[Haskell-cafe] is proof by testing possible?
ekirpichov at gmail.com
Mon Oct 12 13:55:20 EDT 2009
It is possible for functions with compact domain, not just finite.
2009/10/12 Joe Fredette <jfredett at gmail.com>:
> In general? No- If we had an implementation of the `sin` function, how can
> testing a finite number of points along it determine
> if that implementation is correct for every point?
> For specific functions (particularly those with finite domain), it is
> possible. If you know the 'correct' output of every input, then testing each
> input and ensuring correct output will work. Consider the definition of the
> `not` function on booleans. The domain only has two elements (True and
> False) and the range has only two outputs (True and False), so if I test
> every input, and insure it maps appropriately to the specified output, we're
> all set.
> Basically, if you can write your function as a big case statement that
> covers the whole domain, and that domain is finite, then the function can be
> tested to prove it's correctness.
> Now, I should think the Muad'Dib would know that, perhaps you should go back
> to studying with the Mentats. :)
> On Oct 12, 2009, at 1:42 PM, muad wrote:
>> Is it possible to prove correctness of a functions by testing it? I think
>> tests would have to be constructed by inspecting the shape of the function
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