Lint the doctests/examples code

[Luthaf]

I think it could be interesting to have cargo-clippy (maybe clippy too?) run the lints on the doctests/code examples for rustdoc. I don't know how hard this would be, but maybe some code from rustdoc could be reused to extract the code from the examples?

As clippy allow to keep a good code quality, I'd love to be able to run it on my examples too.

[llogiq]

We'd have to coax rustdoc --test into compiling the examples w/ clippy.

[phansch]

This is being tracked in Rust: rust-lang/rust#56232