[Haskell-cafe] Ord for partially ordered sets

[Alexander Solla]

I see it as "morally wrong".  It's like a Monad instance that doesn't obey
the monad laws.  The kind of ticking timebomb strong typing is supposed to
protect us against.  But that only works if we do our part and don't make
non-sense instances.

Can your consumer get away with using a Hashable instance?  (I.e., for use
in unordered-containers).  This would be morally correct -- the graph could
presumably have a valid Hashable instance.


On Fri, Apr 24, 2015 at 6:06 AM, Ivan Lazar Miljenovic <
ivan.miljenovic at gmail.com> wrote:

> What is the validity of defining an Ord instance for types for which
> mathematically the `compare` function is partially ordered?
>
> Specifically, I have a pull request for fgl [1] to add Ord instances
> for the graph types (based upon the Ord instances for Data.Map and
> Data.IntMap, which I believe are themselves partially ordered), and
> I'm torn as to the soundness of adding these instances.  It might be
> useful in Haskell code (the example given is to use graphs as keys in
> a Map) but mathematically-speaking it is not possible to compare two
> arbitrary graphs.
>
> What are people's thoughts on this?  What's more important: potential
> usefulness/practicality or mathematical correctness?
>
> (Of course, the correct answer is to have a function of type a -> a ->
> Maybe Ordering :p)
>
> [1]: https://github.com/haskell/fgl/pull/11
>
> --
> Ivan Lazar Miljenovic
> Ivan.Miljenovic at gmail.com
> http://IvanMiljenovic.wordpress.com
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