Are there any examples of pumping lemmas with "real" languages?

Question

The pumping lemma is a property of regular languages and context-free languages. But all the examples I've seen are things like:

L = {0ⁿ1ⁿ2ⁿ : n ≥ 0}

(which, incidentally, is not a context-free language).

But what I'm interested in is this: are there any examples of its use with any remotely real or useful languages? I haven't been able to find any. Is this one of those things or purely theoretical value with absolutely no practical application?

Answer 1

L = {0ⁿ1ⁿ : n ≥ 0} being a context-free language.

Parenthesis matching in an expression can be considered to be of similar form i.e.

L = { (ⁿ )ⁿ : n ≥ 0}

Answer 2

this python program is valid:

print ((((((((((((((((((((((((1))))))))))))))))))))))))

as well as all other equivalent statements with an equal amount of ( on the left and ) on the right side.

You cannot build a regular expression to verify that, thus you have to use a parser.

It is not at all theoretical. It is the reason why you cannot use regex to parse HTML.