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