Allow type constructors to be associated with traits. This is an incremental step toward a more general feature commonly called “higher-kinded types,” which is often ranked highly as a requested feature by Rust users. This specific feature (associated type constructors) resolves one of the most common use cases for higher-kindedness, is a relatively simple extension to the type system compared to other forms of higher-kinded polymorphism, and is forward compatible with more complex forms of higher-kinded polymorphism that may be introduced in the future.


Consider the following trait as a representative motivating example:

trait StreamingIterator {
    type Item<'a>;
    fn next<'a>(&'a mut self) -> Option<Self::Item<'a>>;

This trait is very useful - it allows for a kind of Iterator which yields values which have a lifetime tied to the lifetime of the reference passed to next. A particular obvious use case for this trait would be an iterator over a vector which yields overlapping, mutable subslices with each iteration. Using the standard Iterator interface, such an implementation would be invalid, because each slice would be required to exist for as long as the iterator, rather than for as long as the borrow initiated by next.

This trait cannot be expressed in Rust as it exists today, because it depends on a sort of higher-kinded polymorphism. This RFC would extend Rust to include that specific form of higher-kinded polymorphism, which is referred to here as associated type constructors. This feature has a number of applications, but the primary application is along the same lines as the StreamingIterator trait: defining traits which yield types which have a lifetime tied to the local borrowing of the receiver type.

Detailed design

Background: What is kindedness?

“Higher-kinded types” is a vague term, conflating multiple language features under a single banner, which can be inaccurate. As background, this RFC includes a brief overview of the notion of kinds and kindedness. Kinds are often called ‘the type of a type,’ the exact sort of unhelpful description that only makes sense to someone who already understands what is being explained. Instead, let’s try to understand kinds by analogy to types.

In a well-typed language, every expression has a type. Many expressions have what are sometimes called ‘base types,’ types which are primitive to the language and which cannot be described in terms of other types. In Rust, the types bool, i64, usize, and char are all prominent examples of base types. In contrast, there are types which are formed by arranging other types - functions are a good example of this. Consider this simple function:

fn not(x: bool) -> bool {

not has the type bool -> bool (my apologies for using a syntax different from Rust’s). Note that this is different from the type of not(true), which is bool. This difference is important to understanding higher-kindedness.

In the analysis of kinds, all of these types - bool, char, bool -> bool and so on - have the kind type. Every type has the kind type. However, type is a base kind, just as bool is a base type, and there are terms with more complex kinds, such as type -> type. An example of a term of this kind is Vec, which takes a type as a parameter and evaluates to a type. The difference between the kind of Vec and the kind of Vec<i32> (which is type) is analogous to the difference between the type of not and not(true). Note that Vec<T> has the kind type, just like Vec<i32>: even though T is a type parameter, Vec is still being applied to a type, just like not(x) still has the type bool even though x is a variable.

A relatively uncommon feature of Rust is that it has two base kinds, whereas many languages which deal with higher-kindedness only have the base kind type. The other base kind of Rust is the lifetime parameter. If you have a type like Foo<'a>, the kind of Foo is lifetime -> type.

Higher-kinded terms can take multiple arguments as well, of course. Result has the kind type, type -> type. Given vec::Iter<'a, T> vec::Iter has the kind lifetime, type -> type.

Terms of a higher kind are often called ‘type operators’; the type operators which evaluate to a type are called ‘type constructors’. There are other type operators which evaluate to other type operators, and there are even higher order type operators, which take type operators as their argument (so they have a kind like (type -> type) -> type). This RFC doesn’t deal with anything as exotic as that.

Specifically, the goal of this RFC is to allow type constructors to be associated with traits, just as you can currently associate functions, types, and consts with traits. There are other forms of polymorphism involving type constructors, such as implementing traits for a type constructor instead of a type, which are not a part of this RFC.

Features of associated type constructors

Declaring & assigning an associated type constructor

This RFC proposes a very simple syntax for defining an associated type constructor, which looks a lot like the syntax for creating aliases for type constructors. The goal of using this syntax is to avoid to creating roadblocks for users who do not already understand higher kindedness.

trait StreamingIterator {
   type Item<'a>;

It is clear that the Item associated item is a type constructor, rather than a type, because it has a type parameter attached to it.

