Data.Map.Lazy

containers-0.6.0.1: Assorted concrete container types

Copyright | (c) Daan Leijen 2002 (c) Andriy Palamarchuk 2008
License | BSD-style
Maintainer | libraries@haskell.org
Portability | portable
Safe Haskell | Safe
Language | Haskell98

Data.Map.Lazy

Contents

- Map type
- Construction
  - From Unordered Lists
  - From Ascending Lists
  - From Descending Lists
- Insertion
- Deletion/Update
- Query
  - Lookup
  - Size
- Combine
  - Union
  - Difference
  - Intersection
  - General combining functions
  - Unsafe general combining function
- Traversal
  - Map
- Folds
  - Strict folds
- Conversion
  - Lists
  - Ordered lists
- Filter
- Submap
- Indexed
- Min/Max
- Debugging

Description

# Finite Maps (lazy interface)

The ``Map` k v` type represents a finite map (sometimes called a dictionary) from keys of type `k` to values of type `v`. A `Map` is strict in its keys but lazy in its values.

The functions in Data.Map.Strict are careful to force values before installing them in a `Map`. This is usually more efficient in cases where laziness is not essential. The functions in this module do not do so.

When deciding if this is the correct data structure to use, consider:

- If you are using `Int` keys, you will get much better performance for most operations using Data.IntMap.Lazy.
- If you don't care about ordering, consider using `Data.HashMap.Lazy` from the unordered-containers package instead.

For a walkthrough of the most commonly used functions see the maps introduction.

This module is intended to be imported qualified, to avoid name clashes with Prelude functions:

    import qualified Data.Map.Lazy as Map

Note that the implementation is generally left-biased. Functions that take two maps as arguments and combine them, such as `union` and `intersection`, prefer the values in the first argument to those in the second.

## Detailed performance information

The amortized running time is given for each operation, with n referring to the number of entries in the map.

Benchmarks comparing Data.Map.Lazy with other dictionary implementations can be found at https://github.com/haskell-perf/dictionaries.

## Warning

The size of a `Map` must not exceed `maxBound::Int`. Violation of this condition is not detected and if the size limit is exceeded, its behaviour is undefined.

## Implementation

The implementation of `Map` is based on size balanced binary trees (or trees of bounded balance) as described by:

- 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.

