path: root/tests/Properties.hs

{-# OPTIONS -fglasgow-exts #-}

import StackSet hiding (filter)
import Operations (tile)

import Debug.Trace
import Data.Word
import Graphics.X11.Xlib.Types (Rectangle(..),Position,Dimension)
import Data.Ratio
import Data.Maybe
import System.Environment
import Control.Exception    (assert)
import Control.Monad
import Test.QuickCheck hiding (promote)
import System.IO
import System.Random hiding (next)
import Text.Printf
import Data.List            (nub,sort,sortBy,group,sort,intersperse,genericLength)
import qualified Data.List as L
import Data.Char            (ord)
import Data.Map             (keys,elems)
import qualified Data.Map as M

-- ---------------------------------------------------------------------
-- QuickCheck properties for the StackSet

-- Some general hints for creating StackSet properties:
--
-- *  ops that mutate the StackSet are usually local
-- *  most ops on StackSet should either be trivially reversible, or 
--    idempotent, or both.

--
-- The all important Arbitrary instance for StackSet.
--
instance (Integral i, Integral s, Eq a, Arbitrary a) => Arbitrary (StackSet i a s) where
    arbitrary = do
        sz <- choose (1,10)     -- number of workspaces
        n  <- choose (0,sz-1)   -- pick one to be in focus
        sc <- choose (1,sz)     -- a number of physical screens
        ls <- vector sz         -- a vector of sz workspaces

        -- pick a random item in each stack to focus
        fs <- sequence [ if null s then return Nothing
                            else liftM Just (choose ((-1),length s-1))
                       | s <- ls ]

        return $ fromList (fromIntegral n, fromIntegral sc,fs,ls)
    coarbitrary = error "no coarbitrary for StackSet"


-- | fromList. Build a new StackSet from a list of list of elements,
-- keeping track of the currently focused workspace, and the total
-- number of workspaces. If there are duplicates in the list, the last
-- occurence wins.
--
-- 'o' random workspace
-- 'm' number of physical screens
-- 'fs' random focused window on each workspace
-- 'xs' list of list of windows
--
fromList :: (Integral i, Integral s, Eq a) => (i, s, [Maybe Int], [[a]]) -> StackSet i a s
fromList (_,_,_,[]) = error "Cannot build a StackSet from an empty list"

fromList (n,m,fs,xs) | n < 0 || n >= genericLength xs
                = error $ "Cursor index is out of range: " ++ show (n, length xs)
                  | m < 1 || m >  genericLength xs
                = error $ "Can't have more screens than workspaces: " ++ show (m, length xs)

fromList (o,m,fs,xs) =
    let s = view o $
                foldr (\(i,ys) s ->
                    foldr insertUp (view i s) ys)
                        (new [0..genericLength xs-1] m) (zip [0..] xs)
    in foldr (\f t -> case f of
                            Nothing -> t
                            Just i  -> foldr (const focusUp) t [0..i] ) s fs

------------------------------------------------------------------------

--
-- Just generate StackSets with Char elements.
--
type T = StackSet (NonNegative Int) Char Int

-- Useful operation, the non-local workspaces
hidden_spaces x = map workspace (visible x) ++ hidden x

-- Basic data invariants of the StackSet
--
-- With the new zipper-based StackSet, tracking focus is no longer an
-- issue: the data structure enforces focus by construction. 
--
-- But we still need to ensure there are no duplicates, and master/and
-- the xinerama mapping aren't checked by the data structure at all.
--
-- * no element should ever appear more than once in a StackSet
-- * the xinerama screen map should be:
--          -- keys should always index valid workspaces
--          -- monotonically ascending in the elements
-- * the current workspace should be a member of the xinerama screens
--
invariant (s :: T) = and
    -- no duplicates
    [ noDuplicates

