Re: [Haskell-cafe] is proof by testing possible?

I mean that, like in the definition of `||` True || _ = True False || x = x If you generalize this to `or`-ing a list of inputs, eg: foldr (||) False list_of_bools you can 'short-circuit' the test as soon as you find a 'True' value. This is actually not the greatest example, since you can't actually test it in finite number of tests, but you can test "half" the function by testing a that lists like [True:undefined] or [False, False, False, ... , True , undefined] return "True". It's "short-circuiting" in the sense that it (like the `||` function) doesn't need to see (necessarily) all of it's arguments to return a correct result. /Joe On Oct 12, 2009, at 2:11 PM, Eugene Kirpichov wrote:

What do you mean under short-circuiting here, and what is the connection? The property that allows to deduce global correctness from correctness on under-defined inputs is just continuity in the topological sense.

2009/10/12 Joe Fredette :

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Oh- thanks for the example, I suppose you can disregard my other message.

I suppose this is a bit like short-circuiting. No?

On Oct 12, 2009, at 1:56 PM, Eugene Kirpichov wrote:

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For example, it is possible to prove correctness of a function "negatedHead :: [Bool] -> Bool" by testing it on "True:undefined" and "False:undefined".

2009/10/12 Eugene Kirpichov :

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It is possible for functions with compact domain, not just finite.

2009/10/12 Joe Fredette :

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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:

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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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-- Eugene Kirpichov Web IR developer, market.yandex.ru

-- Eugene Kirpichov Web IR developer, market.yandex.ru

-- Eugene Kirpichov Web IR developer, market.yandex.ru