Lab 4

[BertLisser]

Ex .5

-- the symmetric closure of a set can be reached by including the reverse of each relation in the set, we do this by adding the reverse, followed by removing any duplicates and sorting these two items and the symmetric closure of the tail.
symClos :: Ord a => Rel a -> Rel a
symClos [] = []
symClos ((x,y):xs) = sort $ nub ((x,y):(y,x):(symClos xs))

Less expensive

symClos' ::  Rel a -> Rel a
symClos' [] = []
symClos' ((x,y):xs) = (x,y):(y,x):(symClos' xs)
symClos :: Ord a => Rel a -> Rel a
symClos  xs =  (sort . nub)  (symClos' xs)

Ex 6

-- helper function that finds all of the missing transitive relations in a set, one layer deep. It also sorts and removes duplicates to maintain set properties
trClosFunc :: Ord a => Rel a -> Rel a
trClosFunc a = nub $ sort (a ++ (a @@ a))

-- the transitive closure of a set can be found by finding missing layers until adding a missing layer does not change the set, because if adding the next layer equals adding the empty set, we have no more missing items to insert into the set. If no items are missing, this means we are done.
trClos :: Ord a => Rel a -> Rel a
trClos a = fp' trClosFunc a

It does a step too much. Less expensive

trClos :: Ord a => Rel a -> Rel a
trClos x= fp' trClosFunc  ((sort.nub) x)

For the readability don't take the same name for the type and argument.