Associated type constructors, part 1: basic concepts and introduction

2 November 2016

So for the end of last week, I was at Rust Belt Rust. This was awesome. And not only because the speakers and attendees at Rust Belt Rust were awesome, though they were. But also because it gave aturon, withoutboats, and I a chance to talk over a lot of stuff in person. We covered a lot of territory and so I wanted to do a series of blog posts trying to write down some of the things we were thinking so as to get other people’s input.

The first topic I’m going to focus on is RFC 1598, which is a proposal by withoutboats to add associated-type constructors (ATC) to the language. ATC makes it possible to have “generic” associated types, which in turn means we can support important patterns like collection and iterable traits.

ATC also (as we will see) potentially subsumes the idea of higher-kinded types. A big focus of our conversation was on elaborating a potential alternative design based on HKT, and trying to see whether choosing to add ATC would lock us into a suboptimal path.

This is quite a big topic, so I’m going to spread it out over many posts. This first post will introduce the basic idea of associated type constructors. It also gives various bits of background information on Rust’s trait system and how type inference works. A certain familiarity with Rust is expected, but expertise should not be necessary.

Aside: Now higher-kinded types especially are one of those PL topics that sound forebodingly complex and kind of abstract (like monads). But once you learn what it is, you realize it’s actually relevant to your life (unlike monads). So I hope to break it down in a relatively simple way.

(Oh, and I’m just trolling about monads. Sorry, couldn’t resist. Don’t hate me. We’ll actually be talking about monads – well, more about functors – in a few posts down the line.)

Background: traits and associated types

Before I can get to RFC 1598, let me lay out a bit of background. This post is going to be talking a lot about traits. Traits are Rust’s version of a generic interface. Naturally, these traits can define a bunch of methods that are part of the interface, but they can also define types that are part of the interface. We call these associated types. So, for example, consider the Iterator trait:

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

This means that every implementation of Iterator must specify both a next() method, which defines how we iterate, as well as the type Item, which defines what kind of values this iterator produces. The two items are linked, since the return value of next() is Self::Item.

The notation Self::Item means “the Item defined in the impl for the type Self” – in other words, the Item type defined for this iterator. This notation is actually shorthand for something more explicit that spells out all the parts: <Self as Iterator>::Item – here we are saying “the Item type defined in the implementation of Iterator for the type Self”. (I prefer to call such paths “fully qualified”, but in the past they have sometimes been called “UFCS” in the Rust community; this stands for “universal functional call syntax”, which is a term borrowed from D, where it unfortunately means something totally different.)

So now we can use the iterator trait to write generic code. For example, we could write a generic routine position that returns the position. I’m going to write this code using a while let loop instead of a for loop, so as to make the iterator protocol more explicit:

fn position<I>(mut iterator: I, value: I::Item) -> Option<usize>
    where I: Iterator, I::Item: Eq,
    let mut index = 0;
    while let Some(v) = {
        if value == v {
            return Some(index); // found it!
        index += 1;
    None // did not find it

Take a look at the types in the signature there. The first argument, iterator is of type I, which is a generic type parameter; the where clause also declares that I: Iterator. So basically we just know that iterator’s type is “some kind of iterator”. The second argument, value, has the type I::Item – this is also a kind of generic type. We’re saying that value is “whatever kind of item I produces”. We could also write that in a slightly different way, using two generic parameters:

fn position<I, T>(mut iterator: I, value: T) -> Option<usize>
    where I: Iterator<Item=T>, T: Eq

Here the where clause states that I: Iterator<Item=T>. This means “I is some sort of iterator producing values of type T”.

Running example: linked list and iterator

OK, let’s elaborate out an example that I can use throughout the post. We’ll start by defining a simple collection type, List<T>, that is a kind of linked list:

/// Very simple linked list. If `cell` is `None`,
/// the list is empty.
pub struct List<T> {
    cell: Option<Box<ListCell<T>>

/// A single cell in a non-empty list. Stores one
/// value and then another list.
struct ListCell<T> {
    value: T,
    next: List<T>

We can define some customary methods on this list:

  • new() – returns an empty list;
  • prepend() – insert a value on the front of the list, which is usually best when working with singly linked lists with no tail pointer;
  • iter() – creates an iterator that yields up shared references to the items in the list.

