Some clarity please!

[Aaron Denney]

On 2008-03-13, Ketil Malde <ketil at malde.org> wrote:
> Aaron Denney <wnoise at ofb.net> writes:
>
>> Well, the way the report specifies that max's default definition
>> is.  I'd actually favor making that not an instance function at
>> all, and instead have max and min be external functions.
>
> If you permit a naïve question:
>
> Prelude> :i Ord
> class (Eq a) => Ord a where
>   compare :: a -> a -> Ordering
>   (<) :: a -> a -> Bool
>   (>=) :: a -> a -> Bool
>   (>) :: a -> a -> Bool
>   (<=) :: a -> a -> Bool
>   max :: a -> a -> a
>   min :: a -> a -> a
>
> ..while all functions could be easily derived from 'compare'.  Or from
> the Eq instance's (==) and (<), say.
>
> What is the reason for this?  Efficiency?  (Which couldn't be handled
> equally well by RULES?)  Otherwise, it looks like an invitation for
> writing inconsistent instances.

My impression (which may not be entirely accurate) is not primarily for
efficiency (though that is one reason), but for ease of implementation.

It may be easier in some cases to think through the various cases of
compare, or to just figure out what (<=) is.  Either of these is
sufficient (perhaps in combination with (==) from the superclass).

You can write things so that any of (<), (<=), (>), or (>=) are
sufficient, but for writing the default compare, it's easiest to know
ahead of time which you are basing it on, so definitions don't get
circular.

max and min seem to have neither justification going for them, although
I suppose it's technically possible to write compare in terms of them
and (==).

I don't think GHC's RULES were around when Haskell 98 was being formalized,
nor is it clear that one compiler's method should let other efficiency
concerns go by the wayside.

Of course, it would be nice to be able to write (==) in terms of
compare.  While doable manually there's no way to default it to that
"smartly".  There are similar issues with Functor and Monad.  ISTR
some discussion about this on the list previously.

-- 
Aaron Denney
-><-