Data.Map, Data.IntMap documentation
Isaac Dupree
isaacdupree at charter.net
Sun Aug 19 06:44:53 EDT 2007
I wrote:
> Maybe there should be a separate FloatOrd class if you want the fourth
> possibility of "false due to NaN" in your comparisons of floating-point
> numbers, so that Float/Double can be made proper members of PrimOrd.
Then there are non-total orderings such as subset relations or many
lattices... which often get demoted to using `lt` and `gt` symbols.
Of course, Floats are not well-behaved even in Eq.
Prelude> let x = 0/0 :: Double in x == x
False
And there is no simple operation based on their (<), (<=)... that
fulfills even the requirements for a partial order...
<http://en.wikipedia.org/wiki/Partially_ordered_set>
A newtype of them that becomes _|_ upon isNaN would make a true total
order AFAIK (the infinities -at least in IEEE arithmetic- are
well-behaved with respect to ordering and equalling themselves).
Isaac
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