Breaking Data.Set integrity without GeneralizedNewtypeDeriving

Question

The code below uses an unsafe GeneralizedNewtypeDeriving extension to break Data.Set by inserting different elements with different Ord

Answer 1

I think that's an important question, so I'll repeat my answer from elsewhere: you can have multiple instances of the same class for the same type in Haskell98 without any extensions at all:

$ cat A.hs
module A where
data U = X | Y deriving (Eq, Show)

$ cat B.hs
module B where
import Data.Set
import A
instance Ord U where
    compare X X = EQ
    compare X Y = LT
    compare Y X = GT
    compare Y Y = EQ
ins :: U -> Set U -> Set U
ins = insert

$ cat C.hs
module C where
import Data.Set
import A
instance Ord U where
    compare X X = EQ
    compare X Y = GT
    compare Y X = LT
    compare Y Y = EQ
ins' :: U -> Set U -> Set U
ins' = insert

$ cat D.hs
module D where
import Data.Set
import A
import B
import C
test = ins' X $ ins X $ ins Y $ empty

$ ghci D.hs
Prelude D> test
fromList [X,Y,X]

And yes, you can prevent this kind of attacks by storing the dictionary internally:

data MSet a where MSet :: Ord a => Set a -> MSet a