QuickCheck is a Haskell’s package used to test properties of programs. The snippets are based on Koen Claessen and John Hughes’s *“QuickCheck: A Lightweight Tool for Random Testing of Haskell Programs”*.

```
module Main where
import Test.QuickCheck
( orderedList,==>),
(
classify,
collect,
forAll,
quickCheck,Property )
-- The programmer must specify a fixed type at which the law is to be tested
-- in some cases, we can use parametricity to argue that a property holds polymorphically
prop_RevUnit :: Int -> Bool
=
prop_RevUnit x reverse [x] == [x]
prop_RevApp :: [Int] -> [Int] -> Bool
=
prop_RevApp xs ys reverse (xs ++ ys) == reverse ys ++ reverse xs
prop_RevRev :: [Int] -> Bool
=
prop_RevRev xs reverse (reverse xs) == xs
-- you can use implication (==>) to express conditional properties
prop_MaxLe :: Int -> Int -> Property
=
prop_MaxLe x y <= y ==> max x y == y
x
-- you can use "classify" and "collect" to monitor test data
ordered :: [Int] -> Bool
= True
ordered [] :xs) = all (>= x) xs && ordered xs
ordered (x
insert :: Int -> [Int] -> [Int]
= [x]
insert x [] :ys) = if x <= y then x : y : ys else y : insert x ys
insert x (y
prop_Insert :: Int -> [Int] -> Property
=
prop_Insert x xs ==> ordered (insert x xs)
ordered xs
-- we sieve out the case of empty lists
prop_InsertClassify :: Int -> [Int] -> Property
=
prop_InsertClassify x xs ==>
ordered xs null xs) "trivial cases" $
classify (
ordered (insert x xs)
-- we list the percent of cases according to the length of the list
prop_InsertCollect :: Int -> [Int] -> Property
=
prop_InsertCollect x xs ==>
ordered xs length xs) $
collect (
ordered (insert x xs)
-- to guide the generator to generate less trivial cases
prop_InsertOrdered :: Int -> Property
=
prop_InsertOrdered x $ \xs ->
forAll orderedList
ordered (insert x xs)
main :: IO ()
= do
main
quickCheck prop_RevUnit
quickCheck prop_RevApp
quickCheck prop_RevRev
quickCheck prop_MaxLe
quickCheck prop_Insert
quickCheck prop_InsertClassify
quickCheck prop_InsertCollect quickCheck prop_InsertOrdered
```

## TODO

- Defining Generators
- Implementing QuickCheck