Modified ECMAScript regular expression grammar

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Regex Grammar
Modified ECMAScript-262
(C++11)
std::basic_regex

This page describes the regular expression grammar that is used when std::basic_regex is constructed with syntax_option_type set to ECMAScript (the default). See syntax_option_type for the other supported regular expression grammars.

The ECMAScript regular expression grammar in C++ is ECMA-262 grammar with modifications marked with (C++ only) below.

Alternatives

A regular expression pattern is sequence of one or more Alternatives, separated by the disjunction operator | (in other words, the disjunction operator has the lowest precedence)

Pattern::

Disjunction

Disjunction::

Alternative
Alternative | Disjunction

The pattern first tries to skip the Disjunction and match the left Alternative followed by the rest of the regular expression (after the Disjunction).

If it fails, it tries to skip the left Alternative and match the right Disjunction (followed by the rest of the regular expression).

If the left Alternative, the right Disjunction, and the remainder of the regular expression all have choice points, all choices in the remainder of the expression are tried before moving on to the next choice in the left Alternative. If choices in the left Alternative are exhausted, the right Disjunction is tried instead of the left Alternative.

Any capturing parentheses inside a skipped Alternative produce empty submatches.

Run this code
#include <iostream>
#include <regex>

void show_matches(const std::string& in, const std::string& re)
{
    std::smatch m;
    std::regex_search(in, m, std::regex(re));
    if(m.empty()) {
        std::cout << "input=[" << in << "], regex=[" << re << "]: NO MATCH\n";
    } else {
        std::cout << "input=[" << in << "], regex=[" << re << "]: ";
        std::cout << "prefix=[" << m.prefix() << "] ";
        for(std::size_t n = 0; n < m.size(); ++n)
            std::cout << " m[" << n << "]=[" << m[n] << "] ";
        std::cout << "suffix=[" << m.suffix() << "]\n";
    }
}
int main()
{
    show_matches("abcdef", "abc|def");
    show_matches("abc", "ab|abc"); // left Alernative matched first

    // Match of the input against the left Alternative (a) followed
    // by the remained of the regex (c|bc) succeeds, which results
    // in m[1]="a" and m[4]="bc".
    // The skipped Alternatives (ab) and (c) leave their submatches
    // m[3] and m[5] empty.
    show_matches("abc", "((a)|(ab))((c)|(bc))");
}

Output: 

input=[abcdef], regex=[abc|def]: prefix=[]  m[0]=[abc] suffix=[def]
input=[abc], regex=[ab|abc]: prefix=[]  m[0]=[ab] suffix=[c]
input=[abc], regex=[((a)|(ab))((c)|(bc))]: prefix=[]  m[0]=[abc]
m[1]=[a]  m[2]=[a]  m[3]=[] m[4]=[bc]  m[5]=[]  m[6]=[bc] suffix=[]

Terms

Each Alternative is either empty or is a sequence of Terms (with no separators between the Terms)

Alternative::

[empty]
Alternative Term

Empty Alternative always matches and does not consume any input.

Consecutive Terms try to simultaneously match consecutive portions of the input.

If the left Alternative, the right Term, and the remainder of the regular expression all have choice points, all choices in the remained of the expression are tried before moving on to the next choice in the right Term, and all choices in the right Term are tried before moving on to the next choice in the left Alternative.

Run this code
#include <iostream>
#include <regex>

void show_matches(const std::string& in, const std::string& re)
{
    std::smatch m;
    std::regex_search(in, m, std::regex(re));
    if(m.empty()) {
        std::cout << "input=[" << in << "], regex=[" << re << "]: NO MATCH\n";
    } else {
        std::cout << "input=[" << in << "], regex=[" << re << "]: ";
        std::cout << "prefix=[" << m.prefix() << "] ";
        for(std::size_t n = 0; n < m.size(); ++n)
            std::cout << " m[" << n << "]=[" << m[n] << "] ";
        std::cout << "suffix=[" << m.suffix() << "]\n";
    }
}
int main()
{
    show_matches("abcdef", ""); // empty regex is a single empty Alternative
    show_matches("abc", "abc|"); // left Alernative matched first
    show_matches("abc", "|abc"); // left Alernative matched first, leaving abc unmatched
}

