How to use 'oneof' in quickCheck (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!

Overtask

Well, what is the type of update? And what do you think will the types of aCandidate and aBlank be? – Araliaceous

I have edited the post, can you please take a look again? – Overtask

Now, check what is the type of [return x | x <- (blanks su)] and therefore of aBlank. – Araliaceous

[return x | x <- (blanks example)] :: (Monad m) => [m Pos] – Overtask

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).

Araliaceous

Does not really work either, but it was very helpful so I'll accept it as an answer. – Overtask

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.

Colwin

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...

Stambul

Well, yes. You don't want to convert a Gen a to a; you want to "lift" candidates instead. – Araliaceous

makes sense. going monadic is the solution. – Stambul