Here are some example implementations of those methods:

impl<T> List<T> {
    pub fn new() -> List<T> {
        List { cell: None }
    pub fn prepend(&mut self, value: T) {
        // get ahold of the current head of the list, if any
        let old_head = self.cell.take();
        // Create a new cell to serve as the new head of the list,
        // and then store it in `self.cell`.
        let cell = ListCell { value: value, next: old_head }; = Some(Box::new(cell));
    pub fn iter<'iter>(&'iter self) -> ListIter<'iter, T> {
        ListIter { cursor: self }

Let’s look more at this last method, and in particular let’s look at how we can define the iterator type ListIter (by the way, if you’d like to read up more on iterators and how they work, you might enjoy this old blog post of mine, which walks through several different kinds of iterators in more detail). The ListIter iterator will basically hold a reference to a List<T>. At each step, if the list is non-empty, it will return a reference to the value field and then update the cursor to the next cell. That struct might look something like this:

/// Iterator over linked lists.
pub struct ListIter<'iter, T> {
    cursor: &'iter List<T>

The 'iter lifetime here is the lifetime of the reference to our list. I called it 'iter because the idea is that it lives as long as the iteration is still ongoing (after that, we don’t need it anymore). Anyway, then we can implement the iterator trait like so:

impl<'iter, T> Iterator for ListIter<'iter, T> {
    type Item = &'iter T;
    fn next(&mut self) -> Option<&'iter T> {
        // If the list is non-empty, borrow a reference
        // to the cell (`cell`).
        if let Some(ref cell) = self.cursor.cell {
            // Point the cursor at the next cell.
            self.cursor = &;
            // Return reference to the value in the
            // the current cell.
        } else {
            // List is empty, return `None`.

Here you see that the impl specifies the type Item to be &'iter T. This is sort of interesting, because, in a sense, it’s not really telling us what the type is, since we don’t yet know what lifetime 'iter is nor what type T is (it’ll depend on what type of values are in the list, of course). But there is a key point here – even though the impl is generic, we know that given any particular type ListIter<'a, Foo>, there is exactly one associated Item type (in this case, &'a Foo).

Background: The role of type inference

Now that we’ve seen the List example, I want to briefly go over the role of type inference in doing trait matching. This will be very important when we talk later about higher-kinded types. Imagine that I have some code that uses a list like this:

fn list(list: &List<u32>) {
    let mut iter = list.iter();
    let value =;

So how does the compiler infer the type of the variable value? The way that this works is by searching the declared impls. In particular, in the call, we know that the type of iter is ListIter<'foo, u32> (for some lifetime 'foo). We also know that the method next() is part of the trait Iterator (actually, figuring this out is a big job in and of itself, but I’m going to ignore that part of it for this post and just assume it is given). So that tells us that we have to go searching for the Iterator impl that applies to ListIter.

We do this, basically, by iterating over all the impls that we see and try to match up the types with the one we are looking for. Eventually we will come to the ListIter impl we saw earlier; it looks like this:

impl<'iter, T> Iterator for ListIter<'iter, T> { ... }

So how do we relate these generic impl parameters ('iter, T) to the type we have at hand ListIter<'foo, u32>? We do this by replacing those parameters with “inference variables”, which I will denote with a leading ? – lifetime variables will be lower-case, type variables up-ercase. So that means that the impl type looks like something like ListIter<?iter, ?T>. We then try to figure out what values of those variables will make the two types the same. In this case, ?iter will map to 'foo and ?T will map to u32.

Once we know how to map ?iter and ?T, we can look at the actual signature of next() as declared in the impl and apply that same mapping:

// Signature as declared, written in a more explicit style:
fn next(self: &mut ListIter<'iter, T>) -> Option<&'iter T>;

// Signature with mapping applied
fn next(self: &mut ListIter<'foo, u32>) -> Option<&'foo u32>;

Now we can see that the type of value is the (mapped) return type of this signature, and hence that it must be Option<&'foo u32>. Very good.