Output: 

input=[abcdef], regex=[]: prefix=[]  m[0]=[] suffix=[abcdef]
input=[abc], regex=[abc|]: prefix=[]  m[0]=[abc] suffix=[]
input=[abc], regex=[|abc]: prefix=[]  m[0]=[] suffix=[abc]

Quantifiers

  • Each Term is either an Assertion (see below), or an Atom (see below), or an Atom immediately followed by a Quantifier

Term::

Assertion
Atom
Atom Quantifier

Each Quantifier is either a greedy quantifier (which consists of just one QuantifierPrefix) or a non-greedy quantifier (which consists of one QuantifierPrefix followed by the question mark ?).

Quantifier::

QuantifierPrefix
QuantifierPrefix ?

Each QuantifierPrefix determines two numbers: the minimum number of repetitions and the maximum number of repetitions, as follows:

QuantifierPrefix Minimum Maximum
* zero infinity
+ one infinity
? zero one
{ DecimalDigits } value of DecimalDigits value of DecimalDigits
{ DecimalDigits , } value of DecimalDigits infinity
{ DecimalDigits , DecimalDigits } value of DecimalDigits before the comma value of DecimalDigits after the comma

The values of the individual DecimalDigits are obtained by calling std::regex_traits::value(C++ only) on each of the digits.

An Atom followed by a Quantifier is repeated the number of times specified by the Quantifier. A Quantifier can be non-greedy, in which case the Atom pattern is repeated as few times as possible while still matching the remainder of the regular expression, or it can be greedy, in which case the Atom pattern is repeated as many times as possible while still matching the remainder of the regular expression.

The Atom pattern is what is repeated, not the input that it matches, so different repetitions of the Atom can match different input substrings.

If the Atom and the remainder of the regular expression all have choice points, the Atom is first matched as many (or as few, if non-greedy) times as possible. All choices in the remainder of the regular expression are tried before moving on to the next choice in the last repetition of Atom. All choices in the last (nth) repetition of Atom are tried before moving on to the next choice in the next-to-last (n1)st repetition of Atom; at which point it may turn out that more or fewer repetitions of Atom are now possible; these are exhausted (again, starting with either as few or as many as possible) before moving on to the next choice in the (n-1)st repetition of Atom and so on.

The Atom's captures are cleared each time it is repeated (see the "(z)((a+)?(b+)?(c))*" example below)

Run this code
#include <iostream>
#include <regex>

void show_matches(const std::string& in, const std::string& re)
{
    std::smatch m;
    std::regex_search(in, m, std::regex(re));
    if(m.empty()) {
        std::cout << "input=[" << in << "], regex=[" << re << "]: NO MATCH\n";
    } else {
        std::cout << "input=[" << in << "], regex=[" << re << "]: ";
        std::cout << "prefix=[" << m.prefix() << "] ";
        for(std::size_t n = 0; n < m.size(); ++n)
            std::cout << " m[" << n << "]=[" << m[n] << "] ";
        std::cout << "suffix=[" << m.suffix() << "]\n";
    }
}
int main()
{
    // greedy match, repeats [a-z] 4 times
    show_matches("abcdefghi", "a[a-z]{2,4}");
    // non-greedy match, repeats [a-z] 2 times
    show_matches("abcdefghi", "a[a-z]{2,4}?");

    // Choice point ordering for quantifiers results in a match
    // with two repetitions, first matching the substring "aa",
    // second matching the substring "ba", leaving "ac" not matched
    // ("ba" appears in the capture clause m[1])
    show_matches("aabaac", "(aa|aabaac|ba|b|c)*");

    // Choice point ordering for quantifiers makes this regex 
    // calculate the greatest common divisor between 10 and 15
    // (the answer is 5, and it populates m[1] with "aaaaa")
    show_matches("aaaaaaaaaa,aaaaaaaaaaaaaaa", "^(a+)\\1*,\\1+$");

