To try some of the examples from paper "Recursion Schemes from Comonads", I wanted to define instances of Show and Observable for types defined as the fixed point of a functor. I defined type recursion and naturals as
newtype Mu f = In {unIn :: f (Mu f)} data N f = S f | Z type Nat = Mu N
An application of Mu should be showable if the functor maps showable types to showable types, so the most natural way to define the instance seemed to be instance (Show a => Show (f a)) => Show (Mu f) where show (In x) = show x Of course that constraint didn't work, so I made a class PShow with a method that witnessed the constraint
class PShow f where pshow :: (Show a) => f a -> String
Now I could define a generic show instance for Mu, and got a Show instance for Nat by defing a PShow instance for N
instance (PShow f) => Show (Mu f) where show (In x) = pshow x
instance PShow N where pshow Z = "Z" pshow (S k) = "S "+show K
show (In (S (In (S (In Z))))) -> "S S Z" This works fine, but you need to be able to use the method of P<Class> in the definition of <Class> (Mu f). I couldn't figure out how to do the same thing with Observable (the use of the class methods is a few layers away from the public interface). I tried to define a set of mutaully recursive definitions instance (Observable (f (Mu f))) => Observable (Mu f) where observer (In x) = send "In" (return In << x) instance (Observable a) => Observable (N a) where observer Z = send "Z" (return Z) observer (S x) = send "S" (return S << x) unfortunately, the class constraint solver doesn't doesn't like this. I get an error message like Constraint Stack Overflow: Observable (N (Mu N)) Observable (Mu N) Observable (N (Mu N)) Observable (Mu N) ... I expected that that constraint solver would realize it could construct a dictionary transformer with a type like Observer Nat -> Observer Nat and take the fixed point to get an instance for Nat. I haven't looked at the implementation, but it seems like it would be easy to add the constraint we are trying to derive to the list of assumptions when trying to construct all the anteceedents of an instance declaration. Can anyone tell me how to 1) get around this 2) modify GHC to handle this :) Brandon