How to use 'oneof' in quickCheck (Haskell) - haskell

Question

I am trying to write a prop that changes a Sudoku and then checks if it's still valid.
However, I am not sure how to use the "oneof"-function properly. Can you give me some hints, please?
prop_candidates :: Sudoku -> Bool
prop_candidates su = isSudoku newSu && isOkay newSu
where
newSu = update su aBlank aCandidate
aCandidate = oneof [return x | x <- candidates su aBlank]
aBlank = oneof [return x | x <- (blanks su)]
Here are some more info...
type Pos = (Int, Int)
update :: Sudoku -> Pos -> Maybe Int -> Sudoku
blanks :: Sudoku -> [Pos]
candidates :: Sudoku -> Pos -> [Int]
[return x | x <- (blanks example)] :: (Monad m) => [m Pos]
I have struggeled with this prop for 3 hours now, so any ideas are welcome!

Answer 1

What I was driving at is that you have a type mix-up. Namely, aBlank is not a Pos, but a Gen Pos, so update su aBlank aCandidate makes no sense! In fact, what you want is a way to generate a new sudoku given an initial sudoku; in other words a function
similarSudoku :: Sudoku -> Gen Sudoku
Now we can write it:
similarSudoku su = do aBlank <- elements (blanks su)
-- simpler than oneOf [return x | x <- blanks su]
aCandidate <- elements (candidates su aBlank)
return (update su aBlank aCandidate)
or even simpler:
similarSudoku su = liftM2 (update su) (elements (blanks su)) (elements (candidates su aBlank))
And the property looks like
prop_similar :: Sudoku -> Gen Bool
prop_similar su = do newSu <- similarSudoku su
return (isSudoku newSu && isOkay newSu)
Since there are instances
Testable Bool
Testable prop => Testable (Gen prop)
(Arbitrary a, Show a, Testable prop) => Testable (a -> prop)
Sudoku -> Gen Bool is Testable as well (assuming instance Arbitrary Sudoku).

Answer 2

On my blog, I wrote a simple craps simulator with QuickCheck tests that use oneof to generate interesting rolls.
Say we have a super-simple Sudoku of a single row:
module Main where
import Control.Monad
import Data.List
import Test.QuickCheck
import Debug.Trace
type Pos = Int
data Sudoku = Sudoku [Char] deriving (Show)
No super-simple Sudoku should have repeated values:
prop_noRepeats :: Sudoku -> Bool
prop_noRepeats s#(Sudoku xs) =
trace (show s) $ all ((==1) . length) $
filter ((/='.') . head) $
group $ sort xs
You might generate a super-simple Sudoku with
instance Arbitrary Sudoku where
arbitrary = sized board :: Gen Sudoku
where board :: Int -> Gen Sudoku
board 0 = Sudoku `liftM` shuffle values
board n | n > 6 = resize 6 arbitrary
| otherwise =
do xs <- shuffle values
let removed = take n xs
dots = take n $ repeat '.'
remain = values \\ removed
ys <- shuffle $ dots ++ remain
return $ Sudoku ys
values = ['1' .. '9']
shuffle :: (Eq a) => [a] -> Gen [a]
shuffle [] = return []
shuffle xs = do x <- oneof $ map return xs
ys <- shuffle $ delete x xs
return (x:ys)
The trace is there to show the randomly generated boards:
*Main> quickCheck prop_noRepeats
Sudoku "629387451"
Sudoku "91.235786"
Sudoku "1423.6.95"
Sudoku "613.4..87"
Sudoku "6..5..894"
Sudoku "7.2..49.."
Sudoku "24....1.."
[...]
+++ OK, passed 100 tests.

Answer 3

it seems that aBlank :: Gen Pos which does not match the way it is used as an argument of candidates :: Sudoku -> Pos -> [Int].
I've been looking through here to find a way to convert Gen a to a which would allow you to use it with candidates. The best i could see is the generate function.
Tell me if I'm missing something...