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The use case question is hard to answer because it's like asking for use cases for a Unix server on the Internet. Any app in this list is a possible use case: https://apps.sandstorm.io/

Another analogy is that it does to server-side apps what Chrome extensions did for client-side apps, but that's not perfect either.

A blockchain is a programmable database, Urbit is a full system software stack rewrite: OS, networking, compiler, PKI, etc. It has superficial similarities to TauChain in that they both have some pretty advanced functional programming theory involved, but otherwise TauChain is a blockchain project and Urbit is not.