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1. lmapWhenMissing :: forall b a (f :: Type -> Type) k x . (b -> a) -> WhenMissing f k a x -> WhenMissing f k b x

   containers	Data.Map.Merge.Lazy

   Map contravariantly over a WhenMissing f k _ x.

2. foldMapWithKey :: Monoid m => (k -> a -> m) -> Map k a -> m

   containers	Data.Map.Strict

   Fold the keys and values in the map using the given monoid, such that

   foldMapWithKey f = fold . mapWithKey f
   

   This can be an asymptotically faster than foldrWithKey or foldlWithKey for some monoids.

3. isProperSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Bool

   containers	Data.Map.Strict

   Is this a proper submap? (ie. a submap but not equal). Defined as (isProperSubmapOf = isProperSubmapOfBy (==)).

4. isProperSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool

   containers	Data.Map.Strict

   Is this a proper submap? (ie. a submap but not equal). The expression (isProperSubmapOfBy f m1 m2) returns True when keys m1 and keys m2 are not equal, all keys in m1 are in m2, and when f returns True when applied to their respective values. For example, the following expressions are all True:

   isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
   isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
   

   But the following are all False:

   isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
   isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
   isProperSubmapOfBy (<)  (fromList [(1,1)])       (fromList [(1,1),(2,2)])
   

5. isSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Bool

   containers	Data.Map.Strict

   This function is defined as (isSubmapOf = isSubmapOfBy (==)).

6. isSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool

   containers	Data.Map.Strict

   The expression (isSubmapOfBy f t1 t2) returns True if all keys in t1 are in tree t2, and when f returns True when applied to their respective values. For example, the following expressions are all True:

   isSubmapOfBy (==) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
   isSubmapOfBy (<=) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
   isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1),('b',2)])
   

   But the following are all False:

   isSubmapOfBy (==) (fromList [('a',2)]) (fromList [('a',1),('b',2)])
   isSubmapOfBy (<)  (fromList [('a',1)]) (fromList [('a',1),('b',2)])
   isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1)])
   

   Note that isSubmapOfBy (_ _ -> True) m1 m2 tests whether all the keys in m1 are also keys in m2.

7. foldMapWithKey :: Monoid m => (k -> a -> m) -> Map k a -> m

   containers	Data.Map.Strict.Internal

   Fold the keys and values in the map using the given monoid, such that

   foldMapWithKey f = fold . mapWithKey f
   

   This can be an asymptotically faster than foldrWithKey or foldlWithKey for some monoids.

8. isProperSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Bool

   containers	Data.Map.Strict.Internal

   Is this a proper submap? (ie. a submap but not equal). Defined as (isProperSubmapOf = isProperSubmapOfBy (==)).

9. isProperSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool

   containers	Data.Map.Strict.Internal

   Is this a proper submap? (ie. a submap but not equal). The expression (isProperSubmapOfBy f m1 m2) returns True when keys m1 and keys m2 are not equal, all keys in m1 are in m2, and when f returns True when applied to their respective values. For example, the following expressions are all True:

   isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
   isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
   

   But the following are all False:

   isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
   isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
   isProperSubmapOfBy (<)  (fromList [(1,1)])       (fromList [(1,1),(2,2)])
   

10. isSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Bool

    containers	Data.Map.Strict.Internal

    This function is defined as (isSubmapOf = isSubmapOfBy (==)).

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