3.7 Regular Expressions

Regular Expressions in The Racket Guide 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.

A literal or printed regular expression starts with #rx or #px. See Reading Regular Expressions for information on reading regular expressions and Printing Regular Expressions for information on printing regular expressions.

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	ex1
	‹pces›	::=	‹pce›		Match ‹pce›
		|	‹pce›‹pces›		Match ‹pce› followed by ‹pces›
	‹pce›	::=	‹repeat›		Match ‹repeat›, longest possible	ex3
		|	‹repeat›?		Match ‹repeat›, shortest possible	ex6
		|	‹atom›		Match ‹atom› exactly once
	‹repeat›	::=	‹atom›*		Match ‹atom› 0 or more times	ex3
		|	‹atom›+		Match ‹atom› 1 or more times	ex4
		|	‹atom›?		Match ‹atom› 0 or 1 times	ex5
	‹atom›	::=	(‹regexp›)		Match sub-expression ‹regexp› and report	ex11
		|	[‹rng›]		Match any character in ‹rng›	ex2
		|	[^‹rng›]		Match any character not in ‹rng›	ex12
		|	.		Match any (except newline in multi mode)	ex13
		|	^		Match start (or after newline in multi mode)	ex14
		|	$		Match end (or before newline in multi mode)	ex15
		|	‹literal›		Match a single literal character	ex1
		|	(?‹mode›:‹regexp›)		Match ‹regexp› using ‹mode›	ex35
		|	(?>‹regexp›)		Match ‹regexp›, only first possible
		|	‹look›		Match empty if ‹look› matches
		|	(?‹tst›‹pces›|‹pces›)		Match 1st ‹pces› if ‹tst›, else 2nd ‹pces›	ex36
		|	(?‹tst›‹pces›)		Match ‹pces› if ‹tst›, empty if not ‹tst›
	‹rng›	::=	]		‹rng› contains ] only	ex27
		|	-		‹rng› contains - only	ex28
		|	‹mrng›		‹rng› contains everything in ‹mrng›
		|	‹mrng›-		‹rng› contains - and everything in ‹mrng›
	‹mrng›	::=	]‹lrng›		‹mrng› contains ] and everything in ‹lrng›	ex29
		|	-‹lrng›		‹mrng› contains - and everything in ‹lrng›	ex29
		|	‹lirng›		‹mrng› contains everything in ‹lirng›
	‹lirng›	::=	‹riliteral›		‹lirng› contains a literal character
		|	‹riliteral›-‹rliteral›		‹lirng› contains Unicode range inclusive	ex22
		|	‹lirng›‹lrng›		‹lirng› contains everything in both
	‹lrng›	::=	^		‹lrng› contains ^	ex30
		|	‹rliteral›-‹rliteral›		‹lrng› contains Unicode range inclusive
		|	^‹lrng›		‹lrng› contains ^ and more
		|	‹lirng›		‹lrng› contains everything in ‹lirng›
	‹look›	::=	(?=‹regexp›)		Match if ‹regexp› matches	ex31
		|	(?!‹regexp›)		Match if ‹regexp› doesn't match	ex32
		|	(?<=‹regexp›)		Match if ‹regexp› matches preceding	ex33
		|	(?<!‹regexp›)		Match if ‹regexp› doesn't match preceding	ex34
	‹tst›	::=	(‹n›)		True if Nth ( has a match
		|	‹look›		True if ‹look› matches	ex36
	‹mode›	::=			Like the enclosing mode
		|	‹mode›i		Like ‹mode›, but case-insensitive	ex35
		|	‹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›	ex21
	‹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	ex7
		|	‹atom›{‹n›,}		Match ‹atom› ‹n› or more times	ex8
		|	‹atom›{,‹m›}		Match ‹atom› between 0 and ‹m› times	ex9
		|	‹atom›{‹n›,‹m›}		Match ‹atom› between ‹n› and ‹m› times	ex10
	‹atom›	::=	...		...
		|	\‹n›		Match latest reported match for ‹n›th (	ex16
		|	‹class›		Match any character in ‹class›
		|	\b		Match \w* boundary	ex17
		|	\B		Match where \b does not	ex18
		|	\p{‹property›}		Match (UTF-8 encoded) in ‹property›	ex19
		|	\P{‹property›}		Match (UTF-8 encoded) not in ‹property›	ex20
	‹literal›	::=	Any character except (, ), *, +, ?, [, ], {, }, ., ^, \, or |
		|	\‹aliteral›		Match ‹aliteral›	ex21
	‹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›	ex26
		|	\‹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	ex23
		|	\D		Contains ASCII other than those in \d
		|	\w		Contains a-z, A-Z, 0-9, _	ex24
		|	\W		Contains ASCII other than those in \w
		|	\s		Contains space, tab, newline, formfeed, return	ex25
		|	\S		Contains ASCII other than those in \s
	‹posix›	::=	[:alpha:]		Contains a-z, A-Z
		|	[:upper:]		Contains A-Z
		|	[:lower:]		Contains a-z	ex26
		|	[: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
		|	[: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	ex19
		|	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