Bounds for `union`, `intersection`, and `difference` are as given by

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

Synopsis

- data Map k a
- empty :: Map k a
- singleton :: k -> a -> Map k a
- fromSet :: (k -> a) -> Set k -> Map k a
- fromList :: Ord k => [(k, a)] -> Map k a
- fromListWith :: Ord k => (a -> a -> a) -> [(k, a)] -> Map k a
- fromListWithKey :: Ord k => (k -> a -> a -> a) -> [(k, a)] -> Map k a
- fromAscList :: Eq k => [(k, a)] -> Map k a
- fromAscListWith :: Eq k => (a -> a -> a) -> [(k, a)] -> Map k a
- fromAscListWithKey :: Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a
- fromDistinctAscList :: [(k, a)] -> Map k a
- fromDescList :: Eq k => [(k, a)] -> Map k a
- fromDescListWith :: Eq k => (a -> a -> a) -> [(k, a)] -> Map k a
- fromDescListWithKey :: Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a
- fromDistinctDescList :: [(k, a)] -> Map k a
- insert :: Ord k => k -> a -> Map k a -> Map k a
- insertWith :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
- insertWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
- insertLookupWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> (Maybe a, Map k a)
- delete :: Ord k => k -> Map k a -> Map k a
- adjust :: Ord k => (a -> a) -> k -> Map k a -> Map k a
- adjustWithKey :: Ord k => (k -> a -> a) -> k -> Map k a -> Map k a
- update :: Ord k => (a -> Maybe a) -> k -> Map k a -> Map k a
- updateWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a
- updateLookupWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> (Maybe a, Map k a)
- alter :: Ord k => (Maybe a -> Maybe a) -> k -> Map k a -> Map k a
- alterF :: (Functor f, Ord k) => (Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a)
- lookup :: Ord k => k -> Map k a -> Maybe a
- (!?) :: Ord k => Map k a -> k -> Maybe a
- (!) :: Ord k => Map k a -> k -> a
- findWithDefault :: Ord k => a -> k -> Map k a -> a
- member :: Ord k => k -> Map k a -> Bool
- notMember :: Ord k => k -> Map k a -> Bool
- lookupLT :: Ord k => k -> Map k v -> Maybe (k, v)
- lookupGT :: Ord k => k -> Map k v -> Maybe (k, v)
- lookupLE :: Ord k => k -> Map k v -> Maybe (k, v)
- lookupGE :: Ord k => k -> Map k v -> Maybe (k, v)
- null :: Map k a -> Bool
- size :: Map k a -> Int
- union :: Ord k => Map k a -> Map k a -> Map k a
- unionWith :: Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a
- unionWithKey :: Ord k => (k -> a -> a -> a) -> Map k a -> Map k a -> Map k a
- unions :: (Foldable f, Ord k) => f (Map k a) -> Map k a
- unionsWith :: (Foldable f, Ord k) => (a -> a -> a) -> f (Map k a) -> Map k a
- difference :: Ord k => Map k a -> Map k b -> Map k a
- (\\) :: Ord k => Map k a -> Map k b -> Map k a
- differenceWith :: Ord k => (a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a
- differenceWithKey :: Ord k => (k -> a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a
- intersection :: Ord k => Map k a -> Map k b -> Map k a
- intersectionWith :: Ord k => (a -> b -> c) -> Map k a -> Map k b -> Map k c
- intersectionWithKey :: Ord k => (k -> a -> b -> c) -> Map k a -> Map k b -> Map k c
- mergeWithKey :: Ord k => (k -> a -> b -> Maybe c) -> (Map k a -> Map k c) -> (Map k b -> Map k c) -> Map k a -> Map k b -> Map k c
- map :: (a -> b) -> Map k a -> Map k b
- mapWithKey :: (k -> a -> b) -> Map k a -> Map k b
- traverseWithKey :: Applicative t => (k -> a -> t b) -> Map k a -> t (Map k b)
- traverseMaybeWithKey :: Applicative f => (k -> a -> f (Maybe b)) -> Map k a -> f (Map k b)
- mapAccum :: (a -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)
- mapAccumWithKey :: (a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)
- mapAccumRWithKey :: (a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)
- mapKeys :: Ord k2 => (k1 -> k2) -> Map k1 a -> Map k2 a
- mapKeysWith :: Ord k2 => (a -> a -> a) -> (k1 -> k2) -> Map k1 a -> Map k2 a
- mapKeysMonotonic :: (k1 -> k2) -> Map k1 a -> Map k2 a
- foldr :: (a -> b -> b) -> b -> Map k a -> b
- foldl :: (a -> b -> a) -> a -> Map k b -> a
- foldrWithKey :: (k -> a -> b -> b) -> b -> Map k a -> b
- foldlWithKey :: (a -> k -> b -> a) -> a -> Map k b -> a
- foldMapWithKey :: Monoid m => (k -> a -> m) -> Map k a -> m
- foldr' :: (a -> b -> b) -> b -> Map k a -> b
- foldl' :: (a -> b -> a) -> a -> Map k b -> a
- foldrWithKey' :: (k -> a -> b -> b) -> b -> Map k a -> b
- foldlWithKey' :: (a -> k -> b -> a) -> a -> Map k b -> a
- elems :: Map k a -> [a]
- keys :: Map k a -> [k]
- assocs :: Map k a -> [(k, a)]
- keysSet :: Map k a -> Set k
- toList :: Map k a -> [(k, a)]
- toAscList :: Map k a -> [(k, a)]
- toDescList :: Map k a -> [(k, a)]
- filter :: (a -> Bool) -> Map k a -> Map k a
- filterWithKey :: (k -> a -> Bool) -> Map k a -> Map k a
- restrictKeys :: Ord k => Map k a -> Set k -> Map k a
- withoutKeys :: Ord k => Map k a -> Set k -> Map k a
- partition :: (a -> Bool) -> Map k a -> (Map k a, Map k a)
- partitionWithKey :: (k -> a -> Bool) -> Map k a -> (Map k a, Map k a)
- takeWhileAntitone :: (k -> Bool) -> Map k a -> Map k a
- dropWhileAntitone :: (k -> Bool) -> Map k a -> Map k a
- spanAntitone :: (k -> Bool) -> Map k a -> (Map k a, Map k a)
- mapMaybe :: (a -> Maybe b) -> Map k a -> Map k b
- mapMaybeWithKey :: (k -> a -> Maybe b) -> Map k a -> Map k b
- mapEither :: (a -> Either b c) -> Map k a -> (Map k b, Map k c)
- mapEitherWithKey :: (k -> a -> Either b c) -> Map k a -> (Map k b, Map k c)
- split :: Ord k => k -> Map k a -> (Map k a, Map k a)
- splitLookup :: Ord k => k -> Map k a -> (Map k a, Maybe a, Map k a)
- splitRoot :: Map k b -> [Map k b]
- isSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Bool
- isSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool
- isProperSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Bool
- isProperSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool
- lookupIndex :: Ord k => k -> Map k a -> Maybe Int
- findIndex :: Ord k => k -> Map k a -> Int
- elemAt :: Int -> Map k a -> (k, a)
- updateAt :: (k -> a -> Maybe a) -> Int -> Map k a -> Map k a
- deleteAt :: Int -> Map k a -> Map k a
- take :: Int -> Map k a -> Map k a
- drop :: Int -> Map k a -> Map k a
- splitAt :: Int -> Map k a -> (Map k a, Map k a)
- lookupMin :: Map k a -> Maybe (k, a)
- lookupMax :: Map k a -> Maybe (k, a)
- findMin :: Map k a -> (k, a)
- findMax :: Map k a -> (k, a)
- deleteMin :: Map k a -> Map k a
- deleteMax :: Map k a -> Map k a
- deleteFindMin :: Map k a -> ((k, a), Map k a)
- deleteFindMax :: Map k a -> ((k, a), Map k a)
- updateMin :: (a -> Maybe a) -> Map k a -> Map k a
- updateMax :: (a -> Maybe a) -> Map k a -> Map k a
- updateMinWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a
- updateMaxWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a
- minView :: Map k a -> Maybe (a, Map k a)
- maxView :: Map k a -> Maybe (a, Map k a)
- minViewWithKey :: Map k a -> Maybe ((k, a), Map k a)
- maxViewWithKey :: Map k a -> Maybe ((k, a), Map k a)
- showTree :: Whoops "showTree has moved to Data.Map.Internal.Debug.showTree." => Map k a -> String
- showTreeWith :: Whoops "showTreeWith has moved to Data.Map.Internal.Debug.showTreeWith." => (k -> a -> String) -> Bool -> Bool -> Map k a -> String
- valid :: Ord k => Map k a -> Bool

