3.7 Regular Expressions

Regular Expressions in Guide: Racket introduces regular expressions.

Regular expressions are specified as strings or byte strings, using the same pattern language as the Unix utility egrep or Perl. A string-specified pattern produces a character regexp matcher, and a byte-string pattern produces a byte regexp matcher. If a character regexp is used with a byte string or input port, it matches UTF-8 encodings (see Encodings and Locales) of matching character streams; if a byte regexp is used with a character string, it matches bytes in the UTF-8 encoding of the string.

Regular expressions can be compiled into a regexp value for repeated matches. The regexp and byte-regexp procedures convert a string or byte string (respectively) into a regexp value using one syntax of regular expressions that is most compatible to egrep. The pregexp and byte-pregexp procedures produce a regexp value using a slightly different syntax of regular expressions that is more compatible with Perl. In addition, Racket constants written with #rx or #px (see The Reader) produce compiled regexp values.

The internal size of a regexp value is limited to 32 kilobytes; this limit roughly corresponds to a source string with 32,000 literal characters or 5,000 operators.

3.7.1 Regexp Syntax

The following syntax specifications describe the content of a string that represents a regular expression. The syntax of the corresponding string may involve extra escape characters. For example, the regular expression (.*)\1 can be represented with the string "(.*)\\1" or the regexp constant #rx"(.*)\\1"; the \ in the regular expression must be escaped to include it in a string or regexp constant.

The regexp and pregexp syntaxes share a common core:

	‹regexp›	::=	‹pces›		Match ‹pces›
		|	‹regexp›|‹regexp›		Match either ‹regexp›, try left first
	‹pces›	::=	‹pce›		Match ‹pce›
		|	‹pce›‹pces›		Match ‹pce› followed by ‹pces›
	‹pce›	::=	‹repeat›		Match ‹repeat›, longest possible
		|	‹repeat›?		Match ‹repeat›, shortest possible
		|	‹atom›		Match ‹atom› exactly once
	‹repeat›	::=	‹atom›*		Match ‹atom› 0 or more times
		|	‹atom›+		Match ‹atom› 1 or more times
		|	‹atom›?		Match ‹atom› 0 or 1 times
	‹atom›	::=	(‹regexp›)		Match sub-expression ‹regexp› and report
		|	[‹rng›]		Match any character in ‹rng›
		|	[^‹rng›]		Match any character not in ‹rng›
		|	.		Match any (except newline in multi mode)
		|	^		Match start (or after newline in multi mode)
		|	$		Match end (or before newline in multi mode)
		|	‹literal›		Match a single literal character
		|	(?‹mode›:‹regexp›)		Match ‹regexp› using ‹mode›
		|	(?>‹regexp›)		Match ‹regexp›, only first possible
		|	‹look›		Match empty if ‹look› matches
		|	(?‹tst›‹pces›|‹pces›)		Match 1st ‹pces› if ‹tst›, else 2nd ‹pces›
		|	(?‹tst›‹pces›)		Match ‹pces› if ‹tst›, empty if not ‹tst›
	‹rng›	::=	]		‹rng› contains ] only
		|	-		‹rng› contains - only
		|	‹mrng›		‹rng› contains everything in ‹mrng›
		|	‹mrng›-		‹rng› contains - and everything in ‹mrng›
	‹mrng›	::=	]‹lrng›		‹mrng› contains ] and everything in ‹lrng›
		|	-‹lrng›		‹mrng› contains - and everything in ‹lrng›
		|	‹lirng›		‹mrng› contains everything in ‹lirng›
	‹lirng›	::=	‹riliteral›		‹lirng› contains a literal character
		|	‹riliteral›-‹rliteral›		‹lirng› contains Unicode range inclusive
		|	‹lirng›‹lrng›		‹lirng› contains everything in both
	‹lrng›	::=	^		‹lrng› contains ^
		|	‹rliteral›-‹rliteral›		‹lrng› contains Unicode range inclusive
		|	^‹lrng›		‹lrng› contains ^ and more
		|	‹lirng›		‹lrng› contains everything in ‹lirng›
	‹look›	::=	(?=‹regexp›)		Match if ‹regexp› matches
		|	(?!‹regexp›)		Match if ‹regexp› doesn't match
		|	(?<=‹regexp›)		Match if ‹regexp› matches preceding
		|	(?<!‹regexp›)		Match if ‹regexp› doesn't match preceding
	‹tst›	::=	(‹n›)		True if Nth ( has a match
		|	‹look›		True if ‹look› matches
	‹mode›	::=			Like the enclosing mode
		|	‹mode›i		Like ‹mode›, but case-insensitive
		|	‹mode›-i		Like ‹mode›, but sensitive
		|	‹mode›s		Like ‹mode›, but not in multi mode
		|	‹mode›-s		Like ‹mode›, but in multi mode
		|	‹mode›m		Like ‹mode›, but in multi mode
		|	‹mode›-m		Like ‹mode›, but not in multi mode

