/r[aeiou]+/g (lowercaser followed by one or more lowercase vowels).Aregular expression (shortened asregex orregexp),[1] sometimes referred to as arational expression,[2][3] is a sequence ofcharacters that specifies amatch pattern intext. Usually such patterns are used bystring-searching algorithms for "find" or "find and replace" operations onstrings, or forinput validation. Regular expression techniques are developed intheoretical computer science andformal language theory.
The concept of regular expressions began in the 1950s, when the American mathematicianStephen Cole Kleene formalized the concept of aregular language. They came into common use withUnix text-processing utilities. Differentsyntaxes for writing regular expressions have existed since the 1980s, one being thePOSIX standard and another, widely used, being thePerl syntax.
Regular expressions are used insearch engines, in search and replace dialogs ofword processors andtext editors, intext processing utilities such assed andAWK, and inlexical analysis. Regular expressions are supported in many programming languages. Library implementations are often called an "engine",[4][5] andmany of these are available for reuse.
Regular expressions originated in 1951, when mathematicianStephen Cole Kleene describedregular languages using his mathematical notation calledregular events.[6][7] These arose intheoretical computer science, in the subfields ofautomata theory (models of computation) and the description and classification offormal languages, motivated by Kleene's attempt to describe earlyartificial neural networks. (Kleene introduced it as an alternative toMcCulloch & Pitts's "prehensible", but admitted "We would welcome any suggestions as to a more descriptive term."[8]) Other early implementations ofpattern matching include theSNOBOL language, which did not use regular expressions, but instead its own pattern matching constructs.
Regular expressions entered popular use from 1968 in two uses: pattern matching in a text editor[9] and lexical analysis in a compiler.[10] Among the first appearances of regular expressions in program form was whenKen Thompson built Kleene's notation into the editorQED as a means to match patterns intext files.[9][11][12][13] For speed, Thompson implemented regular expression matching byjust-in-time compilation (JIT) toIBM 7094 code on theCompatible Time-Sharing System, an important early example of JIT compilation.[14] He later added this capability to the Unix editored, which eventually led to the popular search toolgrep's use of regular expressions ("grep" is a word derived from the command for regular expression searching in the ed editor:g/re/p meaning "Global search for Regular Expression and Print matching lines").[15] Around the same time when Thompson developed QED, a group of researchers includingDouglas T. Ross implemented a tool based on regular expressions that is used for lexical analysis incompiler design.[10]
Many variations of these original forms of regular expressions were used inUnix[13] programs atBell Labs in the 1970s, includinglex,sed,AWK, andexpr, and in other programs such asvi, andEmacs (which has its own, incompatible syntax and behavior). Regexes were subsequently adopted by a wide range of programs, with these early forms standardized in thePOSIX.2 standard in 1992.
In the 1980s, the more complicated regexes arose inPerl, which originally derived from a regex library written byHenry Spencer (1986), who later wrote an implementation forTcl calledAdvanced Regular Expressions.[16] The Tcl library is a hybridNFA/DFA implementation with improved performance characteristics. Software projects that have adopted Spencer's Tcl regular expression implementation includePostgreSQL.[17] Perl later expanded on Spencer's original library to add many new features.[18] Part of the effort in the design ofRaku (formerly named Perl 6) is to improve Perl's regex integration, and to increase their scope and capabilities to allow the definition ofparsing expression grammars.[19] The result is amini-language calledRaku rules, which are used to define Raku grammar as well as provide a tool to programmers in the language. These rules maintain existing features of Perl 5.x regexes, but also allowBNF-style definition of arecursive descent parser via sub-rules.
The use of regexes in structured information standards for document and database modeling started in the 1960s and expanded in the 1980s when industry standards likeISO SGML (precursored by ANSI "GCA 101-1983") consolidated. The kernel of thestructure specification language standards consists of regexes. Its use is evident in theDTD element group syntax. Prior to the use of regular expressions, many search languages allowed simple wildcards, for example "*" to match any sequence of characters, and "?" to match a single character. Relics of this can be found today in theglob syntax for filenames, and in theSQLLIKE operator.
Starting in 1997,Philip Hazel developedPCRE (Perl Compatible Regular Expressions), which attempts to closely mimic Perl's regex functionality and is used by many modern tools includingPHP andApache HTTP Server.[20]
Today, regexes are widely supported in programming languages, text processing programs (particularlylexers), advanced text editors, and some other programs. Regex support is part of thestandard library of many programming languages, includingJava andPython, and is built into the syntax of others, including Perl andECMAScript. In the late 2010s, several companies started to offer hardware,FPGA,[21]GPU[22] implementations ofPCRE compatible regex engines that are faster compared toCPU implementations.
The phraseregular expressions, orregexes, is often used to mean the specific, standard textual syntax for representing patterns for matching text, as distinct from the mathematical notation described below. Each character in a regular expression (that is, each character in the string describing its pattern) is either ametacharacter, having a special meaning, or a regular character that has a literal meaning. For example, in the regexb., 'b' is a literal character that matches just 'b', while '.' is a metacharacter that matches every character except a newline. Therefore, this regex matches, for example, 'b%', or 'bx', or 'b5'. Together, metacharacters and literal characters can be used to identify text of a given pattern or process a number of instances of it. Pattern matches may vary from a precise equality to a very general similarity, as controlled by the metacharacters. For example,. is a very general pattern,[a-z] (match all lowercase letters from 'a' to 'z') is less general andb is a precise pattern (matches just 'b'). The metacharacter syntax is designed specifically to represent prescribed targets in a concise and flexible way to direct the automation of text processing of a variety of input data, in a form easy to type using a standardASCIIkeyboard.
