6. Regular Expressions

Starting with release 2.1.22, BRL includes Dorai Sitaram's `pregexp.scm' package, which provides support for Perl 5.x-style regular expressions. This chapter is taken from the documentation in that package.

6.1 Regexp Introduction

A regexp is a string that describes a pattern. A regexp matcher tries to match this pattern against (a portion of) another string, which we will call the text string. The text string is treated as raw text and not as a pattern.

Most of the characters in a regexp pattern are meant to match occurrences of themselves in the text string. Thus, the pattern "abc" matches a string that contains the characters a, b, c in succession.

In the regexp pattern, some characters act as metacharacters, and some character sequences act as metasequences. That is, they specify something other than their literal selves. For example, in the pattern "a.c", the characters a and c do stand for themselves but the metacharacter . can match any character (other than newline). Therefore, the pattern "a.c" matches an a, followed by any character, followed by a c.

If we needed to match the character . itself, we escape it, ie, precede it with a backslash (\). The character sequence \. is thus a metasequence, since it doesn't match itself but rather just .. So, to match a followed by a literal . followed by c, we use the regexp pattern "a\\.c".(6) Another example of a metasequence is \t, which is a readable way to represent the tab character.

We will call the string representation of a regexp the U-regexp, where U can be taken to mean Unix-style or universal, because this notation for regexps is universally familiar. Our implementation uses an intermediate tree-like representation called the S-regexp, where S can stand for Scheme, symbolic, or s-expression. S-regexps are more verbose and less readable than U-regexps, but they are much easier for Scheme's recursive procedures to navigate.

6.2 Regexp procedures provided

`pregexp.scm' provides the user with the procedures pregexp, pregexp-match-positions, pregexp-match, pregexp-replace, and pregexp-replace*. All the identifiers introduced by `pregexp.scm' have the prefix pregexp, so they are unlikely to clash with other names in Scheme, including those of any natively provided regexp operators.

6.2.1 pregexp

The procedure pregexp takes a U-regexp, which is a string, and returns an S-regexp, which is a tree.

(pregexp "c.r") => (:sub (:or (:seq #\c :any #\r)))

There is rarely any need to look at the S-regexps returned by pregexp.

6.2.2 pregexp-match-positions

The procedure pregexp-match-positions takes a regexp pattern and a text string, and returns a match if the pattern matches the text string. The pattern may be either a U- or an S-regexp. (pregexp-match-positions will internally compile a U-regexp to an S-regexp before proceeding with the matching. If you find yourself calling pregexp-match-positions repeatedly with the same U-regexp, it may be advisable to explicitly convert the latter into an S-regexp once beforehand, using pregexp, to save needless recompilation.)

pregexp-match-positions returns #f if the pattern did not match the string; and a list of index pairs if it did match. Eg,

(pregexp-match-positions "brain" "bird") => #f (pregexp-match-positions "needle" "hay needle stack") => ((4 . 10))

In the second example, the integers 4 and 10 identify the substring that was matched. 1 is the starting (inclusive) index and 2 the ending (exclusive) index of the matching substring.

(substring "hay needle stack" 4 10) => "needle"

Here, pregexp-match-positions's return list contains only one index pair, and that pair represents the entire substring matched by the regexp. When we discuss subpatterns later, we will see how a single match operation can yield a list of submatches.

pregexp-match-positions takes optional third and fourth arguments that specify the indices of the text string within which the matching should take place.

(pregexp-match-positions "needle" "his hay needle stack -- my hay needle stack -- her hay needle stack" 24 43) => ((31 . 37))

Note that the returned indices are still reckoned relative to the full text string.

6.2.3 pregexp-match

The procedure pregexp-match is called like pregexp-match-positions but instead of returning index pairs it returns the matching substrings:

(pregexp-match "brain" "bird") => #f (pregexp-match "needle" "hay needle stack") => ("needle")

pregexp-match also takes optional third and fourth arguments, with the same meaning as does pregexp-match-positions.

