content: -----------------------------------------------------------------------------
  -- |
  -- Module      :  Debug.QuickCheck
  -- Copyright   :  (c) Koen Claessen, John Hughes 2001
  -- License     :  BSD-style (see the file libraries/base/LICENSE)
  -- 
  -- Maintainer  :  libraries@haskell.org
  -- Stability   :  experimental
  -- Portability :  portable
  --
  -- QuickCheck v.0.2
  -- DRAFT implementation; last update 000104.
  -- Koen Claessen, John Hughes.
  -- This file represents work in progress, and might change at a later date.
  --
  -----------------------------------------------------------------------------
  
  module QuickCheck
    -- testing functions
    ( quickCheck    -- :: prop -> IO ()
    , verboseCheck  -- :: prop -> IO ()
    , test          -- :: prop -> IO ()  -- = quickCheck
    
    , Config(..)    -- :: *
    , check         -- :: Config -> prop -> IO ()
   
    -- property combinators
    , forAll        -- :: Gen a -> (a -> prop) -> prop
    , (==>)         -- :: Bool -> prop -> prop
    
    -- gathering test-case information
    , label         -- :: String         -> prop -> prop
    , collect       -- :: Show a => a    -> prop -> prop
    , classify      -- :: Bool -> String -> prop -> prop
    , trivial       -- :: Bool           -> prop -> prop
    
    -- generator combinators
    , Gen           -- :: * -> * ; Functor, Monad
    
    , elements      -- :: [a] -> Gen a
    , two           -- :: Gen a -> Gen (a,a)
    , three         -- :: Gen a -> Gen (a,a,a)
    , four          -- :: Gen a -> Gen (a,a,a,a)
    
    , sized         -- :: (Int -> Gen a) -> Gen a
    , resize        -- :: Int -> Gen a -> Gen a
    , choose        -- :: Random a => (a, a) -> Gen a
    , oneof         -- :: [Gen a] -> Gen a
    , frequency     -- :: [(Int, Gen a)] -> Gen a
    
    , vector        -- :: Arbitrary a => Int -> Gen [a]
  
    -- default generators
    , Arbitrary(..) -- :: class
    , rand          -- :: Gen StdGen
    , promote       -- :: (a -> Gen b) -> Gen (a -> b)
    , variant       -- :: Int -> Gen a -> Gen a
  
    -- testable
    , Testable(..)  -- :: class
    , Property      -- :: *
  
    -- For writing your own driver
    , Result(..)	 -- :: data
    , generate	 -- :: Int -> StdGen -> Gen a -> a
    , evaluate     -- :: Testable a => a -> Gen Result
    )
   where
  
  import Prelude
  
  import Random
  import List( group, sort, intersperse )
  import Monad( liftM2, liftM3, liftM4 )
  
  infixr 0 ==>
  infix  1 `classify`
  
  --------------------------------------------------------------------
  -- Generator
  
  newtype Gen a
    = Gen (Int -> StdGen -> a)
  
  sized :: (Int -> Gen a) -> Gen a
  sized fgen = Gen (\n r -> let Gen m = fgen n in m n r)
  
  resize :: Int -> Gen a -> Gen a
  resize n (Gen m) = Gen (\_ r -> m n r)
  
  rand :: Gen StdGen
  rand = Gen (\n r -> r)
  
  promote :: (a -> Gen b) -> Gen (a -> b)
  promote f = Gen (\n r -> \a -> let Gen m = f a in m n r)
  
  variant :: Int -> Gen a -> Gen a
  variant v (Gen m) = Gen (\n r -> m n (rands r !! (v+1)))
   where
    rands r0 = r1 : rands r2 where (r1, r2) = split r0
  
  generate :: Int -> StdGen -> Gen a -> a
  generate n rnd (Gen m) = m size rnd'
   where
    (size, rnd') = randomR (0, n) rnd
  
  instance Functor Gen where
    fmap f m = m >>= return . f
  
  instance Monad Gen where
    return a    = Gen (\n r -> a)
    Gen m >>= k =
      Gen (\n r0 -> let (r1,r2) = split r0
                        Gen m'  = k (m n r1)
                     in m' n r2)
  
