Empty string

In computer science and formal language theory, the empty string (or null string)^[1] is the unique string of length zero. It is denoted with λ or sometimes Λ or ε.

The empty string is distinct from a null reference in that in an object-oriented programming language a null reference to a string type doesn't point to a string object and will cause an error were one to try to perform any operation on it. The empty string is still a string upon which string operations may be attempted. Some languages however, may treat empty and null strings the same, e.g. if they use COM's strings.

A related concept is the empty language ∅, a formal language that contains no strings.

Properties

When present in a formal language, empty strings have several properties:

• $| \lambda \, | = 0$. The string length is zero.
• $\lambda \, + s = s + \lambda \, = s$. Under concatenation, the empty string is the identity element of the free monoid on the alphabet Σ.
• ${ \lambda \, }^R = \lambda \,$. Reversal of the empty string produces the empty string.
• The empty string precedes any other string in the lexicographical order.^[2]

These properties may hold in some programming languages, but this is left up^{[citation needed]} to the particular implementation.

Representations

The empty string usually represented in a way not different from a generic string. In implementations with string terminating character (C strings or plain text lines) it is just this terminating character placed to the first position.

λ representation	Programming languages
""	C, C++, Perl, Python, C#, Go, PHP, Visual Basic .NET, Java, Turing, JavaScript, Haskell, Objective Caml, Tcl
''	Perl, PHP, Python, JavaScript, Delphi, Pascal
{'\0'}	C, C++
std::string()	C++
@""	Objective-C
qw()	Perl
"""""" str()	Python
string.Empty	C#
String.Empty	Visual Basic .NET
String.make 0 '-'	Objective Caml
{}	Tcl

Occurrence

The empty string is a syntactically valid representation of zero in positional notation (in any base), which does not contain leading zeros. Because handling of empty strings is problematical (particularly in a graphic environment), the zero number traditionally represented by one decimal digit 0 instead.

Zero-filled memory area, interpreted as a C string, is an empty string.

Empty lines (say, two consecutive EOLs) often occurred in text files and sometimes used in text processing to separate paragraphs, e.g. in MediaWiki.

See also

• Empty set
• Null-terminated string

References

1. ^ Kernighan and Ritchie, C, p. 38
2. ^ CSE1002 Lecture Notes - Lexicographic