Picture Of The Cell Theory

Unique string of length zero

In formal linguistic communication theory, the empty string, or empty discussion, is the unique string of length nothing.

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 instance where the sequence has length zero, so there are no symbols in the string. At that place is only ane empty string, because two strings are but different if they accept unlike 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 language ∅, which is a formal language (i.e. a prepare of strings) that contains no strings, non fifty-fifty the empty string.

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 chain operation. The set up of all strings forms a gratis 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.^[two]

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

Employ 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 same string (for instance, the empty string) may exist stored in two or more places in memory.

In this way, in that location could exist multiple empty strings in retention, in contrast with the formal theory definition, for which there is only one possible empty string. Notwithstanding, a string comparing function would indicate that all of these empty strings are equal to each other.

Even a string of length nothing can require memory to shop it, depending on the format existence used. In most programming languages, the empty string is distinct from a null reference (or null pointer) because a zilch reference points to no string at all, not even the empty cord. The empty cord is a legitimate string, upon which most string operations should work. Some languages treat some or all of the post-obit in similar ways: empty strings, null references, the integer 0, the floating signal number 0, the Boolean value false, the ASCII grapheme NUL, or other such values.

The empty string is unremarkably represented similarly to other strings. In implementations with string terminating character (zero-terminated strings or evidently text lines), the empty string is indicated by the immediate utilize of this terminating graphic symbol.

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

Examples of empty strings [edit]

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The empty cord is a syntactically valid representation of zero in positional notation (in whatsoever base of operations), which does non contain leading zeros. Since the empty string does not have a standard visual representation outside of formal linguistic communication theory, the number zero is traditionally represented past a single decimal digit 0 instead.

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

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

Come across also [edit]

Empty set
Null-terminated cord
Concatenation theory

References [edit]

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