    // the substring "bbb" does not appear in the capture clause m[4]
    // because it is cleared when the second repetition of the atom
    // (a+)?(b+)?(c) is matching the substring "ac"
    show_matches("zaacbbbcac", "(z)((a+)?(b+)?(c))*");
}

Output: 

input=[abcdefghi], regex=[a[a-z]{2,4}]: prefix=[]  m[0]=[abcde] suffix=[fghi]
input=[abcdefghi], regex=[a[a-z]{2,4}?]: prefix=[]  m[0]=[abc] suffix=[defghi]
input=[aabaac], regex=[(aa|aabaac|ba|b|c)*]:
 prefix=[]  m[0]=[aaba]  m[1]=[ba] suffix=[ac]
input=[aaaaaaaaaa,aaaaaaaaaaaaaaa], regex=[^(a+)\1*,\1+$]:
 prefix=[]  m[0]=[aaaaaaaaaa,aaaaaaaaaaaaaaa]  m[1]=[aaaaa] suffix=[]
input=[zaacbbbcac], regex=[(z)((a+)?(b+)?(c))*]:
prefix=[]  m[0]=[zaacbbbcac]  m[1]=[z]  m[2]=[ac]  m[3]=[a]  m[4]=[]  m[5]=[c] suffix=[]

Assertions

Assertions match conditions, rather than substrings of the input string. They never consume any characters from the input. Each Assertion is one of the following

Assertion::

^
$
\ b
\ B
( ? = Disjunction )
( ? ! Disjunction )

The assertion ^ (beginning of line) matches

1) The position that immediately follows a LineTerminator character (this may not be supported) (until C++17) (this is only guaranteed if std::regex_constants::multiline(C++ only) is enabled) (since C++17)
2) The beginning of the input (unless std::regex_constants::match_not_bol(C++ only) is enabled)

The assertion $ (end of line) matches

1) The position of a LineTerminator character (this may not be supported) (until C++17)(this is only guaranteed if std::regex_constants::multiline(C++ only) is enabled) (since C++17)
2) The end of the input (unless std::regex_constants::match_not_eol(C++ only) is enabled)

In the two assertions above and in the Atom . below, LineTerminator is one of the following four charactes: U+000A (\n or line feed), U+000D (\r or carriage return), U+2028 (line separator), or U+2029 (paragraph separator)

The assertion \b (word boundary) matches

1) The beginning of a word (current character is a letter, digit, or underscore, and the previous character is not)
2) The end of a word (current character is not a letter, digit, or underscore, and the previous character is one of those)
3) The beginning of input if the first character is a letter, digit, or underscore (unless std::regex_constants::match_not_bow(C++ only) is enabled)
4) The end of input if the last character is a letter, digit, or underscore (unless std::regex_constants::match_not_eow(C++ only) is enabled)

The assertion \B (negative word boundary) matches everything EXCEPT the following

1) The beginning of a word (current character is a letter, digit, or underscore, and the previous character is not one of those or does not exist)
2) The end of a word (current character is not a letter, digit, or underscore (or the matcher is at the end of input), and the previous character is one of those)

The assertion ( ? = Disjunction ) (zero-width positive lookahead) matches if Disjunction would match the input at the current position

The assertion ( ? ! Disjunction ) (zero-width negative lookahead) matches if Disjunction would NOT match the input at the current position.

For both Lookahead assertions, when matching the Disjunction, the position is not advanced before matching the remainder of the regular expression. Also, if Disjunction can match at the current position in several ways, only the first one is tried.

ECMAScript forbids backtracking into the lookahead Disjunctions, which affects the behavior of backreferences into a positive lookahead from the remainder of the regular expression (see example below). Backreferences into the negative lookahead from the rest of the regular expression are always undefined (since the lookahead Disjunction must fail to proceed).