    -- all this xinerama stuff says we don't have the right structure
--  , validScreens
--  , validWorkspaces
--  , inBounds
    ]

  where
    ws = concat [ focus t : up t ++ down t
                  | w <- workspace (current s) : map workspace (visible s) ++ hidden s
                  , t <- maybeToList (stack w)] :: [Char]
    noDuplicates = nub ws == ws

--  validScreens = monotonic . sort . M. . (W.current s : W.visible : W$ s

--  validWorkspaces = and [ w `elem` allworkspaces | w <- (M.keys . screens) s ]
--          where allworkspaces = map tag $ current s : prev s ++ next s

--  inBounds  = and [ w >=0 && w < size s | (w,sc) <- M.assocs (screens s) ]

monotonic []       = True
monotonic (x:[])   = True
monotonic (x:y:zs) | x == y-1  = monotonic (y:zs)
                   | otherwise = False

prop_invariant = invariant

-- and check other ops preserve invariants
prop_empty_I  (n :: Positive Int) = forAll (choose (1,fromIntegral n)) $ \m ->
        invariant $ new [0..fromIntegral n-1] m

prop_view_I (n :: NonNegative Int) (x :: T) =
    n `tagMember` x ==> invariant $ view (fromIntegral n) x

prop_focusUp_I (n :: NonNegative Int) (x :: T) =
    invariant $ foldr (const focusUp) x [1..n]
prop_focusDown_I (n :: NonNegative Int) (x :: T) =
    invariant $ foldr (const focusDown) x [1..n]

prop_focus_I (n :: NonNegative Int) (x :: T) =
    case peek x of
        Nothing -> True
        Just _  -> let w = focus . fromJust . stack . workspace . current $ foldr (const focusUp) x [1..n]
                   in invariant $ focusWindow w x

prop_insertUp_I n (x :: T) = invariant $ insertUp n x

prop_delete_I (x :: T) = invariant $
    case peek x of
        Nothing -> x
        Just i  -> delete i x

prop_swap_master_I (x :: T) = invariant $ swapMaster x

prop_swap_left_I  (n :: NonNegative Int) (x :: T) =
    invariant $ foldr (const swapUp ) x [1..n]
prop_swap_right_I (n :: NonNegative Int) (x :: T) =
    invariant $ foldr (const swapDown) x [1..n]

prop_shift_I (n :: NonNegative Int) (x :: T) =
    n `tagMember` x ==> invariant $ shift (fromIntegral n) x


-- ---------------------------------------------------------------------
-- 'new'

-- empty StackSets have no windows in them
prop_empty (NonEmptyNubList ns) (m :: Positive Int) =
       all (== Nothing) [ stack w | w <- workspace (current x)
                                        : map workspace (visible x) ++ hidden x ]

    where x = new ns (fromIntegral m) :: T

-- empty StackSets always have focus on first workspace
prop_empty_current (NonEmptyNubList ns) (m :: Positive Int) = tag (workspace $ current x) == head ns
    where x = new ns (fromIntegral m) :: T

-- no windows will be a member of an empty workspace
prop_member_empty i (NonEmptyNubList ns) (m :: Positive Int)
    = member i (new ns (fromIntegral m) :: T) == False

-- ---------------------------------------------------------------------
-- viewing workspaces

-- view sets the current workspace to 'n'
prop_view_current (x :: T) (n :: NonNegative Int) = i `tagMember` x ==>
    tag (workspace $ current (view i x)) == i
  where
    i = fromIntegral n

-- view *only* sets the current workspace, and touches Xinerama. 
-- no workspace contents will be changed.
prop_view_local  (x :: T) (n :: NonNegative Int) = i `tagMember` x ==>
    workspaces x == workspaces (view i x)
  where
    workspaces a = sortBy (\s t -> tag s `compare` tag t) $
                                    workspace (current a)
                                    : map workspace (visible a) ++ hidden a
    i = fromIntegral n

-- view should result in a visible xinerama screen
-- prop_view_xinerama (x :: T) (n :: NonNegative Int) = i `tagMember` x ==>
--     M.member i (screens (view i x))
--   where
--     i = fromIntegral n

