[Arch-TK]

There is actually another option.

A more sophisticated type system.

Let's say you had some pseudocode like this:

    let a = 5
    let b = 12
    let c = a + b

The type of a would be Integer[5..5], the type of b would be Integer[12..12], the type of c would therefore be Integer[17..17]. In a more complex example:

    def foo(a: Integer[0..10], b: Integer[0..10]):
        return a + b

The return type of this function would be Integer[0..20].

This kind of type system can solve a number of issues, all but division by zero (which would probably still have to be solved with some kind of optional type).

If type inference dictates that the upper range of an integer would be too large to physically store in a machine data type, then you either resort to bignums or you make it a compilation error. By adding modular and saturating integer types you can handle situations where you want special integer behaviours. By explicitly casting (with the operation returning an optional) you can handle situations where you want to bound the range. This drastically simplifies a lot of code by removing explicit bounds checks in all places except where they are absolutely necessary. If for some reason you care about the space or computational efficiency of the underlying machine type, you can have additional annotations (like C's u?int_(least|fast)[0-9]+_t). If you absolutely must map to a machine type (this is usually misguided, unless you are dealing with existing C interfaces, for which such a language can provide special types) you can have more annotations.

Ada has something resembling this. I believe there are some other languages that implement similar features. I believe this sort of thing has a name, but I am not great with remembering the names of things.

Hopefully this is some food for thought.

[im3w1l]

I think the issue with this is that the worst-case bounds normally grow much faster than the actual values. And it can be easy to see for the programmer that the values can't actually grow that much because a is only big when b is small or some property like that, but then you have to convince the compiler of the same. I might be misremembering though.

[codethief]

> because a is only big when b is small or some property like that

Exactly, the expressiveness of the type system then (typically) becomes the obstacle: How do you express that a and b could each reach INT_MAX but their sum never exceeds INT_MAX?

[Arch-TK]

Those kinds of assumptions are where you explicitly cast to a smaller ranged type with the option of an error if the sum does exceed a limit. The point of this type system is not to be able to fully encode every possible interaction between numbers in a system, but rather to remove unnecessary bounds checking in a bunch of cases and make it explicit in the few cases where you ARE actually making an assumption.

[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.

[wizzwizz4]

> but then you have to convince the compiler of the same.

In conventional parlance, this is known as "handling overflow".

[still_grokking]

> I believe this sort of thing has a name, […]

https://en.wikipedia.org/wiki/Refinement_type

But the concept is just a little bit over 30 years old. So don't expect it shows up in most mainstream languages before the end of the next 20 years, and don't expect it to come to the C languages ever.

Meanwhile in mainstream ML-land:

https://github.com/Iltotore/iron

(Or for the older version of the language: https://github.com/fthomas/refined)

(Please also note that for this feature both versions don't need language support at all but are "just" libraries, as the language is powerful enough to express all kinds of type level / compile time computations in general.)

[Arch-TK]

I know C is never getting anything like this. But C is really just stuck being a very crappy ABI design language.

I do wish things like Rust had native support for stuff like this though.

And it really doesn't have to get in the way of anyone who insists on the more primitive type systems, but it would be nice to have a high level language which didn't have assembly-level (of abstraction) integer types. Why should I care that my machine works with square multiples of 8 bits at a time or care that they have specific wrapping behaviour.

[codethief]

> But the concept is just a little bit over 30 years old. So don't expect it shows up in most mainstream languages before the end of the next 20 years, and don't expect it to come to the C languages ever.

Any specific results/papers from (refinement) type theory you hope/expect to see implemented in the next 20 years?

[JonChesterfield]

Compilers do this sort of range tracking anyway. At least within a function. It's useful for loop optimisations.