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differential-datalog
DDlog is a programming language for incremental computation. It is well suited for writing programs that continuously update their output in response to input changes. A DDlog programmer does not write incremental algorithms; instead they specify the desired input-output mapping in a declarative manner.
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InfluxDB
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I don't know anything about Souffle so I can't directly answer the question. But there is some related material.
The DDlog repo includes a Souffle-to-DDlog converter: https://github.com/vmware/differential-datalog/blob/v0.38.0/...
The Souffle converter is somewhat incomplete: https://github.com/vmware/differential-datalog/issues/174
It's partially inspired by Linq, so the similarity you see is expected.
It's not really arbitrary structures so much, though you're mostly free in what record type you use in a relation (structs and tagged enums are typical, though).
The incremental part is that you can feed it changes to the input (additions/retractions of facts) and get changes to the outputs back with low latency (you can alternatively just use it to keep an index up-to-date, where you can quickly look up based on a key (like a materialized view in SQL)).
This [0] section in the readme of the underlying incremental dataflow framework may help get the concept across, but feel free to follow up if you're still not seeing the incrementality.
[0]: https://github.com/TimelyDataflow/differential-dataflow#an-e...
Yes. Almost exactly what you're describing exists [0] already.
[0]: https://materialize.com/
A related project is declarative dataflow, which is an interactive and reactive dataflow engine built on top of differential dataflow. https://github.com/comnik/declarative-dataflow