{-# LANGUAGE RankNTypes #-}

module Main where

import qualified Data.List as List
import qualified Data.Set as Set

{- TYPES: -}

-- PQ new push pop
-- by intention there is no build-in way to tell if the queue is empty
data PriorityQueue q t = PQ (q t) (t -> q t -> q t) (q t -> (t, q t))
-- there is a concrete way for a particular queue, e.g. List.null
type ListPriorityQueue t = PriorityQueue [] t
-- but there is no method in the abstract setting
newtype AbstractPriorityQueue q = APQ (forall t. Ord t => PriorityQueue q t)


{- SOLUTIONS: -}

-- the basic version
list_selection_sort :: ListPriorityQueue t -> [t] -> [t]
list_selection_sort (PQ new push pop) list = List.unfoldr mypop (List.foldr push new list)
  where
    mypop [] = Nothing -- this is possible because we know that the queue is represented by a list
    mypop ls = Just (pop ls)


-- here we abstract the queue, so we need to keep the queue size ourselves
abstract_selection_sort :: Ord t => AbstractPriorityQueue q -> [t] -> [t]
abstract_selection_sort (APQ (PQ new push pop)) list = List.unfoldr mypop (List.foldr mypush (0,new) list)
  where
    mypush t (n, q) = (n+1, push t q)
    mypop (0, q) = Nothing
    mypop (n, q) = let (t, q') = pop q in Just (t, (n-1, q'))


-- here we generalize the first solution to all the queues that allow checking if the queue is empty
class EmptyCheckable q where
  is_empty :: q -> Bool

generalized_selection_sort :: EmptyCheckable (q t) => PriorityQueue q t -> [t] -> [t]
generalized_selection_sort (PQ new push pop) list = List.unfoldr mypop (List.foldr push new list)
  where
    mypop q | is_empty q = Nothing
    mypop q | otherwise  = Just (pop q)


{- EXAMPLES: -}

-- priority queue based on lists
priority_queue_1 :: Ord t => ListPriorityQueue t
priority_queue_1 = PQ [] List.insert (\ls -> (head ls, tail ls))
instance EmptyCheckable [t] where
  is_empty = List.null

-- priority queue based on sets
priority_queue_2 :: Ord t => PriorityQueue Set.Set t
priority_queue_2 = PQ Set.empty Set.insert Set.deleteFindMin
instance EmptyCheckable (Set.Set t) where
  is_empty = Set.null

-- an arbitrary type and a queue specially designed for it
data ABC = A | B | C deriving (Eq, Ord, Show)

-- priority queue based on counting
data PQ3 t = PQ3 Integer Integer Integer
priority_queue_3 :: PriorityQueue PQ3 ABC
priority_queue_3 = PQ new push pop
  where
    new = (PQ3 0 0 0)
    push A (PQ3 a b c) = (PQ3 (a+1) b c)
    push B (PQ3 a b c) = (PQ3 a (b+1) c)
    push C (PQ3 a b c) = (PQ3 a b (c+1))
    pop (PQ3 0 0 0) = undefined
    pop (PQ3 0 0 c) = (C, (PQ3 0 0 (c-1)))
    pop (PQ3 0 b c) = (B, (PQ3 0 (b-1) c))
    pop (PQ3 a b c) = (A, (PQ3 (a-1) b c))

instance EmptyCheckable (PQ3 t) where
  is_empty (PQ3 0 0 0) = True
  is_empty _ = False


{- MAIN: -}

main :: IO ()
main = do
  print $ list_selection_sort priority_queue_1 [2, 3, 1]
  -- print $ list_selection_sort priority_queue_2 [2, 3, 1] -- fail
  -- print $ list_selection_sort priority_queue_3 [B, C, A] -- fail
  print $ abstract_selection_sort (APQ priority_queue_1) [B, C, A] -- APQ hides the queue
  print $ abstract_selection_sort (APQ priority_queue_2) [B, C, A] -- behind the layer of abstraction
  -- print $ abstract_selection_sort (APQ priority_queue_3) [B, C, A] -- fail
  print $ generalized_selection_sort priority_queue_1 [2, 3, 1]
  print $ generalized_selection_sort priority_queue_2 [B, C, A]
  print $ generalized_selection_sort priority_queue_3 [B, C, A]-- power of generalization

  -- fail
  -- print $ let f q = (list_selection_sort q [2,3,1], list_selection_sort q [B,C,A])
  --         in f priority_queue_1

  -- power of abstraction (rank-n-types actually, but never mind)
  print $ let f q = (abstract_selection_sort q [2,3,1], abstract_selection_sort q [B,C,A])
          in f (APQ priority_queue_1)

  -- fail
  -- print $ let f q = (generalized_selection_sort q [2,3,1], generalized_selection_sort q [B,C,A])
  --         in f priority_queue_1