Examples:

> (regexp-match #rx"a|b" "cat") ; ex1 '("a") > (regexp-match #rx"[at]" "cat") ; ex2 '("a") > (regexp-match #rx"ca*[at]" "caaat") ; ex3 '("caaat") > (regexp-match #rx"ca+[at]" "caaat") ; ex4 '("caaat") > (regexp-match #rx"ca?t?" "ct") ; ex5 '("ct") > (regexp-match #rx"ca*?[at]" "caaat") ; ex6 '("ca") > (regexp-match #px"ca{2}" "caaat") ; ex7, uses #px '("caa") > (regexp-match #px"ca{2,}t" "catcaat") ; ex8, uses #px '("caat") > (regexp-match #px"ca{,2}t" "caaatcat") ; ex9, uses #px '("cat") > (regexp-match #px"ca{1,2}t" "caaatcat") ; ex10, uses #px '("cat") > (regexp-match #rx"(c*)(a*)" "caat") ; ex11 '("caa" "c" "aa") > (regexp-match #rx"[^ca]" "caat") ; ex12 '("t") > (regexp-match #rx".(.)." "cat") ; ex13 '("cat" "a") > (regexp-match #rx"^a|^c" "cat") ; ex14 '("c") > (regexp-match #rx"a$|t$" "cat") ; ex15 '("t") > (regexp-match #px"c(.)\\1t" "caat") ; ex16, uses #px '("caat" "a") > (regexp-match #px".\\b." "cat in hat") ; ex17, uses #px '("t ") > (regexp-match #px".\\B." "cat in hat") ; ex18, uses #px '("ca") > (regexp-match #px"\\p{Ll}" "Cat") ; ex19, uses #px '("a") > (regexp-match #px"\\P{Ll}" "cat!") ; ex20, uses #px '("!") > (regexp-match #rx"\\|" "c|t") ; ex21 '("|") > (regexp-match #rx"[a-f]*" "cat") ; ex22 '("ca") > (regexp-match #px"[a-f\\d]*" "1cat") ; ex23, uses #px '("1ca") > (regexp-match #px" [\\w]" "cat hat") ; ex24, uses #px '(" h") > (regexp-match #px"t[\\s]" "cat\nhat") ; ex25, uses #px '("t\n") > (regexp-match #px"[[:lower:]]+" "Cat") ; ex26, uses #px '("at") > (regexp-match #rx"[]]" "c]t") ; ex27 '("]") > (regexp-match #rx"[-]" "c-t") ; ex28 '("-") > (regexp-match #rx"[]a[]+" "c[a]t") ; ex29 '("[a]") > (regexp-match #rx"[a^]+" "ca^t") ; ex30 '("a^") > (regexp-match #rx".a(?=p)" "cat nap") ; ex31 '("na") > (regexp-match #rx".a(?!t)" "cat nap") ; ex32 '("na") > (regexp-match #rx"(?<=n)a." "cat nap") ; ex33 '("ap") > (regexp-match #rx"(?<!c)a." "cat nap") ; ex34 '("ap") > (regexp-match #rx"(?i:a)[tp]" "cAT nAp") ; ex35 '("Ap") > (regexp-match #rx"(?(?<=c)a|b)+" "cabal") ; ex36 '("ab")

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 an 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 an 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) an end-of-file, whichever comes first.

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 opening 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" "" "")