How can you be sure your validation covered all cases?

Say you have a Circle class, you need a center point so you validate that the center is not null and you check that radius is greater then zero. Do you have an example where is impossible to validate all cases? if so how will your unit tests validate/test all those cases?

In your example, you can't anticipate that center points approximately but not quite equal to pi will cause a ... whatever bug in ... whatever downstream use of the class. One can never really know what states are acceptable.

The circle is valid, what you say is a bug in other section that crashes with valid circles,so types could prevent invalid inputs to functions. What you describe is a bug in an algorithm I don't think that is possible for a compiler to prevent bugs in algorithms, division by zero or precision errors

Type systems can do some pretty miraculous things. For example, you could distinguish between a connected and disconnected socket with types so that you don't accidentally send on a disconnected socket.

I guess I'm arguing both sides now. My point is that one needs to root out the weird cases somehow and that it's often hard to have "100%" validation of inputs. One's initial understanding of what is the valid and invalid state space is often incorrect.