I wonder if Rust or future PL would evolve into allowing multiple borrow checker implementations with varying characteristics (compile speed, runtime speed, algorithm flexibility, etc.) that projects can choose from.
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All have different costs and capabilities across implementation, performance and developer experience.
Then we have what everyone else besides Rust is actually going for, the productivity of automatic resource management (regardless of how), coupled with one of the type systems above, only for performance critical code paths.
I'd just like to interject for a moment. What you’re referring to as "affine types", is in fact, Uniqueness Types. The difference has to do with how they interact with unrestricted types. In Rust, these "unrestricted types" are references (which can be used multiple times due to implementing Copy).
Uniqueness types allow functions to place a constraint on the caller ("this argument cannot be aliased when you pass it to me"), but places no restriction on the callee. This is useful for Rust, because (among other reasons) if a value is not aliased you can free it and be sure that you're not leaving behind references to freed data.
Affine types are the opposite - they allow the caller to place a restriction on the callee ("I'm passing you this value, but you may use it at most once"), which is not something possible to express in Rust's type system, because the callee is always free to create a reference from its argument and pass that reference to multiple functions..
This is often explained via the "do not use more than once rule", but that's not the actual definition, and as your example shows, following that simplified explanation to the letter can cause confusion.
> because the callee is always free to create a reference from its argument and pass that reference to multiple functions..
Passing a reference is not the same thing as passing the actual value, so this does not contradict affinity.
I agree that passing a reference is not the same thing as passing the actual value. If it were, there would really be no point to references. However, it does contradict affinity. Specifically, the fact that multiple references can be created from the same value, combined with the properties of references, contradicts affinity.
> At its core, "affine" means that the type system has exchange and weakening but not contraction, and that exactly characterizes Rust's type system.
Well, the rust type system certainly does support contraction, as I can use a reference multiple times. So what is that if not contraction? It seems like rust at least does support contraction for references.
But in practice, having absolutely no contraction is not a very useful definition of affine, because no practical programming language would ever satisfy it. It prohibits too much and the language would not even be turing complete. Instead, there is usually an "affine world" and an "exponential world". (Exponential meaning "unrestricted" values that you can do whatever you want with). And the convention is that values can go from the exponential world to the affine world, but not back. So a function taking an affine value can be passed any value, but must use in in an affine way, and meanwhile but a function taking an exponential (unrestricted) value can only be passed exponential and not an affine value.
If you don't believe me, you can try using linear haskell, and notice that a function taking a linear argument can be passed a non-linear argument, but not the other way around.
If you interpret Rust's type system this way, it's natural to interpret references as exponentials. But references have the opposite convention. You can go from owned values to references, but not the other way around, which is precisely the opposite situation as the convention around linear/affine type systems. Because these systems feel very different to use and enforce very different properties, I do think it's important that we have separate names for them rather than referring to both as "affine". And the usual name for the rust-like system is "uniqueness types", see https://docs.idris-lang.org/en/latest/reference/uniqueness-t... or https://en.wikipedia.org/wiki/Uniqueness_type .
Good question! For shared references, the answer is that they are `Copy`, so they indeed have contraction. Affinity just means that contraction is not a universal property, but some types/propositions may still have contraction. For mutable references, you can't actually use them multiple times. However, there is a desugaring phase going on before affinity gets checked, so uses of mutable references `r` get replaced by `&mut *r` everywhere. That's not using contraction, it's not literally passing `r` somewhere, it is calling a particular (and interesting) operating on `r` ("reborrowing").
Rust is not just an affine system, it is an affine system extended with borrowing. But I think it is still entirely fair to call it an affine system, for the simple fact that the language will prevent you from "using" a variable twice. "reborrowing" is just not a case of "using", it is its own special case with its own rules.
> But in practice, having absolutely no contraction is not a very useful definition of affine,
Obviously Rust has a class of "duplicable" types, called `Copy`. That's besides the point though.
> If you interpret Rust's type system this way, it's natural to interpret references as exponentials.
Why would that be natural? Mutable references are not even duplicable, so what you say makes little sense for references in general. Maybe you mean shared references -- those are just an example of a duplicable type.
Rust doesn't have a modality in its type system that would make every type duplicable, so there is no equivalent to exponentials. (In particular, `&T` isn't a modality around `T`. It's a different type, with a different representation. And as you noted, even if it were a modality, it wouldn't correspond to exponentials.)
But a type system can be affine/linear without having exponentials so I don't understand the point of this remark.
Uniqueness types seem to be all about how many references there are to a value. You can use linear/affine types to enforce such a uniqueness property (and that is indeed what Rust does), but that doesn't take away from the fact that you have a linear/affine type system.
> Because these systems feel very different to use and enforce very different properties,
I can't talk about the "feel" as I never programmed in an affine language (other than Rust ;), but in terms of the properties, what Rust does is extremely closely related to affine logics: the core property being enforced is that things do not get duplicated. My model of Rust, RustBelt, uses an affine separation logic to encode the properties of the Rust type system, and there's a lot of overlap between separation logic and linear logic. So we have further strong evidence here that it makes perfect sense to call Rust an affine language.
Also, the claims about Curry-Howard correspondence are wrong. It does not prove that rust is an affine language: https://liamoc.net/forest/loc-000S/index.xml
But Swift DOES have affine types with the "Non copyable" types that doesn't allow contraction.
Swift doesn't have references like Rust, and you can't even have unsafe raw pointers to variables without producing a dangling pointer, but this makes Swift more restrictive and less powerful than Rust.
No, they are not. You're not using a value more than once, you are borrowing it, which is an extension of affine logic but keeps true to the core principles of affinity. I have modeled multiple shared references in an affine logic (look up RustBelt), i.e. in a logic that doesn't have contraction, so we have very hard evidence for this claim.