"Functional Database" is contradictory. Honestly this sounds like a bunch of buzzwords concatenated together. Is there an example or a purpose for this?
I think the idea is that it's something simpler than a database. It's more like an append-only file that has on-insert triggers/durable running queries. (Sort of like https://www.pipelinedb.com/ does, or like blockchain nodes do.)
Or, you could think of it as message queue like Kafka, with permanent durability of all "messages", and a single fixed subscriber bolted onto the queue server, where that subscriber is exposed through the queue server's API, allowing users to reprogram it arbitrarily.
Also this still isn't functional. Is adding records to a set not mutation?
Edit: Is a backup mechanism implemented? It's for persistent data, right?