Empty string: Difference between revisions

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{{hatnoteredirect|The term {{green|{{big| "" }}}} redirects here. For |the printed character, see [[|Quotation mark]].}}

{{Short description|Unique string of length zero}}

{{Refimprove|date=November 2009}}

In [[formal language theory]], the '''empty string''', oralso known as the '''empty word''' or '''null string''', is the unique [[String (computer science)|string]] of length zero.

=={{Formal theory<span class="anchor|" id="nullable symbol}}Formal theory"></span>==

Formally, a string is a finite, ordered sequence of [[character (symbol)|characters]] such as letters, digits or spaces. The empty string is the special case where the sequence has length zero, so there are no symbols in the string.

There is only one empty string, because two strings are only different if they have different lengths or a different sequence of symbols.

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* |ε| = 0. Its [[string (computer science)#Formal theory|string length]] is zero.

* ε ⋅ s = s ⋅ ε = s. The empty string is the [[identity element]] of the [[concatenation]] operation. The set of all strings forms a [[free monoid]] with respect to ⋅ and ε.

* ε^R = ε. Reversal of the empty string produces the empty string, so the empty string is a [[palindrome]].

* <math>\forall c \in s: P(c)</math>. Statements that are about all characters in a string are [[vacuous truth|vacuously true]].

* The empty string precedes any other string under [[lexicographical order]], because it is the shortest of all strings.<ref>[http://cs.fit.edu/~ryan/cse1002/lectures/lexicographic.pdf CSE1002 Lecture Notes – Lexicographic]</ref>

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==Use in programming languages==

In most [[programming language]]s, strings are a [[data type]]. Strings are typically stored at distinct [[memory address]]es (locations). Thus, the same string (for examplee.g., the empty string) may be stored in two or more places in memory.

In this way, there could be multiple empty strings in memory, in contrast with the formal theory definition, for which there is only one possible empty string. However, a string comparison function would indicate that all of these empty strings are equal to each other.

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The empty string is usually represented similarly to other strings. In implementations with string terminating character ([[null-terminated string]]s or plain text lines), the empty string is indicated by the immediate use of this terminating character.

Different functions, methods, macros, or [[Programming idiom|idioms]] exist for checking if a string is empty in different languages.{{examples|date=July 2023}}

{| class="wikitable"

|-

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|-

| <code>""</code>

| [[C (programming language)|C]], [[C Sharp (programming language)|C#]], [[C++]], [[Go (programming language)|Go]], [[Haskell (programming language)|Haskell]], [[Java (programming language)|Java]], [[JavaScript]], [[Julia (programming language)|Julia]], [[Lua (programming language)|Lua]], [[MUMPS|M]], [[Objective-C]] (as a C string), [[OCaml]], [[Perl]], [[PHP]], [[PowerShell]], [[Python (programming language)|Python]], [[Ruby (programming language)|Ruby]], [[Scala (programming language)|Scala]], [[Standard ML]], [[Swift (programming language)|Swift]], [[Tcl]], [[Visual Basic .NET]]

|-

| <code>&#39;&#39;</code>

| [[APL (programming language)|APL]], [[Delphi (programming language)|Delphi]], [[JavaScript]], [[Lua (programming language)|Lua]], [[MATLAB]], [[Pascal (programming language)|Pascal]], [[Perl]], [[PHP]], [[PowerShell]], [[Python (programming language)|Python]], [[R (programming language)|R]], [[Ruby (programming language)|Ruby]], [[Smalltalk]], [[SQL]]

|-

| <code>character(0)</code>

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| [[Perl]]

|-

| <code>str()</code><ref>Another way to make an empty string is multiplying a string by 0 or a negative integer.</ref>

| <code>str()</code>

| [[Python (programming language)|Python]]

|-

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| <code><nowiki>[[]]</nowiki></code>

| [[Lua (programming language)|Lua]]

|-

| <code>str()“”</code>

<code>‘’</code>

<code>„”</code>

<code>‚‘</code>{{refn|All 'smart' quotation marks work as both opening and closing marks in any combination, except that single marks must be paired with single marks and double marks with double marks. For example {{code|"Hello, world„}} is valid. Guillemets are not supported. Note that the German-style low single quotation mark given here is {{Unichar|201A}}; the similar-looking character {{Unichar|2C}} does not function as a quotation mark. PowerShell's official documentation recommends using straight quotation marks.<ref>{{cite web |url=https://learn.microsoft.com/en-us/powershell/module/microsoft.powershell.core/about/about_quoting_rules?view=powershell-7.5 |title=about_Quoting_Rules – PowerShell |work=Microsoft Learn |access-date=26 August 2025 |url-status=live |archive-url=https://web.archive.org/web/20250814175659/https://learn.microsoft.com/en-us/powershell/module/microsoft.powershell.core/about/about_quoting_rules?view=powershell-7.5 |archive-date=2025-08-14 |quote=PowerShell treats smart quotation marks, also called typographic or curly quotes, as normal quotation marks for strings. Don't use smart quotation marks to enclose strings.}}</ref>}}

|[[PowerShell]]

|}

=== ExamplesRepresentations of the empty stringsstring ===

{{Expand section|date=March 2010}}

The empty string is a syntactically valid representation of [[0 (number)|zero]] in [[positional notation]] (in any base), which does not contain [[leading zero]]s. Since the empty string does not have a standard visual representation outside of formal language theory, the number zero is traditionally represented by a single [[decimal digit]] '''0''' instead.

Zero-filled memory area, interpreted as a [[null-terminated string]], is an empty string.

Empty lines of text show the empty string. This can occur from two consecutive [[End of line|EOLs]], as often occur in [[text file]]s,. and thisThis is sometimes used in [[text processing]] to separate [[paragraph]]s, e.g. in [[MediaWiki]].

==See also==

* [[Empty set]]

* [[Null-terminated string]]

* [[Concatenation theory]]

* [[String literal]]

==References==