A very simple case of a regular expression in this syntax is to locate a word spelled two different ways in atext editor, the regular expressionseriali[sz]e matches both "serialise" and "serialize".Wildcard characters also achieve this, but are more limited in what they can pattern, as they have fewer metacharacters and a simple language-base.
The usual context of wildcard characters is inglobbing similar names in a list of files, whereas regexes are usually employed in applications that pattern-match text strings in general. For example, the regex^[ \t]+|[ \t]+$ matches excess whitespace at the beginning or end of a line. An advanced regular expression that matches any numeral is[+-]?(\d+(\.\d*)?|\.\d+)([eE][+-]?\d+)?.
Aregex processor translates a regular expression in the above syntax into an internal representation that can be executed and matched against astring representing the text being searched in. One possible approach is theThompson's construction algorithm to construct anondeterministic finite automaton (NFA), which is thenmade deterministic and the resultingdeterministic finite automaton (DFA) is run on the target text string to recognize substrings that match the regular expression.The picture shows the NFA schemeN(s*) obtained from the regular expressions*, wheres denotes a simpler regular expression in turn, which has already beenrecursively translated to the NFAN(s).
A regular expression, often called apattern, specifies aset of strings required for a particular purpose. A simple way to specify a finite set of strings is to list itselements or members. However, there are often more concise ways: for example, the set containing the three strings "Handel", "Händel", and "Haendel" can be specified by the patternH(ä|ae?)ndel; we say that this patternmatches each of the three strings. However, there can be many ways to write a regular expression for the same set of strings: for example,(Hän|Han|Haen)del also specifies the same set of three strings in this example.
Most formalisms provide the following operations to construct regular expressions.
gray|grey can match "gray" or "grey".gray|grey andgr(a|e)y are equivalent patterns which both describe the set of "gray" or "grey".?, theasterisk* (derived from theKleene star), and theplus sign+ (Kleene plus).? | The question mark indicateszero or one occurrences of the preceding element. For example,colou?r matches both "color" and "colour". |
* | The asterisk indicateszero or more occurrences of the preceding element. For example,ab*c matches "ac", "abc", "abbc", "abbbc", and so on. |
+ | The plus sign indicatesone or more occurrences of the preceding element. For example,ab+c matches "abc", "abbc", "abbbc", and so on, but not "ac". |
{n}[23] | The preceding item is matched exactlyn times. |
{min,}[23] | The preceding item is matchedmin or more times. |
{,max}[23] | The preceding item is matched up tomax times. |
{min,max}[23] | The preceding item is matched at leastmin times, but not more thanmax times. |
. matches any character. For example,a.b matches any string that contains an "a", and then any character and then "b".a.*b matches any string that contains an "a", and then the character "b" at some later point.These constructions can be combined to form arbitrarily complex expressions, much like one can construct arithmetical expressions from numbers and the operations +, −, ×, and ÷.
The precisesyntax for regular expressions varies among tools and with context; more detail is given in§ Syntax.
Regular expressions describeregular languages informal language theory. They have the same expressive power asregular grammars. But the language of regular expressions itself, iscontext-free language.
Regular expressions consist of constants, which denote sets of strings, and operator symbols, which denote operations over these sets. The following definition is standard, and found as such in most textbooks on formal language theory.[24][25] Given a finitealphabet Σ, the following constants are definedas regular expressions:
a in Σ denoting the set containing only the charactera.Given regular expressions R and S, the following operations over them are definedto produce regular expressions:
(RS) denotes the set of strings that can be obtained by concatenating a string accepted by R and a string accepted by S (in that order). For example, let R denote {"ab", "c"} and S denote {"d", "ef"}. Then,(RS) denotes {"abd", "abef", "cd", "cef"}.(R|S) denotes theset union of sets described by R and S. For example, if R describes {"ab", "c"} and S describes {"ab", "d", "ef"}, expression(R|S) describes {"ab", "c", "d", "ef"}.(R*) denotes the smallestsuperset of the set described byR that contains ε and isclosed under string concatenation. This is the set of all strings that can be made by concatenating any finite number (including zero) of strings from the set described by R. For example, if R denotes {"0", "1"},(R*) denotes the set of all finitebinary strings (including the empty string). If R denotes {"ab", "c"},(R*) denotes {ε, "ab", "c", "abab", "abc", "cab", "cc", "ababab", "abcab", ...}.To avoid parentheses, it is assumed that the Kleene star has the highest priority followed by concatenation, then alternation. If there is no ambiguity, then parentheses may be omitted. For example,(ab)c can be written asabc, anda|(b(c*)) can be written asa|bc*. Many textbooks use the symbols ∪, +, or ∨ for alternation instead of the vertical bar.
Examples:
a|b* denotes {ε, "a", "b", "bb", "bbb", ...}(a|b)* denotes the set of all strings with no symbols other than "a" and "b", including the empty string: {ε, "a", "b", "aa", "ab", "ba", "bb", "aaa", ...}ab*(c|ε) denotes the set of strings starting with "a", then zero or more "b"s and finally optionally a "c": {"a", "ac", "ab", "abc", "abb", "abbc", ...}(0|(1(01*0)*1))* denotes the set of binary numbers that are multiples of 3: { ε, "0", "00", "11", "000", "011", "110", "0000", "0011", "0110", "1001", "1100", "1111", "00000", ...}The formal definition of regular expressions is minimal on purpose, and avoids defining? and+—these can be expressed as follows:a+=aa*, anda?=(a|ε). Sometimes thecomplement operator is added, to give ageneralized regular expression; hereRc matches all strings over Σ* that do not matchR. In principle, the complement operator is redundant, because it does not grant any more expressive power. However, it can make a regular expression much more concise—eliminating a single complement operator can cause adouble exponential blow-up of its length.[26][27][28]
Regular expressions in this sense can express the regular languages, exactly the class of languages accepted bydeterministic finite automata. There is, however, a significant difference in compactness. Some classes of regular languages can only be described by deterministic finite automata whose size growsexponentially in the size of the shortest equivalent regular expressions. The standard example here is the languagesLk consisting of all strings over the alphabet {a,b} whosekth-from-last letter equals a. On the one hand, a regular expression describingL4 is given by.
