Hi, I have no understanding of template haskell and thus this message is uninformed speculation. Would it not be possible to write a function verifier in TH that, unlike QuickCheck which provides bounds on a function being probably approximately correct, is given a list over properties which are proven over a quasi-quoted syntax tree? For example:
multiply :: Num a => a -> a -> a
multiply_group :: Proof Bool multiply_group = group multiply 1
group :: (a -> a -> a) -> a -> Proof Bool group f ident = [proof| f, [associative, identity 1]]
where `associative` and `ident` are proof-constructing functions that act over the `f` syntax tree. (Maybe some invokation of an Isabelle-like theorem prover or an SMT-like solver as part of the 'proof' module). Then we might even be able to list properties with class declarations. The properties get verified at compile time.
class Monoid a where mzero :: a msum :: a -> a -> a
property a [associative msum, identity mzero msum]
Any thoughts? Vivian