The following completes the grammar for regexp, which treats { and } as literals, \ as a literal within ranges, and \ as a literal producer outside of ranges.

	‹literal›	::=	Any character except (, ), *, +, ?, [, ., ^, \, or |
		|	\‹aliteral›		Match ‹aliteral›
	‹aliteral›	::=	Any character
	‹riliteral›	::=	Any character except ], -, or ^
	‹rliteral›	::=	Any character except ] or -

The following completes the grammar for pregexp, which uses { and } bounded repetition and uses \ for meta-characters both inside and outside of ranges.

	‹repeat›	::=	...		...
		|	‹atom›{‹n›}		Match ‹atom› exactly ‹n› times
		|	‹atom›{‹n›,}		Match ‹atom› ‹n› or more times
		|	‹atom›{,‹m›}		Match ‹atom› between 0 and ‹m› times
		|	‹atom›{‹n›,‹m›}		Match ‹atom› between ‹n› and ‹m› times
	‹atom›	::=	...		...
		|	\‹n›		Match latest reported match for ‹n›th (
		|	‹class›		Match any character in ‹class›
		|	\b		Match \w* boundary
		|	\B		Match where \b does not
		|	\p{‹property›}		Match (UTF-8 encoded) in ‹property›
		|	\P{‹property›}		Match (UTF-8 encoded) not in ‹property›
	‹literal›	::=	Any character except (, ), *, +, ?, [, ], {, }, ., ^, \, or |
		|	\‹aliteral›		Match ‹aliteral›
	‹aliteral›	::=	Any character except a-z, A-Z, 0-9
	‹lirng›	::=	...		...
		|	‹class›		‹lirng› contains all characters in ‹class›
		|	‹posix›		‹lirng› contains all characters in ‹posix›
		|	\‹eliteral›		‹lirng› contains ‹eliteral›
	‹riliteral›	::=	Any character except ], \, -, or ^
	‹rliteral›	::=	Any character except ], \, or -
	‹eliteral›	::=	Any character except a-z, A-Z
	‹class›	::=	\d		Contains 0-9
		|	\D		Contains ASCII other than those in \d
		|	\w		Contains a-z, A-Z, 0-9, _
		|	\W		Contains ASCII other than those in \w
		|	\s		Contains space, tab, newline, formfeed, return
		|	\S		Contains ASCII other than those in \s
	‹posix›	::=	[:alpha:]		Contains a-z, A-Z
		|	[:upper:]		Contains A-Z
		|	[:lower:]		Contains a-z
		|	[:digit:]		Contains 0-9
		|	[:xdigit:]		Contains 0-9, a-f, A-F
		|	[:alnum:]		Contains a-z, A-Z, 0-9
		|	[:word:]		Contains a-z, A-Z, 0-9, _
		|	[:blank:]		Contains space and tab
		|	[:space:]		Contains space, tab, newline, formfeed, return
		|	[:graph:]		Contains all ASCII characters that use ink
		|	[:print:]		Contains space, tab, and ASCII ink users ([:graph:] and [:blank:])
		|	[:cntrl:]		Contains all characters with scalar value < 32
		|	[:ascii:]		Contains all ASCII characters
	‹property›	::=	‹category›		Includes all characters in ‹category›
		|	^‹category›		Includes all characters not in ‹category›

The Unicode categories follow.