Note: Lookahead assertions may be used to create logical AND between multiple regular expressions (see example below)

Run this code
#include <iostream>
#include <regex>

void show_matches(const std::string& in, const std::string& re)
{
    std::smatch m;
    std::regex_search(in, m, std::regex(re));
    if(m.empty()) {
        std::cout << "input=[" << in << "], regex=[" << re << "]: NO MATCH\n";
    } else {
        std::cout << "input=[" << in << "], regex=[" << re << "]: ";
        std::cout << "prefix=[" << m.prefix() << "] ";
        for(std::size_t n = 0; n < m.size(); ++n)
            std::cout << " m[" << n << "]=[" << m[n] << "] ";
        std::cout << "suffix=[" << m.suffix() << "]\n";
    }
}
int main()
{
    // matches the a at the end of input
    show_matches("aaa", "a$");

    // matches the o at the end of the first word
    show_matches("moo goo gai pan", "o\\b");

    // the lookahead matches the empty string immediately after the first b
    // this populates m[1] with "aaa" although m[0] is empty
    show_matches("baaabac", "(?=(a+))");

    // because backtracking into lookaheads is prohibited, 
    // this matches aba rather than aaaba
    show_matches("baaabac", "(?=(a+))a*b\\1");

    // logical AND via lookahead: this password matches IF it contains
    // at least one lowercase letter
    // AND at least one uppercase letter
    // AND at least one punctuation character
    // AND be at least 6 characters long
    show_matches("abcdef", "(?=.*[[:lower:]])(?=.*[[:upper:]])(?=.*[[:punct:]]).{6,}");
    show_matches("aB,def", "(?=.*[[:lower:]])(?=.*[[:upper:]])(?=.*[[:punct:]]).{6,}");
}

Output: 

input=[aaa], regex=[a$]: prefix=[aa]  m[0]=[a] suffix=[]
input=[moo goo gai pan], regex=[o\b]: prefix=[mo]  m[0]=[o] suffix=[ goo gai pan]
input=[baaabac], regex=[(?=(a+))]: prefix=[b]  m[0]=[]  m[1]=[aaa] suffix=[aaabac]
input=[baaabac], regex=[(?=(a+))a*b\1]: prefix=[baa]  m[0]=[aba]  m[1]=[a] suffix=[c]
input=[abcdef], regex=[(?=.*[[:lower:]])(?=.*[[:upper:]])(?=.*[[:punct:]]).{6,}]:
 NO MATCH
input=[aB,def], regex=[(?=.*[[:lower:]])(?=.*[[:upper:]])(?=.*[[:punct:]]).{6,}]:
 prefix=[]  m[0]=[aB,def] suffix=[]

Atoms

An Atom can be one of the following:

Atom::

PatternCharacter
.
\ AtomEscape
CharacterClass
( Disjunction )
( ? : Disjunction )

where AtomEscape::

DecimalEscape
CharacterEscape
CharacterClassEscape

Different kinds of atoms evaluate differently.

Sub-expressions

The Atom ( Disjunction ) is marked subexpression: it executes the Disjunction and stores the copy of the input substring that was consumed by Disjunction in the submatch array at the index that corresponds to the number of times the left open parenthesis ( of marked subexpressions has been encountered in the entire regular expression at this point.

Besides being returned in the std::match_results, the captured submatches are accessible as back-references (\1, \2, ...) and can be referenced in std::regex_replace)

The Atom ( ? : Disjunction ) (non-marking subexpression) simply evaluates the Disjunction and does not store its results in the submatch. This is a purely lexical grouping.

This section is incomplete
Reason: no example

Backreferences

DecimalEscape::

DecimalIntegerLiteral [lookahead DecimalDigit]

If \ is followed by a decimal number N whose first digit is not 0, then the escape sequence is considered to be a backreference. The values N is obtained by calling std::regex_traits::value(C++ only) on each of the digits and combining their results using base-10 arithmetic. It is an error if N is greater than the total number of left capturing parentheses in the entire regular expression.

When a backreference \N appears as an Atom, it matches the same substring as what is currently stored in the N'th element of the submatch array.

