However you're right in a sense, you can't use this scheme to
serialize any functions taking functions, like
something :: (a -> Parser a) -> a -> Parser a
because
data MyParser = FunSomething (a -> MyParser) a
wouldn't be serializable. Well, maybe if your parsers were
arrows... :)
You can't use full arrows because you need to be able to lift an arbitrary function into an arrow type, which precludes meeting the serialization criterion.
You CAN use a CCC, but they are a bit harder to work with. =)
-Edward Kmett