Associated types are a powerful part of Rust’s type system. They’re related to the idea of a ‘type family’, in other words, grouping multiple types together. That description is a bit abstract, so let’s dive right into an example. If you want to write a Graph trait, you have two types to be generic over: the node type and the edge type. So you might write a trait, Graph<N, E>, that looks like this:

# #![allow(unused_variables)]
#fn main() {
trait Graph<N, E> {
    fn has_edge(&self, &N, &N) -> bool;
    fn edges(&self, &N) -> Vec<E>;
    // Etc.
}
#}

While this sort of works, it ends up being awkward. For example, any function that wants to take a Graph as a parameter now also needs to be generic over the Node and Edge types too:

fn distance<N, E, G: Graph<N, E>>(graph: &G, start: &N, end: &N) -> u32 { ... }

Our distance calculation works regardless of our Edge type, so the E stuff in this signature is a distraction.

What we really want to say is that a certain Edge and Node type come together to form each kind of Graph. We can do that with associated types:

# #![allow(unused_variables)]
#fn main() {
trait Graph {
    type N;
    type E;

    fn has_edge(&self, &Self::N, &Self::N) -> bool;
    fn edges(&self, &Self::N) -> Vec<Self::E>;
    // Etc.
}
#}

Now, our clients can be abstract over a given Graph:

fn distance<G: Graph>(graph: &G, start: &G::N, end: &G::N) -> u32 { ... }

No need to deal with the Edge type here!

Let’s go over all this in more detail.

Let’s build that Graph trait. Here’s the definition:

# #![allow(unused_variables)]
#fn main() {
trait Graph {
    type N;
    type E;

    fn has_edge(&self, &Self::N, &Self::N) -> bool;
    fn edges(&self, &Self::N) -> Vec<Self::E>;
}
#}

Simple enough. Associated types use the type keyword, and go inside the body of the trait, with the functions.

These type declarations work the same way as those for functions. For example, if we wanted our N type to implement Display, so we can print the nodes out, we could do this:

# #![allow(unused_variables)]
#fn main() {
use std::fmt;

trait Graph {
    type N: fmt::Display;
    type E;

    fn has_edge(&self, &Self::N, &Self::N) -> bool;
    fn edges(&self, &Self::N) -> Vec<Self::E>;
}
#}

Just like any trait, traits that use associated types use the impl keyword to provide implementations. Here’s a simple implementation of Graph:

# #![allow(unused_variables)]
#fn main() {
# trait Graph {
#     type N;
#     type E;
#     fn has_edge(&self, &Self::N, &Self::N) -> bool;
#     fn edges(&self, &Self::N) -> Vec<Self::E>;
# }
struct Node;

struct Edge;

struct MyGraph;

impl Graph for MyGraph {
    type N = Node;
    type E = Edge;

    fn has_edge(&self, n1: &Node, n2: &Node) -> bool {
        true
    }

    fn edges(&self, n: &Node) -> Vec<Edge> {
        Vec::new()
    }
}
#}

This silly implementation always returns true and an empty Vec<Edge>, but it gives you an idea of how to implement this kind of thing. We first need three structs, one for the graph, one for the node, and one for the edge. If it made more sense to use a different type, that would work as well, we’re going to use structs for all three here.

Next is the impl line, which is an implementation like any other trait.

From here, we use = to define our associated types. The name the trait uses goes on the left of the =, and the concrete type we’re implementing this for goes on the right. Finally, we use the concrete types in our function declarations.

There’s one more bit of syntax we should talk about: trait objects. If you try to create a trait object from a trait with an associated type, like this:

# trait Graph {
#     type N;
#     type E;
#     fn has_edge(&self, &Self::N, &Self::N) -> bool;
#     fn edges(&self, &Self::N) -> Vec<Self::E>;
# }
# struct Node;
# struct Edge;
# struct MyGraph;
# impl Graph for MyGraph {
#     type N = Node;
#     type E = Edge;
#     fn has_edge(&self, n1: &Node, n2: &Node) -> bool {
#         true
#     }
#     fn edges(&self, n: &Node) -> Vec<Edge> {
#         Vec::new()
#     }
# }
let graph = MyGraph;
let obj = Box::new(graph) as Box<Graph>;

You’ll get two errors:

error: the value of the associated type `E` (from the trait `main::Graph`) must
be specified [E0191]
let obj = Box::new(graph) as Box<Graph>;
          ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~
24:44 error: the value of the associated type `N` (from the trait
`main::Graph`) must be specified [E0191]
let obj = Box::new(graph) as Box<Graph>;
          ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We can’t create a trait object like this, because we don’t know the associated types. Instead, we can write this:

# #![allow(unused_variables)]
#fn main() {
# trait Graph {
#     type N;
#     type E;
#     fn has_edge(&self, &Self::N, &Self::N) -> bool;
#     fn edges(&self, &Self::N) -> Vec<Self::E>;
# }
# struct Node;
# struct Edge;
# struct MyGraph;
# impl Graph for MyGraph {
#     type N = Node;
#     type E = Edge;
#     fn has_edge(&self, n1: &Node, n2: &Node) -> bool {
#         true
#     }
#     fn edges(&self, n: &Node) -> Vec<Edge> {
#         Vec::new()
#     }
# }
let graph = MyGraph;
let obj = Box::new(graph) as Box<Graph<N=Node, E=Edge>>;
#}

The N=Node syntax allows us to provide a concrete type, Node, for the N type parameter. Same with E=Edge. If we didn’t provide this constraint, we couldn’t be sure which impl to match this trait object to.