Empty string

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In

of length zero.

Formal theory

Formally, a string is a finite, ordered sequence of 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,

.

The empty string should not be confused with the empty 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 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.
• ${\displaystyle \forall c\in s:P(c)}$. Statements that are about all characters in a string are vacuously true.
• The empty string precedes any other string under
  lexicographical order, because it is the shortest of all strings.^[2]

In

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 languages, strings are a data type. Strings are typically stored at distinct memory addresses (locations). Thus, the same string (for example, 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

(or null pointer) because a null reference points to no string at all, not even the empty string. 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, the ASCII character NUL, or other such values.

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

Different functions, methods, macros, or

]

λ representation	Programming languages
""	Visual Basic .NET
''	Delphi, JavaScript, Lua, MATLAB, Pascal, Perl, PHP, Python, R, Ruby, Smalltalk, SQL
character(0)	R[3]
{'\0'}	C, C++, Objective-C (as a C string)
std::string()	C++
""s	C++ (since the 2014 standard)
@""	Objective-C (as a constant NSString object)
[NSString string]	Objective-C (as a new NSString object)
q(), qq()	Perl
str()	Python
%{} %()	Ruby
String::new()[4]	Rust
string.Empty	Visual Basic .NET
String.make 0 '-'	OCaml
{}	Tcl
[[]]	Lua

Examples of empty strings

This section needs expansion. You can help by adding to it. (March 2010)

The empty string is a syntactically valid representation of

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

.

See also

• Empty set
• Null-terminated string
• Concatenation theory
• String literal

References