Example from sklogic that embeds ML in LISP https://github.com/combinatorylogic/mbase
Take a look at my own Haskell operating system project Hos (https://github.com/tathougies/hos). Written in Haskell 98 using the JHC compiler (a bit outdated, but makes it easy to generate ANSI C from Haskell sources). Currently supports multi-tasking, interrupts, paging, garbage collection. Has the beginnings of a simple user-space ATA driver.
Patches welcome. E-mail me at travis@athougies.net if you want help setting up a development environment!
An example implementation from CHICKEN Scheme: http://wiki.call-cc.org/man/4/Types
Some of that is vastly simpler to do with a dynamic language.
"You can boot into a REPL (Read Evaluate Print Loop) and can inspect or rewrite any part of the OS as you are using it."
As far as I know, nobody has figured out a way to have your cake and eat it too with static typing. Some of the simple things that lisps have been doing for decades are very difficult if not impossible to do with statically compiled languages.
But it's quite a lot of work to get acceptable OS performance if your entire system is interpreted or has to be JIT compiled all the time. People who do that tend to coincidentally decide they're so hardcore they don't even need JPEG support, video, or web browsing…