map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]

map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]

- You will eventually need all the values stored.
- The stored values don't represent large virtual data structures to be lazily computed.

import qualified Data.Map as MapThe implementation of Map is based on

- Stephen Adams, "
*Efficient sets: a balancing act*", Journal of Functional Programming 3(4):553-562, October 1993, http://www.swiss.ai.mit.edu/~adams/BB/. - J. Nievergelt and E.M. Reingold, "
*Binary search trees of bounded balance*", SIAM journal of computing 2(1), March 1973.

- Guy Blelloch, Daniel Ferizovic, and Yihan Sun, "
*Just Join for Parallel Ordered Sets*", https://arxiv.org/abs/1602.02120v3.

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

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")])

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")])

let f k a = if k < 5 then Left (k * 2) else Right (a ++ a) mapEitherWithKey f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) == (fromList [(1,2), (3,6)], fromList [(5,"aa"), (7,"zz")]) mapEitherWithKey (\_ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) == (empty, fromList [(1,"x"), (3,"b"), (5,"a"), (7,"z")])

Map covariantly over a `WhenMatched f k x`, using only a
'Functor f' constraint.

Map covariantly over a `WhenMissing f x`, using only a
'Functor f' constraint.

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"

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

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

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"

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

Map over the entries whose keys are missing from the other map,
optionally removing some. This is the most powerful
SimpleWhenMissing tactic, but others are usually more
efficient.
`mapMaybeMissing` uses fewer unnecessary Applicative
operations.

mapMaybeMissing :: (Key -> x -> Maybe y) -> SimpleWhenMissing x y

mapMaybeMissing f = traverseMaybeMissing (\k x -> pure (f k x))but

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

Map over the entries whose keys are missing from the other map.
`mapMissing` is somewhat faster.

mapMissing :: (k -> x -> y) -> SimpleWhenMissing x y

mapMissing f = mapMaybeMissing (\k x -> Just $ f k x)but

Map covariantly over a `WhenMatched f x y`.

Map covariantly over a `WhenMissing f x`.

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

Map over the entries whose keys are missing from the other map,
optionally removing some. This is the most powerful
SimpleWhenMissing tactic, but others are usually more
efficient.
`mapMaybeMissing` uses fewer unnecessary Applicative
operations.

mapMaybeMissing :: (k -> x -> Maybe y) -> SimpleWhenMissing k x y

mapMaybeMissing f = traverseMaybeMissing (\k x -> pure (f k x))but

Map over the entries whose keys are missing from the other map.
`mapMissing` is somewhat faster.

mapMissing :: (k -> x -> y) -> SimpleWhenMissing k x y

mapMissing f = mapMaybeMissing (\k x -> Just $ f k x)but