Generalizing this pattern toLk gives the expression:
On the other hand, it is known that every deterministic finite automaton accepting the languageLk must have at least 2k states. Luckily, there is a simple mapping from regular expressions to the more generalnondeterministic finite automata (NFAs) that does not lead to such a blowup in size; for this reason NFAs are often used as alternative representations of regular languages. NFAs are a simple variation of the type-3grammars of theChomsky hierarchy.[24]
In the opposite direction, there are many languages easily described by a DFA that are not easily described by a regular expression. For instance, determining the validity of a givenISBN requires computing the modulus of the integer base 11, and can be easily implemented with an 11-state DFA. However, converting it to a regular expression results in a 2,14 megabytes file .[29]
Given a regular expression,Thompson's construction algorithm computes an equivalent nondeterministic finite automaton. A conversion in the opposite direction is achieved byKleene's algorithm.
Finally, many real-world "regular expression" engines implement features that cannot be described by the regular expressions in the sense of formal language theory; rather, they implementregexes. Seebelow for more on this.
As seen in many of the examples above, there is more than one way to construct a regular expression to achieve the same results.
It is possible to write analgorithm that, for two given regular expressions, decides whether the described languages are equal; the algorithm reduces each expression to aminimal deterministic finite state machine, and determines whether they areisomorphic (equivalent).
Algebraic laws for regular expressions can be obtained using a method by Gischer which is best explained along an example: In order to check whether (X+Y)∗ and (X∗Y∗)∗ denote the same regular language, for all regular expressionsX,Y, it is necessary and sufficient to check whether the particular regular expressions (a+b)∗ and (a∗b∗)∗ denote the same language over the alphabet Σ={a,b}. More generally, an equationE=F between regular-expression terms with variables holds if, and only if, its instantiation with different variables replaced by different symbol constants holds.[30][31]
Every regular expression can be written solely in terms of theKleene star andset unions over finite words. This is a surprisingly difficult problem. As simple as the regular expressions are, there is no method to systematically rewrite them to some normal form. The lack of axiom in the past led to thestar height problem. In 1991,Dexter Kozen axiomatized regular expressions as aKleene algebra, using equational andHorn clause axioms.[32]Already in 1964, Redko had proved that no finite set of purely equational axioms can characterize the algebra of regular languages.[33]
A regexpattern matches a targetstring. The pattern is composed of a sequence ofatoms. An atom is a single point within the regex pattern which it tries to match to the target string. The simplest atom is a literal, but grouping parts of the pattern to match an atom will require using( ) as metacharacters. Metacharacters help form:atoms;quantifiers telling how many atoms (and whether it is agreedy quantifier or not); a logical OR character, which offers a set of alternatives, and a logical NOT character, which negates an atom's existence; and backreferences to refer to previous atoms of a completing pattern of atoms. A match is made, not when all the atoms of the string are matched, but rather when all the pattern atoms in the regex have matched. The idea is to make a small pattern of characters stand for a large number of possible strings, rather than compiling a large list of all the literal possibilities.
Depending on the regex processor there are about fourteen metacharacters, characters that may or may not have theirliteral character meaning, depending on context, or whether they are "escaped", i.e. preceded by anescape sequence, in this case, the backslash\. Modern and POSIX extended regexes use metacharacters more often than their literal meaning, so to avoid "backslash-osis" orleaning toothpick syndrome, they have a metacharacter escape to a literal mode; starting out, however, they instead have the four bracketing metacharacters( ) and{ } be primarily literal, and "escape" this usual meaning to become metacharacters. Common standards implement both. The usual metacharacters are {}[]()^$.|*+? and\. The usual characters that become metacharacters when escaped aredswDSW andN.
When entering a regex in a programming language, they may be represented as a usual string literal, hence usually quoted; this is common in C, Java, and Python for instance, where the regexre is entered as"re". However, they are often written with slashes asdelimiters, as in/re/ for the regexre. This originates ined, where/ is the editor command for searching, and an expression/re/ can be used to specify a range of lines (matching the pattern), which can be combined with other commands on either side, most famouslyg/re/p as ingrep ("global regex print"), which is included in mostUnix-based operating systems, such asLinux distributions. A similar convention is used insed, where search and replace is given bys/re/replacement/ and patterns can be joined with a comma to specify a range of lines as in/re1/,/re2/. This notation is particularly well known due to its use inPerl, where it forms part of the syntax distinct from normal string literals. In some cases, such as sed and Perl, alternative delimiters can be used to avoid collision with contents, and to avoid having to escape occurrences of the delimiter character in the contents. For example, in sed the commands,/,X, will replace a/ with anX, using commas as delimiters.
TheIEEEPOSIX standard has three sets of compliance:BRE (Basic Regular Expressions),[34]ERE (Extended Regular Expressions), andSRE (Simple Regular Expressions). SRE isdeprecated,[35] in favor of BRE, as both providebackward compatibility. The subsection below covering thecharacter classes applies to both BRE and ERE.
