Your explanation of why ORDER BY is not efficiently incrementalizable is spot on. At the moment Feldera ignores the outermost ORDER BY clause, unless it is part of the ORDER BY ... LIMIT pattern, which is SQL's way to express the top-k query.
Apologies about the confusion. We indeed only solve incremental computation for Abelian groups, and the paper is making a case that database tables can be modeled as Abelian groups using Z-sets, and all relational operators (plus aggregation, recursion, and more) can be modeled as operations on Z-sets.
Good point. The goal is indeed to be a Postgres of incremental computing: any SQL query should "just work" out of the box with good performance and standard SQL semantics. You shouldn't need a team of experts to use the tool effectively.
The reason DBSP and Differential Dataflow work so well is because they are specialized to relational computations. Relational operators have nice properties that allow evaluating them incrementally. Incremental evaluation for a general purpose language like Rust is a much, much harder problem.
FWIW, DBSP is available as a Rust crate (https://crates.io/crates/dbsp), so you can use it as an embedded incremental compute engine inside your program.
It is indeed inspired by timely/differential, but is not exactly comparable to it. One nice property of DBSP is that the theory is very modular and allows adding new incremental operators with strong correctness guarantees, kind of LEGO brick for incremental computation. For example we have a fully incremental implementation of rolling aggregates (https://www.feldera.com/blog/rolling-aggregates), which I don't think any other system can do today.
The computational complexity of running an analytical query on a database is, at best, O(N), where N is the size of the database. The computational complexity of evaluating queries incrementally over streaming data with a well-designed query engine is O(delta), where delta is the size of the *new* data. If your use case is well served by a database (i.e., can tolerate the latency), then you're certainly better off relying on the more mature technology. But if you need to do some heavy-weight queries and get fresh results in real-time, no DB I can think of can pull that off (including "real-time" databases).
The correct way to think about the problem is in terms of evaluating joins (or any other queries) over changing datasets. And for that you need an engine designed for *incremental* processing from the ground up: algorithms, data structures, the storage layer, and of course the underlying theory. If you don't have such an engine, you're doomed to build layer of hacks, and still fail to do it well.
We've been building such an engine at Feldera (https://www.feldera.com/), and it can compute joins, aggregates, window queries, and much more fully incrementally. All you have to do is write your queries in SQL, attach your data sources (stream or batch), and watch results get incrementally updated in real-time.
A streaming join indeed requires an unbounded buffer in the most general case when inputs keep growing and any input record on one side of the join can match any record on the other side. However, it does not require inputs to be ordered. An incremental query engine such as Feldera or Materialize can handle out-of-order data and offer strong consistency guarantees (disclaimer: I am a developer of Feldera). In practice, unbounded buffers can often be avoided as well. This may require a specialized join such as as-of join (https://www.feldera.com/blog/asof-join) and some GC machinery.
So, a better solution is still future work :)