[Haskell-cafe] the overlapping instance that wasn't?

[Michael Vanier]

  Hi everyone,

Here's some code that's giving me an error message I don't understand:

{-# LANGUAGE EmptyDataDecls,
              MultiParamTypeClasses,
              UndecidableInstances,
              FlexibleInstances #-}

data Z
data S n

class Nat n where
   toInt :: n -> Int

instance Nat Z where
   toInt _ = 0

instance (Nat n) => Nat (S n) where
   toInt _ = 1 + toInt (undefined :: n)

instance (Nat n) => Show n where
   show _ = show $ toInt (undefined :: n)

-- end of code sample

When I run this through ghci, I get this:

test.hs:19:11:
     Overlapping instances for Show Int
       arising from a use of `show' at test.hs:19:11-14
     Matching instances:
       instance Show Int -- Defined in GHC.Show
       instance (Nat n) => Show n -- Defined at test.hs:18:9-25
     In the first argument of `($)', namely `show'
     In the expression: show $ toInt (undefined :: n)
     In the definition of `show': show _ = show $ toInt (undefined :: n)

Adding OverlappingInstances to the language pragmas fixes the problem.  
My question is: why is this an overlapping instance?  It would make 
sense if Int was an instance of Nat, but it isn't.  Is this just a 
limitation in the way overlapping instances are identified?

Mike