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Ironically I've come up a bit short on how to use dependent types to do anything more advanced than matching handlers' to route types, which Servant [2] can do fantastically already.
I would love to be able to write types that describe, e.g., assumptions made about external resources, so that I can prove that "assuming my DB has such-and-such a latency, my page will always render in such-and-such a time" or something similar - but it's a bit beyond me at the moment.
[1] https://github.com/alex-wellbelove/LeanServer
https://sel4.systems
Working on a number of platforms, verified on some. Multicore support is an ongoing effort afaict.
On OS built on this kernel is still subject to some assumptions (like, hardware working correctly, bootloader doing its job, etc). But mostly those assumptions are less of a problem / easier to prove than the properties of a complex software system.
As I understand it, guarantees that seL4 does provide, go well beyond anything else currently out there.
Also a C compiler (https://compcert.org/). I did exaggerate bit in saying that anything non-trivial is "nearly impossible".
However, both CompCert and sel4 took a few years to develop, whereas it would only take months if not weeks to make versions of both which aren't formally verified but heavily tested.
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