Lab 4

[BertLisser]

Exercise 2

integerSetGeneratorFromScratch :: IO (Set Int)
integerSetGeneratorFromScratch = do
    n <- getRandomNatural
    xs <- getRandomIntegers maxNatural
    return (Set (nub xs))

-- Time spent: 1:15

instance (Arbitrary a, Eq a) => Arbitrary (Set a) where 
    arbitrary = do
        xs <- arbitrary
        return (Set (nub xs))

The function sort is missing in return (Set (nub xs)).
It must become: return (Set (sort(nub xs)))

Exercise 6

-- Transitive closure
trClos :: Ord a => Rel a -> Rel a
trClos r = until (\s -> tr s == s) tr r
    where tr r = sort (nub ((r @@ r) ++ r))

will be go wrong in the first step
Solution:

-- Transitive closure
trClos' :: Ord a => Rel a -> Rel a
trClos' r = until (\s -> tr s == s) tr r
    where tr r = sort (nub ((r @@ r) ++ r))
trClos :: Ord a => Rel a -> Rel a
trClos r =  trClos' (sort r)

Ex 8

prop_ClosuresDifference :: Rel Int -> Bool
prop_ClosuresDifference r = symClos (trClos r') == trClos (symClos r') 
    where r' = nub r

the test defined in prop_ClosuresDifference must become

sort(symClos (trClos r') )==sort(trClos (symClos r') )