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Unique string of length zero

In formal language theory, the empty string, or empty discussion, 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 string is the special case where the sequence has length zero, and so there are no symbols in the string. In that location is merely 1 empty string, because two strings are only different if they have different lengths or a different sequence of symbols. In formal treatments,^[one] the empty string is denoted with ε or sometimes Λ or λ.

The empty string should non exist confused with the empty linguistic communication ∅, which is a formal linguistic communication (i.e. a set up of strings) that contains no strings, not fifty-fifty the empty string.

The empty cord has several properties:

|ε| = 0. Its string length is cypher.
ε ⋅ s = due south ⋅ ε = s. The empty string is the identity element of the concatenation operation. The set of all strings forms a gratuitous monoid with respect to ⋅ and ε.
ε^R = ε. Reversal of the empty string produces the empty string.
The empty string precedes whatsoever other string under lexicographical social club, because it is the shortest of all strings.^[2]

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

Use in programming languages [edit]

In almost programming languages, strings are a data type. Strings are typically stored at singled-out memory addresses (locations). Thus, the aforementioned string (for example, the empty string) may be stored in ii or more than places in retention.

In this mode, there could be multiple empty strings in memory, in dissimilarity with the formal theory definition, for which in that location is but one possible empty cord. However, a cord comparing part would point that all of these empty strings are equal to each other.

Even a string of length naught can require retention to store it, depending on the format being used. In most programming languages, the empty string is distinct from a aught reference (or nil pointer) considering a null reference points to no cord at all, not even the empty string. The empty string is a legitimate cord, upon which most cord operations should piece of work. Some languages treat some or all of the post-obit in similar ways: empty strings, null references, the integer 0, the floating indicate number 0, the Boolean value false, the ASCII character NUL, or other such values.

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

λ representation	Programming languages
`""`	C, C#, C++, Become, Haskell, Coffee, JavaScript, Julia, Lua, 1000, Objective-C (as a C string), OCaml, Perl, PHP, Python, Scarlet, Scala, Standard ML, Swift, Tcl, Visual Basic .Cyberspace
`''`	APL, Delphi, JavaScript, Lua, MATLAB, Pascal, Perl, PHP, Python, R, Cherry, Smalltalk, SQL
`character(0)`	R^[3]
`{'\0'}`	C, C++, Objective-C (as a C cord)
`std::string()`	C++
`""s`	C++ (since the 2014 standard)
`@""`	Objective-C (equally a constant `NSString` object)
`[NSString string]`	Objective-C (every bit a new `NSString` object)
`q(), qq()`	Perl
`str()`	Python
`%{}` `%()`	Red
`string.Empty`	C#, Visual Basic .Net
`Cord.make 0 '-'`	OCaml
`{}`	Tcl
`[[]]`	Lua

Examples of empty strings [edit]

This section needs expansion. Y'all tin help past adding to it. (March 2010)

The empty string is a syntactically valid representation of zero in positional note (in any base), which does not comprise leading zeros. Since the empty string does not have a standard visual representation exterior of formal linguistic communication theory, the number zero is traditionally represented by a single decimal digit 0 instead.

Zip-filled memory area, interpreted as a nil-terminated string, is an empty string.

Empty lines of text show the empty cord. This tin occur from ii consecutive EOLs, equally often occur in text files, and this is sometimes used in text processing to separate paragraphs, eastward.chiliad. in MediaWiki.

See likewise [edit]

Empty set
Zip-terminated string
Concatenation theory

References [edit]

^ Corcoran, John; Frank, William; Maloney, Michael (1974). "Cord theory". Journal of Symbolic Logic. 39 (iv): 625–637. doi:x.2307/2272846. JSTOR 2272846.
^ CSE1002 Lecture Notes – Lexicographic
^ At that place are ii ways to create "empty strings" in R; the other is listed here as "". grapheme(0) creates empty graphic symbol vectors, which will output 0 when counted.