{-# LANGUAGE FlexibleInstances #-}
import Data.Set (Set,elems,cartesianProduct,fromList,empty,insert,singleton,
                union,unions)

data CombinatorialProblem a = CP
  {
    bound :: Set a,
    close :: Set a -> Set a
  }

enumerate :: CombinatorialProblem a -> Set a
enumerate cp = iterate' f null (empty, singleton (close cp empty))
  where
    f (old, new) = (union old new, fromList fresh)
      where
        fresh = [close cp (insert a s) | a <- elems (bound cp), s <- elems new]

iterate' :: ((a,a) -> (a,a)) -> (a -> Bool) -> (a,a) -> a
iterate' f p x = let (x0,x1) = iterate'' x in x0
  where
    iterate'' x = if p (let (x0,x1) = x in x1) then x else iterate'' (f x)