But you don't know the MSB at compile time in the general case.

> If you are adding 0(Int18)+1(Int18), you don't need 1(Int36)

No, you’d need an Int19. We were talking about statically typed languages, so you need to decide the type at compile-time. If you add two UInt16’s they could both contain up to 0xFFFF, you need 17 bits to store that answer. Basically, with every addition you need 1 more bit than the largest of the two (types, not values) you are adding together to prevent a potential overflow. It’s even worse for multiplication.

Couldn't you have a constraining operation in there to assert that you have enough bits? You are right that we don't know if `a + b` would need more bits than either a or b. However, we could have an assert that allows us to ensure the static constraints are satisfied. And the type system could be used as a place to know where we haven't checked the constraint.

(Note that I'm not too clear how valuable this would be. Just asking why that isn't a valid path.)

> No, you’d need an Int19.

No, that's completely false. You don't need an Int19 but an Int1.

How do you figure that you can store the result of adding 2 Int18s in an Int1 ? Remember, we’re talking about static types and you don’t know the values at compile time.