Testing asymptotic behaviour is quite simple. It can be done empirically.
Yes, you might make a formal proof of asymptotic behaviour and the property that the iterator returns a set, given a certain approximate model of the system, of course. However, it doesn’t just become simple or practical given the existence of a suitable type system alone.
Also I am not sure of the usefulness of tests of the asymptotic behaviour of an implementation of a data structure over tests over the applicable data and system. Is there a demand for this? What I mean is separate from the proof that a theoretical hash set had X complexity in its operations. That is clearly interesting.
Unit testing might be for the poor man, but how much money will the man doing the formal proof have left at the end of it?
Yes, you might make a formal proof of asymptotic behaviour and the property that the iterator returns a set, given a certain approximate model of the system, of course. However, it doesn’t just become simple or practical given the existence of a suitable type system alone.
Also I am not sure of the usefulness of tests of the asymptotic behaviour of an implementation of a data structure over tests over the applicable data and system. Is there a demand for this? What I mean is separate from the proof that a theoretical hash set had X complexity in its operations. That is clearly interesting.
Unit testing might be for the poor man, but how much money will the man doing the formal proof have left at the end of it?