How can I define an instance for a specific type application in Haskell 98?

Question

I noticed that the test suite for Data.Set only really defines Arbitrary Set a sensibly for a ~ Int, but to avoid the GHC special ~ it uses

instance Enum a => Arbitrary (Set a)

How can I make sure only the Arbitrary (Set Int) instance is used without needing any GHC extensions? In GHC-only code, I'd use either FlexibleInstances or GADTs and then either

instance Arbitrary (Set Int)

or

instance a ~ Int => Arbitrary (Set a)

Answer 1

This is possible using an idea I think I first encountered in a paper by Oleg Kiselyov, and which underlies Control.Lens.Equality.

import Data.Functor.Identity

class IsInt a where
  fromIntF :: f Int -> f a

instance IsInt Int where
  fromIntF fx = fx

toIntF :: IsInt a => g a -> g Int
toIntF = unf . fromIntF . F $ id

newtype F g a b = F {unf :: g b -> a}

fromInt :: IsInt a => Int -> a
fromInt = runIdentity . fromIntF . Identity

toInt :: IsInt a => a -> Int
toInt = runIdentity . toIntF . Identity

Now I can use

instance IsInt a => Arbitrary (Set a)

and be confident that I'm really dealing with Int. For convenience, I can constrain the IsInt class with any classes I need of which Int is an instance:

class (Show a, Read a, Integral a, Arbitrary a) => IsInt a where ...