Recursive patterns

Consider the problem of matching a string in parentheses, allowing for unlimited nested parentheses. Without the use of recursion, the best that can be done is to use a pattern that matches up to some fixed depth of nesting. It is not possible to handle an arbitrary nesting depth. Perl 5.6 has provided an experimental facility that allows regular expressions to recurse (among other things). The special item (?R) is provided for the specific case of recursion. This PCRE pattern solves the parentheses problem (assume the PCRE_EXTENDED option is set so that white space is ignored): \( ( (?>[^()]+) | (?R) )* \)

First it matches an opening parenthesis. Then it matches any number of substrings which can either be a sequence of non-parentheses, or a recursive match of the pattern itself (i.e. a correctly parenthesized substring). Finally there is a closing parenthesis.

This particular example pattern contains nested unlimited repeats, and so the use of a once-only subpattern for matching strings of non-parentheses is important when applying the pattern to strings that do not match. For example, when it is applied to (aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa() it yields "no match" quickly. However, if a once-only subpattern is not used, the match runs for a very long time indeed because there are so many different ways the + and * repeats can carve up the subject, and all have to be tested before failure can be reported.

The values set for any capturing subpatterns are those from the outermost level of the recursion at which the subpattern value is set. If the pattern above is matched against (ab(cd)ef) the value for the capturing parentheses is "ef", which is the last value taken on at the top level. If additional parentheses are added, giving \( ( ( (?>[^()]+) | (?R) )* ) \) then the string they capture is "ab(cd)ef", the contents of the top level parentheses. If there are more than 15 capturing parentheses in a pattern, PCRE has to obtain extra memory to store data during a recursion, which it does by using pcre_malloc, freeing it via pcre_free afterwards. If no memory can be obtained, it saves data for the first 15 capturing parentheses only, as there is no way to give an out-of-memory error from within a recursion.

(?1), (?2) and so on can be used for recursive subpatterns too. It is also possible to use named subpatterns: (?P>name) or (?&name).

If the syntax for a recursive subpattern reference (either by number or by name) is used outside the parentheses to which it refers, it operates like a subroutine in a programming language. An earlier example pointed out that the pattern (sens|respons)e and \1ibility matches "sense and sensibility" and "response and responsibility", but not "sense and responsibility". If instead the pattern (sens|respons)e and (?1)ibility is used, it does match "sense and responsibility" as well as the other two strings. Such references must, however, follow the subpattern to which they refer.

The maximum length of a subject string is the largest positive number that an integer variable can hold. However, PCRE uses recursion to handle subpatterns and indefinite repetition. This means that the available stack space may limit the size of a subject string that can be processed by certain patterns.

User Contributed Notes

horvath at webarticum dot hu

3 years ago


With the (?R) item you can link only to the full pattern, because it quasi equals to (?0). You can not use anchors, asserts etc., and you can only check that string CONTAINS a valid hierarchy or not.

This is wrong: ^\(((?>[^()]+)|(?R))*\)$

However, you can bracketing the full expression, and replace (?R) to the relative link (?-2). This make it reusable. So you can check complex expressions, for example:
<?php

$bracket_system = "(\\(((?>[^()]+)|(?-2))*\\))"; // (reuseable)
$bracket_systems = "((?>[^()]+)?$bracket_system)*(?>[^()]+)?"; // (reuseable)
$equation = "$bracket_systems=$bracket_systems"; // Both side of the equation must be contain valid bracket systems
var_dump(preg_match("/^$equation\$/","a*(a-(2a+2))=4(a+3)-2(a-(a-2))")); // Outputs 'int(1)'
var_dump(preg_match("/^$equation\$/","a*(a-(2a+2)=4(a+3)-2(a-(a-2)))")); // Outputs 'int(0)'

?>

You can also catch multibyte quotes with the 'u' modifier (if you use UTF-8), eg:
<?php

$quoted = "(»((?>[^»«]+)|(?-2))*«)"; // (reuseable)
$prompt = "[\\w ]+: $quoted";
var_dump(preg_match("/^$prompt\$/u","Your name: »write here«")); // Outputs 'int(1)'

?>

emanueledelgrande at email dot it

6 years ago


The recursion in regular expressions is the only way to allow the parsing of HTML code with nested tags of indefinite depth.
It seems it's not yet a spreaded practice; not so much contents are available on the web regarding regexp recursion, and until now no user contribute notes have been published on this manual page.
I made several tests with complex patterns to get tags with specific attributes or namespaces, studying the recursion of a subpattern only instead of the full pattern.
Here's an example that may power a fast LL parser with recursive descent (http://en.wikipedia.org/wiki/Recursive_descent_parser):

$pattern = "/<([\w]+)([^>]*?) (([\s]*\/>)| (>((([^<]*?|<\!\-\-.*?\-\->)| (?R))*)<\/\\1[\s]*>))/xsm";

The performances of a preg_match or preg_match_all function call over an avarage (x)HTML document are quite fast and may drive you to chose this way instead of classic DOM object methods, which have a lot of limits and are usually poor in performance with their workarounds, too.
I post a sample application in a brief function (easy to be turned into OOP), which returns an array of objects:

