This came up before (see the prior thread): https://mail.haskell.org/pipermail/libraries/2015-February/024943.html The thread at that time grew rather large, and only at the end did I come up with what I continue to think is a satisfactory formulation of the law. However, at that point nobody really acted to do anything about it. I would like to _formally request that the core libraries committee review_ the final version of the law as proposed, for addition to Foldable documentation: == Given a fresh newtype GenericSet = GenericSet Integer deriving (Eq, Ord), where GenericSet is otherwise fully abstract: forall (g :: forall a. f a -> Maybe a), (x :: f GenericSet). maybe True (`Foldable.elem` x) (g x) =/= False == The intuition is: "there is no general way to get an `a` out of `f a` which cannot be seen by the `Foldable` instance". The use of `GenericSet` is to handle the case of GADTs, since even parametric polymorphic functions on them may at given _already known_ types have specific behaviors. This law also works over infinite structures. It rules out "obviously wrong" instances and accepts all the instances we want to that I am aware of. My specific motivation for raising this again is that I am rather tired of people saying "well, Foldable has no laws, and it is in base, so things without laws are just fine." Foldable does a have a law we all know to obey. It just has been rather tricky to state. The above provides a decent way to state it. So we should state it. Cheers, Gershom