	‹category›	::=	Ll		Letter, lowercase
		|	Lu		Letter, uppercase
		|	Lt		Letter, titlecase
		|	Lm		Letter, modifier
		|	L&		Union of Ll, Lu, Lt, and Lm
		|	Lo		Letter, other
		|	L		Union of L& and Lo
		|	Nd		Number, decimal digit
		|	Nl		Number, letter
		|	No		Number, other
		|	N		Union of Nd, Nl, and No
		|	Ps		Punctuation, open
		|	Pe		Punctuation, close
		|	Pi		Punctuation, initial quote
		|	Pf		Punctuation, final quote
		|	Pc		Punctuation, connector
		|	Pd		Punctuation, dash
		|	Po		Punctuation, other
		|	P		Union of Ps, Pe, Pi, Pf, Pc, Pd, and Po
		|	Mn		Mark, non-spacing
		|	Mc		Mark, spacing combining
		|	Me		Mark, enclosing
		|	M		Union of Mn, Mc, and Me
		|	Sc		Symbol, currency
		|	Sk		Symbol, modifier
		|	Sm		Symbol, math
		|	So		Symbol, other
		|	S		Union of Sc, Sk, Sm, and So
		|	Zl		Seaprator, line
		|	Zp		Seaparator, paragraph
		|	Zs		Separator, space
		|	Z		Union of Zl, Zp, and Zs
		|	Cc		Other, control
		|	Cf		Other, format
		|	Cs		Other, surrogate
		|	Cn		Other, not assigned
		|	Co		Other, private use
		|	C		Union of Cc, Cf, Cs, Cn, and Co
		|	.		Union of all Unicode categories

3.7.2 Additional Syntactic Constraints

In addition to matching a grammar, regular expressions must meet two syntactic restrictions:

• In a ‹repeat› other than ‹atom›?, the ‹atom› must not match an empty sequence.

• In a (?<=‹regexp›) or (?<!‹regexp›), the ‹regexp› must match a bounded sequence only.

These contraints are checked syntactically by the following type system. A type [n, m] corresponds to an expression that matches between n and m characters. In the rule for (‹Regexp›), N means the number such that the opening parenthesis is the Nth opening parenthesis for collecting match reports. Non-emptiness is inferred for a backreference pattern, \‹N›, so that a backreference can be used for repetition patterns; in the case of mutual dependencies among backreferences, the inference chooses the fixpoint that maximizes non-emptiness. Finiteness is not inferred for backreferences (i.e., a backreference is assumed to match an arbitrarily large sequence).

‹regexp›1 : [n1, m1]   ‹regexp›2 : [n2, m2]   ‹regexp›1|‹regexp›2 : [min(n1, n2), max(m1, m2)]

‹pce› : [n1, m1]   ‹pces› : [n2, m2]   ‹pce›‹pces› : [n1+n2, m1+m2]

‹repeat› : [n, m]   ‹repeat›? : [0, m]       ‹atom› : [n, m]   n > 0   ‹atom›* : [0, ∞]

‹atom› : [n, m]   n > 0   ‹atom›+ : [1, ∞]       ‹atom› : [n, m]   ‹atom›? : [0, m]

‹atom› : [n, m]   n > 0   ‹atom›{‹n›} : [n*‹n›, m*‹n›]

‹atom› : [n, m]   n > 0   ‹atom›{‹n›,} : [n*‹n›, ∞]

‹atom› : [n, m]   n > 0   ‹atom›{,‹m›} : [0, m*‹m›]

‹atom› : [n, m]   n > 0   ‹atom›{‹n›,‹m›} : [n*‹n›, m*‹m›]

‹regexp› : [n, m]   (‹regexp›) : [n, m]   αN=n

‹regexp› : [n, m]   (?‹mode›:‹regexp›) : [n, m]

