Lab 4

[BertLisser]

Ex. 2

instance Arbitrary a => Arbitrary (Set a) where
    arbitrary = fmap Set arbitrary

Is wrong because the array belonging to

{-- START OF LECTURE CODE --}
{-- Sets implemented as ordered lists without duplicates --}

newtype Set a = Set [a] deriving (Eq,Ord)

must have no duplicates and must be ordered.
A solution is:

instance (Eq a,  Ord a, Arbitrary a) => Arbitrary (Set a) where
    arbitrary = fmap Set (liftM (sort.nub) arbitrary)

Ex. 3
Then you don't need to define 'testIntIntersection' and 'quickCheck' on a list of Integers
but instead directly

quickCheckIntersection = verboseCheck (testIntersection::(Set Int->Set Int->Bool))

and so on.

Ex 7

isTransitive :: Eq a => Rel a -> Bool
isTransitive xs = and [ elem(a,c) xs | (a,b) <- xs, (c,d) <- xs, b == c ]

is wrong. Must become

isTransitive :: Eq a => Rel a -> Bool
isTransitive xs = and [ elem(a,d) xs | (a,b) <- xs, (c,d) <- xs, b == c ]