-- view is idempotent
prop_view_idem (x :: T) (i :: NonNegative Int) = i `tagMember` x ==> view i (view i x) == (view i x)

-- view is reversible, though shuffles the order of hidden/visible
prop_view_reversible (i :: NonNegative Int) (x :: T) =
    i `tagMember` x ==> normal (view n (view i x)) == normal x
    where n  = tag (workspace $ current x)

-- normalise workspace list
normal s = s { hidden = sortBy g (hidden s), visible = sortBy f (visible s) }
    where
        f = \a b -> tag (workspace a) `compare` tag (workspace b)
        g = \a b -> tag a `compare` tag b

-- ---------------------------------------------------------------------
-- Xinerama

-- every screen should yield a valid workspace
-- prop_lookupWorkspace (n :: NonNegative Int) (x :: T) =
--       s < M.size (screens x) ==>
--       fromJust (lookupWorkspace s x) `elem` (map tag $ current x : prev x ++ next x)
--     where
--        s = fromIntegral n

-- ---------------------------------------------------------------------
-- peek/index

-- peek either yields nothing on the Empty workspace, or Just a valid window
prop_member_peek (x :: T) =
    case peek x of
        Nothing -> True {- then we don't know anything -}
        Just i  -> member i x

-- ---------------------------------------------------------------------
-- index

-- the list returned by index should be the same length as the actual
-- windows kept in the zipper
prop_index_length (x :: T) =
    case stack . workspace . current $ x of
        Nothing   -> length (index x) == 0
        Just it -> length (index x) == length (focus it : up it ++ down it)

-- ---------------------------------------------------------------------
-- rotating focus
--

-- master/focus
-- 
-- The tiling order, and master window, of a stack is unaffected by focus changes.
--
prop_focus_left_master (n :: NonNegative Int) (x::T) =
    index (foldr (const focusUp) x [1..n]) == index x
prop_focus_right_master (n :: NonNegative Int) (x::T) =
    index (foldr (const focusDown) x [1..n]) == index x
prop_focusWindow_master (n :: NonNegative Int) (x :: T) =
    case peek x of
        Nothing -> True
        Just _  -> let s = index x
                       i = fromIntegral n `mod` length s
                   in index (focusWindow (s !! i) x) == index x

-- shifting focus is trivially reversible
prop_focus_left  (x :: T) = (focusUp  (focusDown x)) == x
prop_focus_right (x :: T) = (focusDown (focusUp  x)) ==  x

-- focusWindow actually leaves the window focused...
prop_focusWindow_works (n :: NonNegative Int) (x :: T) =
    case peek x of
        Nothing -> True
        Just _  -> let s = index x
                       i = fromIntegral n `mod` length s
                   in (focus . fromJust . stack . workspace . current) (focusWindow (s !! i) x) == (s !! i)

-- rotation through the height of a stack gets us back to the start
prop_focus_all_l (x :: T) = (foldr (const focusUp) x [1..n]) == x
  where n = length (index x)
prop_focus_all_r (x :: T) = (foldr (const focusDown) x [1..n]) == x
  where n = length (index x)

-- prop_rotate_all (x :: T) = f (f x) == f x
--     f x' = foldr (\_ y -> rotate GT y) x' [1..n]

-- focus is local to the current workspace
prop_focus_local (x :: T) = hidden_spaces (focusDown x) == hidden_spaces x

prop_focusWindow_local (n :: NonNegative Int) (x::T ) =
    case peek x of
        Nothing -> True
        Just _  -> let s = index x
                       i = fromIntegral n `mod` length s
                   in hidden_spaces (focusWindow (s !! i) x) == hidden_spaces x

-- ---------------------------------------------------------------------
-- member/findIndex

--
-- For all windows in the stackSet, findIndex should identify the
-- correct workspace
--
prop_findIndex (x :: T) =
    and [ tag w == fromJust (findIndex i x)
        | w <- workspace (current x) : map workspace (visible x)  ++ hidden x
        , t <- maybeToList (stack w)
        , i <- focus t : up t ++ down t
        ]

