Test.QuickCheck does not generate random values ​​correctly

Question

I use Test.QuickCheck to generate random Sudoku puzzles.

data Sudoku = Sudoku { getSudoku :: [[Maybe Int]] } deriving (Show, Eq)

rows :: Sudoku -> [[Maybe Int]]
rows (Sudoku rs) = rs

--B1
printSudoku :: Sudoku -> IO ()
printSudoku s = do
    putStrLn . unlines . map (map (maybe '.' (head . show))) $ rows s

--C1
cell :: Gen (Maybe Int)
cell = suchThatMaybe (frequency [(90, choose (0,0)),(10, choose(1,9))]) (/=0)

--C2
instance Arbitrary Sudoku where
    arbitrary = do
        rows <- sequence [ sequence [ cell | j <- [1..9] ] | i <- [1..9] ]
        return (Sudoku rows)

--C3
prop_Sudoku :: Sudoku -> Bool
prop_Sudoku = isSudoku

checkRandomSudoku :: IO [Bool]
checkRandomSudoku = do
    s <- sample' (arbitrary :: Gen Sudoku)
    return $ map isSudoku s

The code is working fine. However, when I perform

a <- sample '(arbitrary :: Gen Sudoku)

sequence $ map printSudoku a

it returns something like this:

....5..3.
...4.....
...2.....
...5.....
.........
...33....
...5.....
...2.4...
.........

.........
.343.....
.........
......9.2
.........
45....5.1
.2......7
.7..88.34
.9....6..

....2..8.
.2121638.
.7.7...9.
4..45.6..
.....6.2.
..6.6....
53..9.6..
..9....7.
.47892...

.373411..
5...3282.
...45..9.
8989..18.
31.8113..
9..35.6..
4.685....
.4....39.
7..6.5.76

48.178.53
1.871.4.4
3165.17..
.1...7.59
.98126.51
6.6...775
9.4636952
.5..239..
372.....8

.34.73129
.5.8.27.1
344.34931
28.6.94.1
6327.3..8
3743.5496
93...7984
..82.8...
..3.54.93

273847853
5568.7465
832.73515
3766..6.7
.7.196256
1.96.9.3.
.7156.268
1615.196.
.392..633

731652284
863.8.768
31..5.5.6
961.5.467
1245.1159
5..275471
52.727759
6.656.849
99.72352.

which is obviously not random. The distribution of empty cells is initially very high, and then slowly decreases. Am I using the wrong function or the wrong? Thanks

Answer 1

The reason you see this behavior is because QuickCheck is trying to get more serious test cases. This is described in the resizing section of the manual.

suchThatMaybe , , . http://hackage.haskell.org/package/QuickCheck-2.6/docs/src/Test-QuickCheck-Gen.html#suchThatMaybe. :

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)

, suchThatMaybe n , n , .

sample' [0,2..20], suchThatMaybe.

, resize :

>>> a <- sample' $ (resize 2 arbitrary :: Gen Sudoku)
>>> sequence $ map printSudoku a
.....8.5.
.......4.
.........
4..25...5
......9..
....5....
........7
.....7...
...4.....

...5.....
.......4.
...6...6.
..14.....
...7...7.
....2....
.....6...
...4..572
.4.....6.

..6..8...
..4......
.........
......9..
839......
67..4....
.5.......
....5....
........3

4...1....
7..9.39..
....6....
...4.1...
.........
.........
..9....6.
.2.9...84
.....8...

.64......
..3.44...
4.......4
....1..8.
.9.......
34.......
.....6...
18.2..593
.4.7.....

.........
...8..6..
.2......5
...5.....
.2.......
........6
.3....13.
8.1.2..85
....5....

..7......
..67...5.
..6......
27....1.9
.9.......
78.....7.
......34.
.......2.
..81...81

3.1......
.........
.....6...
.........
.16.71...
.........
.2.......
.........
.....9.1.

..65..6.9
........5
..1.4....
....86...
.2..2..2.
.....9...
..6......
.........
...7..855

.......94
...14..8.
.....4...
...3....9
.........
.....5...
.5.......
45.....8.
..48.....

4........
......3..
5......4.
.4..6..2.
..3......
.........
..9......
6..9.....
....7....