  -- derived
  
  choose :: Random a => (a, a) -> Gen a
  choose bounds = (fst . randomR bounds) `fmap` rand
  
  elements :: [a] -> Gen a
  elements xs = (xs !!) `fmap` choose (0, length xs - 1)
  
  vector :: Arbitrary a => Int -> Gen [a]
  vector n = sequence [ arbitrary | i <- [1..n] ]
  
  oneof :: [Gen a] -> Gen a
  oneof gens = elements gens >>= id
  
  frequency :: [(Int, Gen a)] -> Gen a
  frequency xs = choose (1, tot) >>= (`pick` xs)
   where
    tot = sum (map fst xs)
  
    pick n ((k,x):xs)
      | n <= k    = x
      | otherwise = pick (n-k) xs
  
  -- general monadic
  
  two :: Monad m => m a -> m (a, a)
  two m = liftM2 (,) m m
  
  three :: Monad m => m a -> m (a, a, a)
  three m = liftM3 (,,) m m m
  
  four :: Monad m => m a -> m (a, a, a, a)
  four m = liftM4 (,,,) m m m m
  
  --------------------------------------------------------------------
  -- Arbitrary
  
  class Arbitrary a where
    arbitrary   :: Gen a
    coarbitrary :: a -> Gen b -> Gen b
  
  instance Arbitrary () where
    arbitrary     = return ()
    coarbitrary _ = variant 0
  
  instance Arbitrary Bool where
    arbitrary     = elements [True, False]
    coarbitrary b = if b then variant 0 else variant 1
  
  instance Arbitrary Int where
    arbitrary     = sized $ \n -> choose (-n,n)
    coarbitrary n = variant (if n >= 0 then 2*n else 2*(-n) + 1)
  
  instance Arbitrary Integer where
    arbitrary     = sized $ \n -> choose (-fromIntegral n,fromIntegral n)
    coarbitrary n = variant (fromInteger (if n >= 0 then 2*n else 2*(-n) + 1))
  
  instance Arbitrary Float where
    arbitrary     = liftM3 fraction arbitrary arbitrary arbitrary 
    coarbitrary x = coarbitrary (decodeFloat x)
  
  instance Arbitrary Double where
    arbitrary     = liftM3 fraction arbitrary arbitrary arbitrary 
    coarbitrary x = coarbitrary (decodeFloat x)
  
  fraction a b c = fromInteger a + (fromInteger b / (abs (fromInteger c) + 1))
  
  instance (Arbitrary aa, Arbitrary bb) => Arbitrary (aa, bb) where
    arbitrary          = liftM2 (,) arbitrary arbitrary
    coarbitrary (a, b) = coarbitrary a . coarbitrary b
  
  instance (Arbitrary aa, Arbitrary bb, Arbitrary cc) => Arbitrary (aa, bb, cc) where
    arbitrary             = liftM3 (,,) arbitrary arbitrary arbitrary
    coarbitrary (a, b, c) = coarbitrary a . coarbitrary b . coarbitrary c
  
  instance (Arbitrary aa, Arbitrary bb, Arbitrary cc, Arbitrary dd)
        => Arbitrary (aa, bb, cc, dd)
   where
    arbitrary = liftM4 (,,,) arbitrary arbitrary arbitrary arbitrary
    coarbitrary (a, b, c, d) =
      coarbitrary a . coarbitrary b . coarbitrary c . coarbitrary d
  
  instance Arbitrary aa => Arbitrary [aa] where
    arbitrary          = sized (\n -> choose (0,n) >>= vector)
    coarbitrary []     = variant 0
    coarbitrary (a:as) = coarbitrary a . variant 1 . coarbitrary as
  
  instance (Arbitrary aa, Arbitrary bb) => Arbitrary (aa -> bb) where
    arbitrary         = promote (`coarbitrary` arbitrary)
    coarbitrary f gen = arbitrary >>= ((`coarbitrary` gen) . f)
  