BRE and ERE work together. ERE adds?,+, and|, and it removes the need to escape the metacharacters( ) and{ }, which arerequired in BRE. Furthermore, as long as the POSIX standard syntax for regexes is adhered to, there can be, and often is, additional syntax to serve specific (yet POSIX compliant) applications. Although POSIX.2 leaves some implementation specifics undefined, BRE and ERE provide a "standard" which has since been adopted as the default syntax of many tools, where the choice of BRE or ERE modes is usually a supported option. For example,GNUgrep has the following options: "grep -E" for ERE, and "grep -G" for BRE (the default), and "grep -P" forPerl regexes.
Perl regexes have become a de facto standard, having a rich and powerful set of atomic expressions. Perl has no "basic" or "extended" levels. As in POSIX EREs,( ) and{ } are treated as metacharacters unless escaped; other metacharacters are known to be literal or symbolic based on context alone. Additional functionality includeslazy matching,backreferences, named capture groups, andrecursive patterns.
In thePOSIX standard, Basic Regular Syntax (BRE) requires that themetacharacters( ) and{ } be designated\(\) and\{\}, whereas Extended Regular Syntax (ERE) does not.
| Metacharacter | Description |
|---|---|
^ | Matches the starting position within the string. In line-based tools, it matches the starting position of any line. |
. | Matches any single character (many applications excludenewlines, and exactly which characters are considered newlines is flavor-, character-encoding-, and platform-specific, but it is safe to assume that the line feed character is included). Within POSIX bracket expressions, the dot character matches a literal dot. For example,a.c matches "abc", etc., but[a.c] matches only "a", ".", or "c". |
[ ] | A bracket expression. Matches a single character that is contained within the brackets. For example,[abc] matches "a", "b", or "c".[a-z] specifies a range which matches any lowercase letter from "a" to "z". These forms can be mixed:[abcx-z] matches "a", "b", "c", "x", "y", or "z", as does[a-cx-z].The |
[^ ] | Matches a single character that is not contained within the brackets. For example,[^abc] matches any character other than "a", "b", or "c".[^a-z] matches any single character that is not a lowercase letter from "a" to "z". Likewise, literal characters and ranges can be mixed. |
$ | Matches the ending position of the string or the position just before a string-ending newline. In line-based tools, it matches the ending position of any line. |
( ) | Defines a marked subexpression, also called a capturing group, which is essential for extracting the desired part of the text (See also the next entry,\n).BRE mode requires\( \). |
\n | Matches what thenth marked subexpression matched, wheren is a digit from 1 to 9. This construct is defined in the POSIX standard.[36] Some tools allow referencing more than nine capturing groups. Also known as a back-reference, this feature is supported in BRE mode. |
* | Matches the preceding element zero or more times. For example,ab*c matches "ac", "abc", "abbbc", etc.[xyz]* matches "", "x", "y", "z", "zx", "zyx", "xyzzy", and so on.(ab)* matches "", "ab", "abab", "ababab", and so on. |
{m,n} | Matches the preceding element at leastm and not more thann times. For example,a{3,5} matches only "aaa", "aaaa", and "aaaaa". This is not found in a few older instances of regexes. BRE mode requires\{m,n\}. |
Examples:
.at matches any three-character string ending with "at", including "hat", "cat", "bat", "4at", "#at" and " at" (starting with a space).[hc]at matches "hat" and "cat".[^b]at matches all strings matched by.at except "bat".[^hc]at matches all strings matched by.at other than "hat" and "cat".^[hc]at matches "hat" and "cat", but only at the beginning of the string or line.[hc]at$ matches "hat" and "cat", but only at the end of the string or line.\[.\] matches any single character surrounded by "[" and "]" since the brackets are escaped, for example: "[a]", "[b]", "[7]", "[@]", "[]]", and "[ ]" (bracket space bracket).s.* matches s followed by zero or more characters, for example: "s", "saw", "seed", "s3w96.7", and "s6#h%(>>>m n mQ".According to Russ Cox, the POSIX specification requires ambiguous subexpressions to be handled in a way different from Perl's. The committee replaced Perl's rules with one that is simple to explain, but the new "simple" rules are actually more complex to implement: they were incompatible with pre-existing tooling and made it essentially impossible to define a "lazy match" (see below) extension. As a result, very few programs actually implement the POSIX subexpression rules (even when they implement other parts of the POSIX syntax).[37]
The meaning of metacharactersescaped with a backslash is reversed for some characters in the POSIX Extended Regular Expression (ERE) syntax. With this syntax, a backslash causes the metacharacter to be treated as a literal character. So, for example,\( \) is now( ) and\{ \} is now{ }. Additionally, support is removed for\n backreferences and the following metacharacters are added:
| Metacharacter | Description |
|---|---|
? | Matches the preceding element zero or one time. For example,ab?c matches only "ac" or "abc". |
+ | Matches the preceding element one or more times. For example,ab+c matches "abc", "abbc", "abbbc", and so on, but not "ac". |
| | The choice (also known as alternation or set union) operator matches either the expression before or the expression after the operator. For example,abc|def matches "abc" or "def". |
Examples:
[hc]?at matches "at", "hat", and "cat".[hc]*at matches "at", "hat", "cat", "hhat", "chat", "hcat", "cchchat", and so on.[hc]+at matches "hat", "cat", "hhat", "chat", "hcat", "cchchat", and so on, but not "at".cat|dog matches "cat" or "dog".POSIX Extended Regular Expressions can often be used with modern Unix utilities by including thecommand line flag-E.
