QC-basics.hs

import Test.QuickCheck
import Data.List

-- testing a sort routine
qsort :: Ord a => [a] -> [a]
qsort [] = []
qsort (x:xs) = qsort lhs ++ [x] ++ qsort rhs
    where lhs = filter (< x) xs
          rhs = filter (>= x) xs

prop_idempotent xs = qsort (qsort xs) == qsort xs

prop_minimum xs = head (qsort xs) == minimum xs
-- fails on empty lists
prop_minimum' xs = not (null xs) ==> head (qsort xs) == minimum xs

prop_ordered xs = ordered (qsort xs)
    where ordered [] = True
          ordered [x] = True
          ordered (x:y:ys) = x <= y && ordered (y:xs)

prop_permutation xs = permutation xs (qsort xs)
    where permutation xs ys = null (xs \\ ys) && null (ys \\ xs)
    
prop_maximum xs = not (null xs) ==> last (qsort xs) == maximum xs

prop_append xs ys = not (null xs) ==> 
        head (qsort (xs ++ ys)) == min (minimum xs) (minimum ys)
        
prop_sort_model xs = sort xs == qsort xs