[jarrettc]

Lately I've been playing around with static dimensional analysis in Rust. The overall idea is similar: Use PhantomData to add a type parameter and define an empty struct for each unit. So you might end up with, say, Scalar<Newtons> or Vec3<Meters>.

Dividing and multiplying units statically is where I've had trouble so far. I think I've found a way, but it would depend on negative trait bounds, as discussed here:

https://github.com/rust-lang/rfcs/issues/1053

Ideally, I'd like to be able to do something like this:

    let a: Scalar<Joules> = Scalar::new(2.0);
    let b: Scalar<Seconds> = Scalar::new(3.0);
    let c: Scalar<Watts> = a / b;
    // Watts is a type synonym for Over<Joules, Seconds>.
    // Other derived units would use Times<U, V>. E.g.:
    type Pascals = Times<Newton, Times<Meter, Meter>>.

[wyager]

If you aren't aware of it, the dimensional library for Haskell does this. https://hackage.haskell.org/package/dimensional

[jarrettc]

Yep! That was my inspiration. I'd love to be able to do this in Rust. Soon, hopefully!

[dastbe]

You should take a look at its source code. You'll see that the path you're taking is not the path that library takes.

[TJSomething]

But what makes Times<Times<Newton, Meter>, Meter> the same as Times<Newton, Times<Meter, Meter>>?

[dastbe]

Canonicalization is tough, and requires you to define some common ordering on your units.

Systems will use an array of unit powers, so that if the array were defined as <Joules, Seconds, Newtons, Meters>, then acceleration would be <0,-2,0,1> and watts would be <1,-1,0,0>. Addition and subtraction require that your arrays are equal, and multiplication and division are pairwise additive/subtractive.

[sigterm]

Is it tough? There are only seven fundamental units. https://en.wikipedia.org/wiki/SI_base_unit

Just represent every unit in terms of them then it's good.

One problem with the array you came up is that the units are not orthogonal, since Joules = Newtons * Meters.

[jcranmer]

Actually, there's more "kinds" of units: radians (versus degrees) and steradians come to mind.

[masklinn]

These are dimensionless derived units in SI equivalence (respectively m/m and m2/m2)

[dastbe]

Sorry! I never really spent much time in the physical sciences, so I didn't know that. You would obviously not want to pick Joules as a fundamental unit.

[jarrettc]

Will the Rust compiler ever understand numbers in types? I.e. will the numbers ever be more than just part of the string that is the type name? If not, then I don't know how possible powers will be. Maybe the solution would be to define some types for commonly-used powers, e.g. PowN4, PowN3, PowN2, PowN1, Pow2, Pow3, Pow4. Users who needed higher powers could define those types themselves, I guess.

[steveklabnik]

We do desire type-level integers, yes. There hasn't been an RFC yet, though.

[jarrettc]

Great question. I believe each unit struct would need to implement PartialEq or something similar. That would define the canonical nesting order. Alphabetical would make sense.

We would to resolve the nesting during multiplication and division. For example:

    let a: Scalar<Times<A, B>> = Scalar::new(10.0);
    let b: Scalar<Times<A, Times<B, C>>> = Scalar::new(5.0);
    let c: Scalar<Times<A, Times<A, Times<B, Times<C>>>> = a * b;
    

Another challenge is that the type of c is ugly. But this could be mitigated by generous use of type synonyms.