{-# 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 :: Ord a => CombinatorialProblem a -> Set (Set a)
enumerate cp = iterate' f null (empty, singleton (close cp empty) :: Set (Set a))
  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)



minimal.hs:12:40: error:
    • Couldn't match type ‘a1’ with ‘a’
      ‘a1’ is a rigid type variable bound by
        an expression type signature:
          forall a1. Set (Set a1)
        at minimal.hs:12:70-80
      ‘a’ is a rigid type variable bound by
        the type signature for:
          enumerate :: forall a.
                       Ord a =>
                       CombinatorialProblem a -> Set (Set a)
        at minimal.hs:11:1-59
      Expected type: Set (Set a1)
        Actual type: Set (Set a)
    • In the expression: singleton (close cp empty) :: Set (Set a)
      In the third argument of ‘iterate'’, namely
        ‘(empty, singleton (close cp empty) :: Set (Set a))’
      In the expression:
        iterate' f null (empty, singleton (close cp empty) :: Set (Set a))
    • Relevant bindings include
        f :: (Set (Set a), Set (Set a)) -> (Set (Set a), Set (Set a))
          (bound at minimal.hs:14:5)
        cp :: CombinatorialProblem a (bound at minimal.hs:12:11)
        enumerate :: CombinatorialProblem a -> Set (Set a)
          (bound at minimal.hs:12:1)
   |
12 | enumerate cp = iterate' f null (empty, singleton (close cp empty) :: Set (Set a))
   |