Brainmoda | Staffan Nöteberg’s blog

The IP address problem is well known in the regex community. Here I present an extended regex syntax that would make it possible to match IP addresses in a less chatty way.

Ip-address problem

Let’s say I want to validate an IP address. It is four integers with interleaved dots such as 123.125.126.107. The naïve regex would be:

• \d*\.\d*\.\d*\.\d*

But it is so imprecise that it matches both 9999.9999.9999.9999 and …. Since the four integers in a IP address must be in the range 0-255, I can be certain that they consist of one, two, or three digits. With the Limiting Repetition operator, I can formulate this requirement:

• \d{1,3}\.\d{1,3}\.\d{1,3}\.\d{1,3}

Now 0.1.2.3 and 101.0.202.1 matches, while 9999.9999.9999.9999 doesn’t match because there are too many digits in the integers. Unfortunately 999.888.777.666 matches as well. That’s not an acceptable IP address. I told you that the integers can be up to 255. But, don’t give up. In Friedl’s seminal book “Mastering Regular Expressions”, he describes two ways to shrink the match set. Both are, however, very chatty. The first way is to list all authorized integers in a super chubby alternation:

• (0|1|2|3|4|5|6|7|8|9|10|11|12|13|14|15|16|17|18|19|20
|21|22|23|24|25|26|27|28|29|30|31|32|33|34|35
|36|37|38|39|40|41|42|43|44|45|46|47|48|49|50
|51|52|53|54|55|56|57|58|59|60|61|62|63|64|65
|66|67|68|69|70|71|72|73|74|75|76|77|78|79|80
|81|82|83|84|85|86|87|88|89|90|91|92|93|94|95
|96|97|98|99|100|101|102|103|104|105|106|107
|108|109|110|111|112|113|114|115|116|117|118
|119|120|121|122|123|124|125|126|127|128|129
|130|131|132|133|134|135|136|137|138|139|140
|141|142|143|144|145|146|147|148|149|150|151
|152|153|154|155|156|157|158|159|160|161|162
|163|164|165|166|167|168|169|170|171|172|173
|174|175|176|177|178|179|180|181|182|183|184
|185|186|187|188|189|190|191|192|193|194|195
|196|197|198|199|200|201|202|203|204|205|206
|207|208|209|210|211|212|213|214|215|216|217
|218|219|220|221|222|223|224|225|226|227|228
|229|230|231|232|233|234|235|236|237|238|239
|240|241|242|243|244|245|246|247|248|249|250
|251|252|253|254|255)

Note that the above is just one integer in the IP address. I have to write the super chubby alternation four times with interleaved dots to get the correct regex.

The second way to specify an integer in the range 0-255 is to decompose the problem into sub problems based on the initial character. If the first digit is 0 or 1, then all integers consisting of 1-3 digits are acceptable – I also allow leading zeros as in e.g. 054. When the initial digit is 2 and the second number is in the range 0-4, then I accept digits in the ranges 20-24 and 200-249. Finally, if the integer starts with 25, then I only tolerate it if it’s followed by a digit in the range 0-5. Like this:

• [01]?\d\d?|2[0-4]\d|25[0-5]

(Does this regex really match 25? The third part of this alternation only matches integers in the range 250-255. Yes, it does. The first part matches any integer consisting of one or two digits.)

Again I must rewrite my regex four times with interleaved dots to match an entire IP address.

Integer Class – a new operator suggested

So far I’ve talked about how regex works right now. Let’s imagine now that I can add a new operator. I call the new operator Integer Class.

Both regexes above solve the problem, but they demand so many characters that it reminds me of chatter from a group of monkeys (i.e. not easy to understand). My proposal is to extend the regex syntax with a new operator: Integer Class. It matches integers of any length, if they are in a specific range. For IP numbers — which should be in the range 0-255 — it would look like this:

• [0..255]

Square brackets surrounds two integers – a lower and an upper limit. There are double dots in-between the integers. Integer Class would work almost as a syntactic sugar for the super chubby alternation above — but not quite. Here are some details:

• Backwards compability: most regex interpreters permits Character Classes with repeated characters. A regex [0..255] is syntactically correct already today. But now it means something entirely different than what I want. The regex interpreter doesn’t care about the double fives and the double dots. Right now, [0..255] is a redundant way of writing [0.25], i.e. it matches exactly one character and it must be either 0, dot, 2 or 5. With my syntax and semantics, the regex interpreter would notice the double dots and say “Hey, this isn’t a Character Class, because it’s an Integer Class.” How cool is that?
• Leading Zeroes: An Integer Class matches leading zeros in the candidate, but only if you specify it. How? Well, by writing a zero in front of the lower limit. For example: [00..255] means that even sequences like 012, 0004 and 00255 are appropriate integers.
• Negative integers: Of course, negative integers are permitted. For example, [-1..1] matches -1, 0 or 1. Sidenote: a leading dash in a Character Class means that dashes are allowed. It may sound trivial, but then you should know that in a Character Class [A-Z], the dash means from/to – the range A to Z. A dash in a Character Class has a different meaning depending of if it’s in the beginning or the middle of an expression. Anyway, if there is a double point, it is an Integer Class and then dash means minus.
• Greedy: Like many other regex operators – such as repetition – the Integer Class is greedy of type longest-leftmost-match, but charity obedient. This means that [0..255] rather match 255 than 2 in candidate 255. But the regex engine is prepared to release the fives if it means the whole expression match. This differs from the super chubby alternation above. At least a Traditional NFA engine often matches the first one it finds, i.e. 2 rather than 255.
• Meta Characters inside Integer class: There’s no need for rules to escape characters since only digits, double dots and dashes are permitted in an Integer class. Backslash is not allowed to reside in an Integer Class.
• Negated Integer Class: A caret ^ after the right square bracket will negate the Integer Class. Any integer except those stated in the Integer Class will be matched. E.g. [^5..7] match any integer except 5, 6 and 7. Note that a negated Integer Class still must match an integer. Match exactly one integer, but not 5, 6 or 7.
• Not accepting nothing: A Character Class doesn’t match nothing – the empty string. The same is true for an Integer Class. There must be an integer matched in the range. The exception is, of course, when an Integer Class is followed by * or ? — for example: [0..255]*

With the suggested Integer Class, an IP address can be matched with this regex:

• ([0..255]\.){3}[0..255]

Relevant questions:

• Is this syntax possible or would it be ambiguous?2
• There are many possible operators to add to the regex syntax – is Integer Class the most needed?
• Should the Integer Class be even more capable, e.g. be able to match floats?