[Haskell-cafe] is proof by testing possible?

[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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