[SkiFire13]

Expanding the logic to union of intervals looks cool, but what is the complexity of that? Since you introduce the the possibility of an operation on an interval producing two intervals I suspect executing N operations might have an exponential complexity, which unfortunately makes this unfeasible to use for some common intervals applciations like abstract interpretation, unless you start introducing approximations once you have enough intervals.

[lou1306]

Yes, this is well-known (eg. in abstract interpretation). As you said, usually you can set a "cap" to the size of these objects, and start merging intervals when you hit the cap. But at least in abstract interpretation it seems that they simply consider more sophisticated domains than intervals.