Binder and Higher ranked regions

Sometimes we define generic parameters not on an item but as part of a type or a where clauses. As an example the type for<'a> fn(&'a u32) or the where clause for<'a> T: Trait<'a> both introduce a generic lifetime named 'a. Currently there is no stable syntax for for<T> or for<const N: usize> but on nightly feature(non_lifetime_binders) feature can be used to write where clauses (but not types) using for<T>/for<const N: usize>.

The for is referred to as a "binder" because it brings new names into scope. In rustc we use the Binder type to track where these parameters are introduced and what the parameters are (i.e. how many and whether the parameter is a type/const/region). A type such as for<'a> fn(&'a u32) would be represented in rustc as:

Binder(
    fn(&RegionKind::Bound(DebruijnIndex(0), BoundVar(0)) u32) -> (),
    &[BoundVariableKind::Region(...)],
)

Usages of these parameters is represented by the RegionKind::Bound (or TyKind::Bound/ConstKind::Bound variants). These bound regions/types/consts are composed of two main pieces of data:

• A DebruijnIndex to specify which binder we are referring to.
• A BoundVar which specifies which of the parameters the Binder introduces we are referring to.
• We also sometimes store some extra information for diagnostics reasons via the BoundTyKind/BoundRegionKind but this is not important for type equality or more generally the semantics of Ty. (omitted from the above example)

In debug output (and also informally when talking to eachother) we tend to write these bound variables in the format of ^DebruijnIndex_BoundVar. The above example would instead be written as Binder(fn(&'^0_0), &[BoundVariableKind::Region]). Sometimes when the DebruijnIndex is 0 we just omit it and would write ^0.

Another concrete example, this time a mixture of for<'a> in a where clause and a type:

where
    for<'a> Foo<for<'b> fn(&'a &'b T)>: Trait,

This would be represented as

Binder(
    Foo<Binder(
        fn(&'^1_0 &'^0 T/#0),
        [BoundVariableKind::Region(...)]
    )>: Trait,
    [BoundVariableKind::Region(...)]
)

Note how the '^1_0 refers to the 'a parameter. We use a DebruijnIndex of 1 to refer to the binder one level up from the innermost one, and a var of 0 to refer to the first parameter bound which is 'a. We also use '^0 to refer to the 'b parameter, the DebruijnIndex is 0 (referring to the innermost binder) so we omit it, leaving only the boundvar of 0 referring to the first parameter bound which is 'b.

We did not always explicitly track the set of bound vars introduced by each Binder, this caused a number of bugs (read: ICEs #81193, #79949, #83017). By tracking these explicitly we can assert when constructing higher ranked where clauses/types that there are no escaping bound variables or variables from a different binder. See the following example of an invalid type inside of a binder:

Binder(
    fn(&'^1_0 &'^1 T/#0),
    &[BoundVariarbleKind::Region(...)],
)

This would cause all kinds of issues as the region '^1_0 refers to a binder at a higher level than the outermost binder i.e. it is an escaping bound var. The '^1 region (also writeable as '^0_1) is also ill formed as the binder it refers to does not introduce a second parameter. Modern day rustc will ICE when constructing this binder due to both of those regions, in the past we would have simply allowed this to work and then ran into issues in other parts of the codebase.