[Haskell-cafe] Re: [Haskell] Abusing quickcheck to check existential properties

[Sterling Clover]

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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