[Haskell-cafe] Re: [Haskell] Abusing quickcheck to check
existential properties
Sterling Clover
s.clover at gmail.com
Sun Oct 12 16:31:28 EDT 2008
My understanding is that SmallCheck and lazy SmallCheck[1] are much
better suited to handle existential properties, and indeed have
combinators especially for that task.
--Sterl.
[1] http://www-users.cs.york.ac.uk/~mfn/lazysmallcheck/
smallcheck.pdf, http://hackage.haskell.org/cgi-bin/hackage-scripts/
package/smallcheck, http://hackage.haskell.org/cgi-bin/hackage-
scripts/package/lazysmallcheck
On Oct 12, 2008, at 1:38 PM, Norman Ramsey wrote:
> I recently used QuickCheck to check on some calculations for image
> compression.
> (I love exact rational arithmetic!) But I thought only to check for
> inverse properties, and I realized afterward I had failed to check for
> ranges. For example I should have checked that
>
> boundedB block = -1 <= b && b <= 1
> where Cos a b c d = cos_of_block block
>
> which turns out to be correct. But actually my calculations were
> wrong, and the real bounds on b are not +/- 1 but rather +/- 0.5, so I
> might equally well have passed a more stringent test. It's quite
> embarrassing as I have only 5 bits of precision to represent b, and
> throwing away a bit on values that don't exist is not the best idea I
> have had recently.
>
> What I would really like to do is write some combinators for interval
> checking that say
>
> * It is a *universal* property that for *every* input, the output
> lies within the stated interval.
>
> * It is an *existential* property of *some* input that the output
> lies close to the ends of the stated interval.
>
> But how do I use QuickCheck to check an existential?
> I realize I could run
>
> boundsNotAchieved block = -0.9 <= b && b <= 0.9
> where Cos a b c d = cos_of_block block
>
> and then if the test of boundsNotAcheived fails, my test passes
> (by exists x : P(x) iff not forall(x) : not P(x)).
>
> But if I set up a test suite in which some tests are supposed to fail
> and others are supposed to succeed, I will never keep track of which
> is which. I would like to build an existential test. Is it
> sufficient for me to write
>
> boundsAchieved block = expectFailure (-0.9 <= b && b <= 0.9)
> where Cos a b c d = cos_of_block block
>
> and then run 'quickCheck boundsAchieved'?
>
> In the long run I'd love something like
>
> fillsIntervalWithin :: (Num a, Ord a, Arbitrary a) => (a, a) -> a
> -> a -> Property
>
> with the idea that I want to test the partial application
>
> fillsIntervalWithin (lo, hi) epsilon
>
> and have the test succeed if every input x satisfies lo <= x <= hi
> and if some input x satisfies not (lo + epsilon <= x <= hi - epsilon).
>
> I'm betting someone on this list has already thought about similar
> problems and can advise me. (Because I have yet to write the
> specialized instance declaration for Arbitrary that guarantees the
> numerical invariants of the inputs, I have yet to test any of the
> examples in this email.)
>
>
> Norman
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