% Traits

Do you remember the `impl` keyword, used to call a function with method
syntax?

```{rust}
struct Circle {
    x: f64,
    y: f64,
    radius: f64,
}

impl Circle {
    fn area(&self) -> f64 {
        std::f64::consts::PI * (self.radius * self.radius)
    }
}
```

Traits are similar, except that we define a trait with just the method
signature, then implement the trait for that struct. Like this:

```{rust}
struct Circle {
    x: f64,
    y: f64,
    radius: f64,
}

trait HasArea {
    fn area(&self) -> f64;
}

impl HasArea for Circle {
    fn area(&self) -> f64 {
        std::f64::consts::PI * (self.radius * self.radius)
    }
}
```

As you can see, the `trait` block looks very similar to the `impl` block,
but we don't define a body, just a type signature. When we `impl` a trait,
we use `impl Trait for Item`, rather than just `impl Item`.

So what's the big deal? Remember the error we were getting with our generic
`inverse` function?

```text
error: binary operation `==` cannot be applied to type `T`
```

We can use traits to constrain our generics. Consider this function, which
does not compile, and gives us a similar error:

```{rust,ignore}
fn print_area<T>(shape: T) {
    println!("This shape has an area of {}", shape.area());
}
```

Rust complains:

```text
error: type `T` does not implement any method in scope named `area`
```

Because `T` can be any type, we can't be sure that it implements the `area`
method. But we can add a *trait constraint* to our generic `T`, ensuring
that it does:

```{rust}
# trait HasArea {
#     fn area(&self) -> f64;
# }
fn print_area<T: HasArea>(shape: T) {
    println!("This shape has an area of {}", shape.area());
}
```

The syntax `<T: HasArea>` means `any type that implements the HasArea trait`.
Because traits define function type signatures, we can be sure that any type
which implements `HasArea` will have an `.area()` method.

Here's an extended example of how this works:

```{rust}
trait HasArea {
    fn area(&self) -> f64;
}

struct Circle {
    x: f64,
    y: f64,
    radius: f64,
}

impl HasArea for Circle {
    fn area(&self) -> f64 {
        std::f64::consts::PI * (self.radius * self.radius)
    }
}

struct Square {
    x: f64,
    y: f64,
    side: f64,
}

impl HasArea for Square {
    fn area(&self) -> f64 {
        self.side * self.side
    }
}

fn print_area<T: HasArea>(shape: T) {
    println!("This shape has an area of {}", shape.area());
}

fn main() {
    let c = Circle {
        x: 0.0f64,
        y: 0.0f64,
        radius: 1.0f64,
    };

    let s = Square {
        x: 0.0f64,
        y: 0.0f64,
        side: 1.0f64,
    };

    print_area(c);
    print_area(s);
}
```

This program outputs:

```text
This shape has an area of 3.141593
This shape has an area of 1
```

As you can see, `print_area` is now generic, but also ensures that we
have passed in the correct types. If we pass in an incorrect type:

```{rust,ignore}
print_area(5);
```

We get a compile-time error:

```text
error: failed to find an implementation of trait main::HasArea for int
```

So far, we've only added trait implementations to structs, but you can
implement a trait for any type. So technically, we _could_ implement
`HasArea` for `i32`:

```{rust}
trait HasArea {
    fn area(&self) -> f64;
}

impl HasArea for i32 {
    fn area(&self) -> f64 {
        println!("this is silly");

        *self as f64
    }
}

5.area();
```

It is considered poor style to implement methods on such primitive types, even
though it is possible.

This may seem like the Wild West, but there are two other restrictions around
implementing traits that prevent this from getting out of hand. First, traits
must be `use`d in any scope where you wish to use the trait's method. So for
example, this does not work:

```{rust,ignore}
mod shapes {
    use std::f64::consts;

    trait HasArea {
        fn area(&self) -> f64;
    }

    struct Circle {
        x: f64,
        y: f64,
        radius: f64,
    }

    impl HasArea for Circle {
        fn area(&self) -> f64 {
            consts::PI * (self.radius * self.radius)
        }
    }
}

fn main() {
    let c = shapes::Circle {
        x: 0.0f64,
        y: 0.0f64,
        radius: 1.0f64,
    };

    println!("{}", c.area());
}
```

Now that we've moved the structs and traits into their own module, we get an
error:

```text
error: type `shapes::Circle` does not implement any method in scope named `area`
```

