Not all splices are the same

I've been a bit upset by the challenges Template Haskell poses for type inference. For example, (3 :: Int) == $$(...) may typecheck when $$(...) == (3 :: Int) does not. I don't imagine this problem can be solved in general, but I'm rather curious whether it might be possible to solve for "pure" splices, with types that look like forall m. Quote m => Code m a Would it be possible to get full bidirectional inference for these if they were somehow marked specially by the user? For instance, if I wrote $$$e that could mean e should be interpreted as having some type PCode a where newtype PCode a = PCode (forall m. Quote m => a)