[Haskell-cafe] QuickCheck, (Ord a)=> [a] -> Property problem

[Nick Smallbone]

"larry.liuxinyu" <liuxinyu95 at gmail.com> writes:

> prop_foo :: (Ord a) => [a] -> Property
> prop_foo xs = not (null xs) ==> maximum xs == minimum xs
>
> This is an extreme case that the property is always wrong.
>
> However, QuickCheck produces:
> *Main> test prop_foo
> OK, passed 100 tests.
>
> Why this happen? If I use verboseCheck, I can find the sample test
> data are as the following:
> *Main>verboseCheck prop_foo
> ...
> 97:
> [(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),()]
> 98:
> [(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),
> (),(),(),(),(),(),()]
> 99:
> [(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),(),
> (),(),()]
> OK, passed 100 tests.

This is an unfortunate feature of GHCi: if the thing you want to
evaluate has a polymorphic type then all the type variables default to
(), see:
  http://www.haskell.org/ghc/docs/7.0.3/html/users_guide/interactive-evaluation.html#extended-default-rules
So prop_foo is only tested for lists of (). Nasty.

The usual way to work around it is to declare all your properties
monomorphic, so write:
  prop_foo :: [Integer] -> Property

> This works at least, However, since 'a'<'b', they are order-able, what
> if I want to test prop_foo works for char?

Testing with Integers should always[*] be enough because of
parametricity.

Nick

[*] For certain values of "always" :)