The character class is the most basic regex concept after a literal match. It makes one small sequence of characters match a larger set of characters. For example,[A-Z] could stand for any uppercase letter in the English alphabet, and\d could mean any digit. Character classes apply to both POSIX levels.
When specifying a range of characters, such as[a-Z] (i.e. lowercasea to uppercaseZ), the computer's locale settings determine the contents by the numeric ordering of the character encoding. They could store digits in that sequence, or the ordering could beabc...zABC...Z, oraAbBcC...zZ. So the POSIX standard defines a character class, which will be known by the regex processor installed. Those definitions are in the following table:
| Description | POSIX | Perl/Tcl | Vim | Java | ASCII |
|---|---|---|---|---|---|
| ASCII characters | \p{ASCII} | [\x00-\x7F] | |||
| Alphanumeric characters | [:alnum:] | \p{Alnum} | [A-Za-z0-9] | ||
| Alphanumeric characters plus "_" | \w | \w | \w | [A-Za-z0-9_] | |
| Non-word characters | \W | \W | \W | [^A-Za-z0-9_] | |
| Alphabetic characters | [:alpha:] | \a | \p{Alpha} | [A-Za-z] | |
| Space and tab | [:blank:] | \s | \p{Blank} | [ \t] | |
| Word boundaries | \b | \< \> | \b | (?<=\W)(?=\w)|(?<=\w)(?=\W) | |
| Non-word boundaries | \B | (?<=\W)(?=\W)|(?<=\w)(?=\w) | |||
| Control characters | [:cntrl:] | \p{Cntrl} | [\x00-\x1F\x7F] | ||
| Digits | [:digit:] | \d | \d | \p{Digit} or\d | [0-9] |
| Non-digits | \D | \D | \D | [^0-9] | |
| Visible characters | [:graph:] | \p{Graph} | [\x21-\x7E] | ||
| Lowercase letters | [:lower:] | \l | \p{Lower} | [a-z] | |
| Visible characters and the space character | [:print:] | \p | \p{Print} | [\x20-\x7E] | |
| Punctuation characters | [:punct:] | \p{Punct} | [][!"#$%&'()*+,./:;<=>?@\^_`{|}~-] | ||
| Whitespace characters | [:space:] | \s | \_s | \p{Space} or\s | [\t\r\n\v\f] |
| Non-whitespace characters | \S | \S | \S | [^ \t\r\n\v\f] | |
| Uppercase letters | [:upper:] | \u | \p{Upper} | [A-Z] | |
| Hexadecimal digits | [:xdigit:] | \x | \p{XDigit} | [A-Fa-f0-9] |
POSIX character classes can only be used within bracket expressions. For example,[[:upper:]ab] matches the uppercase letters and lowercase "a" and "b".
An additional non-POSIX class understood by some tools is[:word:], which is usually defined as[:alnum:] plus underscore. This reflects the fact that in many programming languages these are the characters that may be used in identifiers. The editorVim further distinguishesword andword-head classes (using the notation\w and\h) since in many programming languages the characters that can begin an identifier are not the same as those that can occur in other positions: numbers are generally excluded, so an identifier would look like\h\w* or[[:alpha:]_][[:alnum:]_]* in POSIX notation.
Note that what the POSIX regex standards callcharacter classes are commonly referred to asPOSIX character classes in other regex flavors which support them. With most other regex flavors, the termcharacter class is used to describe what POSIX callsbracket expressions.
Because of its expressive power and (relative) ease of reading, many other utilities and programming languages have adopted syntax similar toPerl's—for example,Java,JavaScript,Julia,Python,Ruby,Qt, Microsoft's.NET Framework, andXML Schema. Some languages and tools such asBoost andPHP support multiple regex flavors. Perl-derivative regex implementations are not identical and usually implement a subset of features found in Perl 5.0, released in 1994. Perl sometimes does incorporate features initially found in other languages. For example, Perl 5.10 implements syntactic extensions originally developed in PCRE and Python.[38]
In Python and some other implementations (e.g. Java), the three common quantifiers (*,+ and?) aregreedy by default because they match as many characters as possible.[39] The regex".+" (including the double-quotes) applied to the string
"Ganymede," he continued, "is the largest moon in the Solar System."
matches the entire line (because the entire line begins and ends with a double-quote) instead of matching only the first part,"Ganymede,". The aforementioned quantifiers may, however, be madelazy orminimal orreluctant, matching as few characters as possible, by appending a question mark:".+?" matches only"Ganymede,".[39]
In Java and Python 3.11+,[40] quantifiers may be madepossessive by appending a plus sign, which disables backing off (in a backtracking engine), even if doing so would allow the overall match to succeed:[41] While the regex".*" applied to the string
"Ganymede," he continued, "is the largest moon in the Solar System."
matches the entire line, the regex".*+" doesnot match at all, because.*+ consumes the entire input, including the final". Thus, possessive quantifiers are most useful with negated character classes, e.g."[^"]*+", which matches"Ganymede," when applied to the same string.
Another common extension serving the same function is atomic grouping, which disables backtracking for a parenthesized group. The typical syntax is(?>group). For example, while^(wi|w)i$ matches bothwi andwii,^(?>wi|w)i$ only matcheswii because the engine is forbidden from backtracking and so cannot try setting the group to "w" after matching "wi".[42]
Possessive quantifiers are easier to implement than greedy and lazy quantifiers, and are typically more efficient at runtime.[41]
IETF RFC 9485 describes "I-Regexp: An Interoperable Regular Expression Format". It specifies a limited subset of regular-expression idioms designed to be interoperable, i.e. produce the same effect, in a large number of regular-expression libraries. I-Regexp is also limited to matching, i.e. providing a true or false match between a regular expression and a given piece of text. Thus, it lacks advanced features such as capture groups, lookahead, and backreferences.[43]
Many features found in virtually all modern regular expression libraries provide an expressive power that exceeds theregular languages. For example, many implementations allow grouping subexpressions with parentheses and recalling the value they match in the same expression (backreferences). This means that, among other things, a pattern can match strings of repeated words like "papa" or "WikiWiki", calledsquares in formal language theory. The pattern for these strings is(.+)\1.
