.

<div class="mw-heading mw-heading2"><h2 id="Criticisms">Criticisms</h2></div>

Operator overloading has often been criticized<a href="#cite_note-2">[2]</a> because it allows programmers to reassign the semantics of operators depending on the types of their operands. For example, the use of the <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr"><<</code> operator in <a href="C%2B%2B" title="C++">C++</a> <code class="mw-highlight mw-highlight-lang-cpp mw-content-ltr" dir="ltr">a << b</code> shifts the bits in the variable <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">a</code> left by <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">b</code> bits if <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">a</code> and <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">b</code> are of an integer type, but if <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">a</code> is an output stream then the above code will attempt to write a <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">b</code> to the stream. Because operator overloading allows the original programmer to change the usual semantics of an operator and to catch any subsequent programmers by surprise, it is considered good practice to use operator overloading with care (the creators of <a href="Java_(programming_language)" title="Java (programming language)">Java</a> decided not to use this feature,<a href="#cite_note-3">[3]</a> although not necessarily for this reason).

Another, more subtle, issue with operators is that certain rules from mathematics can be wrongly expected or unintentionally assumed. For example, the <a href="Commutative_property" title="Commutative property">commutativity</a> of + (i.e. that <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">a + b == b + a</code>) does not always apply; an example of this occurs when the operands are strings, since + is commonly overloaded to perform a concatenation of strings (i.e. <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">"bird" + "song"</code> yields <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">"birdsong"</code>, while <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">"song" + "bird"</code> yields <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">"songbird"</code>). A typical counter to this argument comes directly from mathematics: While + is commutative on integers (and more generally any complex number), it is not commutative for other "types" of variables. In practice, + is not even always <a href="Operator_associativity" title="Operator associativity">associative</a>, for example with floating-point values due to rounding errors. Another example: In mathematics, multiplication is commutative for real and complex numbers but not commutative in <a href="Matrix_multiplication" title="Matrix multiplication">matrix multiplication</a>.

<div class="mw-heading mw-heading2"><h2 id="Catalog">Catalog</h2></div>

A classification of some common programming languages is made according to whether their operators are overloadable by the programmer and whether the operators are limited to a predefined set.

<th>Operators

</th>

<th>Not overloadable

</th>

<th>Overloadable

</th></tr>

<tr>

<th>New definable<a href="#cite_note-4">[4]</a>

</th>

<td>

<li><a href="Prolog" title="Prolog">Prolog</a><a href="#cite_note-6">[6]</a></li></ul>

</td>

<td>

<ul><li><a href="ALGOL_68#op:_Operators" title="ALGOL 68">ALGOL 68</a></li>

<li><a href="Clojure" title="Clojure">Clojure</a></li>

<li><a href="Eiffel_(programming_language)" title="Eiffel (programming language)">Eiffel</a><a href="#cite_note-7">[7]</a></li>

<li><a href="Fortran" title="Fortran">Fortran</a><a href="#cite_note-8">[8]</a><a href="#cite_note-9">[9]</a></li>

<li><a href="Futhark_(programming_language)" title="Futhark (programming language)">Futhark</a><a href="#cite_note-10">[10]</a></li>

<li><a href="Haskell_(programming_language)" class="mw-redirect" title="Haskell (programming language)">Haskell</a><a href="#cite_note-12">[12]</a></li>

<li><a href="Julia_(programming_language)" title="Julia (programming language)">Julia</a><a href="#cite_note-14">[14]</a></li>

<li><a href="Scala_(programming_language)" title="Scala (programming language)">Scala</a><a href="#cite_note-18">[18]</a></li>

<li><a href="Smalltalk" title="Smalltalk">Smalltalk</a><a href="#cite_note-Hunt2012-20">[20]</a></li>

<li><a href="Swift_(programming_language)" title="Swift (programming language)">Swift</a><a href="#cite_note-21">[21]</a></li></ul>

