[Haskell] Abusing quickcheck to check existential properties

[Colin Runciman]

Norman,

> I guess what I would like is to reuse most of the mechanisms in
> QuickCheck to have it say one of these two things:
> 
>   1. Found an satisfying instance after 73 tries: [gives instance]
> 
>   2. After 100 tries, could not find a satisfying instance.
> 
> Like failure, the first tells you something definite about your
> program.  And like passing 100 tests, the second tells you nothing.

What you're asking for is similar to what SmallCheck could give you, but 
in the context of exhaustive testing of small values not sample testing 
  of random values.  However:

1. As most existentials are within the scope of a universal, there are 
many instances tested, so when a witness is indeed found nothing is 
reported.

2. A report is given only when no witness can be found within the 
specified search depth -- or when more than one can be found in the case 
of a unique existential.

Perhaps your final remark is tongue-in-cheek?  I agree the question of 
what "passed 100 tests" tells you is tricky; but it isn't "nothing". 
Anyway, in SmallCheck knowing that any witness could only be beyond the 
search depth does tell you something (eg. the expected witness might be 
a position in a list where the search depth is the length of the list).

Colin R