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In [[formal language theory]], the '''empty string''' (or '''null string''')<ref name="Kernighan and Ritchie, C, p. 38">Kernighan and Ritchie, ''C'', p. 38</ref> is the unique [[string (computer science)|string]] of [[String (computer science)#Formal theory|length]] [[zero]].
 
==Formal theory==
Formally, a string is a finite sequence of symbols such as letters or digits.
The empty string is the extreme 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>JOHN CORCORAN, WILLIAM FRANK, and MICHAEL MALONEY, String theory, Journal of Symbolic Logic, vol. 39 (1974) pp. 625&ndash; 637</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:
*<math>| \epsilon \, | = 0</math>. The '''[[String (computer science)#Formal theory|string length]]''' is zero.
*<math>\epsilon \, + s = s + \epsilon \, = s</math>. The empty string is the [[identity element]] of the '''[[union]]''' operation (which forms a [[free monoid]] on the [[alphabet]] Σ).
*<math>{ \epsilon \, }^R = \epsilon \,</math>. '''Reversal''' of the empty string produces the empty string.
* 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>
 
==Use in programming languages==
In most programming languages, strings are a [[data type]]. Individual strings are typically stored in consecutive [[Memory address|memory locations]].
This means that the same string (for example the empty string) could be stored in two different places in memory.
(Note that even a string of length zero can require memory to store it, depending on the format being used.)
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.
 
The empty string is distinct from a [[null pointer|null]] [[Reference (computer science)|reference]] (or null pointer) because a null reference does not point to any 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, which can lessen the danger: 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.
{| class="wikitable"
|-
! λ representation
! Programming languages
|-
| <code>""</code>
| [[C (programming language)|C]], [[C++]], [[Perl]], [[Python (programming language)|Python]], [[C Sharp (programming language)|C#]], [[Go (programming language)|Go]], [[PHP]], [[Visual Basic .NET]], [[Java (programming language)|Java]], [[Turing (programming language)|Turing]], [[JavaScript]], [[Haskell (programming language)|Haskell]], [[Objective-C]] (as a C string), [[OCaml]], [[Standard ML]], [[Scala (programming language)|Scala]], [[Seed7]], [[Tcl (programming language)|Tcl]]
|-
| <code>&#39;&#39;</code>
| [[Perl]], [[PHP]], [[Python (programming language)|Python]], [[JavaScript]], [[Delphi (programming language)|Delphi]], [[Pascal (programming language)|Pascal]], [[Matlab (programming language)|Matlab]]
|-
| <code>{'\0'}</code>
| [[C (programming language)|C]], [[C++]], [[Objective-C]] (as a C string)
|-
| <code>std::string()</code>
| [[C++]]
|-
| <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>%{}</code>
| [[Ruby]]
|-
| <code>""""""</code><br/><code>str()</code>
| [[Python (programming language)|Python]]
|-
| <code>string.Empty</code>
| [[C Sharp (programming language)|C#]], [[VB.NET|Visual Basic .NET]]
|-
| <code>String.make 0 '-'</code>
| [[OCaml]]
|-
| <code>{}</code>
| [[Tcl]]
|-
|}
 
=== Examples of empty strings ===
{{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 this is sometimes used in [[text processing]] to separate [[paragraph]]s, e.g. in [[MediaWiki]].
 
==See also==
*[[Empty set]]
*[[Null-terminated string]]
*[[Concatenation theory]]
*[[Concatenation]]
 
==References==
{{Reflist}}
 
{{nulls}}
 
{{DEFAULTSORT:Empty String}}
[[Category:Formal languages]]
[[Category:String (computer science)]]
[[Category:Zero]]

Revision as of 18:46, 16 February 2014

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The son of any , is aware of persistence and perseverance are important elements in relation to a prosperous career- . His to start with album, Keep Me, produced the best hits “All My Buddies “Country and Say” Guy,” when his effort, Doin’ Point, identified the vocalist-a few straight No. 3 single men and women: Else Calling Is actually a Fantastic Point.”

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