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1. mapKeys :: Ord k2 => (k1 -> k2) -> Map k1 a -> Map k2 a

   containers	Data.Map.Strict

   mapKeys f s is the map obtained by applying f to each key of s. The size of the result may be smaller if f maps two or more distinct keys to the same new key. In this case the value at the greatest of the original keys is retained.

   mapKeys (+ 1) (fromList [(5,"a"), (3,"b")])                        == fromList [(4, "b"), (6, "a")]
   mapKeys (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "c"
   mapKeys (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "c"
   

2. mapKeysMonotonic :: (k1 -> k2) -> Map k1 a -> Map k2 a

   containers	Data.Map.Strict

   mapKeysMonotonic f s == mapKeys f s, but works only when f is strictly monotonic. That is, for any values x and y, if x < y then f x < f y. The precondition is not checked. Semi-formally, we have:

   and [x < y ==> f x < f y | x <- ls, y <- ls]
   ==> mapKeysMonotonic f s == mapKeys f s
   where ls = keys s
   

   This means that f maps distinct original keys to distinct resulting keys. This function has better performance than mapKeys.

   mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")]) == fromList [(6, "b"), (10, "a")]
   valid (mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")])) == True
   valid (mapKeysMonotonic (\ _ -> 1)     (fromList [(5,"a"), (3,"b")])) == False
   

3. mapKeysWith :: Ord k2 => (a -> a -> a) -> (k1 -> k2) -> Map k1 a -> Map k2 a

   containers	Data.Map.Strict

   mapKeysWith c f s is the map obtained by applying f to each key of s. The size of the result may be smaller if f maps two or more distinct keys to the same new key. In this case the associated values will be combined using c. The value at the greater of the two original keys is used as the first argument to c.

   mapKeysWith (++) (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "cdab"
   mapKeysWith (++) (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "cdab"
   

   Also see the performance note on fromListWith.

4. mapMaybe :: (a -> Maybe b) -> Map k a -> Map k b

   containers	Data.Map.Strict

   Map values and collect the Just results.

   let f x = if x == "a" then Just "new a" else Nothing
   mapMaybe f (fromList [(5,"a"), (3,"b")]) == singleton 5 "new a"
   

5. mapMaybeWithKey :: (k -> a -> Maybe b) -> Map k a -> Map k b

   containers	Data.Map.Strict

   Map keys/values and collect the Just results.

   let f k _ = if k < 5 then Just ("key : " ++ (show k)) else Nothing
   mapMaybeWithKey f (fromList [(5,"a"), (3,"b")]) == singleton 3 "key : 3"
   

6. mapWithKey :: (k -> a -> b) -> Map k a -> Map k b

   containers	Data.Map.Strict

   Map a function over all values in the map.

   let f key x = (show key) ++ ":" ++ x
   mapWithKey f (fromList [(5,"a"), (3,"b")]) == fromList [(3, "3:b"), (5, "5:a")]
   

7. mapAccum :: (a -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)

   containers	Data.Map.Strict.Internal

   The function mapAccum threads an accumulating argument through the map in ascending order of keys.

   let f a b = (a ++ b, b ++ "X")
   mapAccum f "Everything: " (fromList [(5,"a"), (3,"b")]) == ("Everything: ba", fromList [(3, "bX"), (5, "aX")])
   

8. mapAccumRWithKey :: (a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)

   containers	Data.Map.Strict.Internal

   The function mapAccumRWithKey threads an accumulating argument through the map in descending order of keys.

9. mapAccumWithKey :: (a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)

   containers	Data.Map.Strict.Internal

   The function mapAccumWithKey threads an accumulating argument through the map in ascending order of keys.

   let f a k b = (a ++ " " ++ (show k) ++ "-" ++ b, b ++ "X")
   mapAccumWithKey f "Everything:" (fromList [(5,"a"), (3,"b")]) == ("Everything: 3-b 5-a", fromList [(3, "bX"), (5, "aX")])
   

10. mapEither :: (a -> Either b c) -> Map k a -> (Map k b, Map k c)

    containers	Data.Map.Strict.Internal

    Map values and separate the Left and Right results.

    let f a = if a < "c" then Left a else Right a
    mapEither f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
    == (fromList [(3,"b"), (5,"a")], fromList [(1,"x"), (7,"z")])
    
    mapEither (\ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
    == (empty, fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
    

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