-- ---------------------------------------------------------------------
-- 'insert'

-- inserting a item into an empty stackset means that item is now a member
prop_insert_empty i (NonEmptyNubList ns) (m :: Positive Int) = member i (insertUp i x)
    where x = new ns (fromIntegral m) :: T

-- insert should be idempotent
prop_insert_idem i (x :: T) = insertUp i x == insertUp i (insertUp i x)

-- insert when an item is a member should leave the stackset unchanged
prop_insert_duplicate i (x :: T) = member i x ==> insertUp i x == x

-- push shouldn't change anything but the current workspace
prop_insert_local (x :: T) i = not (member i x) ==> hidden_spaces x == hidden_spaces (insertUp i x)

-- Inserting a (unique) list of items into an empty stackset should
-- result in the last inserted element having focus.
prop_insert_peek (NonEmptyNubList ns) (m :: Positive Int) (NonEmptyNubList is) =
    peek (foldr insertUp x is) == Just (head is)
    where x = new ns (fromIntegral m) :: T

-- insert >> delete is the identity, when i `notElem` .
-- Except for the 'master', which is reset on insert and delete.
--
prop_insert_delete n x = not (member n x) ==> delete n (insertUp n y) == (y :: T)
    where
        y = swapMaster x -- sets the master window to the current focus.
                         -- otherwise, we don't have a rule for where master goes.

-- inserting n elements increases current stack size by n
prop_size_insert is (NonEmptyNubList ns) (m :: Positive Int) =
        size (foldr insertUp x ws ) ==  (length ws)
  where
    ws   = nub is
    x    = new ns (fromIntegral m) :: T
    size = length . index


-- ---------------------------------------------------------------------
-- 'delete'

-- deleting the current item removes it.
prop_delete x =
    case peek x of
        Nothing -> True
        Just i  -> not (member i (delete i x))
    where _ = x :: T

-- delete is reversible with 'insert'.
-- It is the identiy, except for the 'master', which is reset on insert and delete.
--
prop_delete_insert (x :: T) =
    case peek x of
        Nothing -> True
        Just n  -> insertUp n (delete n y) == y
    where
        y = swapMaster x

-- delete should be local
prop_delete_local (x :: T) = 
    case peek x of
        Nothing -> True
        Just i  -> hidden_spaces x == hidden_spaces (delete i x)

-- delete should not affect focus unless the focused element is what is being deleted
prop_delete_focus n (x :: T) = member n x && Just n /= peek x ==> peek (delete n x) == peek x

-- ---------------------------------------------------------------------
-- swapUp, swapDown, swapMaster: reordiring windows

-- swap is trivially reversible
prop_swap_left  (x :: T) = (swapUp  (swapDown x)) == x
prop_swap_right (x :: T) = (swapDown (swapUp  x)) ==  x
-- TODO swap is reversible
-- swap is reversible, but involves moving focus back the window with
-- master on it. easy to do with a mouse...
{-
prop_promote_reversible x b = (not . null . fromMaybe [] . flip index x . current $ x) ==>
                            (raiseFocus y . promote . raiseFocus z . promote) x == x
  where _            = x :: T
        dir          = if b then LT else GT
        (Just y)     = peek x
        (Just (z:_)) = flip index x . current $ x
-}

-- swap doesn't change focus
prop_swap_master_focus (x :: T) = peek x == (peek $ swapMaster x)
--    = case peek x of
--        Nothing -> True
--        Just f  -> focus (stack (workspace $ current (swap x))) == f
prop_swap_left_focus   (x :: T) = peek x == (peek $ swapUp   x)
prop_swap_right_focus  (x :: T) = peek x == (peek $ swapDown  x)

