# Associated Types

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:

fn main() { trait Graph<N, E> { fn has_edge(&self, &N, &N) -> bool; fn edges(&self, &N) -> Vec<E>; // etc } }

    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 `N`ode and `E`dge types too:

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

    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 `E`dge and `N`ode type come together to form each kind of `Graph`. We can do that with associated types:

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 } }

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

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

No need to deal with the `E`dge type here!

Let’s go over all this in more detail.

## Defining associated types

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

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>; } }

    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 can have all the same thing as functions do. For example, if we wanted our `N` type to implement `Display`, so we can print the nodes out, we could do this:

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>; } }

    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>;
    }

## Implementing associated types

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

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() } } }

    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 `struct`s, 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 `struct`s 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 `impl`ementing this for goes on the right. Finally, we use the concrete types in our function declarations.

## Trait objects with associated types

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:

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>; }

    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:

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>>; }

    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.