I myselft don't understand why GHCi doesn't accept the type it infered as an explicit signature ...
I think it has to do with the following: Looking at the type errors, they seem to indicate that the type checker is being general and does not assume the |From| and |To| "relations" are between a type |t| and (s (t x) x)| but, in general, between |t| and |s (t' x) x|. Given that from :: (From a1 c1 x) => a1 x -> c1 x to :: (To a2 c2 y) => c2 y -> a2 y bimap :: Bifunctor s => (t1 -> t3) -> (t2 -> t4) -> s t1 t2 -> s t3 t4 During type checking the following equations spring up: c2 y = s t3 t4 c1 x = s t1 t2 t2 = x t4 = y t1 = a1 x t3 = a2 y That'd give the same type as that inferred, but somehow new variables |a11| and |a12| appear.
caused by a lack of functional dependencies. class From a c x | a -> c where class To a c y | c -> a where ... hushes GHCi. The question now is, of course, if the new dependencies are too restrictive for your problem.
They are of little avail given the instances I define: instance Bifunctor s => From (Fix s) (s (Fix s x)) x where from = out instance Bifunctor s => To (Fix s) (s (Fix s y)) y where to = In