Lab 4

[BertLisser]

Ex. 6

trClos :: Ord a => Rel a -> Rel a
trClos xs = keepSearching (sort.nub) xs 

keepSearching :: Ord a => Rel a -> Rel a -> Rel a
keepSearching rel1 rel2 = if (nub(rel1++(rel1@@rel2)) == nub(rel1++rel2))
  then nub(rel1++rel2)
  else keepSearching (rel1++(rel1@@rel2)) rel2

Too expensive. It does too much steps. Better:

trClos :: Ord a => Rel a -> Rel a
trClos xs = keepSearching xs xs

keepSearching :: Ord a => Rel a -> Rel a
keepSearching rel1 = if ((sort.nub)(rel1++(rel1@@rel1)) == rel1)
  then rel1
  else keepSearching ((sort.nub) (rel1++(rel1@@rel1))) 

Ex. 7

-- Test  trClos
prop_trClos :: Ord a => Rel a -> Bool
prop_trClos r = let rclos = trClos r
                    transitiveChecks :: [Bool]
                    transitiveChecks = [ ((a, c) `elem` rclos) | (a, b) <- rclos, (c, d) <- rclos, b == c ]
                in  (nub r) `isSublist` (nub rclos) -- Check if r is subset of rclos
                 && foldr (&&) True transitiveChecks -- Check transitive property of rclos

must become

prop_trClos :: Ord a => Rel a -> Bool
prop_trClos r = let rclos = trClos r
                    transitiveChecks :: [Bool]
                    transitiveChecks = [ ((a, d) `elem` rclos) | (a, b) <- rclos, (c, d) <- rclos, b == c ]
                in  (nub r) `isSublist` (nub rclos) -- Check if r is subset of rclos
                 && foldr (&&) True transitiveChecks -- Check transitive property of rclos