意外地反向非二元函数会产生奇怪的行为

这是有问题的代码(也在lpaste.net上):

module Data.Graph.Dijkstra
       ( dijkstra
       , dijkstraPath
       ) where

-- Graph library import
import Data.Graph.Inductive hiding (dijkstra)

-- Priority queue import
import qualified Data.PQueue.Prio.Min as PQ

-- Standard imports
import Data.List (find)
import Data.Maybe (fromJust)
import Data.Monoid

-- Internal routine implementing Dijkstra's shortest paths
-- algorithm. Deemed internal because it needs to be kickstarted with
-- a singleton node queue. Based on FGL's current implementation of
-- Dijkstra.
dijkstraInternal ::
  (Graph gr, Ord b, Monoid b) => gr a b -> PQ.MinPQueue b [Node] -> [[Node]]
dijkstraInternal g q
  | PQ.null q = []
  | otherwise =
    case match v g of
      (Just cxt,g') -> p:dijkstraInternal  g' (PQ.unions (q' : expand cxt minDist p))
      (Nothing, g') -> dijkstraInternal g' q'
  where ((minDist,p@(v:_)), q') = PQ.deleteFindMin q
        expand (_,_,_,s) dist pathToC =
          map (\(edgeCost,n) -> PQ.singleton (dist `mappend` edgeCost) (n:pathToC)) s

-- Given a graph and a start node, returns a list of lists of nodes
-- corresponding to the shortest paths from the start to all other
-- nodes, where the edge costs are accumulated according to the Monoid
-- instance of the edge label type and costs are compared by the edge
-- label's Ord instance.
dijkstra :: (Graph gr, Ord b, Monoid b) => gr a b -> Node -> [[Node]]
dijkstra g start = dijkstraInternal g (PQ.singleton `mempty` [start])  -- !!!

dijkstraPath :: (Graph gr, Ord b, Monoid b) => gr a b -> Node -> Node -> [LNode a]
dijkstraPath g start goal =
  let paths = dijkstra g start
      pathNodes  = find ((goal ==) . head) paths -- Can paths be empty?
  in
   case pathNodes of
     Nothing -> []
     Just ps -> reverse $ map (\n -> (n, fromJust $ lab g n)) ps

奇怪的是在第39行,标有-- !!!评论.此代码编译,但运行时错误是无论如何,该PQ.singleton函数返回一个空的优先级队列.我意识到我不小心添加了反引号mempty,所以当我删除那些代码编译并按预期工作时.

然而这让我感到奇怪.如何用反引号正确编译代码mempty,这根本不是二进制函数(mempty :: a)？

在对#haskell提供了一些非常慷慨的帮助之后,我发现它与函数的Monoid实例有关:

instance Monoid b => Monoid (a -> b)

我现在非常模糊地理解为什么这个错误成功地进行了类型检查,但我仍然觉得在某种程度上受到了道德冤枉.有人能解释这是怎么发生的吗？

另外,我还想关注singleton我正在使用的优先级队列的功能:根据源,它不返回空队列.但是,在第24行,相同的优先级队列立即被评估为空.(我通过跟踪调用验证了这一点.)