6.2.4 pregexp-replace

The procedure pregexp-replace replaces the matched portion of the text string by another string. The first argument is the regexp, the second the text string, and the third is the insert string (string to be inserted).

(pregexp-replace "te" "liberte" "ty") => "liberty"

6.2.5 pregexp-replace*

The procedure pregexp-replace* replaces all matches in the text string by the insert string:

(pregexp-replace* "te" "liberte egalite fraternite" "ty") => "liberty egality fratyrnity"

6.3 The regexp pattern language

Here is a complete description of the regexp pattern language recognized by the pregexp procedures.

6.3.1 Basic assertions

The assertions ^ and $ identify the beginning and the end of the text string respectively. They ensure that their adjoining regexps match at one or other end of the text string. Examples:

(pregexp-match-positions "^contact" "first contact") => #f

The regexp fails to match because contact does not occur at the beginning of the text string.

(pregexp-match-positions "laugh$" "laugh laugh laugh laugh") => ((18 . 23))

The regexp matches the last laugh.

The metasequence \b asserts that a word boundary exists.

(pregexp-match-positions "yack\\b" "yackety yack") => ((8 . 12))

The yack in yackety doesn't end at a word boundary so it isn't matched. The second yack does and is.

The metasequence \B has the opposite effect to \b. It asserts that a word boundary does not exist.

(pregexp-match-positions "an\\B" "an analysis") => ((3 . 5))

The an that doesn't end in a word boundary is matched.

6.3.2 Characters and character classes

Typically a character in the regexp matches the same character in the text string. Sometimes it is necessary or convenient to use a regexp metasequence to refer to a single character. Thus, metasequences \n, \r, \t, and \. match the newline, return, tab and period characters respectively.

The metacharacter period (.) matches any character other than newline.

(pregexp-match "p.t" "pet") => ("pet")

It also matches pat, pit, pot, put, and p8t but not peat or pfffft.

A character class [...] matches any one character from the set enclosed within the brackets. Thus "p[aeiou]t" matches pat, pet, pit, pot, put and nothing else.

Inside the brackets, a hyphen (-) between two characters specifies the ascii range between the characters. Eg, "ta[b-dgn-p]" matches tab, tac, tad, and tag, and tan, tao, tap.

An initial caret (^) after the left bracket inverts the set specified by the rest of the contents, ie, it specifies the set of characters other than those identified in the brackets. Eg, "do[^g]" matches all three-character sequences starting with do except dog.

Note that the metacharacter ^ inside brackets means something quite different from what it means outside. Most other metacharacters (., *, +, ?, etc) cease to be metacharacters when inside brackets, although you may still escape them for peace of mind. - is a metacharacter only when it's inside brackets.

6.3.2.1 Some frequently used character classes

Some standard character classes can be conveniently represented as metasequences instead of as explicit bracketed expressions. \d matches a digit ([0-9]); \s matches a whitespace character; and \w matches a character that could be part of a "word".(7)

The upper-case versions of these metasequences stand for the inversions of the corresponding character classes. Thus \D matches a non-digit, \S a non-whitespace character, and \W a non-"word" character.

Remember to include a double backslash when putting these metasequences in a Scheme string:

(pregexp-match "\\d\\d" "0 dear, 1 have 2 read catch 22 before 9") => ("22")

These character classes can be used inside a bracketed expression. Eg, "[a-z\\d]" matches a lower-case letter or a digit.

6.3.2.2 POSIX character classes

A POSIX character class is a special metasequence of the form [:...:] that can be used only inside a bracketed expression. The POSIX classes supported are

[:alnum:]

letters and digits

[:alpha:]

letters

[:algor:]

the letters c, h, a and d

[:ascii:]

7-bit ascii characters

[:blank:]

widthful whitespace, ie, space and tab

[:cntrl:]

"control" characters, viz, those with code < 32

[:digit:]

digits, same as \d

[:graph:]

characters that use ink

[:lower:]

lower-case letters

[:print:]

ink-users plus widthful whitespace

[:space:]

whitespace, same as \s

[:upper:]

upper-case letters

[:word:]

letters, digits, and underscore, same as \w

[:xdigit:]

ex digits

For example, the regexp "[[:alpha:]_]" matches a letter or underscore.

