It kind of asks "What if we built an OS, but with all data sourced from immutable, append-only logs processed by pure functios?"

Probably not literally realizable right now, but IMHO, the closer we can get, the better

You could easily make CUNIX by starting with a log containing the state of a PDP11 at boot and a pure function which appends ignore previous input and the next PDP11 state to it.