> I don't think you're really correct about "email addresses" being context-free, or at least, citation, please?
> When I look at a generic "email address" entry field on a random form on the Internet, say on the sign-up page for some hot new startup's service, I expect it to take what RFC 5322 §3.4.1[1] calls an `addr-spec`; specifically, I don't ever expect such fields to take the grammar of what that RFC calls an `address`.
Well, sure. Let's look at what RFC 5322 defines as an addr-spec[1]:
addr-spec = local-part "@" domain
And how does it define a local-part?
local-part = dot-atom / quoted-string / obs-local-part
Let's ignore quoted-string and obs-local-part for the moment. What is a dot-atom?
dot-atom = [CFWS] dot-atom-text [CFWS]
And what is CFWS?
CFWS = (1*([FWS] comment) [FWS]) / FWS
What's a comment?
comment = "(" *([FWS] ccontent) [FWS] ")"
So far, all of this has been matchable with a regular expression. But what's a ccontent?
ccontent = ctext / quoted-pair / comment
See that there? A comment is composed of a balanced pair of parentheses around, perhaps, another comment! Thus (this (is (a (heavily (commented (email \(address))))))foo@bar.example(some more (to prove (the point))) is a perfectly viable RFC5322 address!
Pair-balancing, of course, is impossible with regular expressions, since matching pairs requires push-down automata (which match CFGs) and cannot be done with finite-state machines, (which match regular expressions).
QED.
> Also, using that assumption, your "perfectly valud[sic] email addresses such as …" would appear to not be valid, as it has unbalanced quotes.
Nope, there are no unbalanced quotes in (this)"()[]:,;@\\\"!#$%&'-/=?^_`{}| ~.a"(is)@(valid)example.org(honest): the first quote balances with the third, while the second quote is one of a quoted pair \" (which is allowed within a quoted-string, which is allowed within a local-part). It's all allowed per the spec.
I'll admit that it's a bit surprising, but it's true. One simply cannot match a valid RFC5322 addr-spec with a regular expression. One can, of course, match it with something which pretends to be regular but isn't really (as I noted).