+-- | Fold through all elements less than or equal to the supplied key,
+-- in decreasing order.
+foldFM_LE :: Ord key => (key -> elt -> a -> a) -> a -> key ->
+ FiniteMap key elt -> a
+foldFM_LE k z fr EmptyFM = z
+foldFM_LE k z fr (Branch key elt _ fm_l fm_r)
+ | key <= fr = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r
+ | otherwise = foldFM_LE k z fr fm_l
+
+-- | List elements greater than or equal to the supplied key, in decreasing
+-- order
+fmToList_LE :: Ord key => FiniteMap key elt -> key -> [(key,elt)]
+fmToList_LE fm fr = foldFM_LE (\ key elt rest -> (key,elt) : rest) [] fr fm
+
+-- | List keys greater than or equal to the supplied key, in decreasing order
+keysFM_LE :: Ord key => FiniteMap key elt -> key -> [key]
+keysFM_LE fm fr = foldFM_LE (\ key elt rest -> key : rest) [] fr fm
+
+-- | List elements corresponding to keys greater than or equal to the supplied
+-- key, in decreasing order of key.
+eltsFM_LE :: Ord key => FiniteMap key elt -> key -> [elt]
+eltsFM_LE fm fr = foldFM_LE (\ key elt rest -> elt : rest) [] fr fm
+
+-- ---------------------------------------------------------------------------
+-- Getting minimum and maximum key out.
+-- ---------------------------------------------------------------------------
+
+-- | Extract minimum key, or Nothing if the map is empty.
+minFM :: Ord key => FiniteMap key elt -> Maybe key
+minFM EmptyFM = Nothing
+minFM (Branch key _ _ fm_l _) =
+ case minFM fm_l of
+ Nothing -> Just key
+ Just key1 -> Just key1
+
+-- | Extract maximum key, or Nothing if the map is empty.
+maxFM :: Ord key => FiniteMap key elt -> Maybe key
+maxFM EmptyFM = Nothing
+maxFM (Branch key _ _ _ fm_r) =
+ case maxFM fm_r of
+ Nothing -> Just key
+ Just key1 -> Just key1
+
+