[Haskell-cafe] NaN as Integer value

[wren ng thornton]

On 4/14/13 8:53 PM, Kim-Ee Yeoh wrote:
> On Sun, Apr 14, 2013 at 3:28 PM, wren ng thornton <wren at freegeek.org>
wrote:
>> Whereas the problematic
>> values due to infinities are overspecified, so no matter which answer you
>> pick it's guaranteed to be the wrong answer half the time.
>>
>> Part of this whole problem comes from the fact that floats *do* decide to
>> give a meaning to 1/0 (namely Infinity).
>
> I'm not sure what you mean about overspecification here, but in
> setting 1/0 as +infinity (as opposed to -infinity), there's an easily
> overlooked assumption that the limit is obtained "from above" as
> opposed to "from below."

Setting 1/0 = +inf isn't the problem, or at least not the main one. Of
course, there's always the question about which completion of the reals to
use--- i.e., whether we have +inf vs -inf, or whether we just have a
single point infinity.

Rather, the NaN problem comes from trying to resolve things like:

    inf - inf
    inf * 0
    inf / inf
    0 / 0

The overspecification problem I mentioned is that each of these
expressions has "too many" solutions. For example, we have the following
equations:

    x   * 0 == 0               -- where x is finite
    inf * y == inf * signum y  -- where y /= 0
    inf * 0 == ??

    x   - inf == -inf  -- where x is finite
    inf - y   == inf   -- where y is finite
    inf - inf == ??

    x / 0 == inf * signum x  -- where x /= 0
    0 / y == 0               -- where y /= 0
    0 / 0 == ??

-- 
Live well,
~wren