(pregexp-match "[[:alpha:]_]" "--x--") => ("x") (pregexp-match "[[:alpha:]_]" "--_--") => ("_") (pregexp-match "[[:alpha:]_]" "--:--") => #f

The POSIX class notation is valid only inside a bracketed expression. For instance, [:alpha:], when not inside a bracketed expression, will not be read as the letter class. Rather it is (from previous principles) the character class containing the characters :, a, l, p, h.

(pregexp-match "[:alpha:]" "--a--") => ("a") (pregexp-match "[:alpha:]" "--_--") => #f

By placing a caret (^) immediately after [:, you get the inversion of that POSIX character class. Thus, [:^alpha] is the class containing all characters except the letters.

6.3.3 Quantifiers

The quantifiers *, +, and ? match respectively: zero or more, one or more, and zero or one instances of the preceding subpattern.

(pregexp-match-positions "c[ad]*r" "cadaddadddr") => ((0 . 11)) (pregexp-match-positions "c[ad]*r" "cr") => ((0 . 2)) (pregexp-match-positions "c[ad]+r" "cadaddadddr") => ((0 . 11)) (pregexp-match-positions "c[ad]+r" "cr") => #f (pregexp-match-positions "c[ad]?r" "cadaddadddr") => #f (pregexp-match-positions "c[ad]?r" "cr") => ((0 . 2)) (pregexp-match-positions "c[ad]?r" "car") => ((0 . 3))

6.3.3.1 Numeric quantifiers

You can use braces to specify much finer-tuned quantification than is possible with *, +, ?.

The quantifier {m} matches exactly m instances of the preceding subpattern. m must be a nonnegative integer.

The quantifier {m,n} matches at least m and at most n instances. m and n are nonnegative integers with m <= n. You may omit either or both numbers, in which case m defaults to 0 and n to infinity.

It is evident that + and ? are abbreviations for {1,} and {0,1} respectively. * abbreviates {,}, which is the same as {0,}.

(pregexp-match "[aeiou]{3}" "vacuous") => ("uou") (pregexp-match "[aeiou]{3}" "evolve") => #f (pregexp-match "[aeiou]{2,3}" "evolve") => #f (pregexp-match "[aeiou]{2,3}" "zeugma") => ("eu")

6.3.3.2 Non-greedy quantifiers

The quantifiers described above are greedy, ie, they match the maximal number of instances that would still lead to an overall match for the full pattern.

(pregexp-match "<.*>" " <tag2> <tag3>") => ("<tag1> <tag2> <tag3>")

To make these quantifiers non-greedy, append a ? to them. Non-greedy quantifiers match the minimal number of instances needed to ensure an overall match.

(pregexp-match "<.*?>" " <tag2> <tag3>") => ("<tag1>")

The non-greedy quantifiers are respectively: *?, +?, ??, {m}?, {m,n}?. Note the two uses of the metacharacter ?.

6.3.4 Clusters

Clustering, ie, enclosure within parens (...), identifies the enclosed subpattern as a single entity. It causes the matcher to capture the submatch, or the portion of the string matching the subpattern, in addition to the overall match.

(pregexp-match "([a-z]+) ([0-9]+), ([0-9]+)" "jan 1, 1970") => ("jan 1, 1970" "jan" "1" "1970")

Clustering also causes a following quantifier to treat the entire enclosed subpattern as an entity.

(pregexp-match "(poo )*" "poo poo platter") => ("poo poo " "poo ")

The number of submatches returned is always equal to the number of subpatterns specified in the regexp, even if a particular subpattern happens to match more than one substring or no substring at all.