</td></tr>

<tr>

<th>Limited set

</th>

<td>

<ul><li><a href="BASIC" title="BASIC">BASIC</a></li>

<li><a href="JavaScript" title="JavaScript">JavaScript</a></li>

<li><a href="Modula-2" title="Modula-2">Modula-2</a></li>

<li><a href="Objective-C" title="Objective-C">Objective-C</a></li>

<li><a href="Pascal_(programming_language)" title="Pascal (programming language)">Pascal</a><a href="#cite_note-23">[23]</a></li>

<li><a href="TypeScript" title="TypeScript">TypeScript</a><a href="#cite_note-24">[24]</a></li>

<li><a href="Visual_Basic" title="Visual Basic">Visual Basic</a></li></ul>

</td>

<td>

<li><a href="Ceylon_(programming_language)" title="Ceylon (programming language)">Ceylon</a><a href="#cite_note-28">[28]</a></li>

<li><a href="FreeBASIC" title="FreeBASIC">FreeBASIC</a><a href="#cite_note-31">[31]</a></li>

<li><a href="Groovy_(programming_language)" class="mw-redirect" title="Groovy (programming language)">Groovy</a><a href="#cite_note-32">[32]</a></li>

<li><a href="Kotlin_(programming_language)" title="Kotlin (programming language)">Kotlin</a><a href="#cite_note-33">[33]</a></li>

<li><a href="MATLAB" title="MATLAB">MATLAB</a><a href="#cite_note-35">[35]</a></li>

<li><a href="Object_Pascal" title="Object Pascal">Object Pascal</a> (<a href="Free_Pascal" title="Free Pascal">Free Pascal</a>,<a href="#cite_note-36">[36]</a> <a href="Delphi_(programming_language)" class="mw-redirect" title="Delphi (programming language)">Delphi</a> (since 2005)<a href="#cite_note-37">[37]</a>)</li>

<li><a href="PHP" title="PHP">PHP</a> (using magic methods,<a href="#cite_note-38">[38]</a> ArrayAccess interface, or Operator extension)</li>

<li><a href="Python_(programming_language)" title="Python (programming language)">Python</a><a href="#cite_note-40">[40]</a></li>

<li><a href="Visual_Basic_.NET" class="mw-redirect" title="Visual Basic .NET">Visual Basic .NET</a><a href="#cite_note-43">[43]</a></li></ul>

</td></tr></tbody></table>

<div class="mw-heading mw-heading2"><h2 id="Timeline_of_operator_overloading">Timeline of operator overloading</h2></div>

The <a href="ALGOL_68" title="ALGOL 68">ALGOL 68</a> specification allowed operator overloading.<a href="#cite_note-44">[44]</a>

Extract from the ALGOL 68 language specification (page 177) where the overloaded operators ¬, =, ≠, and abs are defined:

<pre>10.2.2. Operations on Boolean Operands

a) op ∨ = (bool a, b) bool:( a | true | b );

b) op ∧ = (bool a, b) bool: ( a | b | false );

c) op ¬ = (bool a) bool: ( a | false | true );

d) op = = (bool a, b) bool:( a∧b ) ∨ ( ¬b∧¬a );

e) op ≠ = (bool a, b) bool: ¬(a=b);

f) op abs = (bool a)int: ( a | 1 | 0 );

</pre>

Note that no special declaration is needed to overload an operator, and the programmer is free to create new operators. For dyadic operators their priority compared to other operators can be set:

<pre> prio max = 9;

op max = (int a, b) int: ( a>b | a | b );

op ++ = ( ref int a ) int: ( a +:= 1 );

</pre>

<a href="Ada_(programming_language)" title="Ada (programming language)">Ada</a> supports overloading of operators from its inception, with the publication of the Ada 83 language standard. However, the language designers chose to preclude the definition of new operators. Only extant operators in the language may be overloaded, by defining new functions with identifiers such as "+", "*", "&" etc. Subsequent revisions of the language (in 1995 and 2005) maintain the restriction to overloading of extant operators.