-- swap is local
prop_swap_master_local (x :: T) = hidden_spaces x == hidden_spaces (swapMaster x)
prop_swap_left_local   (x :: T) = hidden_spaces x == hidden_spaces (swapUp   x)
prop_swap_right_local  (x :: T) = hidden_spaces x == hidden_spaces (swapDown  x)

-- rotation through the height of a stack gets us back to the start
prop_swap_all_l (x :: T) = (foldr (const swapUp)  x [1..n]) == x
  where n = length (index x)
prop_swap_all_r (x :: T) = (foldr (const swapDown) x [1..n]) == x
  where n = length (index x)

prop_swap_master_idempotent (x :: T) = swapMaster (swapMaster x) == swapMaster x

-- ---------------------------------------------------------------------
-- shift

-- shift is fully reversible on current window, when focus and master
-- are the same. otherwise, master may move.
prop_shift_reversible i (x :: T) =
    i `tagMember` x ==> case peek y of
                          Nothing -> True
                          Just _  -> normal ((view n . shift n . view i . shift i) y) == normal y
    where
        y = swapMaster x
        n = tag (workspace $ current y)

------------------------------------------------------------------------
-- some properties for layouts:

-- 1 window should always be tiled fullscreen
{-
prop_tile_fullscreen rect = tile pct rect 1 1 == [rect]

-- multiple windows 
prop_tile_non_overlap rect windows nmaster = noOverlaps (tile pct rect nmaster windows)
  where _ = rect :: Rectangle

pct = 3 % 100

noOverlaps []  = True
noOverlaps [_] = True
noOverlaps xs  = and [ verts a `notOverlap` verts b
                     | a <- xs
                     , b <- filter (a /=) xs
                     ]
    where
      verts (Rectangle a b w h) = (a,b,a + fromIntegral w - 1, b + fromIntegral h - 1)

      notOverlap (left1,bottom1,right1,top1)
                 (left2,bottom2,right2,top2)
        =  (top1 < bottom2 || top2 < bottom1)
        || (right1 < left2 || right2 < left1)

-}

------------------------------------------------------------------------

main :: IO ()
main = do
    args <- getArgs
    let n = if null args then 100 else read (head args)
    (results, passed) <- liftM unzip $ mapM (\(s,a) -> printf "%-25s: " s >> a n) tests
    printf "Passed %d tests!\n" (sum passed)
    when (not . and $ results) $ fail "Not all tests passed!"
 where

    tests =
        [("StackSet invariants" , mytest prop_invariant)

        ,("empty: invariant"    , mytest prop_empty_I)
        ,("empty is empty"      , mytest prop_empty)
        ,("empty / current"     , mytest prop_empty_current)
        ,("empty / member"      , mytest prop_member_empty)

        ,("view : invariant"    , mytest prop_view_I)
        ,("view sets current"   , mytest prop_view_current)
        ,("view idempotent"     , mytest prop_view_idem)
        ,("view reversible"    , mytest prop_view_reversible)
--      ,("view / xinerama"     , mytest prop_view_xinerama)
        ,("view is local"       , mytest prop_view_local)

--      ,("valid workspace xinerama", mytest prop_lookupWorkspace)

        ,("peek/member "        , mytest prop_member_peek)

        ,("index/length"        , mytest prop_index_length)

        ,("focus left : invariant", mytest prop_focusUp_I)
        ,("focus right: invariant", mytest prop_focusDown_I)
        ,("focusWindow: invariant", mytest prop_focus_I)
        ,("focus left/master"   , mytest prop_focus_left_master)
        ,("focus right/master"  , mytest prop_focus_right_master)
        ,("focusWindow master"  , mytest prop_focusWindow_master)
        ,("focus left/right"    , mytest prop_focus_left)
        ,("focus right/left"    , mytest prop_focus_right)
        ,("focus all left  "    , mytest prop_focus_all_l)
        ,("focus all right "    , mytest prop_focus_all_r)
        ,("focus is local"      , mytest prop_focus_local)
        ,("focusWindow is local", mytest prop_focusWindow_local)
        ,("focusWindow works"   , mytest prop_focusWindow_works)