(pregexp-match "([a-z ]+;)*" "lather; rinse; repeat;") => ("lather; rinse; repeat;" " repeat;")

Here the *-quantified subpattern matches three times, but it is the last submatch that is returned.

It is also possible for a quantified subpattern to fail to match, even if the overall pattern matches. In such cases, the failing submatch is represented by #f.

(define date-re ;match `month year' or `month day, year'. ;subpattern matches day, if present (pregexp "([a-z]+) +([0-9]+,)? *([0-9]+)")) (pregexp-match date-re "jan 1, 1970") => ("jan 1, 1970" "jan" "1," "1970") (pregexp-match date-re "jan 1970") => ("jan 1970" "jan" #f "1970")

6.3.4.1 Backreferences

Submatches can be used in the insert string argument of the procedures pregexp-replace and pregexp-replace*. The insert string can use \n as a backreference to refer back to the nth submatch, ie, the substring that matched the nth subpattern. \0 refers to the entire match, and it can also be specified as \&.

(pregexp-replace "_(.+?)_" "the _nina_, the _pinta_, and the _santa maria_" "*\\1*") => "the *nina*, the _pinta_, and the _santa maria_" (pregexp-replace* "_(.+?)_" "the _nina_, the _pinta_, and the _santa maria_" "*\\1*") => "the *nina*, the *pinta*, and the *santa maria*" ;recall: \S stands for non-whitespace character (pregexp-replace "(\\S+) (\\S+) (\\S+)" "eat to live" "\\3 \\2 \\1") => "live to eat"

Use \\ in the insert string to specify a literal backslash. Also, \$ stands for an empty string, and is useful for separating a backreference \n from an immediately following number.

Backreferences can also be used within the regexp pattern to refer back to an already matched subpattern in the pattern. \n stands for an exact repeat of the nth submatch.(8)

(pregexp-match "([a-z]+) and \\1" "billions and billions") => ("billions and billions" "billions")

Note that the backreference is not simply a repeat of the previous subpattern. Rather it is a repeat of the particular substring already matched by the subpattern.

In the above example, the backreference can only match billions. It will not match millions, even though the subpattern it harks back to -- ([a-z]+) --- would have had no problem doing so:

(pregexp-match "([a-z]+) and \\1" "billions and millions") => #f

The following corrects doubled words:

(pregexp-replace* "(\\S+) \\1" "now is the the time for all good men to to come to the aid of of the party" "\\1") => "now is the time for all good men to come to the aid of the party"

The following marks all immediately repeating patterns in a number string:

(pregexp-replace* "(\\d+)\\1" "123340983242432420980980234" "{\\1,\\1}") => "12{3,3}40983{24,24}3242{098,098}0234"

6.3.4.2 Non-capturing clusters

It is often required to specify a cluster (typically for quantification) but without triggering the capture of submatch information. Such clusters are called non-capturing. In such cases, use (?: instead of ( as the cluster opener. In the following example, the non-capturing cluster eliminates the "directory" portion of a given pathname, and the capturing cluster identifies the basename.

(pregexp-match "^(?:[a-z]*/)*([a-z]+)$" "/usr/local/bin/mzscheme") => ("/usr/local/bin/mzscheme" "mzscheme")

6.3.4.3 Cloisters

The location between the ? and the : of a non-capturing cluster is called a cloister.(9) You can put modifiers there that will cause the enclustered subpattern to be treated specially. The modifier i causes the subpattern to match case-insensitively:

(pregexp-match "(?i:hearth)" "HeartH") => ("HeartH")

The modifier x causes the subpattern to match space-insensitively, ie, spaces and comments within the subpattern are ignored. Comments are introduced as usual with a semicolon (;) and extend till the end of the line. If you need to include a literal space or semicolon in a space-insensitized subpattern, escape it with a backslash.