In <a href="C%2B%2B" title="C++">C++</a>, operator overloading is more refined than in <a href="ALGOL_68" title="ALGOL 68">ALGOL 68</a>.<a href="#cite_note-45">[45]</a>

<a href="Java_(programming_language)" title="Java (programming language)">Java</a> language designers at <a href="Sun_Microsystems" title="Sun Microsystems">Sun Microsystems</a> chose to omit overloading.<a href="#cite_note-46">[46]</a><a href="#cite_note-47">[47]</a><a href="#cite_note-48">[48]</a>

<a href="Python_(programming_language)" title="Python (programming language)">Python</a> allows operator overloading through the implementation of methods with special names.<a href="#cite_note-49">[49]</a> For example, the addition (+) operator can be overloaded by implementing the method <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">obj.__add__(self, other)</code>.

<a href="Ruby_(programming_language)" title="Ruby (programming language)">Ruby</a> allows operator overloading as syntactic sugar for simple method calls.

<a href="Lua_(programming_language)" class="mw-redirect" title="Lua (programming language)">Lua</a> allows operator overloading as syntactic sugar for method calls with the added feature that if the first operand doesn't define that operator, the method for the second operand will be used.

Microsoft added operator overloading to <a href="C_Sharp_(programming_language)" title="C Sharp (programming language)">C#</a> in 2001 and to <a href="Visual_Basic_.NET" class="mw-redirect" title="Visual Basic .NET">Visual Basic .NET</a> in 2003.

<a href="Scala_(programming_language)" title="Scala (programming language)">Scala</a> treats all operators as methods and thus allows operator overloading by proxy.

In <a href="Raku_(programming_language)" title="Raku (programming language)">Raku</a>, the definition of all operators is delegated to lexical functions, and so, using function definitions, operators can be overloaded or new operators added. For example, the function defined in the <a href="Rakudo" title="Rakudo">Rakudo</a> source for incrementing a Date object with "+" is:

<div class="mw-highlight mw-highlight-lang-perl6 mw-content-ltr" dir="ltr"><pre>multi infix:<+>(Date:D $d, Int:D $x) {

Date.new-from-daycount($d.daycount + $x)

}

</pre></div>

Since "multi" was used, the function gets added to the list of <a href="Multidispatch" class="mw-redirect" title="Multidispatch">multidispatch</a> candidates, and "+" is only overloaded for the case where the type constraints in the function signature are met.

While the capacity for overloading includes +, *, >=, the <a href="Imaginary_unit" title="Imaginary unit">postfix and term i</a>, and so on, it also allows for overloading various brace operators: "[x, y]", "x[y]", "x{y}", and "x(y)".

<a href="Kotlin_(programming_language)" title="Kotlin (programming language)">Kotlin</a> has supported operator overloading since its creation.

<ul><li><a href="Function_overloading" title="Function overloading">Function overloading</a></li>

<li><a href="Polymorphism_(computer_science)" title="Polymorphism (computer science)">Polymorphism (computer science)</a></li>

<li><a href="Subroutine" class="mw-redirect" title="Subroutine">Subroutine</a></li>

<li><a href="Operator_(programming)" class="mw-redirect" title="Operator (programming)">Operator (programming)</a></li>

<li><a href="Operators_in_C_and_C%2B%2B" title="Operators in C and C++">Operators in C and C++</a></li>

<li><a href="Mutator_method" title="Mutator method">Mutator method</a></li>

<li><a href="Indexer_(programming)" title="Indexer (programming)">Indexer (programming)</a></li>

<li><a href="Property_(programming)" title="Property (programming)">Property (programming)</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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<li id="cite_note-4"><a href="#cite_ref-4">^</a> Completely new operators can be added.

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<li id="cite_note-5"><a href="#cite_ref-5">^</a> Binary functions with a symbolic name can be called infix.

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<li id="cite_note-9"><a href="#cite_ref-9">^</a> Introduced in Fortran 90.

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