Some key points here:

  • When doing trait selection, we replace the generic parameters on the impl (e.g., T, 'iter) with variables (?T, ?iter).
  • We use unification to then figure out what those variables must be.

Associated type constructors: the iterable trait

OK, so far we’ve seen that we can define an Iterator trait that lets us operate generically over iterators like ListIter<'iter, T>. That’s very useful, but you might be wondering if it’s possible to define a Collection trait that lets us operate generically over collections, like List<T>. Perhaps something like this:

// Collection trait, take 1.
trait Collection<T> {
    // create an empty collection of this type:
    fn empty() -> Self;
    // add `value` to this collection in some way:
    fn add(&mut self, value: T);

    // iterate over this collection:
    fn iterate(&self) -> Self::Iter;
    // the type of an iterator for this collection (e.g., `ListIter`)
    type Iter: Iterator<Item=T>;

If we try to write an impl of this collection for List<T>, we will find that it almost works, but not quite. Let’s give it a try!

impl<T> Collection<T> for List<T> {
    fn empty() -> List<T> {

    fn add(&mut self, value: T) {
    fn iterate<'iter>(&'iter self) -> ListIter<'iter, T> {
    type Iter = ListIter<'iter, T>;
    //                   ^^^^^ oh, wait, this is not in scope!

Everything seems to be going great until we get to the last item, the associated type Iter. Then we see that we can’t actually write out the full type – that’s because the full type needs to talk about the lifetime 'iter of the iteration, and that is not in scope at this point. Remember that each call to iterate() will require a distinct lifetime 'iter.

This shows that in fact modeling collections is actually harder than modeling iterators. Recall that, with iterators, we said that once we know the type of an iterator, we know everything we need to know to figure out the type of items that iterator produces. But with collections, knowing the collection type (List<T>) does not tell us everything we need to know to get the type of an iterator (ListIter<'iter, T>).

RFC 1598 proposes to solve this problem by making it possible to have not only associated types but associated type constructors. Basically, associated types can themselves have generic type parameters:

// Collection trait, take 2, using RFC 1598.
trait Collection<T> {
    // as before
    fn empty() -> Self;
    fn add(&mut self, value: T);

    // Here, we use associated type constructors:
    fn iterate<'iter>(&'iter self) -> Self::Iter<'iter>;
    type Iter<'iter>: Iterator<Item=T>;

Now, writing the impl of Collection for List becomes fairly straightforward. In fact, the only difference is the definition of the type Iter:

impl<T> Collection<T> for List<T> {
    ... // same as above
    type Iter<'iter> = ListIter<'iter, T>;
    //        ^^^^^ brings `'iter` into scope

We could also imagine writing impls for other types, like Vec<T> in the standard library:

use std::slice;
impl<T> Collection<T> for Vec<T> {
    fn empty() -> Self { vec![] }
    fn add(&mut self, value: T) { self.push(value); }
    fn iterate<'iter>(&'iter self) -> slice::Iter<'self, T> { self.iter() }
    type Iter<'iter> = slice::Iter<'iter, T>;

Writing code that is generic over collections

Now that we have a collection trait, we can write code that works generically over collections. That’s pretty nifty. For example, this function takes in a collection of floating point numbers and returns to you another collection with the same numbers, but rounded down to the nearest integer:

fn round_all<C>(collection: &C) -> C
    where C: Collection<f32>
    let mut rounded = C::empty();
    for &f in c.iterate() {


That’s it for today. Let’s review what we covered thus far:

  • Traits today can define associated types;
    • but, this type cannot make use of any types or lifetimes that aren’t part of the implementing type
  • Whenever you have something with generic parameters, like an impl, fn, or struct, inference is used to determine the value of those parameters;
    • this means that if you try to extend the sorts of thing that a generic parameter can be used to represent (such as permitting things that are generic over constants), you have to think about how it will interact with inference.
  • If you have a collection type like List<T>, the iterator usually includes a lifetime 'iter that is not part of the original type (ListIter<'iter, T>);
    • therefore, you cannot model a Collection trait today in Rust, at least not in a nice way.
      • There are some tricks I didn’t cover. =)
  • Associated type constructors are basically just “generic” associated types;
    • this is great for modeling Collection.


Please leave comments on this internals thread.