-- | Core data type for the game.

> module Core.Constraints
>     ( Constraints
>     , initConstraints
>     , setSum
>     , solutions
>     , distribution
>     , clearProb
>     ) where

> import Data.SetClass (fromList, size)

> import Core.Square
> import Core.BitField
> import Core.SetContainer
> import Core.Constraint

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

> type Constraints 
>   = CachedSize
>       (Maybe 
>           (EitherC Clear
>               (EitherC Bomb
>                   [Constraint SquareSet]
>               )
>           )
>       )

> solutions :: Constraints -> Integer
> solutions = numOfLayouts

> setSum :: SquareSet -> Int -> Constraints -> Constraints
> setSum ps v c
>     = addConstraint ps v c


> initConstraints :: Board -> Int -> Constraints
> initConstraints s m 
>     = newLayout (squares s) m

> clearProb :: Square -> Constraints -> Rational
> clearProb p g
>    = fromIntegral (solutions $ setSum (fromList [p]) 0 g) / fromIntegral (solutions g)

> distribution :: SquareSet -> Constraints -> [Constraints]
> distribution ps cs 
>     = at ((/=0) . solutions) 
>          (takeWhile ((/=0) . solutions))
>          [setSum ps i cs | i<-[0..size ps]]


Auxiliary
---------

> foldrUntil :: (a -> Bool) -> (a -> b -> b) -> ([a] -> b) -> [a] -> b
> foldrUntil p c n (x:xs) | p x = x `c` foldrUntil p c n xs
> foldrUntil _ _ n xs = n xs

> at :: (a -> Bool) -> ([a] -> [a]) -> [a] -> [a]
> at p = foldrUntil (not . p) (:)