[codethief]

> Those kinds of assumptions are where you explicitly cast to a smaller ranged type

But how exactly do you do that? As mentioned, a and b individually can still reach INT_MAX.

I agree with your overall assessment, though. If a type system could represent (and recognize, and evaluate / automatically draw conclusions from) any possible restriction on the values of variables this would probably amount to the type system being able to carry out arbitrary mathematical proofs. The existence of such a type system seems rather unlikely.

[Arch-TK]

In some pretend rust. Pretend Integer exists and has the properties I described:

    fn special_sum(a: Integer<0..(1<<32)>, b: Integer<0..(1<<32)>) -> Option<Integer<0..(1<<32)>>
    {
        Integer<0..(1<<32)>::try_from(a + b)
    }

The type of the expression a+b would be Integer<0..(1<<33)-1>.

Obviously you can design a language which makes this much more ergonomic. That language can also avoid needing to use a type larger than a 32 bit wide unsigned integer to perform the operation through a special optimisation. Moreover, there's nothing stopping the type system from being able to maintain more sophisticated rules, for example there's nothing stopping a product type of two Integer<0..(1<<32)> having a rule applied which ensures that the sum of the two values cannot exceed 2*32-1.