Re^2: Why machine-generated solutions will never cease to amaze me

[hv]

in reply to Re: Why machine-generated solutions will never cease to amaze me
in thread Why machine-generated solutions will never cease to amaze me

The proof for the (x?|y) case follows immediately from regex union being commutative.

Regexp union is not commutative when one of the alternates is a leading substring of another: then order becomes important - (E|x) will always match E in preference to x.

It is the presence of the outer anchors in the original pattern that disambiguates and thus makes it commutative.

Hugo

[tmoertel]

hv wrote:

Regexp union is not commutative when one of the alternates is a leading substring of another: then order becomes important - (E|x) will always match E in preference to x.

Excellent point. (However, union is commutative even in the face of overlapping operands when the union is forced to match all of the target string or not match at all.)

It is the presence of the outer anchors in the original pattern that disambiguates and thus makes (regexp union) commutative.

Even anchoring isn't sufficient. What if one of the anchors matches the difference between the union operands? Consider (a|aa) in:

  "aaaa" =~ /a(a|aa)a/

Fortunately, in the case of the OP's regexes – s(?:al|pre)?ad and s(?:(?:al)?|pre)ad) – the union operands don't overlap, and so classical equivalence (do the regexps generate the same language?) predicts the equivalence of Perl's matching behavior (do the regexps match the same strings identically?)

Cheers,
Tom