Determine trait inheritance hierarchies for core and std traits

[bstrie]

Lines like fn map_reduce<K1: Copy Send, K2: Hash IterBytes Eq Const Copy Send, V: Copy Send> can probably be compressed a bit with the aid of trait inheritance. Figure out the places where trait inheritance would be useful and determine the appropriate hierarchies.

[brendanzab]

It's been raised a number of times on IRC, but it'd be really handy if we had:

pub trait Num: Ord, Eq, Add<self, self>, Sub<self, self>, Mul<self, self>, Div<self, self>, Modulo<self, self>, Neg<self> {
    pure fn to_int() -> int;
    static pure fn from_int(n: int) -> self;
}

[bstrie]

Regarding the Num trait, would it also implement Copy? And would Ord inherit from Eq?

[brendanzab]

I believe that pcwalton has to implement 'kind inheritance' before we can inherit Copy - 'kind' referring to Rust's magic in-built traits like Const, Copy, Send and Owned (I think).

Float, Integer, Signed and Unsigned traits might also be useful:

trait Float: Num, FuzzyEq {}

trait Integer: Num {}

trait Signed: Num, Neg<self> {}

trait Unsigned: Num {}

[catamorphism]

Blocked on #3984

[alexcrichton]

I don't think that we're in as bad as a situation as we were when this was opened, but this is also kind of a vague issue.

@bstrie, do you know of any existing specific locations which could use improvement. I think that @bjz has been tracking all the numeric-related things in another issue, so I'm tempted to close this due to lack of actionable work unless there are things left to take care of.

[bstrie]

This was mostly a call-to-action for getting people thinking about our trait hierarchies (and numeric traits in particular), and I'd say it's served its purpose. Closing. Feel free to file more specific issues as they arise.