{-# LANGUAGE TemplateHaskell #-}

module TestSets where

import Test.QuickCheck
import SetsAsList

-- The type of elements for testing:
type Elem = Int

-- ADT equations:

prop_empty_elem :: Elem -> Bool
prop_empty_elem x = not (isElem x empty)

prop_insert_elem :: Elem -> Set Elem -> Bool
prop_insert_elem x s = isElem x (insert x s)

prop_insert2_elem :: Elem -> Elem -> Set Elem -> Bool
prop_insert2_elem x y s = isElem x (insert y (insert x s))

prop_union :: Elem -> Set Elem -> Set Elem -> Bool
prop_union x s1 s2 =
  isElem x (union s1 s2) == (isElem x s1 || isElem x s2)

instance (Eq a, Arbitrary a) => Arbitrary (Set a) where
  arbitrary = do
    xs <- arbitrary
    return ((foldr :: (a -> b -> b) -> b -> [a] -> b) insert empty xs)

-- Executing all tests:
return []
testAll = $quickCheckAll