Hi, I just read the API of Data.Map and the source code of it. The documentation of "insertWithKey" is not precise. The following is copied from API. *insertWithKey* :: Ord http://www.haskell.org/ghc/docs/6.4/html/libraries/base/Prelude.html#t%3AOrd k => (k -> a -> a -> a) -> k -> a -> Map http://www.haskell.org/ghc/docs/6.4/html/libraries/base/Data.Map.html#t%3AMa... k a -> Map http://www.haskell.org/ghc/docs/6.4/html/libraries/base/Data.Map.html#t%3AMa... k a /O(log n)/. Insert with a combining function. This function take a function to solve collision, which can be considered as an operator. However the documentation does not specify the order of arguments to the operator. Because of that we can only supply operator which is communitive. But we all know that there must exist an ordering of arguments. I explored the source code of it as the following. -- | /O(log n)/. Insert with a combining function. insertWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a insertWithKey f kx x t = case t of Tip -> singleton kx x Bin sy ky y l r -> case compare kx ky of LT -> balance ky y (insertWithKey f kx x l) r GT -> balance ky y l (insertWithKey f kx x r) EQ -> Bin sy ky (f ky x y) l r By the last line the ordering is clear such that the inserted value goes the first. Shiqi Cao