The decimal escape \0 is NOT a backreference: it is a character escape that represents the nul character. It cannot be followed by a decimal digit.

This section is incomplete
Reason: no example

Single character matches

The Atom . matches and consumes any one character from the input string except for LineTerminator (U+000D, U+000A, U+2029, or U+2028)

The Atom PatternCharacter, where PatternCharacter is any SourceCharacter EXCEPT the characters ^ $ \ . * +? ( ) [ ] { } |, matches and consumes one character from the input if it is equal to this PatternCharacter.

The equality for this and all other single character matches is defined as follows:

1) If std::regex_constants::icase is set, the characters are equal if the return values of std::regex_traits::translate_nocase are equal.(C++ only)
2) otherwise, if std::regex_constants::collate is set, the characters are equal if the return values of std::regex_traits::translate are equal.(C++ only)
3) otherwise, the characters are equal if operator== returns true.

Each Atom that consists of the escape character \ followed by CharacterEscape as well as the special DecimalEscape \0, matches and consumes one character from the input if it is equal to the character represented by the CharacterEscape. The following character escape sequences are recognized:

CharacterEscape::

ControlEscape
c ControlLetter
HexEscapeSequence
UnicodeEscapeSequence
IdentityEscape

Here, ControlEscape is one of the following five characters: f n r t v

ControlEscape Code Unit Name
f U+000C form feed
n U+000A new line
r U+000D carriage return
t U+0009 horizontal tab
v U+000B vertical tab

ControlLetter is any lowercase or uppercase ASCII letters and this character escape matches the character whose code unit equals the remainder of dividing the value of the code unit of ControlLetter by 32, for example, \cD and \cd both match code unit U+0004 (EOT) because 'D' is U+0044, and 0x44% 32 == 4 and 'd' is U+0064 and 0x64% 32 == 4.

HexEscapeSequence is the letter x followed by exactly two HexDigits (where HexDigit is one of 0 1 2 3 4 5 6 7 8 9 a b c d e f A B C D E F). This character escape matches the character whose code unit equals the numeric value of the two-digit hexadecimal number

UnicodeEscapeSequence is the letter u followed by exactly four HexDigits. This character escape matches the character whose code unit equals the numeric value of this four-digit hexadecimal number. If the value does not fit in this std::basic_regex's CharT, std::regex_error is thrown(C++ only).

IdentityEscape can be any non-alphanumeric character: for example, another backslash. It matches the character as-is.

This section is incomplete
Reason: no example

Character classes

An Atom can represent a character class, that is, it will match and consume one character if it belongs to one of the predefined groups of characters.

A character class can be introduced through a character class escape:

Atom::

\ CharacterClassEscape

or directly

Atom::

CharacterClass

The character class escapes are shorthands for some of the common characters classes, as follows:

CharacterClassEscape ClassName expression(C++ only) Meaning
d [[:digit:]] digits
D [^[:digit:]] non-digits
s [[:space:]] whitespace characters
S [^[:space:]] non-whitespace characters
w [_[:alnum:]] alphanumeric characters and the character _
W [^_[:alnum:]] characters other than alphanumeric or _
The exact meaning of each of these character class escapes in C++ is defined in terms of the locale-dependent named character classes, and not by explicitly listing the acceptable characters as in ECMAScript.

A CharacterClass is a bracket-enclosed sequence of ClassRanges, optionally beginning with the negation operator ^. If it begins with ^, this Atom matches any character that is NOT in the set of characters represented by the union of all ClassRanges. Otherwise, this Atom matches any character that IS in the set of the characters represented by the union of all ClassRanges.

