April 2007 — Flagrant Badassery

Mastering Regular Expressions, 3rd Edition

After reading positive reviews about the second edition it since I started using regular expressions a little over a year ago, I finally purchased O'Reilly Media's Mastering Regular Expressions by Jeffrey E. F. Friedl, since I discovered that a third edition came out in August 2006. The book arrived today, and it is indeed pretty damn excellent (I'm as excited about it as I can be about a tech book, anyway). I've only spent a few minutes with it so far, but I can see that it is very well presented and demonstrates some cool techniques. Hopefully I'll post about some nifty things I learn over the next few weeks, if I get a chance to actually sit down and read through a significant portion of the book.

Mimicking Conditionals

Excited by the fact that I can mimic atomic groups when using most regex libraries which don't support them, I set my sights on another of my most wanted features which is commonly lacking: conditionals (which provide an if-then-else construct). Of the regex libraries I'm familiar with, conditionals are only supported by .NET, Perl, PCRE (and hence, PHP's preg functions), and JGsoft products (including RegexBuddy).

There are two common types of regex conditionals in those libraries: capturing-group-based and lookaround-based. I'll get to the latter type in a bit, but first I'll address capturing-group-based conditionals, which are able to base logic on whether a capturing group has participated in the match so far. Here's an example:

(a)?b(?(1)c|d)

That matches only "bd" and "abc". The pattern can be expressed as follows:

(if_matched)?inner_pattern(?(1)then|else)

Here's a comparable pattern I created which doesn't require support for conditionals:

(?=(a)()|())\1?b(?:\2c|\3d)

Note that to use it without an "else" part, you still need to include the second empty backreference (in this case, \3) at the end, like this:

(?=(a)()|())\1?b(?:\2c|\3)

As a brief explanation of how that works, there's a zero-length alternation option within the lookahead at the beginning which is used to cancel the effect of the lookahead, while at the same time, the intentionally empty capturing groups within the lookahead are exploited to base the then/else part on which option in the lookahead matched. However, there are a couple issues:

This doesn't work with some regex engines, due to how they handle backreferences for non-participating capturing groups.
It interacts with backtracking differently than a real conditional (the "a" part is treated as if it were within an optional, atomic group, e.g., (?>(a))? instead of (a)?), so it might be better to think of this as a new operator which is similar to a conditional.

Here are the regex engines I've briefly tested this pattern with:

Language	Supports fake cond.	Supports real cond.	Notes
.NET	Yes	Yes	Tested using Expresso.
ColdFusion	Yes	No	Tested using ColdFusion MX7.
Java	Yes	No	Tested using Regular Expression Test Applet.
JavaScript	No	No	According to ECMA-262v3, backreferences to non-participating capturing groups always succeed, and most browsers respect that. Unfortunately, this pattern depends on the way most other regex engines handle such groups.
JGsoft	Yes	Yes	(Edit:) Works as of RegexBuddy version 2.4.0. Previous versions contained two bugs (which I reported to JGsoft) which prevented this from working reliably.

As for lookaround-based conditionals, we can mimic them using the same concepts. Here's what a real lookaround-based conditional looks like (this example uses a positive lookahead for the assertion):

(?(?=if_assertion)then|else)

And here's how you can mimic it:

(?:(?=if_assertion()|())\1then|\2else)

Again, to use it without an "else" part, you still need to include the second empty backreference (in this case, \2) at the end, like this:

(?:(?=if_assertion()|())\1then|\2)

Notes:

The above compatibility table applies just the same.
Backtracking does not come into play with lookaround-based conditionals in the same way as with capturing-group-based conditionals. As a result, mimicked lookaround-based conditionals are functionally identical to their "real" counterparts.
In some regex flavors, it may be necessary to write it in the the somewhat less lucid form (?=a()|())(?:\1b|\2c).
Another, potentially more verbose and less efficient way to mimic a lookaround-based conditional is to alternate two opposite lookarounds. E.g., (?=if_assertion)then|(?!if_assertion)else. That will work even in the case of flavors like JavaScript where backreferences to non-participating groups match the empty string.

Mimicking Atomic Groups

So, I was messing around with RegexBuddy and discovered that capturing groups work inside lookarounds (e.g., "(?=(captured))"), even though, of course, lookarounds only match a position. Consider that by using this technique, you can return text to your application (using backreferences) which wasn't contained within your actual match (backreference zero)!

Thinking back to the regex I just posted about (which matches innermost HTML elements, supporting an infinite amount of nesting), I realized this technique could actually be used to fake an atomic grouping. So, I've added a note on the end of the last post with an improved non-atomic-group-reliant version, which sure enough is nearly identical in speed to the regex which uses a real atomic grouping.

Here's how it's done:

(?=(pattern to make atomic))\1

Basically, it uses a capturing group inside a positive lookahead (which captures but doesn't actually consume anything, so the rest of the regex can't backtrack into it), followed by "\1" (the backreference you just captured), to act just like an atomic group. That produces the exactly same result as "(?>pattern to make atomic)", but can be used in programming languages which don't support atomic groups or possessive quantifiers (assuming they do support lookaheads). I can now use such constructs in languages like JavaScript and ColdFusion, and I think that's pretty freaking sweet.

