Instantiating Binders

Much like EarlyBinder, when accessing the inside of a Binder we must first discharge it by replacing the bound vars with some other value. This is for much the same reason as with EarlyBinder, types referencing parameters introduced by the Binder do not make any sense outside of that binder, for example:

fn foo<'a>(a: &'a u32) -> &'a u32 {
    a
}
fn bar<T>(a: fn(&u32) -> T) -> T {
    a(&10)
}

fn main() {
    let higher_ranked_fn_ptr = foo as for<'a> fn(&'a u32) -> &'a u32;
    let references_bound_vars = bar(higher_ranked_fn_ptr);
}

In this example we are providing an argument of type for<'a> fn(&'^0 u32) -> &'^0 u32 to bar, we do not want to allow T to be inferred to the type &'^0 u32 as it would be rather nonsensical (and likely unsound if we did not happen to ICE, main has no idea what 'a is so how would the borrow checker handle a borrow with lifetime 'a).

Unlike EarlyBinder we typically do not instantiate Binder with some concrete set of arguments from the user, i.e. ['b, 'static] as arguments to a for<'a1, 'a2> fn(&'a1 u32, &'a2 u32). Instead we usually instantiate the binder with inference variables or placeholders.

Instantiating with inference variables

We instantiate binders with inference variables when we are trying to infer a possible instantiation of the binder, e.g. calling higher ranked function pointers or attempting to use a higher ranked where-clause to prove some bound. For example, given the higher_ranked_fn_ptr from the example above, if we were to call it with &10_u32 we would:

• Instantiate the binder with infer vars yielding a signature of fn(&'?0 u32) -> &'?0 u32)
• Equate the type of the provided argument &10_u32 (&'static u32) with the type in the signature, &'?0 u32, inferring '?0 = 'static
• The provided arguments were correct as we were successfully able to unify the types of the provided arguments with the types of the arguments in fn ptr signature

As another example of instantiating with infer vars, given some for<'a> T: Trait<'a> where-clause, if we were attempting to prove that T: Trait<'static> holds we would:

• Instantiate the binder with infer vars yielding a where clause of T: Trait<'?0>
• Equate the goal of T: Trait<'static> with the instantiated where clause, inferring '?0 = 'static
• The goal holds because we were successfully able to unify T: Trait<'static> with T: Trait<'?0>

Instantiating binders with inference variables can be accomplished by using the instantiate_binder_with_fresh_vars method on InferCtxt. Binders should be instantiated with infer vars when we only care about one specific instantiation of the binder, if instead we wish to reason about all possible instantiations of the binder then placeholders should be used instead.

Instantiating with placeholders

Placeholders are very similar to Ty/ConstKind::Param/ReEarlyParam, they represent some unknown type that is only equal to itself. Ty/Const and Region all have a Placeholder variant that is comprised of a Universe and a BoundVar.

The Universe tracks which binder the placeholder originated from, and the BoundVar tracks which parameter on said binder that this placeholder corresponds to. Equality of placeholders is determined solely by whether the universes are equal and the BoundVars are equal. See the chapter on Placeholders and Universes for more information.

When talking with other rustc devs or seeing Debug formatted Ty/Const/Regions, Placeholder will often be written as '!UNIVERSE_BOUNDVARS. For example given some type for<'a> fn(&'a u32, for<'b> fn(&'b &'a u32)), after instantiating both binders (assuming the Universe in the current InferCtxt was U0 beforehand), the type of &'b &'a u32 would be represented as &'!2_0 &!1_0 u32.

When the universe of the placeholder is 0, it will be entirely omitted from the debug output, i.e. !0_2 would be printed as !2. This rarely happens in practice though as we increase the universe in the InferCtxt when instantiating a binder with placeholders so usually the lowest universe placeholders encounterable are ones in U1.

Binders can be instantiated with placeholders via the enter_forall method on InferCtxt. It should be used whenever the compiler should care about any possible instantiation of the binder instead of one concrete instantiation.

Note: in the original example of this chapter it was mentioned that we should not infer a local variable to have type &'^0 u32. This code is prevented from compiling via universes (as explained in the linked chapter)

Why have both RePlaceholder and ReBound?

You may be wondering why we have both of these variants, afterall the data stored in Placeholder is effectively equivalent to that of ReBound: something to track which binder, and an index to track which parameter the Binder introduced.

