How so? If you specify the type int how would that save you from an overflow/underflow at runtime?

Not sure if types are supposed to protect against overflow/underflow, it's more in the arithmetic territory. Interesting idea though, I wonder if some programming language allows overflow/underflow checks directly in the types.

Yes, it's actually quite easy:

    +: (int<N>, int<N>) -> int<N+1>    // or (int<N>, bit) as the return type
    *: (int<N>, int<N>) -> int<2*N>

etc. Those are the actual types of those arithmetic operations.