Ord (FiniteMap key elt)

[Christian Maeder]

> There's a lot more missing: Test for disjointness, subset-relation as
> well as instances for Show and Ord (lexical order, not subset-relation).
> Also FiniteMap should have these instances (also for Eq), if the
> elements have. These instances would allow nested sets and maps.

Since you had difficulties to supply an instance Ord for FiniteMap (see
below), here is my proposal:

instance (Ord key, Ord elt) => Ord (FiniteMap key elt) where
    fm_1 <= fm_2 =    
	if sizeFM fm_1 == sizeFM fm_2 -- quick test (unnecessary)
           && keysFM fm_1 == keysFM fm_2
	then eltsFM fm_1 <= eltsFM fm_2
	else keysFM fm_1 <= keysFM fm_2   -- or "<" if you wish 


That - besides Set - FiniteMap is an instance of Eq may almost be
obvious but wasn't documented!

("show . fmToList" for "Show" would be enough for me.)

Cheers Christian

The sources "/ghc-5.02.2/hslibs/data/FiniteMap.lhs" showed:

instance (Eq key, Eq elt) => Eq (FiniteMap key elt) where
  fm_1 == fm_2 = (sizeFM   fm_1 == sizeFM   fm_2) &&   -- quick test
                 (fmToList fm_1 == fmToList fm_2)

{- NO: not clear what The Right Thing to do is:
instance (Ord key, Ord elt) => Ord (FiniteMap key elt) where
  fm_1 <= fm_2 = (sizeFM   fm_1 <= sizeFM   fm_2) &&   -- quick test
                 (fmToList fm_1 <= fmToList fm_2)
-}