The language of squares is not regular, nor is itcontext-free, due to thepumping lemma. However,pattern matching with an unbounded number of backreferences, as supported by numerous modern tools, is stillcontext sensitive.[44] The general problem of matching any number of backreferences isNP-complete, and the execution time for known algorithms grows exponentially by the number of backreference groups used.[45]
However, many tools, libraries, and engines that provide such constructions still use the termregular expression for their patterns. This has led to a nomenclature where the term regular expression has different meanings informal language theory and pattern matching. For this reason, some people have taken to using the termregex,regexp, or simplypattern to describe the latter.Larry Wall, author of the Perl programming language, writes in an essay about the design of Raku:
"Regular expressions" […] are only marginally related to real regular expressions. Nevertheless, the term has grown with the capabilities of our pattern matching engines, so I'm not going to try to fight linguistic necessity here. I will, however, generally call them "regexes" (or "regexen", when I'm in an Anglo-Saxon mood).[19]
| Assertion | Lookbehind | Lookahead |
|---|---|---|
| Positive | (?<=pattern) | (?=pattern) |
| Negative | (?<!pattern) | (?!pattern) |
| Lookbehind and lookahead assertions inPerl regular expressions | ||
Other features not found in describing regular languages include assertions. These include the ubiquitous^ and$, used since at least 1970,[46] as well as some more sophisticated extensions like lookaround that appeared in 1994.[47] Lookarounds define the surrounding of a match and do not spill into the match itself, a feature only relevant for the use case of string searching.[citation needed] Some of them can be simulated in a regular language by treating the surroundings as a part of the language as well.[48]
Thelook-ahead assertions(?=...) and(?!...) have been attested since at least 1994, starting with Perl 5.[47] The lookbehind assertions(?<=...) and(?<!...) are attested since 1997 in a commit by Ilya Zakharevich to Perl 5.005.[49]
There are at least three differentalgorithms that decide whether and how a given regex matches a string.
The oldest and fastest relies on a result in formal language theory that allows everynondeterministic finite automaton (NFA) to be transformed into adeterministic finite automaton (DFA). The DFA can be constructed explicitly and then run on the resulting input string one symbol at a time. Constructing the DFA for a regular expression of sizem has the time and memory cost ofO(2m), but it can be run on a string of sizen in timeO(n). Note that the size of the expression is the size after abbreviations, such as numeric quantifiers, have been expanded.
An alternative approach is to simulate the NFA directly, essentially building each DFA state on demand and then discarding it at the next step. This keeps the DFA implicit and avoids the exponential construction cost, but running cost rises toO(mn). The explicit approach is called the DFA algorithm and the implicit approach the NFA algorithm. Adding caching to the NFA algorithm is often called the "lazy DFA" algorithm, or just the DFA algorithm without making a distinction. These algorithms are fast, but using them for recalling grouped subexpressions, lazy quantification, and similar features is tricky.[50][51] Modern implementations include the re1-re2-sregex family based on Cox's code.
The third algorithm is to match the pattern against the input string bybacktracking. This algorithm is commonly called NFA, but this terminology can be confusing. Its running time can be exponential, which simple implementations exhibit when matching against expressions like(a|aa)*b that contain both alternation and unbounded quantification and force the algorithm to consider an exponentially increasing number of sub-cases. This behavior can cause a security problem calledRegular expression Denial of Service (ReDoS).
Although backtracking implementations only give an exponential guarantee in the worst case, they provide much greater flexibility and expressive power. For example, any implementation which allows the use of backreferences, or implements the various extensions introduced by Perl, must include some kind of backtracking. Some implementations try to provide the best of both algorithms by first running a fast DFA algorithm, and revert to a potentially slower backtracking algorithm only when a backreference is encountered during the match. GNU grep (and the underlying gnulib DFA) uses such a strategy.[52]
Sublinear runtime algorithms have been achieved usingBoyer-Moore (BM) based algorithms and related DFA optimization techniques such as the reverse scan.[53] GNU grep, which supports a wide variety of POSIX syntaxes and extensions, uses BM for a first-pass prefiltering, and then uses an implicit DFA. Wuagrep, which implements approximate matching, combines the prefiltering into the DFA in BDM (backward DAWG matching). NR-grep's BNDM extends the BDM technique with Shift-Or bit-level parallelism.[54]
A few theoretical alternatives to backtracking for backreferences exist, and their "exponents" are tamer in that they are only related to the number of backreferences, a fixed property of some regexp languages such as POSIX. One naive method that duplicates a non-backtracking NFA for each backreference note has a complexity of time and space for a haystack of length n and k backreferences in the RegExp.[55] A very recent theoretical work based on memory automata gives a tighter bound based on "active" variable nodes used, and a polynomial possibility for some backreferenced regexps.[56]
In theoretical terms, any token set can be matched by regular expressions as long as it is pre-defined. In terms of historical implementations, regexes were originally written to useASCII characters as their token set though regex libraries have supported numerous othercharacter sets. Many modern regex engines offer at least some support forUnicode. In most respects it makes no difference what the character set is, but some issues do arise when extending regexes to support Unicode.
