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Unique string of length aught

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 cord is the special instance where the sequence has length nada, so in that location are no symbols in the cord. There is only 1 empty cord, because two strings are only different if they have different lengths or a unlike 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 ready of strings) that contains no strings, not even the empty string.

The empty cord has several properties:

|ε| = 0. Its string length is zero.
ε ⋅ s = s ⋅ ε = s. The empty string is the identity element of the chain operation. The ready of all strings forms a free 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 social club, because it is the shortest of all strings.^[2]

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

Utilize in programming languages [edit]

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

In this way, at that place could be multiple empty strings in retentiveness, in contrast with the formal theory definition, for which there is only one possible empty string. Notwithstanding, a string comparing function would betoken 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 singled-out from a null reference (or cypher arrow) because a zero reference points to no string at all, not even the empty string. The empty string is a legitimate string, upon which most string operations should piece of work. Some languages care for 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 cord is usually represented similarly to other strings. In implementations with string terminating character (null-terminated strings or plain text lines), the empty cord is indicated by the immediate use of this terminating character.

λ representation	Programming languages
`""`	C, C#, C++, Go, Haskell, Java, JavaScript, Julia, Lua, G, Objective-C (every bit 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, Ruby, Smalltalk, SQL
`grapheme(0)`	R^[3]
`{'\0'}`	C, C++, Objective-C (equally a C cord)
`std::string()`	C++
`""southward`	C++ (since the 2014 standard)
`@""`	Objective-C (as a constant `NSString` object)
`[NSString string]`	Objective-C (as a new `NSString` object)
`q(), qq()`	Perl
`str()`	Python
`%{}` `%()`	Red
`cord.Empty`	C#, Visual Basic .Cyberspace
`String.make 0 '-'`	OCaml
`{}`	Tcl
`[[]]`	Lua

Examples of empty strings [edit]

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

The empty string is a syntactically valid representation of zilch in positional notation (in any base), which does non incorporate leading zeros. Since the empty cord 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.

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

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

References [edit]

^ Corcoran, John; Frank, William; Maloney, Michael (1974). "String theory". Journal of Symbolic Logic. 39 (iv): 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 as "". grapheme(0) creates empty character vectors, which will output 0 when counted.