# Map type

data Map k a #

A Map from keys `k` to values `a`.

Instances

Eq2 Map # | Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Map a c -> Map b d -> Bool Source #
Ord2 Map # | Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Map a c -> Map b d -> Ordering Source #
Show2 Map # | Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Map a b -> ShowS Source # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Map a b] -> ShowS Source #
Functor (Map k) # |
Instance details Defined in Data.Map.Internal Methods fmap :: (a -> b) -> Map k a -> Map k b Source # (<$) :: a -> Map k b -> Map k a Source #
Foldable (Map k) # |
Instance details Defined in Data.Map.Internal Methods fold :: Monoid m => Map k m -> m Source # foldMap :: Monoid m => (a -> m) -> Map k a -> m Source # foldr :: (a -> b -> b) -> b -> Map k a -> b Source # foldr' :: (a -> b -> b) -> b -> Map k a -> b Source # foldl :: (b -> a -> b) -> b -> Map k a -> b Source # foldl' :: (b -> a -> b) -> b -> Map k a -> b Source # foldr1 :: (a -> a -> a) -> Map k a -> a Source # foldl1 :: (a -> a -> a) -> Map k a -> a Source # toList :: Map k a -> [a] Source # null :: Map k a -> Bool Source # length :: Map k a -> Int Source # elem :: Eq a => a -> Map k a -> Bool Source # maximum :: Ord a => Map k a -> a Source # minimum :: Ord a => Map k a -> a Source # sum :: Num a => Map k a -> a Source # product :: Num a => Map k a -> a Source #
Traversable (Map k) # |
Instance details Defined in Data.Map.Internal Methods traverse :: Applicative f => (a -> f b) -> Map k a -> f (Map k b) Source # sequenceA :: Applicative f => Map k (f a) -> f (Map k a) Source # mapM :: Monad m => (a -> m b) -> Map k a -> m (Map k b) Source # sequence :: Monad m => Map k (m a) -> m (Map k a) Source #
Eq k => Eq1 (Map k) # | Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods liftEq :: (a -> b -> Bool) -> Map k a -> Map k b -> Bool Source #
Ord k => Ord1 (Map k) # | Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods liftCompare :: (a -> b -> Ordering) -> Map k a -> Map k b -> Ordering Source #
(Ord k, Read k) => Read1 (Map k) # | Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Map k a) Source # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Map k a] Source # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Map k a) Source # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Map k a] Source #
Show k => Show1 (Map k) # | Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Map k a -> ShowS Source # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Map k a] -> ShowS Source #
Ord k => IsList (Map k v) # | Since: containers-0.5.6.2
Instance details Defined in Data.Map.Internal Associated Types type Item (Map k v) :: Type Source # Methods fromList :: [Item (Map k v)] -> Map k v Source # fromListN :: Int -> [Item (Map k v)] -> Map k v Source # toList :: Map k v -> [Item (Map k v)] Source #
(Eq k, Eq a) => Eq (Map k a) # |
Instance details Defined in Data.Map.Internal Methods (==) :: Map k a -> Map k a -> Bool Source # (/=) :: Map k a -> Map k a -> Bool Source #
(Data k, Data a, Ord k) => Data (Map k a) # |
Instance details Defined in Data.Map.Internal Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Map k a -> c (Map k a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Map k a) Source # toConstr :: Map k a -> Constr Source # dataTypeOf :: Map k a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Map k a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Map k a)) Source # gmapT :: (forall b. Data b => b -> b) -> Map k a -> Map k a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Map k a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Map k a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Map k a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Map k a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) Source #
(Ord k, Ord v) => Ord (Map k v) # |
Instance details Defined in Data.Map.Internal Methods compare :: Map k v -> Map k v -> Ordering Source # (<) :: Map k v -> Map k v -> Bool Source # (<=) :: Map k v -> Map k v -> Bool Source # (>) :: Map k v -> Map k v -> Bool Source # (>=) :: Map k v -> Map k v -> Bool Source # max :: Map k v -> Map k v -> Map k v Source # min :: Map k v -> Map k v -> Map k v Source #
(Ord k, Read k, Read e) => Read (Map k e) # |
Instance details Defined in Data.Map.Internal Methods readsPrec :: Int -> ReadS (Map k e) Source # readList :: ReadS [Map k e] Source # readPrec :: ReadPrec (Map k e) Source # readListPrec :: ReadPrec [Map k e] Source #
(Show k, Show a) => Show (Map k a) # |
Instance details Defined in Data.Map.Internal Methods showsPrec :: Int -> Map k a -> ShowS Source # show :: Map k a -> String Source # showList :: [Map k a] -> ShowS Source #
Ord k => Semigroup (Map k v) # |
Instance details Defined in Data.Map.Internal Methods (<>) :: Map k v -> Map k v -> Map k v Source # sconcat :: NonEmpty (Map k v) -> Map k v Source # stimes :: Integral b => b -> Map k v -> Map k v Source #
Ord k => Monoid (Map k v) # |
Instance details Defined in Data.Map.Internal Methods mempty :: Map k v Source # mappend :: Map k v -> Map k v -> Map k v Source # mconcat :: [Map k v] -> Map k v Source #
(NFData k, NFData a) => NFData (Map k a) # |
Instance details Defined in Data.Map.Internal Methods rnf :: Map k a -> () Source #
type Item (Map k v) # |
Instance details Defined in Data.Map.Internal type Item (Map k v) = (k, v)

