How can I fill in arbitrary sets?

Question

The current Arbitraryinstance used for testing Data.Setis too complex for my taste. I really do not understand this, so I do not believe it. I came up with the idea of ​​separating form generation from value generation.

Using

class Monad m => MonadGen m where
  liftGen :: Gen a -> m a
instance MonadGen Gen where
  liftGen = id
instance MonadGen m => MonadGen (StateT s m) where
  liftGen = lift . liftGen

I can write

mkArb :: MonadGen m => m a -> Int -> m (Set a)
mkArb step n
  | n <= 0 = pure Tip
  | n == 1 = singleton <$> step
  | n == 2 = do
     dir <- liftGen arbitrary
     p <- step
     q <- step
     if dir
       then pure (Bin 2 q (singleton p) Tip)
       else pure (Bin 2 p Tip (singleton q))
  | otherwise = do
      let upper = (3*(n - 1)) `quot` 4
      let lower = (n + 2) `quot` 4
      ln <- liftGen $ choose (lower, upper)
      let rn = n - ln - 1
      (\lt x rt -> Bin n x lt rt) <$> mkArb step ln <*> step <*> mkArb step rn

Then I can use something like StateT s Gento populate the set with strictly ascending elements.

I have two questions:

• Am I successfully creating all balanced tree shapes? How can i check?

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