[Haskell-cafe] Justification for Ord inheriting from Eq?
robdockins at fastmail.fm
Fri Apr 7 12:49:38 EDT 2006
On Apr 7, 2006, at 9:43 AM, Jacques Carette wrote:
> Robert Dockins wrote:
>>> The behaviour of NaN actually makes perfect sense when you
>>> realise that
>>> it is Not a Number. Things that are not numbers are incomparable
>>> things that are.
>>> Yes, NaN can be of type Float. But it's not a Float.
>> If you take that tack, then you have to concede that the type
>> system isn't doing what it should (keeping me from having
>> something not-a-float where I expect a float). Any way you slice
>> it, its an unfortunate situation.
>> I'd personally rather that any operation generating NaN raises an
>> exception, a la divide by 0 at Int. I think (although I'm not
>> sure) that the floating point infinities play nice wrt equality
>> and ordering, so getting rid of NaN would restore at least _some_
>> semblance of proper algebraic behavior to the floating point
>> representations. (And the FFI already has CFloat/CDouble, so you
>> should use those when you really need to actually do something
>> with NaN generated by external code, and CFloat/CDobule should not
>> be members of Eq and Ord).
>> Or at the very least, attempting to compare NaN using (==) or (<)
>> and friends should raise an exception, rather than just returning
>> broken results.
>> Rob Dockins
> The IEEE 754 standard explicitly specifies that complete
> implementations can have either or both 'signalling' NaNs and
> 'quiet' NaNs. It appears that current Haskell implementations have
> chosen to go with quiet NaNs, which is very surprising indeed, as
> that does go "against" the type system. Signalling NaNs are more
> consistent with the rest of Haskell's semantics.
> However, it is also important to note that IEEE 754 also mandates
> 'trap handlers' for signalling NaNs, so that implementors may
> choose (even at run-time, on a per-instance basis) what to do with
> any given occurence of NaN. In particular, it is possible to
> resume the computation with a _value_ being substituted in for that
> NaN. These 'trap handlers' are also in there for division-by-zero,
> so that one may _choose_ to return either infinity or raise an
> actual exception.
> If one reads the standard (IEEE 754) carefully enough, it is
> possible to 'pick' an implementation of it which actually fits in
> with Haskell fairly well. Yes, the standard is explicitly written
> to have *choices* in it for implementors. The current
> implementation is generally standard-compliant, but does not seem
> to 'pick' a path of least-resistance wrt the rest of Haskell.
Is this an H' worthy item?
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