> 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.
Well, it can if we write it in a bit different way:
instance (Show (f (Mu f))) => Show (Mu f) where
show (In x) = show x
instance Show (N (Mu N)) where
show Z = "Z"
show (S k) = "S "++show k
*Main> show (In (S (In (S (In Z)))))
"S S Z"
This solution is akin to that of breaking the type recursion when
defining the fixpoint combinator fix. Only here we face the recursion
on constraints. I believe the same solution should work for the
Observable class. You didn't post the definition of the Observable
class, so I couldn't test my claim.
Flags used:
ghci -fglasgow-exts -fallow-undecidable-instances /tmp/a.hs
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