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Unique string of length zero

In formal language theory, the empty string, or empty give-and-take, is the unique string of length zip.

Formal theory [edit]

Formally, a cord is a finite, ordered sequence of characters such as letters, digits or spaces. The empty string is the special instance where the sequence has length nothing, then at that place are no symbols in the cord. There is just 1 empty string, because two strings are just dissimilar if they accept different lengths or a dissimilar sequence of symbols. In formal treatments,^[1] the empty cord is denoted with ε or sometimes Λ or λ.

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

The empty string has several backdrop:

|ε| = 0. Its string length is zero.
ε ⋅ due south = due south ⋅ ε = s. The empty string is the identity element of the concatenation operation. The set of all strings forms a complimentary monoid with respect to ⋅ and ε.
ε^R = ε. Reversal of the empty string produces the empty string.
The empty string precedes any other string under lexicographical order, because information technology is the shortest of all strings.^[2]

In context-free grammars, a product dominion that allows a symbol to produce the empty cord is known as an ε-production, and the symbol is said to exist "nullable".

Use in programming languages [edit]

In most programming languages, strings are a data blazon. Strings are typically stored at singled-out memory addresses (locations). Thus, the same cord (for example, the empty cord) may exist stored in two or more than places in memory.

In this mode, there could be multiple empty strings in retention, in contrast with the formal theory definition, for which there is only one possible empty cord. However, a string comparing function would bespeak that all of these empty strings are equal to each other.

Even a string of length zero can require memory to shop information technology, depending on the format being used. In well-nigh programming languages, the empty string is distinct from a null reference (or zilch pointer) considering a cipher reference points to no cord at all, not fifty-fifty the empty string. The empty string is a legitimate string, upon which near string operations should work. Some languages treat some or all of the following in similar ways: empty strings, nil references, the integer 0, the floating point number 0, the Boolean value false, the ASCII grapheme NUL, or other such values.

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

λ representation	Programming languages
`""`	C, C#, C++, Go, Haskell, Java, JavaScript, Julia, Lua, Chiliad, Objective-C (as a C string), OCaml, Perl, PHP, Python, Cerise, Scala, Standard ML, Swift, Tcl, Visual Basic .NET
`''`	APL, Delphi, JavaScript, Lua, MATLAB, Pascal, Perl, PHP, Python, R, Reddish, Smalltalk, SQL
`character(0)`	R^[three]
`{'\0'}`	C, C++, Objective-C (as a C cord)
`std::cord()`	C++
`""due south`	C++ (since the 2014 standard)
`@""`	Objective-C (equally a abiding `NSString` object)
`[NSString string]`	Objective-C (as a new `NSString` object)
`q(), qq()`	Perl
`str()`	Python
`%{}` `%()`	Ruby
`string.Empty`	C#, Visual Basic .Cyberspace
`Cord.make 0 '-'`	OCaml
`{}`	Tcl
`[[]]`	Lua

Examples of empty strings [edit]

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

The empty string is a syntactically valid representation of zero in positional annotation (in whatever base), which does not incorporate leading zeros. Since the empty string does not take a standard visual representation outside of formal linguistic communication theory, the number zilch is traditionally represented by a single decimal digit 0 instead.

Goose egg-filled retentiveness area, interpreted every bit a null-terminated cord, is an empty string.

Empty lines of text show the empty string. This can occur from 2 consecutive EOLs, every bit often occur in text files, and this is sometimes used in text processing to separate paragraphs, eastward.g. in MediaWiki.

References [edit]

^ Corcoran, John; Frank, William; Maloney, Michael (1974). "String theory". Journal of Symbolic Logic. 39 (4): 625–637. doi:10.2307/2272846. JSTOR 2272846.
^ CSE1002 Lecture Notes – Lexicographic
^ There are 2 ways to create "empty strings" in R; the other is listed here equally "". character(0) creates empty graphic symbol vectors, which volition output 0 when counted.