Associated type constructors can be bounded, just like associated types can be:

trait Iterable {
    type Item<'a>;
    type Iter<'a>: Iterator<Item = Self::Item<'a>>;
    fn iter<'a>(&'a self) -> Self::Iter<'a>;

This bound is applied to the “output” of the type constructor, and the parameter is treated as a higher rank parameter. That is, the above bound is roughly equivalent to adding this bound to the trait:

for<'a> Self::Iter<'a>: Iterator<Item = Self::Item<'a>>

Assigning associated type constructors in impls is very similar to the syntax for assigning associated types:

impl<T> StreamingIterator for StreamIterMut<T> {
    type Item<'a> = &'a mut [T];

Using an associated type constructor to construct a type

Once a trait has an associated type constructor, it can be applied to any parameters or concrete terms that are in scope. This can be done both inside the body of the trait and outside of it, using syntax which is analogous to the syntax for using associated types. Here are some examples:

trait StreamingIterator {
    type Item<'a>;
    // Applying the lifetime parameter `'a` to `Self::Item` inside the trait.
    fn next<'a>(&'a self) -> Option<Self::Item<'a>>;

struct Foo<T: StreamingIterator> {
    // Applying a concrete lifetime to the constructor outside the trait.
    bar: <T as StreamingIterator>::Item<'static>;

Associated type constructors can also be used to construct other type constructors:

trait Foo {
    type Bar<'a, 'b>;

trait Baz {
    type Quux<'a>;

impl<T> Baz for T where T: Foo {
    type Quux<'a> = <T as Foo>::Bar<'a, 'static>;

Lastly, lifetimes can be elided in associated type constructors in the same manner that they can be elided in other type constructors. Considering lifetime elision, the full definition of StreamingIterator is:

trait StreamingIterator {
    type Item<'a>;
    fn next(&mut self) -> Option<Self::Item>;

Using associated type constructors in bounds

Users can bound parameters by the type constructed by that trait’s associated type constructor of a trait using HRTB. Both type equality bounds and trait bounds of this kind are valid:

fn foo<T: for<'a> StreamingIterator<Item<'a>=&'a [i32]>>(iter: T) { ... }

fn foo<T>(iter: T) where T: StreamingIterator, for<'a> T::Item<'a>: Display { ... }

This RFC does not propose allowing any sort of bound by the type constructor itself, whether an equality bound or a trait bound (trait bounds of course are also impossible).

Associated type constructors of type arguments

All of the examples in this RFC have focused on associated type constructors of lifetime arguments, however, this RFC proposes adding ATCs of types as well:

trait Foo {
    type Bar<T>;

This RFC does not propose extending HRTBs to take type arguments, which makes these less expressive than they could be. Such an extension is desired, but out of scope for this RFC.

Type arguments can be used to encode other forms of higher kinded polymorphism using the “family” pattern. For example, Using the PointerFamily trait, you can abstract over Arc and Rc:

trait PointerFamily {
    type Pointer<T>: Deref<Target = T>;
    fn new<T>(value: T) -> Self::Pointer<T>;

struct ArcFamily;

impl PointerFamily for ArcFamily {
    type Pointer<T> = Arc<T>;
    fn new<T>(value: T) -> Self::Pointer<T> {

struct RcFamily;

impl PointerFamily for RcFamily {
    type Pointer<T> = Rc<T>;
    fn new<T>(value: T) -> Self::Pointer<T> {

struct Foo<P: PointerFamily> {
    bar: P::Pointer<String>,

Evaluating bounds and where clauses

Bounds on associated type constructors

Bounds on associated type constructors are treated as higher rank bounds on the trait itself. This makes their behavior consistent with the behavior of bounds on regular associated types. For example:

trait Foo {
    type Assoc<'a>: Trait<'a>;

Is equivalent to:

trait Foo where for<'a> Self::Assoc<'a>: Trait<'a> {
    type Assoc<'a>;

where clauses on associated types

In contrast, where clauses on associated types introduce constraints which must be proven each time the associated type is used. For example:

trait Foo {
    type Assoc where Self: Sized;

Each invocation of <T as Foo>::Assoc will need to prove T: Sized, as opposed to the impl needing to prove the bound as in other cases.

(@nikomatsakis believes that where clauses will be needed on associated type constructors specifically to handle lifetime well formedness in some cases. The exact details are left out of this RFC because they will emerge more fully during implementation.)

Benefits of implementing only this feature before other higher-kinded polymorphisms

This feature is not full-blown higher-kinded polymorphism, and does not allow for the forms of abstraction that are so popular in Haskell, but it does provide most of the unique-to-Rust use cases for higher-kinded polymorphism, such as streaming iterators and collection traits. It is probably also the most accessible feature for most users, being somewhat easy to understand intuitively without understanding higher-kindedness.

This feature has several tricky implementation challenges, but avoids all of these features that other kinds of higher-kinded polymorphism require:

  • Defining higher-kinded traits
  • Implementing higher-kinded traits for type operators
  • Higher order type operators
  • Type operator parameters bound by higher-kinded traits
  • Type operator parameters applied to a given type or type parameter

Advantages of proposed syntax

The advantage of the proposed syntax is that it leverages syntax that already exists. Type constructors can already be aliased in Rust using the same syntax that this used, and while type aliases play no polymorphic role in type resolution, to users they seem very similar to associated types. A goal of this syntax is that many users will be able to use types which have associated type constructors without even being aware that this has something to do with a type system feature called higher-kindedness.

