Merge branch 'master' of https://github.com/FFPiHaskell/slides

exampleCode/lecture8/sort.hs

+module Main where
+
+import Data.List
+import Test.QuickCheck
+
+-- Sorting twice changes nothing
+prop_idempotency :: Ord a => [a] -> Bool
+prop_idempotency xs = qsort xs == qsort (qsort xs)
+
+-- Sorting doesn't change the length
+prop_len :: Ord a => [a] -> Bool
+prop_len xs = length xs == length (qsort xs)
+
+-- Sorted result is a permutation of input
+prop_perm :: Ord a => [a] -> Bool
+prop_perm xs = (qsort xs) `elem` (permutations xs)
+
+-- Sorting produces sorted list
+prop_sort :: Ord a => [a] -> Bool
+prop_sort = isSorted . qsort
+  where
+    isSorted :: Ord a => [a] -> Bool
+    isSorted []       = True
+    isSorted [x]      = True
+    isSorted (x:y:zs) = (x <= y) && isSorted (y:zs)
+
+qsort :: Ord a => [a] -> [a]
+qsort []     = []
+qsort (p:xs) = (qsort lesser) ++ p:(qsort greater)
+  where
+    lesser  = filter (< p) xs
+    greater = filter (>= p) xs