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*Lab6> lengthCar 500 10
"500"
*Lab6>lengthMR 500 10
"0"

The numbers that give True for the first argument in the tuple are indeed known Mersenne numbers as can
be found on http://en.wikipedia.org/wiki/Mersenne_prime.

-- functions to show the difference in result of Fermat's primality and Miller-Rabin's 
primality check
lengthCar :: Integer -> Int -> IO String
lengthCar n k= do
    f <- testMore1 n k
    return $ show (length f)

lengthMR :: Integer -> Int -> IO String
lengthMR n k = do
    f <- test2More n k
    return $ show (length f)

trClos :: ( Ord a) => Rel a -> Rel a
trClos x = trClos2 x []
-- If the closure n+1 is a subset of n than all closures are found
-- because no new elements were found
trClos2 :: ( Ord a) => Rel a -> Rel a -> Rel a
trClos2 = fix (\ f x y ->
if subSet ( list2set x) ( list2set y) then ( nub x)
else f ((x @@ x )++ x) x)

trClos :: ( Ord a) => Rel a -> Rel a
trClos x = trClos2$nub x []
-- If the closure n+1 is a subset of n than all closures are found
-- because no new elements were found
trClos2 :: ( Ord a) => Rel a -> Rel a -> Rel a
trClos2 = fix (\ f x y ->
if  ( length x == length y) then x
else f$nub ((x @@ x )++ x)  x)

testTrClos :: ( Ord a) => Rel a -> Rel a -> Bool
testTrClos [] _ = True
testTrClos (x:xs) z = (all (\y -> elem y z) ([x] @@ z)) && ( testTrClos xs z)