Matching Innermost HTML Elements

On a regular expression forum I visit every once in awhile, a user asked how he could match all innermost tables within HTML source code. In other words, he wanted to match all tables which did not contain other tables. The regex should match <table>…</table>, but should only match the inner table within <table>…<table>…</table>…</table>. This logic needed to support an unlimited amount of nested tables.

One of the resident regex experts quickly claimed that regexes are not suited for parsing nested HTML data, and that this was therefore impossible using regular expressions, period.

It's true that many regex libraries are incapable of recursion (although even then it's often possible to fake it to an acceptable level). However, when people make claims like that, it encourages me to try to prove otherwise. wink

Here's the solution I offered (though there were a few steps to get there):

<table\b[^>]*>(?:(?>[^<]+)|<(?!table\b[^>]*>))*?</table>

That matches all innermost (or deepest level) tables, and supports an unlimited amount of nesting. It's also quite fast, and can easily be modified to work with other HTML elements (just change the three instances of "table" to whatever element name you want).

To demonstrate, the above regex matches the three highlighted segments of the text below:

<table><td><table><td> </td></table></td></table> <table><tr><td> </td></tr></table><table></table>

In order to explain how it works, I'll show the progression of gradually more solid regexes I tried along the way to the final result. Here was my first stab at the regex, which is probably easiest to follow (note that it's somewhat flawed, and comparatively slow):

<table>(?:.(?!<table>))*?</table>

(Make sure to turn on the "dot matches newline" modifier with the above, or change the dot to [\S\s].)

Basically, the way that works is it matches an opening <table> tag, then it looks at each following character one at a time, checking if they are followed by another instance of <table> before </table>. If so, the match fails, because it's not an innermost table. (In theory, at least.)

Within a couple minutes I realized there was a slight flaw. In order for it to work, there must be at least one character before it encounters a nested table (e.g., "<table>1<table></table></table>" has no problem, but "<table><table></table></table>" would return incorrect results). This is easily fixable by using another negative lookahead immediately after the opening <table>, but in any case this regex is also slower than it needs to be, since it tests a negative lookahead against every character contained within table tags.

To address both of those issues, I used the following regex:

<table>(?:[^<]+|<(?!table>))*?</table>

First, that increases speed (in theory… you'll see that there is now a much bigger issue than before), because within each <table> tag it will greedily jump between all characters which are not < in single steps (using [^<]+), and it will only use the negative lookahead when it encounters <. Secondly, it solves the previously noted error by using <(?!table>) instead of .(?!<table>).

If you're wondering about table tags which contain attributes, that's not a problem. Here's an updated regex to accomplish this (the added parts are highlighted in yellow):

<table\b[^>]*>(?:[^<]+|<(?!table\b[^>]*>))*?</table>

At first I thought this closed the case… The regex supports an unlimited amount of recursion within its context, despite the traditional wisdom that regexes are incapable of recursion. However, one of the forum moderators noted that its performance headed south very quickly when run against certain examples of real world data. This was a result of the regex triggering catastrophic backtracking. Although this is something I should've anticipated (nested quantifiers should always warrant extra attention and care), it's very easy to fix using an atomic grouping or possessive quantifier (I'll use an atomic grouping here since they're more widely supported). The addition to the regex is highlighted:

<table\b[^>]*>(?:(?>[^<]+)|<(?!table\b[^>]*>))*?</table>

And that's it. As a result of all this, the regex not only does its job, but it performs quite impressively. When running it over a source code test case (which previously triggered catastrophic backtracking) containing nearly 100,000 characters and lots of nested tables, it correctly returned all innermost tables in a couple milliseconds on my system.

However, note that neither possessive quantifiers nor atomic groupings are supported by some programming languages, such as JavaScript. If you want to pull this off in JavaScript, an approach which is not susceptible to catastrophic backtracking would be:

<table\b[^>]*>(?!<table\b[^>]*>)(?:[\S\s](?!<table\b[^>]*>))*?</table>

That runs a little bit slower than (but produces the same result as) the earlier regex which relied on an atomic grouping.

If you have a copy of RegexBuddy (and if you don't, I highly recommend it), run these regexes through its debugger for an under-the-hood look at how they're handled by a regex engine.

Edit: Using a trick I just stumbled upon (which I'll have to blog about in a second), the regex can be rewritten in a way that does not rely on an atomic grouping but is nearly as fast as the one that does:

<table\b[^>]*>(?:(?=([^<]+))\1|<(?!table\b[^>]*>))*?</table>

Basically, that uses a capturing group inside a positive lookahead followed by \1 to act just like an atomic group!

Update: See Matching Nested Constructs in JavaScript, Part 2 for a way to match outermost HTML elements using JavaScript.