<?php
// test function:
function parse($html) {
    // I have split the pattern in two lines not to have long lines alerts by the PHP.net form:
    $pattern = "/<([\w]+)([^>]*?)(([\s]*\/>)|".
    "(>((([^<]*?|<\!\-\-.*?\-\->)|(?R))*)<\/\\1[\s]*>))/sm";
    preg_match_all($pattern, $html, $matches, PREG_OFFSET_CAPTURE);
    $elements = array();
    
    foreach ($matches[0] as $key => $match) {
        $elements[] = (object)array(
            'node' => $match[0],
            'offset' => $match[1],
            'tagname' => $matches[1][$key][0],
            'attributes' => isset($matches[2][$key][0]) ? $matches[2][$key][0] : '',
            'omittag' => ($matches[4][$key][1] > -1), // boolean
            'inner_html' => isset($matches[6][$key][0]) ? $matches[6][$key][0] : ''
        );
    }
    return $elements;
}

// random html nodes as example:
$html = <<<EOD
<div id="airport">
    <div geo:position="1.234324,3.455546" class="index">
        <!-- comment test:
        <div class="index_top" />
        -->
        <div class="element decorator">
                <ul class="lister">
                    <li onclick="javascript:item.showAttribute('desc');">
                        <h3 class="outline">
                            <a href="http://php.net/manual/en/regexp.reference.recursive.php" onclick="openPopup()">Link</a>
                        </h3>
                        <div class="description">Sample description</div>
                    </li>
                </ul>
        </div>
        <div class="clean-line"></div>
    </div>
</div>
<div id="omittag_test" rel="rootChild" />
EOD;

// application:
$elements = parse($html);

if (count($elements) > 0) {
    echo "Elements found: <b>".count($elements)."</b><br />";
    
    foreach ($elements as $element) {
        echo "<p>Tpl node: <pre>".htmlentities($element->node)."</pre>
        Tagname: <tt>".$element->tagname."</tt><br />
        Attributes: <tt>".$element->attributes."</tt><br />
        Omittag: <tt>".($element->omittag ? 'true' : 'false')."</tt><br />
        Inner HTML: <pre>".htmlentities($element->inner_html)."</pre></p>";
    }
}
?>

Daniel Klein

3 years ago


The order of non-mutually exclusive alternatives within a recursed sub-pattern is important.
<?php
$pattern = '/^(?<octet>[01]?\d?\d|2[0-4]\d|25[0-5])(?:\.(?P>octet)){3}$/';
?>

You might expect that this pattern will match any IP address in dotted-decimal notation (e.g. '123.45.67.89'). The pattern is intended to match four octets in the following ranges: 0-9, 00-99 & 000-255, each separated by a single dot. However, only the first octet can include values from 200-255; the remainder can only have values less than 200. The reason for this is that if the rest of the pattern fails, recursion is not back-tracked into to find an alternative match. The first part of the sub-pattern will match the first two digits of any octet from 200-255. The rest of the pattern will then fail because the third digit in the octet does not match either '\.' or '$'.

<?php
var_export(preg_match($pattern, '255.123.45.67')); // 1 (true)
var_export(preg_match($pattern, '255.200.45.67')); // 0 (false)
var_export(preg_match($pattern, '255.123.45.200')); // 0 (false)
?>

The correct pattern is:
<?php
$pattern = '/^(?<octet>25[0-5]|2[0-4]\d|[01]?\d?\d)(?:\.(?P>octet)){3}$/';
?>

Note that the first two alternatives are mutually exclusive so their order is unimportant. The third alternative, however, is not mutually exclusive but it will now only match when the first two fail.

<?php
var_export(preg_match($pattern, '255.123.45.67')); // 1 (true)
var_export(preg_match($pattern, '255.200.45.67')); // 1 (true)
var_export(preg_match($pattern, '255.123.45.200')); // 1 (true)
?>

Onyxagargaryll

5 years ago


Here's an approach to create a multidimensional array according to a string's delimiters, i.e. we want to analyze...

"some text (aaa(b(c1)(c2)d)e)(test) more text"

... as multidimensional layers.

<?php
$string = "some text (aaa(b(c1)(c2)d)e)(test) more text";

/*
 * Analyses the string multidimensionally by its opening and closing delimiters
 */
function recursiveSplit($string, $layer) {
    preg_match_all("/\((([^()]*|(?R))*)\)/",$string,$matches);
    // iterate thru matches and continue recursive split
    if (count($matches) > 1) {
        for ($i = 0; $i < count($matches[1]); $i++) {
            if (is_string($matches[1][$i])) {
                if (strlen($matches[1][$i]) > 0) {
                    echo "<pre>Layer ".$layer.":   ".$matches[1][$i]."</pre><br />";
                    recursiveSplit($matches[1][$i], $layer + 1);
                }
            }
        }
    }
}

recursiveSplit($string, 0);

/*

Output:

Layer 0:   aaa(b(c1)(c2)d)e

Layer 1:   b(c1)(c2)d

Layer 2:   c1

Layer 2:   c2

Layer 0:   test
*/
?>

jonah at nucleussystems dot com

5 years ago


An unexpected behavior came up that introduced a very hard-to-track bug in some code I was working on.  It has to do with the preg_match_all PREG_OFFSET_CAPTURE flag.  When you capture the offset of a sub-match, it's offset is given _relative_ to it's parent.  For example, if you extract the value between < and > recursively in this string:

<this is a <string>>

You will get an array that looks like this:

Array
(
    [0] => Array
    (
        [0] => Array
        (
            [0] => <this is a <string>>
            [1] => 0
        )
        [1] => Array
        (
            [0] => this is a <string>
            [1] => 1
        )
    )
    [1] => Array
    (
        [0] => Array
        (
            [0] => <string>
            [1] => 0
        )
        [1] => Array
        (
            [0] => string
            [1] => 1
        )
    )
)

Notice that the offset in the last index is one, not the twelve we expected.  The best way to solve this problem is to run over the results with a recursive function, adding the parent's offset.

horvath at webarticum dot hu

3 years ago


Below are some reusable patterns. I used comments with the 'x' modifier for human-readability.

You can write also a function, that generates patterns for specified bracket/quote pairs.

<?php

/* normal paretheses */
$simple_pattern = "(    (?#root pattern)
  (                     (?#text or expression)
    (?>[^\\(\\)]+)      (?#text)
    |
    \\((?-2)\\)         (?#expression and recursion)
  )*
)";

$simple_okay_text = "5( 2a + (b - c) ) - a * ( 2b - (c * 3(b - (c + a) ) ) )";
$simple_bad_text = "5( 2)a + (b - c) ) - )a * ( ((2b - (c * 3(b - (c + a) ) ) )";

echo "Simple pattern results:\n";
var_dump(preg_match("/^$simple_pattern\$/x",$simple_okay_text));
var_dump(preg_match("/^$simple_pattern\$/x",$simple_bad_text));
echo "\n----------\n";

/* some brackets */
$full_pattern = "(                  (?#root pattern)
  (                                 (?#text or expression)
    (?>[^\\(\\)\\{\\}\\[\\]<>]+)    (?#text not contains brackets)
    |
    (
      [\\(\\{\\[<]                  (?#start bracket)
        (?(?<=\\()(?-3)\\)|           (?#if normal)
        (?(?<=\\{)(?-3)\\}|           (?#if coursed)
        (?(?<=\\[)(?-3)\\]|           (?#if squared)
        (?1)\\>                       (?#else so if tag)
      )))                           (?#close nested-but-logically-the-some-level subpatterns)
    )
  )*
)";

$full_okay_text = "5( 2a + [b - c] ) - a * ( 2b - {c * 3<b - (c + a) > } )";
$full_bad_text = "5[ 2a + [b - c} ) - a * ( 2b - [c * 3(b - c + a) ) ) }";

echo "Full pattern results:\n";
var_dump(preg_match("/^$full_pattern\$/x",$simple_okay_text));
var_dump(preg_match("/^$full_pattern\$/x",$full_okay_text));
var_dump(preg_match("/^$full_pattern\$/x",$full_bad_text));
echo "\n----------\n";

/* some brackets and quotes */
$extrafull_pattern = "(             (?#root pattern)
  (                                 (?#text or expression)
    (?>[^\\(\\)\\{\\}\\[\\]<>'\"]+) (?#text not contains brackets and quotes)
    |
    (
      ([\\(\\{\\[<'\"])             (?#start bracket)
        (?(?<=\\()(?-4)\\)|           (?#if normal)
        (?(?<=\\{)(?-4)\\}|           (?#if coursed)
        (?(?<=\\[)(?-4)\\]|           (?#if squared)
        (?(?<=\\<)(?-4)\\>|           (?#if tag)
        ['\"]                         (?#else so if static)
      ))))                          (?#close nested-but-logically-the-some-level subpatterns)
    )
  )*
)";

$extrafull_okay_text = "5( 2a + ['b' - c] ) - a * ( 2b - \"{c * 3<b - (c + a) > }\" )";
$extrafull_bad_text = "5( 2a + ['b' - c] ) - a * ( 2b - \"{c * 3<b - (c + a) > }\" )";

echo "Extra-full pattern results:\n";
var_dump(preg_match("/^$extrafull_pattern\$/x",$simple_okay_text));
var_dump(preg_match("/^$extrafull_pattern\$/x",$full_okay_text));
var_dump(preg_match("/^$extrafull_pattern\$/x",$extrafull_okay_text));
var_dump(preg_match("/^$extrafull_pattern\$/x",$extrafull_bad_text));

/*

Outputs:

Simple pattern results:
int(0)
int(0)

----------
Full pattern results:
int(0)
int(0)
int(0)

----------
Extra-full pattern results:
int(0)
int(0)
int(0)
int(0)

*/

?>