[x-y] are valid whereverx andy havecode points in the range [0x00,0x7F] and codepoint(x) ≤ codepoint(y). The natural extension of such character ranges to Unicode would simply change the requirement that the endpoints lie in [0x00,0x7F] to the requirement that they lie in [0x0000,0x10FFFF]. However, in practice this is often not the case. Some implementations, such as that ofgawk, do not allow character ranges to cross Unicode blocks. A range like [0x61,0x7F] is valid since both endpoints fall within the Basic Latin block, as is [0x0530,0x0560] since both endpoints fall within the Armenian block, but a range like [0x0061,0x0532] is invalid since it includes multiple Unicode blocks. Other engines, such as that of theVim editor, allow block-crossing but the character values must not be more than 256 apart.[57]java.util.regex library, properties of the form\p{InX} or\p{Block=X} match characters in blockX and\P{InX} or\P{Block=X} matches code points not in that block. Similarly,\p{Armenian},\p{IsArmenian}, or\p{Script=Armenian} matches any character in the Armenian script. In general,\p{X} matches any character with either the binary propertyX or the general categoryX. For example,\p{Lu},\p{Uppercase_Letter}, or\p{GC=Lu} matches any uppercase letter. Binary properties that arenot general categories include\p{White_Space},\p{Alphabetic},\p{Math}, and\p{Dash}. Examples of non-binary properties are\p{Bidi_Class=Right_to_Left},\p{Word_Break=A_Letter}, and\p{Numeric_Value=10}.Mostgeneral-purpose programming languages support regex capabilities, either natively or vialibraries.
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Regexes are useful in a wide variety of text processing tasks, and more generallystring processing, where the data need not be textual. Common applications includedata validation,data scraping (especiallyweb scraping),data wrangling, simpleparsing, the production ofsyntax highlighting systems, and many other tasks.
Some high-enddesktop publishing software has the ability to use regexes to automatically apply text styling, saving the person doing the layout from laboriously doing this by hand for anything that can be matched by a regex. For example, by defining acharacter style that makes text intosmall caps and then using the regex[A-Z]{4,} to apply that style, any word of four or more consecutive capital letters will be automatically rendered as small caps instead.
While regexes would be useful on Internetsearch engines, processing them across the entire database could consume excessive computer resources depending on the complexity and design of the regex. Although in many cases system administrators can run regex-based queries internally, most search engines do not offer regex support to the public. Notable exceptions includeGoogle Code Search andExalead. However, Google Code Search was shut down in January 2012.[59]
The specific syntax rules vary depending on the specific implementation,programming language, orlibrary in use. Additionally, the functionality of regex implementations can vary betweenversions.
Because regexes can be difficult to both explain and understand without examples, interactive websites for testing regexes are a useful resource for learning regexes by experimentation.This section provides a basic description of some of the properties of regexes by way of illustration.
The following conventions are used in the examples.[60]
metacharacter(s) ;; the metacharacters column specifies the regex syntax being demonstrated=~ m// ;; indicates a regexmatch operation in Perl=~ s/// ;; indicates a regexsubstitution operation in Perl
These regexes are all Perl-like syntax. StandardPOSIX regular expressions are different.
Unless otherwise indicated, the following examples conform to thePerl programming language, release 5.8.8, January 31, 2006. This means that other implementations may lack support for some parts of the syntax shown here (e.g. basic vs. extended regex,\( \) vs.(), or lack of\d instead ofPOSIX[:digit:]).
The syntax and conventions used in these examples coincide with that of other programming environments as well.[61]
| Metacharacter(s) | Description | Example[62] |
|---|---|---|
. | Normally matches any character except a newline. Within square brackets the dot is literal. | $string1="Hello World\n";if($string1=~m/...../){print"$string1 has length >= 5.\n";} Output: Hello World has length >= 5. |
( ) | Groups a series of pattern elements to a single element. When you match a pattern within parentheses, you can use any of $1,$2, ... later to refer to the previously matched pattern. Some implementations may use a backslash notation instead, like\1,\2. | $string1="Hello World\n";if($string1=~m/(H..).(o..)/){print"We matched '$1' and '$2'.\n";} Output: We matched 'Hel' and 'o W'. |
+ | Matches the preceding pattern element one or more times. | $string1="Hello World\n";if($string1=~m/l+/){print"There are one or more consecutive letter \"l\"'s in $string1.\n";} Output: There are one or more consecutive letter "l"'s in Hello World. |
? | Matches the preceding pattern element zero or one time. | $string1="Hello World\n";if($string1=~m/H.?e/){print"There is an 'H' and a 'e' separated by ";print"0-1 characters (e.g., He Hue Hee).\n";} Output: There is an 'H' and a 'e' separated by 0-1 characters (e.g., He Hue Hee). |
? | Modifies the*,+,? or{M,N}'d regex that comes before to match as few times as possible. | $string1="Hello World\n";if($string1=~m/(l.+?o)/){print"The non-greedy match with 'l' followed by one or ";print"more characters is 'llo' rather than 'llo Wo'.\n";} Output: The non-greedy match with 'l' followed by one or more characters is 'llo' rather than 'llo Wo'. |
* | Matches the preceding pattern element zero or more times. | $string1="Hello World\n";if($string1=~m/el*o/){print"There is an 'e' followed by zero to many ";print"'l' followed by 'o' (e.g., eo, elo, ello, elllo).\n";} Output: There is an 'e' followed by zero to many 'l' followed by 'o' (e.g., eo, elo, ello, elllo). |
