Well… I’m not sure how helpful that example is, but yes you could probably find something in common between SQL and Haskell, and on the other hand, no, what I said did not mean that.

Look up Graham Hutton’s writings on relations. He has published quite a bit about this, and he knows a thing or two about functional programming.

I think relations are not a precondition for something to be called declarative programming. Most definitions I‘ve found are way broader and generic.

I never claimed they were, and I don't know if they are. But relations are in the category of declarative, and are a generalization of functions.

I'm a biologist that doesn't understand what's being talked about on this thread at all (a definition of "state", and its relation to other computational parameters would be nice). But I think I can pull an analogy from ecology that might be useful here.

When a bird population starts speciating along, say, the arctic circle, you have a line of a bunch of closely related sub-species that can interbreed with the sub-species nearest them.

Sub-species 1 ... Sub-species 2 ... Sub-species 3 ... Sub-species 4 ...

1 can breed with 2. 2 can breed with 1 and 3. 2 can't breed with 4 because they are too far apart, but if a 4 came to the territory of a 2 they could breed. Etcetera.

Eventually You get a whole circle of interbreedable sub-species as they spread across a circle of arctic latitude around the world:

1 ... 2 ... 3 ... 4 ... 5 ... 6 ... 7 ... 8 ... 9 ... 1

But once you get to that point you find that sub-species 9 and sub-species 1 can't, or won't, interbreed anymore. They are now two entirely separate species despite coming from the same origin and living right next to each other.

However none of them can interbreed with a complete separate lineage, such as wolves.

TLDR: The overlap is before the extremes, not between them.