        ,("findIndex"           , mytest prop_findIndex)

        ,("insert: invariant"   , mytest prop_insertUp_I)
        ,("insert/new"          , mytest prop_insert_empty)
        ,("insert is idempotent", mytest prop_insert_idem)
        ,("insert is reversible", mytest prop_insert_delete)
        ,("insert is local"     , mytest prop_insert_local)
        ,("insert duplicates"   , mytest prop_insert_duplicate)
        ,("insert/peek "        , mytest prop_insert_peek)
        ,("insert/size"         , mytest prop_size_insert)

        ,("delete: invariant"   , mytest prop_delete_I)
        ,("delete/empty"        , mytest prop_empty)
        ,("delete/member"       , mytest prop_delete)
        ,("delete is reversible", mytest prop_delete_insert)
        ,("delete is local"     , mytest prop_delete_local)
        ,("delete/focus"        , mytest prop_delete_focus)

        ,("swapMaster: invariant", mytest prop_swap_master_I)
        ,("swapUp: invariant" , mytest prop_swap_left_I)
        ,("swapDown: invariant", mytest prop_swap_right_I)
        ,("swapMaster id on focus", mytest prop_swap_master_focus)
        ,("swapUp id on focus", mytest prop_swap_left_focus)
        ,("swapDown id on focus", mytest prop_swap_right_focus)
        ,("swapMaster is idempotent", mytest prop_swap_master_idempotent)
        ,("swap all left  "     , mytest prop_swap_all_l)
        ,("swap all right "     , mytest prop_swap_all_r)
        ,("swapMaster is local" , mytest prop_swap_master_local)
        ,("swapUp is local"   , mytest prop_swap_left_local)
        ,("swapDown is local"  , mytest prop_swap_right_local)

        ,("shift: invariant"    , mytest prop_shift_I)
        ,("shift is reversible" , mytest prop_shift_reversible)

{-
        ,("tile 1 window fullsize", mytest prop_tile_fullscreen)
        ,("tiles never overlap",    mytest prop_tile_non_overlap)
-}

        ]

------------------------------------------------------------------------
--
-- QC driver
--

debug = False

mytest :: Testable a => a -> Int -> IO (Bool, Int)
mytest a n = mycheck defaultConfig
    { configMaxTest=n
    , configEvery   = \n args -> let s = show n in s ++ [ '\b' | _ <- s ] } a
 -- , configEvery= \n args -> if debug then show n ++ ":\n" ++ unlines args else [] } a

mycheck :: Testable a => Config -> a -> IO (Bool, Int)
mycheck config a = do
    rnd <- newStdGen
    mytests config (evaluate a) rnd 0 0 []

mytests :: Config -> Gen Result -> StdGen -> Int -> Int -> [[String]] -> IO (Bool, Int)
mytests config gen rnd0 ntest nfail stamps
    | ntest == configMaxTest config = done "OK," ntest stamps >> return (True, ntest)
    | nfail == configMaxFail config = done "Arguments exhausted after" ntest stamps >> return (True, ntest)
    | otherwise               =
      do putStr (configEvery config ntest (arguments result)) >> hFlush stdout
         case ok result of
           Nothing    ->
             mytests config gen rnd1 ntest (nfail+1) stamps
           Just True  ->
             mytests config gen rnd1 (ntest+1) nfail (stamp result:stamps)
           Just False ->
             putStr ( "Falsifiable after "
                   ++ show ntest
                   ++ " tests:\n"
                   ++ unlines (arguments result)
                    ) >> hFlush stdout >> return (False, ntest)
     where
      result      = generate (configSize config ntest) rnd2 gen
      (rnd1,rnd2) = split rnd0

done :: String -> Int -> [[String]] -> IO ()
done mesg ntest stamps = 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) ++ "%"

