It is possible for functions with compact domain, not just finite.
2009/10/12 Joe Fredette
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. :)
/Joe
On Oct 12, 2009, at 1:42 PM, muad wrote:
Is it possible to prove correctness of a functions by testing it? I think the tests would have to be constructed by inspecting the shape of the function definition.
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