{M,N} | Denotes the minimum M and the maximum N match count. N can be omitted and M can be 0: {M} matches "exactly" M times;{M,} matches "at least" M times;{0,N} matches "at most" N times.x* y+ z? is thus equivalent tox{0,} y{1,} z{0,1}. | $string1="Hello World\n";if($string1=~m/l{1,2}/){print"There exists a substring with at least 1 ";print"and at most 2 l's in $string1\n";} Output: There exists a substring with at least 1 and at most 2 l's in Hello World |
[…] | Denotes a set of possible character matches. | $string1="Hello World\n";if($string1=~m/[aeiou]+/){print"$string1 contains one or more vowels.\n";} Output: Hello World contains one or more vowels. |
| | Separates alternate possibilities. | $string1="Hello World\n";if($string1=~m/(Hello|Hi|Pogo)/){print"$string1 contains at least one of Hello, Hi, or Pogo.";} Output: Hello World contains at least one of Hello, Hi, or Pogo. |
\b | Matches a zero-width boundary between a word-class character (see next) and either a non-word class character or an edge; same as
| $string1="Hello World\n";if($string1=~m/llo\b/){print"There is a word that ends with 'llo'.\n";} Output: There is a word that ends with 'llo'. |
\w | Matches an alphanumeric character, including "_"; same as [A-Za-z0-9_] in ASCII, and
in Unicode,[58] where the | $string1="Hello World\n";if($string1=~m/\w/){print"There is at least one alphanumeric ";print"character in $string1 (A-Z, a-z, 0-9, _).\n";} Output: There is at least one alphanumeric character in Hello World (A-Z, a-z, 0-9, _). |
\W | Matches anon-alphanumeric character, excluding "_"; same as [^A-Za-z0-9_] in ASCII, and
in Unicode. | $string1="Hello World\n";if($string1=~m/\W/){print"The space between Hello and ";print"World is not alphanumeric.\n";} Output: The space between Hello and World is not alphanumeric. |
\s | Matches a whitespace character, which in ASCII are tab, line feed, form feed, carriage return, and space; in Unicode, also matches no- | $string1="Hello World\n";if($string1=~m/\s.*\s/){print"In $string1 there are TWO whitespace characters, which may";print" be separated by other characters.\n";} Output: In Hello World there are TWO whitespace characters, which may be separated by other characters. |
\S | Matches anythingbut a whitespace. | $string1="Hello World\n";if($string1=~m/\S.*\S/){print"In $string1 there are TWO non-whitespace characters, which";print" may be separated by other characters.\n";} Output: In Hello World there are TWO non-whitespace characters, which may be separated by other characters. |
\d | Matches a digit; same as [0-9] in ASCII;in Unicode, same as the \p{Digit} or\p{GC=Decimal_Number} property, which itself the same as the\p{Numeric_Type=Decimal} property. | $string1="99 bottles of beer on the wall.";if($string1=~m/(\d+)/){print"$1 is the first number in '$string1'\n";} Output: 99 is the first number in '99 bottles of beer on the wall.' |
\D | Matches a non-digit; same as [^0-9] in ASCII or\P{Digit} in Unicode. | $string1="Hello World\n";if($string1=~m/\D/){print"At least one character in $string1";print" is not a digit.\n";} Output: At least one character in Hello World is not a digit. |
^ | Matches the beginning of a line or string. | $string1="Hello World\n";if($string1=~m/^He/){print"$string1 starts with the characters 'He'.\n";} Output: Hello World starts with the characters 'He'. |
$ | Matches the end of a line or string. | $string1="Hello World\n";if($string1=~m/rld$/){print"$string1 is a line or string ";print"that ends with 'rld'.\n";} Output: Hello World is a line or string that ends with 'rld'. |
\A | Matches the beginning of a string (but not an internal line). | $string1="Hello\nWorld\n";if($string1=~m/\AH/){print"$string1 is a string ";print"that starts with 'H'.\n";} Output: HelloWorld is a string that starts with 'H'. |
\z | Matches the end of a string (but not an internal line).[63] | $string1="Hello\nWorld\n";if($string1=~m/d\n\z/){print"$string1 is a string ";print"that ends with 'd\\n'.\n";} Output: HelloWorld is a string that ends with 'd\n'. |
[^…] | Matches every character except the ones inside brackets. | $string1="Hello World\n";if($string1=~m/[^abc]/){print"$string1 contains a character other than ";print"a, b, and c.\n";} Output: Hello World contains a character other than a, b, and c. |
Regular expressions can often be created ("induced" or "learned") based on a set of example strings. This is known as theinduction of regular languages and is part of the general problem ofgrammar induction incomputational learning theory. Formally, given examples of strings in a regular language, and perhaps also given examples of stringsnot in that regular language, it is possible to induce a grammar for the language, i.e., a regular expression that generates that language. Not all regular languages can be induced in this way (seelanguage identification in the limit), but many can. For example, the set of examples {1, 10, 100}, and negative set (of counterexamples) {11, 1001, 101, 0} can be used to induce the regular expression 1⋅0* (1 followed by zero or more 0s).
The concept of regular events was introduced by Kleene via the definition of regular expressions.
This property need not hold for extended regular expressions, even if they describe no larger class than regular languages; cf. p.121.
Digression: POSIX Submatching
If the scanner detects a transition on backref, it returns a kind of "semi-success" indicating that the match will have to be verified with a backtracking matcher.
m/[^abc]/ could also be rendered as/[^abc]/. The 'm' is only necessary if the user wishes to specify a match operation without using a forward-slash as the regexdelimiter. Sometimes it is useful to specify an alternate regex delimiter in order to avoid "delimiter collision". See 'perldoc perlreArchived 2009-12-31 at theWayback Machine' for more details.
Media related toRegex at Wikimedia Commons