CharacterClass::

[ [ lookahead {^}] ClassRanges ]
[ ^ ClassRanges ]

ClassRanges::

[empty]
NonemptyClassRanges

NonemptyClassRanges::

ClassAtom
ClassAtom NonemptyClassRangesNoDash
ClassAtom - ClassAtom ClassRanges

If non-empty class range has the form ClassAtom - ClassAtom, it matches any character from a range defined as follows: (C++ only)

The first ClassAtom must match a single collating element c1 and the second ClassAtom must match a single collating element c2. To test if the input character c is matched by this range, the following steps are taken:

1) If std::regex_constants::collate is not on, the character is matched by direct comparison of code points: c is matched if c1 <= c && c <= c2
1) Otherwise (if std::regex_constants::collate is enabled):
1) If std::regex_constants::icase is enabled, all three characters (c, c1, and c2) are passed std::regex_traits::translate_nocase
2) Otherwise (if std::regex_constants::icase is not set), all three characters (c, c1, and c2) are passed std::regex_traits::translate
2) The resulting strings are compared using std::regex_traits::transform and the character c is matched if transformed c1 <= transformed c && transformed c <= transformed c2

The character - is treated literally if it is

  • the first or last character of ClassRanges
  • the beginning or end ClassAtom of a dash-separated range specification
  • immediately follows a dash-separated range specification.
  • escaped with a backslash as a CharacterEscape

NonemptyClassRangesNoDash::

ClassAtom
ClassAtomNoDash NonemptyClassRangesNoDash
ClassAtomNoDash - ClassAtom ClassRanges

ClassAtom::

-
ClassAtomNoDash
ClassAtomExClass(C++ only)
ClassAtomCollatingElement(C++ only)
ClassAtomEquivalence(C++ only)

ClassAtomNoDash::

SourceCharacter but not one of \ or ] or -
\ ClassEscape

Each ClassAtomNoDash represents a single character -- either SourceCharacter as-is or escaped as follows:

ClassEscape::

DecimalEscape
b
CharacterEscape
CharacterClassEscape

The special ClassEscape \b produces a character set that matches the code unit U+0008 (backspace). Outside of CharacterClass, it is the word-boundary Assertion.

The use of \B and the use of any backreference (DecimalEscape other than zero) inside a CharacterClass is an error.

The characters - and ] may need to be escaped in some situations in order to be treated as atoms. Other characters that have special meaning outside of CharacterClass, such as * or ?, do not need to be escaped.

This section is incomplete
Reason: no example

POSIX-based character classes

These character classes are an extension to the ECMAScript grammar, and are equivalent to character classes found in the the POSIX regular expressions.

ClassAtomExClass(C++ only)::

[: ClassName :]

Represents all characters that are members of the named character class ClassName. The name is valid only if std::regex_traits::lookup_classname returns non-zero for this name. As described in std::regex_traits::lookup_classname, the following names are guaranteed to be recognized: alnum, alpha, blank, cntrl, digit, graph, lower, print, punct, space, upper, xdigit, d, s, w. Additional names may be provided by system-supplied locales (such as jdigit or jkanji in Japanese) or implemented as a user-defined extension.

ClassAtomCollatingElement(C++ only)::

[. ClassName .]

Represents the named collating element, which may represent a single character or a sequence of characters that collates as a single unit under the imbued locale, such as [.tilde.] or [.ch.] in Czech. The name is valid only if std::regex_traits::lookup_collatename is not an empty string.

When using std::regex_constants::collate, collating elements can always be used as ends points of a range (e.g. [[.dz.]-g] in Hungarian).

ClassAtomEquivalence(C++ only)::

[= ClassName =]

Represents all characters that are members of the same equivalence class as the named collating element, that is, all characters whose whose primary collation key is the same as that for collating element ClassName. The name is valid only if std::regex_traits::lookup_collatename for that name is not an empty string and if the value returned by std::regex_traits::transform_primary for the result of the call to std::regex_traits::lookup_collatename is not an empty string.

A primary sort key is one that ignores case, accentation, or locale-specific tailorings; so for example [[=a=]] matches any of the characters: a, , , , , , , A, , , , , and .

ClassName(C++ only)::

ClassNameCharacter
ClassNameCharacter ClassName

ClassNameCharacter(C++ only)::

SourceCharacter but not one of . =:
This section is incomplete
Reason: no example
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