(pregexp-match "(?x: a lot)" "alot") => ("alot") (pregexp-match "(?x: a \\ lot)" "a lot") => ("a lot") (pregexp-match "(?x: a \\ man \\; \\ ; ignore a \\ plan \\; \\ ; me a \\ canal ; completely )" "a man; a plan; a canal") => ("a man; a plan; a canal")

The global variable *pregexp-comment-char* contains the comment character (#\;). For Perl-like comments,

(set! *pregexp-comment-char* #\#)

You can put more than one modifier in the cloister.

(pregexp-match "(?ix: a \\ man \\; \\ ; ignore a \\ plan \\; \\ ; me a \\ canal ; completely )" "A Man; a Plan; a Canal") => ("A Man; a Plan; a Canal")

A minus sign before a modifier inverts its meaning. Thus, you can use -i and -x in a subcluster to overturn the insensitivities caused by an enclosing cluster.

(pregexp-match "(?i:the (?-i:TeX)book)" "The TeXbook") => ("The TeXbook")

This regexp will allow any casing for the and book but insists that TeX not be differently cased.

6.3.5 Alternation

You can specify a list of alternate subpatterns by separating them by `|'. The `|' separates subpatterns in the nearest enclosing cluster (or in the entire pattern string if there are no enclosing parens).

(pregexp-match "f(ee|i|o|um)" "a small, final fee") => ("fi" "i") (pregexp-replace* "([yi])s(e[sdr]?|ing|ation)" "it is energising to analyse an organisation pulsing with noisy organisms" "\\1z\\2") => "it is energizing to analyze an organization pulsing with noisy organisms"

Note again that if you wish to use clustering merely to specify a list of alternate subpatterns but do not want the submatch, use (?: instead of (.

(pregexp-match "f(?:ee|i|o|um)" "fun for all") => ("fo")

An important thing to note about alternation is that the leftmost matching alternate is picked regardless of its length. Thus, if one of the alternates is a prefix of a later alternate, the latter may not have a chance to match.

(pregexp-match "call|call-with-current-continuation" "call-with-current-continuation") => ("call")

To allow the longer alternate to have a shot at matching, place it before the shorter one:

(pregexp-match "call-with-current-continuation|call" "call-with-current-continuation") => ("call-with-current-continuation")

In any case, an overall match for the entire regexp is always preferred to an overall nonmatch. In the following, the longer alternate still wins, because its preferred shorter prefix fails to yield an overall match.

(pregexp-match "(?:call|call-with-current-continuation) constrained" "call-with-current-continuation constrained") => ("call-with-current-continuation constrained")

6.3.6 Backtracking

We've already seen that greedy quantifiers match the maximal number of times, but the overriding priority is that the overall match succeed. Consider

(pregexp-match "a*a" "aaaa")

The regexp consists of two subregexps, a* followed by a. The subregexp a* cannot be allowed to match all four a's in the text string "aaaa", even though * is a greedy quantifier. It may match only the first three, leaving the last one for the second subregexp. This ensures that the full regexp matches successfully.

The regexp matcher accomplishes this via a process called backtracking. The matcher tentatively allows the greedy quantifier to match all four a's, but then when it becomes clear that the overall match is in jeopardy, it backtracks to a less greedy match of three a's. If even this fails, as in the call

(pregexp-match "a*aa" "aaaa")

the matcher backtracks even further. Overall failure is conceded only when all possible backtracking has been tried with no success.

Backtracking is not restricted to greedy quantifiers. Nongreedy quantifiers match as few instances as possible, and progressively backtrack to more and more instances in order to attain an overall match. There is backtracking in alternation too, as the more rightward alternates are tried when locally successful leftward ones fail to yield an overall match.

6.3.6.1 Disabling backtracking

Sometimes it is efficient to disable backtracking. For example, we may wish to commit to a choice, or we know that trying alternatives is fruitless. A nonbacktracking regexp is enclosed in (?>...).

(pregexp-match "(?>a+)." "aaaa") => #f

In this call, the subregexp ?>a* greedily matches all four a's, and is denied the opportunity to backpedal. So the overall match is denied. The effect of the regexp is therefore to match one or more a's followed by something that is definitely non-a.