How We Teach This

This RFC uses the terminology “associated type constructor,” which has become the standard way to talk about this feature in the Rust community. This is not a very accessible framing of this concept; in particular the term “type constructor” is an obscure piece of jargon from type theory which most users cannot be expected to be familiar with.

Upon accepting this RFC, we should begin (with haste) referring to this concept as simply “generic associated types.” Today, associated types cannot be generic; after this RFC, this will be possible. Rather than teaching this as a separate feature, it will be taught as an advanced use case for associated types.

Patterns like “family traits” should also be taught in some way, possible in the book or possibly just through supplemental forms of documentation like blog posts.

This will also likely increase the frequency with which users have to employ higher rank trait bounds; we will want to put additional effort into teaching and making teachable HRTBs.


Adding language complexity

This would add a somewhat complex feature to the language, being able to polymorphically resolve type constructors, and requires several extensions to the type system which make the implementation more complicated.

Additionally, though the syntax is designed to make this feature easy to learn, it also makes it more plausible that a user may accidentally use it when they mean something else, similar to the confusion between impl .. for Trait and impl<T> .. for T where T: Trait. For example:

// The user means this
trait Foo<'a> {
    type Bar: 'a;

// But they write this
trait Foo<'a> {
    type Bar<'a>;

Not full “higher-kinded types”

This does not add all of the features people want when they talk about higher- kinded types. For example, it does not enable traits like Monad. Some people may prefer to implement all of these features together at once. However, this feature is forward compatible with other kinds of higher-kinded polymorphism, and doesn’t preclude implementing them in any way. In fact, it paves the way by solving some implementation details that will impact other kinds of higher- kindedness as well, such as partial application.

Syntax isn’t like other forms of higher-kinded polymorphism

Though the proposed syntax is very similar to the syntax for associated types and type aliases, it is probably not possible for other forms of higher-kinded polymorphism to use a syntax along the same lines. For this reason, the syntax used to define an associated type constructor will probably be very different from the syntax used to e.g. implement a trait for a type constructor.

However, the syntax used for these other forms of higher-kinded polymorphism will depend on exactly what features they enable. It would be hard to design a syntax which is consistent with unknown features.


Push HRTBs harder without associated type constructors

An alternative is to push harder on HRTBs, possibly introducing some elision that would make them easier to use.

Currently, an approximation of StreamingIterator can be defined like this:

trait StreamingIterator<'a> {
   type Item: 'a;
   fn next(&'a self) -> Option<Self::Item>;

You can then bound types as T: for<'a> StreamingIterator<'a> to avoid the lifetime parameter infecting everything StreamingIterator appears.

However, this only partially prevents the infectiveness of StreamingIterator, only allows for some of the types that associated type constructors can express, and is in generally a hacky attempt to work around the limitation rather than an equivalent alternative.

Impose restrictions on ATCs

What is often called “full higher kinded polymorphism” is allowing the use of type constructors as input parameters to other type constructors - higher order type constructors, in other words. Without any restrictions, multiparameter higher order type constructors present serious problems for type inference.

For example, if you are attempting to infer types, and you know you have a constructor of the form type, type -> Result<(), io::Error>, without any restrictions it is difficult to determine if this constructor is (), io::Error -> Result<(), io::Error> or io::Error, () -> Result<(), io::Error>.

Because of this, languages with first class higher kinded polymorphism tend to impose restrictions on these higher kinded terms, such as Haskell’s currying rules.

If Rust were to adopt higher order type constructors, it would need to impose similar restrictions on the kinds of type constructors they can receive. But associated type constructors, being a kind of alias, inherently mask the actual structure of the concrete type constructor. In other words, if we want to be able to use ATCs as arguments to higher order type constructors, we would need to impose those restrictions on all ATCs.

We have a list of restrictions we believe are necessary and sufficient; more background can be found in this blog post by nmatsakis:

  • Each argument to the ATC must be applied
  • They must be applied in the same order they appear in the ATC
  • They must be applied exactly once
  • They must be the left-most arguments of the constructor

These restrictions are quite constrictive; there are several applications of ATCs that we already know about that would be frustrated by this, such as the definition of Iterable for HashMap (for which the item (&'a K, &'a V), applying the lifetime twice).

For this reason we have decided not to apply these restrictions to all ATCs. This will mean that if higher order type constructors are ever added to the language, they will not be able to take an abstract ATC as an argument. However, this can be maneuvered around using newtypes which do meet the restrictions, for example:

struct IterItem<'a, I: Iterable>(I::Item<'a>);

Unresolved questions