What's an example of a "functional database"? Datomic? What's the most deployed functional database?
It's misleading to say that compilers are databases if they're not anything like databases people use and know. Probably a more accurate title would have been "Compilers are like functional databases".
Storage is obviously an important part of database architecture. If a compiler doesn't deal with storage, there's only so much resemblance that a compiler and a database can have.
I think "functional database" can be seen as a wider data pattern than just a datastore that exclusively implements that pattern. It's a design principle where a piece of data once created is never changed. That leads to event sourcing or Twitters "lambda architecture".
The compiler is a database in the sense that it has a memory across incremental invocations. So the 'storage' happens to be in memory but could be on disk.
I'm definitely not a DB guy, but Datomic was the first thing that came to mind. You could also include databases that require linear consistency like etcd if you consider "functional databases" to be any database that represents state as a function of time.
There was an early slide that explicitly said FRP and functional databases were inspiration for the compiler design, but I do agree that the title should have reflected that fact.
It's misleading to say that compilers are databases if they're not anything like databases people use and know. Probably a more accurate title would have been "Compilers are like functional databases".
Storage is obviously an important part of database architecture. If a compiler doesn't deal with storage, there's only so much resemblance that a compiler and a database can have.