------------------------------------------------------------------------

instance Arbitrary Char where
    arbitrary = choose ('a','z')
    coarbitrary n = coarbitrary (ord n)

instance Random Word8 where
  randomR = integralRandomR
  random = randomR (minBound,maxBound)

instance Arbitrary Word8 where
  arbitrary     = choose (minBound,maxBound)
  coarbitrary n = variant (fromIntegral ((fromIntegral n) `rem` 4))

instance Random Word64 where
  randomR = integralRandomR
  random = randomR (minBound,maxBound)

instance Arbitrary Word64 where
  arbitrary     = choose (minBound,maxBound)
  coarbitrary n = variant (fromIntegral ((fromIntegral n) `rem` 4))

integralRandomR :: (Integral a, RandomGen g) => (a,a) -> g -> (a,g)
integralRandomR  (a,b) g = case randomR (fromIntegral a :: Integer,
                                         fromIntegral b :: Integer) g of
                            (x,g) -> (fromIntegral x, g)

instance Arbitrary Position  where
    arbitrary = do n <- arbitrary :: Gen Word8
                   return (fromIntegral n)
    coarbitrary = undefined

instance Arbitrary Dimension where
    arbitrary = do n <- arbitrary :: Gen Word8
                   return (fromIntegral n)
    coarbitrary = undefined

instance Arbitrary Rectangle where
    arbitrary = do
        sx <- arbitrary
        sy <- arbitrary
        sw <- arbitrary
        sh <- arbitrary
        return $ Rectangle sx sy sw sh
    coarbitrary = undefined

instance Arbitrary Rational where
    arbitrary = do
        n <- arbitrary
        d' <- arbitrary
        let d =  if d' == 0 then 1 else d'
        return (n % d)
    coarbitrary = undefined

------------------------------------------------------------------------
-- QC 2

-- from QC2
-- | NonEmpty xs: guarantees that xs is non-empty.
newtype NonEmptyList a = NonEmpty [a]
 deriving ( Eq, Ord, Show, Read )

instance Arbitrary a => Arbitrary (NonEmptyList a) where
  arbitrary   = NonEmpty `fmap` (arbitrary `suchThat` (not . null))
  coarbitrary = undefined

newtype NonEmptyNubList a = NonEmptyNubList [a]
 deriving ( Eq, Ord, Show, Read )

instance (Eq a, Arbitrary a) => Arbitrary (NonEmptyNubList a) where
  arbitrary   = NonEmptyNubList `fmap` ((liftM nub arbitrary) `suchThat` (not . null))
  coarbitrary = undefined

type Positive a = NonZero (NonNegative a)

newtype NonZero a = NonZero a
 deriving ( Eq, Ord, Num, Integral, Real, Enum, Show, Read )

instance (Num a, Ord a, Arbitrary a) => Arbitrary (NonZero a) where
  arbitrary = fmap NonZero $ arbitrary `suchThat` (/= 0)
  coarbitrary = undefined

newtype NonNegative a = NonNegative a
 deriving ( Eq, Ord, Num, Integral, Real, Enum, Show, Read )

instance (Num a, Ord a, Arbitrary a) => Arbitrary (NonNegative a) where
  arbitrary =
    frequency
      [ (5, (NonNegative . abs) `fmap` arbitrary)
      , (1, return 0)
      ]
  coarbitrary = undefined

-- | Generates a value that satisfies a predicate.
suchThat :: Gen a -> (a -> Bool) -> Gen a
gen `suchThat` p =
  do mx <- gen `suchThatMaybe` p
     case mx of
       Just x  -> return x
       Nothing -> sized (\n -> resize (n+1) (gen `suchThat` p))

-- | Tries to generate a value that satisfies a predicate.
suchThatMaybe :: Gen a -> (a -> Bool) -> Gen (Maybe a)
gen `suchThatMaybe` p = sized (try 0 . max 1)
 where
  try _ 0 = return Nothing
  try k n = do x <- resize (2*k+n) gen
               if p x then return (Just x) else try (k+1) (n-1)