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Unique string of length nil

In formal language theory, the empty string, or empty word, is the unique string of length zero.

Formal theory [edit]

Formally, a string is a finite, ordered sequence of characters such as letters, digits or spaces. The empty cord is the special case where the sequence has length zero, so there are no symbols in the string. There is only i empty string, because two strings are merely dissimilar if they have different lengths or a different sequence of symbols. In formal treatments,^[1] the empty string is denoted with ε or sometimes Λ or λ.

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

The empty cord has several properties:

|ε| = 0. Its cord length is zero.
ε ⋅ due south = southward ⋅ ε = s. The empty string is the identity element of the chain operation. The set of all strings forms a costless monoid with respect to ⋅ and ε.
ε^R = ε. Reversal of the empty string produces the empty string.
The empty cord precedes any other string under lexicographical club, considering information technology is the shortest of all strings.^[two]

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

Use in programming languages [edit]

In nearly programming languages, strings are a data type. Strings are typically stored at distinct retentivity addresses (locations). Thus, the same cord (for case, the empty string) may be stored in two or more places in memory.

In this way, there could be multiple empty strings in retention, in contrast with the formal theory definition, for which there is simply ane possible empty string. However, a string comparison function would indicate that all of these empty strings are equal to each other.

Fifty-fifty a string of length cipher tin can require memory to shop it, depending on the format being used. In nearly programming languages, the empty string is distinct from a nix reference (or zippo pointer) because a null reference points to no string at all, non even the empty string. The empty string is a legitimate string, upon which most string operations should work. Some languages care for some or all of the post-obit in like ways: empty strings, nix 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 cord terminating grapheme (zippo-terminated strings or plain text lines), the empty string is indicated by the immediate use of this terminating character.

λ representation	Programming languages
`""`	C, C#, C++, Get, Haskell, Java, JavaScript, Julia, Lua, G, Objective-C (as a C cord), OCaml, Perl, PHP, Python, Carmine, Scala, Standard ML, Swift, Tcl, Visual Bones .NET
`''`	APL, Delphi, JavaScript, Lua, MATLAB, Pascal, Perl, PHP, Python, R, Ruby, Smalltalk, SQL
`grapheme(0)`	R^[3]
`{'\0'}`	C, C++, Objective-C (as a C cord)
`std::string()`	C++
`""southward`	C++ (since the 2014 standard)
`@""`	Objective-C (as a constant `NSString` object)
`[NSString cord]`	Objective-C (every bit a new `NSString` object)
`q(), qq()`	Perl
`str()`	Python
`%{}` `%()`	Cherry-red
`string.Empty`	C#, Visual Basic .Cyberspace
`Cord.make 0 '-'`	OCaml
`{}`	Tcl
`[[]]`	Lua

Examples of empty strings [edit]

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

The empty string is a syntactically valid representation of cypher in positional notation (in any base), which does not contain leading zeros. Since the empty string does non take a standard visual representation exterior of formal language theory, the number naught is traditionally represented past a single decimal digit 0 instead.

Nil-filled memory area, interpreted as a null-terminated cord, is an empty string.

Empty lines of text show the empty string. This can occur from two consecutive EOLs, as oftentimes occur in text files, and this is sometimes used in text processing to separate paragraphs, east.one thousand. in MediaWiki.

Run into also [edit]

Empty fix
Nil-terminated string
Concatenation theory

References [edit]

^ Corcoran, John; Frank, William; Maloney, Michael (1974). "String theory". Journal of Symbolic Logic. 39 (4): 625–637. doi:ten.2307/2272846. JSTOR 2272846.
^ CSE1002 Lecture Notes – Lexicographic
^ There are two ways to create "empty strings" in R; the other is listed here equally "". character(0) creates empty character vectors, which will output 0 when counted.