Empty string
In formal language theory, the empty string, or empty word is the unique string 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 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 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.
- εR = ε. 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.
Use in programming languages
In most programming languages, strings are a data type. Strings are typically stored at distinct memory locations.This means that the same string could 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 because a null reference does not point to any 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, the empty string is indicated by the immediate use of this terminating character.
| λ representation | Programming languages |
"" | C, C#, C++, Go, Haskell, Java, JavaScript, Lua, Objective-C, OCaml, Perl, PHP, Python, Ruby, Scala, Standard ML, Swift, Tcl, Visual Basic.NET |
'' | APL, Delphi, JavaScript, Matlab, Pascal, Perl, PHP, Python, Ruby, Smalltalk, SQL |
| C, C++, Objective-C |
std::string | C++ |
""s | C++ |
@"" | Objective-C |
| Objective-C |
q, qq | Perl |
%% | Ruby |
string.Empty | C#, Visual Basic.NET |
String.make 0 '-' | OCaml |
| Tcl |
| Lua |
Examples of empty strings
The empty string is a syntactically valid representation of zero in positional notation, which does not contain leading zeros. 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 EOLs, as often occur in text files, and this is sometimes used in text processing to separate paragraphs, e.g. in MediaWiki.