If we add a `use` line right above `main` and make the right things public,
everything is fine:

```{rust}
use shapes::HasArea;

mod shapes {
    use std::f64::consts;

    pub trait HasArea {
        fn area(&self) -> f64;
    }

    pub struct Circle {
        pub x: f64,
        pub y: f64,
        pub radius: f64,
    }

    impl HasArea for Circle {
        fn area(&self) -> f64 {
            consts::PI * (self.radius * self.radius)
        }
    }
}


fn main() {
    let c = shapes::Circle {
        x: 0.0f64,
        y: 0.0f64,
        radius: 1.0f64,
    };

    println!("{}", c.area());
}
```

This means that even if someone does something bad like add methods to `int`,
it won't affect you, unless you `use` that trait.

There's one more restriction on implementing traits. Either the trait or the
type you're writing the `impl` for must be inside your crate. So, we could
implement the `HasArea` type for `i32`, because `HasArea` is in our crate.  But
if we tried to implement `Float`, a trait provided by Rust, for `i32`, we could
not, because both the trait and the type aren't in our crate.

One last thing about traits: generic functions with a trait bound use
*monomorphization* (*mono*: one, *morph*: form), so they are statically
dispatched. What's that mean? Well, let's take a look at `print_area` again:

```{rust,ignore}
fn print_area<T: HasArea>(shape: T) {
    println!("This shape has an area of {}", shape.area());
}

fn main() {
    let c = Circle { ... };

    let s = Square { ... };

    print_area(c);
    print_area(s);
}
```

When we use this trait with `Circle` and `Square`, Rust ends up generating
two different functions with the concrete type, and replacing the call sites with
calls to the concrete implementations. In other words, you get something like
this:

```{rust,ignore}
fn __print_area_circle(shape: Circle) {
    println!("This shape has an area of {}", shape.area());
}

fn __print_area_square(shape: Square) {
    println!("This shape has an area of {}", shape.area());
}

fn main() {
    let c = Circle { ... };

    let s = Square { ... };

    __print_area_circle(c);
    __print_area_square(s);
}
```

The names don't actually change to this, it's just for illustration. But
as you can see, there's no overhead of deciding which version to call here,
hence *statically dispatched*. The downside is that we have two copies of
the same function, so our binary is a little bit larger.

## Our `inverse` Example

Back in [Generics](generics.html), we were trying to write code like this:

```{rust,ignore}
fn inverse<T>(x: T) -> Result<T, String> {
    if x == 0.0 { return Err("x cannot be zero!".to_string()); }

    Ok(1.0 / x)
}
```

If we try to compile it, we get this error:

```text
error: binary operation `==` cannot be applied to type `T`
```

This is because `T` is too generic: we don't know if a random `T` can be
compared. For that, we can use trait bounds. It doesn't quite work, but try
this:

```{rust,ignore}
fn inverse<T: PartialEq>(x: T) -> Result<T, String> {
    if x == 0.0 { return Err("x cannot be zero!".to_string()); }

    Ok(1.0 / x)
}
```

You should get this error:

```text
error: mismatched types:
 expected `T`,
    found `_`
(expected type parameter,
    found floating-point variable)
```

So this won't work. While our `T` is `PartialEq`, we expected to have another `T`,
but instead, we found a floating-point variable. We need a different bound. `Float`
to the rescue:

```
use std::num::Float;

fn inverse<T: Float>(x: T) -> Result<T, String> {
    if x == Float::zero() { return Err("x cannot be zero!".to_string()) }

    let one: T = Float::one();
    Ok(one / x)
}
```

We've had to replace our generic `0.0` and `1.0` with the appropriate methods
from the `Float` trait. Both `f32` and `f64` implement `Float`, so our function
works just fine:

```
# use std::num::Float;
# fn inverse<T: Float>(x: T) -> Result<T, String> {
#     if x == Float::zero() { return Err("x cannot be zero!".to_string()) }
#     let one: T = Float::one();
#     Ok(one / x)
# }
println!("the inverse of {} is {:?}", 2.0f32, inverse(2.0f32));
println!("the inverse of {} is {:?}", 2.0f64, inverse(2.0f64));

println!("the inverse of {} is {:?}", 0.0f32, inverse(0.0f32));
println!("the inverse of {} is {:?}", 0.0f64, inverse(0.0f64));
```
