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Unique string of length nix

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


Formal theory


[edit]

Formally, a cord is a finite, ordered sequence of characters such equally letters, digits or spaces. The empty string is the special case where the sequence has length naught, so at that place are no symbols in the string. There is just one empty string, because two strings are but unlike 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 non be dislocated with the empty linguistic communication ∅, which is a formal language (i.e. a prepare of strings) that contains no strings, non even the empty cord.

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 costless monoid with respect to ⋅ and ε.
  • εR
    = ε. Reversal of the empty string produces the empty cord.
  • The empty string precedes any other string under lexicographical gild, because it is the shortest of all strings.[2]

In context-gratis grammars, a production rule that allows a symbol to produce the empty string is known every bit an ε-production, 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 singled-out memory addresses (locations). Thus, the same cord (for example, the empty string) may be stored in two or more places in retention.

In this mode, there could be multiple empty strings in memory, in contrast with the formal theory definition, for which at that place is only one possible empty string. However, a string comparison office would indicate that all of these empty strings are equal to each other.

Even a string of length zero can crave retentivity to store it, depending on the format being used. In most programming languages, the empty string is distinct from a zero reference (or null arrow) because a null reference points to no string at all, non even the empty string. The empty cord is a legitimate cord, upon which nearly string operations should work. Some languages care for some or all of the following in similar ways: empty strings, nil references, the integer 0, the floating signal 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 graphic symbol (null-terminated strings or plain text lines), the empty cord is indicated by the firsthand use of this terminating character.

λ representation Programming languages
"" C, C#, C++, Become, Haskell, Coffee, JavaScript, Julia, Lua, Thou, Objective-C (every bit a C string), OCaml, Perl, PHP, Python, Ruby, Scala, Standard ML, Swift, Tcl, Visual Bones .NET
'' APL, Delphi, JavaScript, Lua, MATLAB, Pascal, Perl, PHP, Python, R, Carmine, Smalltalk, SQL
character(0) R[3]
{'\0'} C, C++, Objective-C (as a C string)
std::cord() C++
""s C++ (since the 2014 standard)
@"" Objective-C (as a constant
NSString
object)
[NSString string] Objective-C (every bit a new
NSString
object)
q(), qq() Perl
str() Python
%{}

%()
Crimson
String::new()
[4]
Rust
string.Empty C#, Visual Bones .Internet
Cord.make 0 '-' OCaml
{} Tcl
[[]] Lua

Examples of empty strings

[edit]

The empty string is a syntactically valid representation of nix in positional notation (in any base), which does not incorporate leading zeros. Since the empty string does non 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 surface area, interpreted equally a null-terminated string, is an empty string.

Empty lines of text show the empty cord. This can occur from two sequent EOLs, equally often occur in text files, and this is sometimes used in text processing to separate paragraphs, e.g. in MediaWiki.

See also

[edit]

  • Empty set
  • Nothing-terminated string
  • Chain theory

References

[edit]


  1. ^


    Corcoran, John; Frank, William; Maloney, Michael (1974). “String theory”.
    Periodical of Symbolic Logic.
    39
    (4): 625–637. doi:ten.2307/2272846. JSTOR 2272846. S2CID 2168826.



  2. ^

    CSE1002 Lecture Notes – Lexicographic

  3. ^

    There are two 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.

  4. ^


    “Cord in std::string – Rust”.
    doc.rust-lang.org
    . Retrieved
    2022-11-30
    .




Source: https://en.wikipedia.org/wiki/Empty_string

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