# 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:

```
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 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:

```
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 `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:

```
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:

```
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:

```
# 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
`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 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:

```
# 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.