[Haskell] Abusing quickcheck to check existential properties
Norman Ramsey
nr at cs.tufts.edu
Sun Oct 12 13:38:05 EDT 2008
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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