The main reason for this is that Bound is a more syntactic representation of bound variables whereas Placeholder is a more semantic representation. As a concrete example:

#![allow(unused)]
fn main() {
impl<'a> Other<'a> for &'a u32 { }

impl<T> Trait for T
where
    for<'a> T: Other<'a>,
{ ... }

impl<T> Bar for T
where
    for<'a> &'a T: Trait
{ ... }
}

Given these trait implementations u32: Bar should not hold. &'a u32 only implements Other<'a> when the lifetime of the borrow and the lifetime on the trait are equal. However if we only used ReBound and did not have placeholders it may be easy to accidentally believe that trait bound does hold. To explain this let's walk through an example of trying to prove u32: Bar in a world where rustc did not have placeholders:

• We start by trying to prove u32: Bar
• We find the impl<T> Bar for T impl, we would wind up instantiating the EarlyBinder with u32 (note: this is not quite accurate as we first instantiate the binder with an inference variable that we then infer to be u32 but that distinction is not super important here)
• There is a where clause for<'a> &'^0 T: Trait on the impl, as we instantiated the early binder with u32 we actually have to prove for<'a> &'^0 u32: Trait
• We find the impl<T> Trait for T impl, we would wind up instantiating the EarlyBinder with &'^0 u32
• There is a where clause for<'a> T: Other<'^0>, as we instantiated the early binder with &'^0 u32 we actually have to prove for<'a> &'^0 u32: Other<'^0>
• We find the impl<'a> Other<'a> for &'a u32 and this impl is enough to prove the bound as the lifetime on the borrow and on the trait are both '^0

This end result is incorrect as we had two separate binders introducing their own generic parameters, the trait bound should have ended up as something like for<'a1, 'a2> &'^1 u32: Other<'^0> which is not satisfied by the impl<'a> Other<'a> for &'a u32.

While in theory we could make this work it would be quite involved and more complex than the current setup, we would have to:

• "rewrite" bound variables to have a higher DebruijnIndex whenever instantiating a Binder/EarlyBinder with a Bound ty/const/region
• When inferring an inference variable to a bound var, if that bound var is from a binder enterred after creating the infer var, we would have to lower the DebruijnIndex of the var.
• Separately track what binder an inference variable was created inside of, also what the innermost binder it can name parameters from (currently we only have to track the latter)
• When resolving inference variables rewrite any bound variables according to the current binder depth of the infcx
• Maybe more (while writing this list items kept getting added so it seems naive to think this is exhaustive)

Fundamentally all of this complexity is because Bound ty/const/regions have a different representation for a given parameter on a Binder depending on how many other Binders there are between the binder introducing the parameter, and its usage. For example given the following code:

#![allow(unused)]
fn main() {
fn foo<T>()
where
    for<'a> T: Trait<'a, for<'b> fn(&'b T, &'a u32)>
{ ... }
}

That where clause would be written as:
for<'a> T: Trait<'^0, for<'b> fn(&'^0 T, &'^1_0 u32)>
Despite there being two references to the 'a parameter they are both represented differently: ^0 and ^1_0, due to the fact that the latter usage is nested under a second Binder for the inner function pointer type.

This is in contrast to Placeholder ty/const/regions which do not have this limitation due to the fact that Universes are specific to the current InferCtxt not the usage site of the parameter.

It is trivially possible to instantiate EarlyBinders and unify inference variables with existing Placeholders as no matter what context the Placeholder is in, it will have the same representation. As an example if we were to instantiate the binder on the higher ranked where clause from above, it would be represented like so:
T: Trait<'!1_0, for<'b> fn(&'^0 T, &'!1_0 u32)>
the RePlaceholder representation for both usages of 'a are the same despite one being underneath another Binder.

If we were to then instantiate the binder on the function pointer we would get a type such as:
fn(&'!2_0 T, ^'!1_0 u32)
the RePlaceholder for the 'b parameter is in a higher universe to track the fact that its binder was instantiated after the binder for 'a.

Instantiating with ReLateParam

As discussed in a previous chapter, RegionKind has two variants for representing generic parameters, ReLateParam and ReEarlyParam. ReLateParam is conceptually a Placeholder that is always in the root universe (U0). It is used when instantiating late bound parameters of functions/closures while inside of them. Its actual representation is relatively different from both ReEarlyParam and RePlaceholder:

• A DefId for the item that introduced the late bound generic parameter
• A BoundRegionKind which either specifies the DefId of the generic parameter and its name (via a Symbol), or that this placeholder is representing the anonymous lifetime of a Fn/FnMut closure's self borrow. There is also a variant for BrAnon but this is not used for ReLateParam.

For example, given the following code:

impl Trait for Whatever {
    fn foo<'a>(a: &'a u32) -> &'a u32 {
        let b: &'a u32 = a;
        b
    }
}

the lifetime 'a in the type &'a u32 in the function body would be represented as:

ReLateParam(
    {impl#0}::foo,
    BoundRegionKind::BrNamed({impl#0}::foo::'a, "'a")
)

In this specific case of referencing late bound generic parameters of a function from inside the body this is done implicitly during hir_ty_lowering rather than explicitly when instantiating a Binder somewhere. In some cases however, we do explicitly instantiate a Binder with ReLateParams.

Generally whenever we have a Binder for late bound parameters on a function/closure and we are conceptually inside of the binder already, we use liberate_late_bound_regions to instantiate it with ReLateParams. That makes this operation the Binder equivalent to EarlyBinder's instantiate_identity.

As a concrete example, accessing the signature of a function we are type checking will be represented as EarlyBinder<Binder<FnSig>>. As we are already "inside" of these binders, we would call instantiate_identity followed by liberate_late_bound_regions.