Proposal: Remove Show and Eq superclasses of Num

Edward Kmett ekmett at
Sun Sep 18 05:43:23 CEST 2011

On Sat, Sep 17, 2011 at 7:33 PM, Paterson, Ross <R.Paterson at>wrote:

> Sebastian Fischer writes:
> > Then Eq and Show must be superclasses of Num forever, which is the
> > wart Ian wants to address. I think that these superclasses should be
> > removed *and* the classes should be restructured along the lines of
> > yap. I don't care in which order, so +1 from me.
> If we had a Ring class, the superclasses of Num would be of much less
> consequence.

The problem that comes in is that this at the next proposal someone will
come along and just say the same thing.

"Now you have rings, but we really need semirings", so we can make a Bool
instance that folks understand rather than the ugly boolean ring.

"Now you have semirings, but we really need right seminearrings" to model
recognizing parsers.

Moreover, to properly factor out abs and signum you need MPTCs and,
regardless, any instance of Ring for Float and Double is lying to you, due
to the fact that associativity just flat out doesn't hold, so I would have
reservations about introducing it as a superclass for Num.

At least in its current lawless state I don't feel guilty making instances
for IEEE floats.

I favor this proposal because it is simple, has easily understood
consequences, and doesn't require people who implement Num to do anything
different, merely requires a few extra annotations in places where people
were using Num but also wanted to be able to show or compare, while letting
far more Num instances be defined without lying.

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