Really? How? That sounds very interesting, I've got a fair knowledge
of basic topology, I'd love to see an application
to programming...
On Oct 12, 2009, at 1:55 PM, Eugene Kirpichov wrote:
It is possible for functions with compact domain, not just finite.
2009/10/12 Joe Fredette <[email protected]>:
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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--
Eugene Kirpichov
Web IR developer, market.yandex.ru
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