Allow a trait to implement its parent trait

The Rust Reference says:

the syntax Circle : Shape means that types that implement Circle must also have an implementation for Shape

Traditionally this is accomplished by adding an implementation to the underlying struct, and thus the trait Circle can only be applied to structs that supply an implementation for Shape.

However, I think it is very often useful (including in the example in the reference) to allow the trait to supply the supertrait implementation all by itself. In the reference example, does it really make sense for every struct : Circle to provide its own implementation of area? No. The area of a circle is always π*r^2.

Notably, it is still true that "types that implement Circle must also have an implementation for Shape." The difference is whether this implementation is supplied by each struct separately, or by Circle itself. The latter is better DRY.

Proposed syntax:

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

trait Circle : Shape { 
    fn radius(&self) -> f64;
    fn area(&self) -> f64 { //here we supply an implementation for Shape
        self.radius().powf(2.0) * 3.14
    }
}

struct MyCircle;
//impl Shape for MyCircle not required since all Circles are known to have an implementation for Shape.
impl Circle for MyCircle { fn radius (&self) -> f64 { 2.0 } }

fn main() {
    let b = MyCircle;
    println!("{}",b.area());
}

Read the Rust Reference traits example and the proposed syntax in this issue first. Compare the requested supertrait behavior with current Rust trait rules; done means a settled, implementable design for allowing Circle to provide Shape's implementation, with its interaction with implementing structs made explicit.