‹regexp› : [n, m]   (?=‹regexp›) : [0, 0]       ‹regexp› : [n, m]   (?!‹regexp›) : [0, 0]

‹regexp› : [n, m]   m < ∞   (?<=‹regexp›) : [0, 0]       ‹regexp› : [n, m]   m < ∞   (?<!‹regexp›) : [0, 0]

‹regexp› : [n, m]   (?>‹regexp›) : [n, m]

‹tst› : [n0, m0]   ‹pces›1 : [n1, m1]   ‹pces›2 : [n2, m2]   (?‹tst›‹pces›1|‹pces›2) : [min(n1, n2), max(m1, m2)]

‹tst› : [n0, m0]   ‹pces› : [n1, m1]   (?‹tst›‹pces›) : [0, m1]

(‹n›) : [αN, ∞]     [‹rng›] : [1, 1]     [^‹rng›] : [1, 1]

. : [1, 1]     ^ : [0, 0]     $ : [0, 0]

‹literal› : [1, 1]     \‹n› : [αN, ∞]     ‹class› : [1, 1]

\b : [0, 0]     \B : [0, 0]

\p{‹property›} : [1, 6]     \P{‹property›} : [1, 6]

3.7.3 Regexp Constructors

The object-name procedure returns the source string for a regexp value.

Examples:

> (regexp "ap*le")

#rx"ap*le"

> (object-name #rx"ap*le")

"ap*le"

Examples:

> (pregexp "ap*le")

#px"ap*le"

> (regexp? #px"ap*le")

#t

The object-name procedure returns the source byte string for a regexp value.

Examples:

> (byte-regexp #"ap*le")

#rx#"ap*le"

> (object-name #rx#"ap*le")

#"ap*le"

> (byte-regexp "ap*le")

byte-regexp: expects argument of type <byte string>; given

"ap*le"

Example:

> (byte-pregexp #"ap*le")

#px#"ap*le"

Examples:

> (regexp-match "." "apple.scm")

'("a")

> (regexp-match (regexp-quote ".") "apple.scm")

'(".")

3.7.4 Regexp Matching

If input is a path, it is converted to a byte string with path->bytes if pattern is a byte string or a byte-based regexp. Otherwise, input is converted to a string with path->string.

The optional start-pos and end-pos arguments select a portion of input for matching; the default is the entire string or the stream up to an end-of-file. When input is a string, start-pos is a character position; when input is a byte string, then start-pos is a byte position; and when input is an input port, start-pos is the number of bytes to skip before starting to match. The end-pos argument can be #f, which corresponds to the end of the string or the end-of-file in the stream; otherwise, it is a character or byte position, like start-pos. If input is an input port, and if the end-of-file is reached before start-pos bytes are skipped, then the match fails.

In pattern, a start-of-string ^ refers to the first position of input after start-pos, assuming that input-prefix is #"". The end-of-input $ refers to the end-posth position or (in the case of an input port) the end of file, whichever comes first, assuming that output-prefix is #f.

The input-prefix specifies bytes that effectively precede input for the purposes of ^ and other look-behind matching. For example, a #"" prefix means that ^ matches at the beginning of the stream, while a #"\n" input-prefix means that a start-of-line ^ can match the beginning of the input, while a start-of-file ^ cannot.

If the match fails, #f is returned. If the match succeeds, a list containing strings or byte string, and possibly #f, is returned. The list contains strings only if input is a string and pattern is not a byte regexp. Otherwise, the list contains byte strings (substrings of the UTF-8 encoding of input, if input is a string).

The first [byte] string in a result list is the portion of input that matched pattern. If two portions of input can match pattern, then the match that starts earliest is found.

Additional [byte] strings are returned in the list if pattern contains parenthesized sub-expressions (but not when the open parenthesis is followed by ?). Matches for the sub-expressions are provided in the order of the opening parentheses in pattern. When sub-expressions occur in branches of an | “or” pattern, in a * “zero or more” pattern, or other places where the overall pattern can succeed without a match for the sub-expression, then a #f is returned for the sub-expression if it did not contribute to the final match. When a single sub-expression occurs within a * “zero or more” pattern or other multiple-match positions, then the rightmost match associated with the sub-expression is returned in the list.

