Some total ordering relations can only be expressed as partial orders

TL;DR: one cannot impl Ord<Foo> for Bar.

Currently, we can stablish strict and non-strict partial ordering relations between types:

impl PartialEq<Foo> for Bar { ... }
impl PartialOrd<Foo> for Bar { ... }

but there is no way to state that such a relation is a total order because Ord and Eq are not generic over the RHS like PartialOrd and PartialEq are.

Is this an oversight?

I would find this useful when implementing ordering relations for wrapper types for which it makes no sense to implement Deref. For example:

impl PartialOrd<Wrapping<i32>> for i32 { ... } // TODAY OK
impl PartialEq<Wrapping<i32>> for i32 { ... } // TODAY OK

impl Eq<Wrapping<i32>> for i32 { ... }  // TODAY ERROR
impl Ord<Wrapping<i32>> for i32 { ... }  // TODAY ERROR

To solve this we would probably need to change Eq and Ord from:

pub trait Eq: PartialEq<Self> { ... }
pub trait Ord: Eq + PartialOrd<Self> { ... }

to

pub trait Eq<RHS=Self>: PartialEq<RHS> { ... }
pub trait Ord<RHS=Self>: Eq<RHS> + PartialOrd<RHS> { ... }

Would this be a breaking change? (if so, could it be fixed automatically by rustfix?)

Start by reviewing the issue's proposed changes to Rust's Eq, Ord, PartialEq, and PartialOrd traits, including the wrapper-type examples. Determine whether making Eq and Ord generic would be breaking and whether rustfix could automate compatibility changes. Done means documenting a resolved design direction or turning the proposal into an RFC-ready change.