  --------------------------------------------------------------------
  -- Testable
  
  data Result
    = Result { ok :: Maybe Bool, stamp :: [String], arguments :: [String] }
  
  nothing :: Result
  nothing = Result{ ok = Nothing, stamp = [], arguments = [] }
  
  newtype Property
    = Prop (Gen Result)
  
  result :: Result -> Property
  result res = Prop (return res)
  
  evaluate :: Testable a => a -> Gen Result
  evaluate a = gen where Prop gen = toProperty a
  
  class Testable a where
    toProperty :: a -> Property
  
  instance Testable () where
    toProperty _ = result nothing
  
  instance Testable Bool where
    toProperty b = result (nothing{ ok = Just b })
  
  instance Testable Result where
    toProperty res = result res
  
  instance Testable Property where
    toProperty prop = prop
  
  instance (Arbitrary a, Show a, Testable b) => Testable (a -> b) where
    toProperty f = forAll arbitrary f
  
  forAll :: (Show a, Testable b) => Gen a -> (a -> b) -> Property
  forAll gen body = Prop $
    do a   <- gen
       res <- evaluate (body a)
       return (argument a res)
   where
    argument a res = res{ arguments = show a : arguments res }
  
  (==>) :: Testable a => Bool -> a -> Property
  True  ==> a = toProperty a
  False ==> a = toProperty ()
  
  label :: Testable a => String -> a -> Property
  label s a = Prop (add `fmap` evaluate a)
   where
    add res = res{ stamp = s : stamp res }
  
  classify :: Testable a => Bool -> String -> a -> Property
  classify True  name = label name
  classify False _    = toProperty
  
  trivial :: Testable a => Bool -> a -> Property
  trivial = (`classify` "trivial")
  
  collect :: (Show a, Testable b) => a -> b -> Property
  collect v = label (show v)
  
  --------------------------------------------------------------------
  -- Testing
  
  data Config = Config
    { configMaxTest :: Int
    , configMaxFail :: Int
    , configSize    :: Int -> Int
    , configEvery   :: Int -> [String] -> String
    }
  
  quick :: Config
  quick = Config
    { configMaxTest = 100
    , configMaxFail = 1000
    , configSize    = (+ 3) . (`div` 2)
    , configEvery   = \n args -> let s = show n in s ++ [ '\b' | _ <- s ]
    }
           
  verbose :: Config
  verbose = quick
    { configEvery = \n args -> show n ++ ":\n" ++ unlines args
    }
  
  test, quickCheck, verboseCheck :: Testable a => a -> IO ()
  test         = check quick
  quickCheck   = check quick
  verboseCheck = check verbose
           
  check :: Testable a => Config -> a -> IO ()
  check config a =
    do rnd <- newStdGen
       tests config (evaluate a) rnd 0 0 []
  
  tests :: Config -> Gen Result -> StdGen -> Int -> Int -> [[String]] -> IO () 
  tests config gen rnd0 ntest nfail stamps
    | ntest == configMaxTest config = do done "OK, passed" ntest stamps
    | nfail == configMaxFail config = do done "Arguments exhausted after" ntest stamps
    | otherwise               =
        do putStr (configEvery config ntest (arguments result))
           case ok result of
             Nothing    ->
               tests config gen rnd1 ntest (nfail+1) stamps
             Just True  ->
               tests config gen rnd1 (ntest+1) nfail (stamp result:stamps)
             Just False ->
               putStr ( "Falsifiable, after "
                     ++ show ntest
                     ++ " tests:\n"
                     ++ unlines (arguments result)
                      )
       where
        result      = generate (configSize config ntest) rnd2 gen
        (rnd1,rnd2) = split rnd0
  
  done :: String -> Int -> [[String]] -> IO ()
  done mesg ntest stamps =
    do putStr ( mesg ++ " " ++ show ntest ++ " tests" ++ table )
   where
    table = display
          . map entry
          . reverse
          . sort
          . map pairLength
          . group
          . sort
          . filter (not . null)
          $ stamps
  
    display []  = ".\n"
    display [x] = " (" ++ x ++ ").\n"
    display xs  = ".\n" ++ unlines (map (++ ".") xs)
  
    pairLength xss@(xs:_) = (length xss, xs)
    entry (n, xs)         = percentage n ntest
                         ++ " "
                         ++ concat (intersperse ", " xs)
  
    percentage n m        = show ((100 * n) `div` m) ++ "%"
  
  --------------------------------------------------------------------
  -- the end.
  