Ord instance for Data.Map?

[Bertram Felgenhauer]

Henning Thielemann wrote:
> 
> I wonder whether the Ord instance is a good choice as constraint for
> Data.Map, Data.Set and so on.

In the case where there are Ord instances they are a good choice. Adding
another type class for this purpose has the disadvantage that you have
to write class instances for them, for all existing types that have Ord
instances; while trivial this still adds up to quite a few lines of
boilerplate code. This has to be weighted against the added boilerplate
code for cases where a total order can be defined but is rather
artificial. Right now I think that this is the exception rather than the
rule. Changing the library interface should also not be done lightly.

[snip examples: Complex numbers and Haskore notes]
>
> I have a work-around in mind: I could introduce
>
> class Eq a => Indexable a where
>   compareIndex :: a -> a -> Ordering
[snip]

Personally I'd do it without an Indexable class; just

> newtype Index a = Index a

> instance Ord x => Ord (Index (Complex x)) where
>    (Index (Complex a b)) `compare` (Index (Complex c d)) =
>        (a, b) `compare` (c, d)

should be good enough. 'Index' marks the purpose for the type.

Note that for me, Ord alone really only implies a total order. If a
type has both Num and Ord instances that is different; I understand
your concerns about providing an Ord instance for Complex numbers
directly.

> Then I do not insert complex numbers immediately in a set, but wrap them
> in IndexableToOrd and insert the wrapped values in a set.
>  Cumbersome, isn't it?

Of course you still need that index wrapping. If this gets out of hand
it can be put into a simple wrapper around Data.Map though, without
changing any existing libraries.

> So my question is: Was the Ord constraint for Data.Map a good idea?

I still think it was.

Bertram