6.3.7 Looking ahead and behind

You can have assertions in your pattern that look ahead or behind to ensure that a subpattern does or does not occur. These "look around" assertions are specified by putting the subpattern checked for in a cluster whose leading characters are: ?= (for positive lookahead), ?! (negative lookahead), ?<= (positive lookbehind), ?<! (negative lookbehind). Note that the subpattern in the assertion does not generate a match in the final result. It merely allows or disallows the rest of the match.

6.3.7.1 Lookahead

Positive lookahead (?=) peeks ahead to ensure that its subpattern could match.

(pregexp-match-positions "grey(?=hound)" "i left my grey socks at the greyhound") => ((28 . 32))

The regexp "grey(?=hound)" matches grey, but only if it is followed by hound. Thus, the first grey in the text string is not matched.

Negative lookahead (?!) peeks ahead to ensure that its subpattern could not possibly match.

(pregexp-match-positions "grey(?!hound)" "the gray greyhound ate the grey socks") => ((27 . 31))

The regexp "grey(?!hound)" matches grey, but only if it is not followed by hound. Thus the grey just before socks is matched.

6.3.7.2 Lookbehind

Positive lookbehind (?<=) checks that its subpattern could match immediately to the left of the current position in the text string.

(pregexp-match-positions "(?<=grey)hound" "the hound in the picture is not a greyhound") => ((38 . 43))

The regexp (?<=grey)hound matches hound, but only if it is preceded by grey.

Negative lookbehind (?<!) checks that its subpattern could not possibly match immediately to the left.

(pregexp-match-positions "(?

The regexp (?<!grey)hound matches hound, but only if it is not preceded by grey.

Lookaheads and lookbehinds can be convenient when they are not confusing.

6.4 An extended example

Here's an extended example from Friedl [Mastering Regular Expressions, p123] that covers many of the features described above. The problem is to fashion a regexp that will match any and only IP addresses or dotted quads, ie, four numbers separated by three dots, with each number between 0 and 255. We will use the commenting mechanism to build the final regexp with clarity. First, a subregexp n0-255 that matches 0 through 255.

(define n0-255 "(?x: \\d ; 0 through 9 | \\d\\d ; 00 through 99 | [01]\\d\\d ;000 through 199 | 2[0-4]\\d ;200 through 249 | 25[0-5] ;250 through 255 )")

The first two alternates simply get all single- and double-digit numbers. Since 0-padding is allowed, we need to match both 1 and 01. We need to be careful when getting 3-digit numbers, since numbers above 255 must be excluded. So we fashion alternates to get 000 through 199, then 200 through 249, and finally 250 through 255.(10)

An IP-address is a string that consists of four n0-255s with three dots separating them.

(define ip-re1 (string-append "^" ;nothing before n0-255 ;the first n0-255, "(?x:" ;then the subpattern of "\\." ;a dot followed by n0-255 ;an n0-255, ")" ;which is "{3}" ;repeated exactly 3 times "$" ;with nothing following ))

Let's try it out.

(pregexp-match ip-re1 "1.2.3.4") => ("1.2.3.4") (pregexp-match ip-re1 "55.155.255.265") => #f

which is fine, except that we also have

(pregexp-match ip-re1 "0.00.000.00") => ("0.00.000.00")

All-zero sequences are not valid IP addresses! Lookahead to the rescue. Before starting to match ip-re1, we look ahead to ensure we don't have all zeros. We could use positive lookahead to ensure there is a digit other than zero.

(define ip-re (string-append "(?=.*[1-9])" ;ensure there's a non-0 digit ip-re1))

Or we could use negative lookahead to ensure that what's ahead isn't composed of only zeros and dots.

(define ip-re (string-append "(?![0.]*$)" ;not just zeros and dots ;(note: dot is not metachar inside []) ip-re1))

The regexp ip-re will match all and only valid IP addresses.

(pregexp-match ip-re "1.2.3.4") => ("1.2.3.4") (pregexp-match ip-re "0.0.0.0") => #f