View source for Empty string

{{redirect|""|the printed character|Quotation mark}}
{{Short description|Unique string of length zero}}
{{Refimprove|date=November 2009}}
In [[formal language theory]], the '''empty string''', or '''empty word''', is the unique [[String (computer science)|string]] of length zero.

==Formal theory<span class="anchor" id="nullable symbol"></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.
In formal treatments,<ref>{{cite journal |first1=John |last1=Corcoran |first2=William |last2=Frank |first3=Michael |last3=Maloney |title=String theory |journal=Journal of Symbolic Logic |volume=39 |issue=4 |year=1974 |pages=625–637 |doi=10.2307/2272846 |jstor=2272846|s2cid=2168826 }}</ref> the empty string is denoted with '''[[ε]]''' or sometimes '''[[Λ]]''' or '''[[λ]]'''.

The empty string should not be confused with the empty language [[∅]], which is a [[formal language]] (i.e. a set of strings) that contains no strings, not even the empty string.

The empty string has several properties:
* |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<sup>R</sup> = 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>

In [[context-free grammar]]s, a [[production (computer science)|production rule]] that allows a [[symbol (logic)|symbol]] to produce the empty string is known as an ε-production, and the symbol is said to be "nullable".

==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 (e.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.

Even a string of length zero can require memory to store it, depending on the format being used. In most programming languages, the empty string is distinct from a [[null reference]] (or null pointer) because a null reference points to no string at all, not even the empty string.
<!---A null reference is likely to cause an error if one tries to perform any operation on it, but an empty string is less likely to do so.--->
The empty string is a legitimate string, upon which most string operations should work. Some languages treat some or all of the following in similar ways: empty strings, null references, the integer 0, the floating point number 0, the Boolean value [[False (logic)|false]], the [[ASCII]] character [[null character|NUL]], or other such values.

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"
|-
! λ representation
! Programming languages
|-
| <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>
| [[R (programming language)|R]]{{Refn|There are two ways to create "empty strings" in R; the other is listed here as <code>""</code>. <code>character(0)</code> creates empty character vectors, which will output 0 when counted.}}
|-
| <code>{'\0'}</code>
| [[C (programming language)|C]], [[C++]], [[Objective-C]] (as a C string)
|-
| <code>std::string()</code>
| [[C++]]
|-
| <code>""s</code>
| [[C++]] (since the [[C++14|2014 standard]])
|-
| <code>@""</code>
| [[Objective-C]] (as a constant <code>NSString</code> object)
|-
| <code>[NSString string]</code>
| [[Objective-C]] (as a new <code>NSString</code> object)
|-
| <code>q(), qq()</code>
| [[Perl]]
|-
| <code>str()</code><ref>Another way to make an empty string is multiplying a string by 0 or a negative integer.</ref>
| [[Python (programming language)|Python]]
|-
| <code>%{}</code><br /><code>%()</code>
| [[Ruby (programming language)|Ruby]]
|-
| <code>String::new()</code><ref>{{Cite web |title=String in std::string - Rust |url=https://doc.rust-lang.org/std/string/struct.String.html#method.new |access-date=2022-11-30 |website=doc.rust-lang.org}}</ref>
| [[Rust (programming language)|Rust]]
|-
| <code>string.Empty</code>
| [[C Sharp (programming language)|C#]], [[VB.NET|Visual Basic .NET]]
|- 
| <code>String.make 0 '-'</code>
| [[OCaml]]
|- 
| <code>{}</code>
| [[Tcl]]
|-
| <code><nowiki>[[]]</nowiki></code>
| [[Lua (programming language)|Lua]]
|-
|<code>“”</code>
<code>‘’</code>
|[[PowerShell]]
|}

=== Representations of the empty string ===
{{Expand section|date=March 2010}}
The empty string is a syntactically valid representation of [[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. This 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==
{{Reflist}}

{{DEFAULTSORT:Empty String}}
[[Category:Formal languages]]
[[Category:String (computer science)]]
[[Category:Zero (linguistics)]]