If the optional output-port is provided as an output port, the part of input from its beginning (not start-pos) that precedes the match is written to the port. All of input up to end-pos is written to the port if no match is found. This functionality is most useful when input is an input port.

When matching an input port, a match failure reads up to end-pos bytes (or end-of-file), even if pattern begins with a start-of-string ^; see also regexp-try-match. On success, all bytes up to and including the match are eventually read from the port, but matching proceeds by first peeking bytes from the port (using peek-bytes-avail!), and then (re‑)reading matching bytes to discard them after the match result is determined. Non-matching bytes may be read and discarded before the match is determined. The matcher peeks in blocking mode only as far as necessary to determine a match, but it may peek extra bytes to fill an internal buffer if immediately available (i.e., without blocking). Greedy repeat operators in pattern, such as * or +, tend to force reading the entire content of the port (up to end-pos) to determine a match.

If the input port is read simultaneously by another thread, or if the port is a custom port with inconsistent reading and peeking procedures (see Custom Ports), then the bytes that are peeked and used for matching may be different than the bytes read and discarded after the match completes; the matcher inspects only the peeked bytes. To avoid such interleaving, use regexp-match-peek (with a progress-evt argument) followed by port-commit-peeked.

Examples:

> (regexp-match #rx"x." "12x4x6")

'("x4")

> (regexp-match #rx"y." "12x4x6")

#f

> (regexp-match #rx"x." "12x4x6" 3)

'("x6")

> (regexp-match #rx"x." "12x4x6" 3 4)

#f

> (regexp-match #rx#"x." "12x4x6")

'(#"x4")

> (regexp-match #rx"x." "12x4x6" 0 #f (current-output-port))

12

'("x4")

> (regexp-match #rx"(-[0-9]*)+" "a-12--345b")

'("-12--345" "-345")

The pattern is used in order to find matches, where each match attempt starts at the end of the last match, and ^ is allowed to match the beginning of the input (if input-prefix is #"") only for the first match. Empty matches are handled like other matches, returning a zero-length string or byte sequence (they are more useful in the complementing regexp-split function), but pattern is restricted from matching an empty sequence immediately after an empty match.

If input contains no matches (in the range start-pos to end-pos), null is returned. Otherwise, each item in the resulting list is a distinct substring or byte sequence from input that matches pattern. The end-pos argument can be #f to match to the end of input (which corresponds to an end-of-file if input is an input port).

Examples:

> (regexp-match* #rx"x." "12x4x6")

'("x4" "x6")

> (regexp-match* #rx"x*" "12x4x6")

'("" "" "x" "" "x" "" "")

This procedure is especially useful with a pattern that begins with a start-of-string ^ or with a non-#f end-pos, since each limits the amount of peeking into the port. Otherwise, beware that a large portion of the stream may be peeked (and therefore pulled into memory) before the match succeeds or fails.

Range results are returned in a substring- and subbytes-compatible manner, independent of start-pos. In the case of an input port, the returned positions indicate the number of bytes that were read, including start-pos, before the first matching byte.

Examples:

> (regexp-match-positions #rx"x." "12x4x6")

'((2 . 4))

> (regexp-match-positions #rx"x." "12x4x6" 3)

'((4 . 6))

> (regexp-match-positions #rx"(-[0-9]*)+" "a-12--345b")

'((1 . 9) (5 . 9))

Example:

> (regexp-match-positions* #rx"x." "12x4x6")

'((2 . 4) (4 . 6))

Examples:

> (regexp-match? #rx"x." "12x4x6")

#t

> (regexp-match? #rx"y." "12x4x6")

#f

Examples:

> (regexp-match-exact? #rx"x." "12x4x6")

#f

> (regexp-match-exact? #rx"1.*x." "12x4x6")

#t