How can I test a higher-order function using QuickCheck?

I have a higher-order function that I want to test, and one of the properties I want to test is what it does with the functions that are passed in. For purposes of illustration, here is a contrived example:

gen :: a -> ([a] -> [a]) -> ([a] -> Bool) -> a

The idea is roughly that this is an example generator. I'm going to start with a single a, create a singleton list of [a], then make new lists of [a] until a predicate tells me to stop. A call might look like this:

gen init next stop

where

init :: a
next :: [a] -> [a]
stop :: [a] -> Bool

Here's the property I'd like to test:

On any call to gen init next stop, gen promises never to pass an empty list to next.

Can I test this property using QuickCheck, and if so, how?