How to represent externally certified enclosures with `trv` decoration?

[ChangheYang1999]

Hi, I have a question about decorations in IntervalArithmetic.jl.

In my project, some intervals are not obtained directly from decorated interval evaluation. Instead, they are certified by an external error estimate.

For example, suppose I have an approximate value x_approx and a rigorous error bound E, with an external proof that

abs(x_true - x_approx) <= E

Then I know that the true value is contained in

[x_approx - E, x_approx + E]

In code this is roughly:

lo = x_approx - E
hi = x_approx + E
Y = hull(lo, hi)

The result may have decoration trv. I understand that this can happen because hull is a set operation, not a continuous function evaluation, so it should not automatically preserve com.

My question is: how should such externally certified enclosures be represented?

More specifically:

1. Does trv mean only that the decoration-based function-evaluation information is lost, or does it also mean the interval should not be trusted as an enclosure?
2. Is it reasonable to keep the trv decoration while relying on the external proof abs(x_true - x_approx) <= E?
3. Is there a recommended pattern for this, such as wrapping the interval in a separate CertifiedEnclosure type?

I do not want to manually reconstruct the interval as com, since that would misrepresent the decoration semantics. I only want a clean way to express: the interval is not certified by decorations, but its bounds are certified by an external theorem or error bound.

Thanks!

[OlivierHnt]

You could use hull(x, y; dec = :auto). But I think you should just call interval(x_approx, R; format = :midpoint), no?

[ChangheYang1999]

Thanks a lot!