# Construction

empty :: Map k a #

O(1). The empty map.

    empty      == fromList []
    size empty == 0

singleton :: k -> a -> Map k a #

O(1). A map with a single element.

    singleton 1 'a'        == fromList [(1, 'a')]
    size (singleton 1 'a') == 1

fromSet :: (k -> a) -> Set k -> Map k a #

O(n). Build a map from a set of keys and a function which for each key computes its value.

    fromSet (\k -> replicate k 'a') (Data.Set.fromList [3, 5]) == fromList [(5,"aaaaa"), (3,"aaa")]
    fromSet undefined Data.Set.empty == empty

## From Unordered Lists

fromList :: Ord k => [(k, a)] -> Map k a #

O(n*log n). Build a map from a list of key/value pairs. See also `fromAscList`. If the list contains more than one value for the same key, the last value for the key is retained.

If the keys of the list are ordered, linear-time implementation is used, with the performance equal to `fromDistinctAscList`.

    fromList [] == empty
    fromList [(5,"a"), (3,"b"), (5, "c")] == fromList [(5,"c"), (3,"b")]
    fromList [(5,"c"), (3,"b"), (5, "a")] == fromList [(5,"a"), (3,"b")]

fromListWith :: Ord k => (a -> a -> a) -> [(k, a)] -> Map k a #

O(n*log n). Build a map from a list of key/value pairs with a combining function. See also `fromAscListWith`.

    fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"a")] == fromList [(3, "ab"), (5, "aba")]
    fromListWith (++) [] == empty

fromListWithKey :: Ord k => (k -> a -> a -> a) -> [(k, a)] -> Map k a #

O(n*log n). Build a map from a list of key/value pairs with a combining function. See also `fromAscListWithKey`.

    let f k a1 a2 = (show k) ++ a1 ++ a2
    fromListWithKey f [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"a")] == fromList [(3, "3ab"), (5, "5a5ba")]
    fromListWithKey f [] == empty

## From Ascending Lists

fromAscList :: Eq k => [(k, a)] -> Map k a #

O(n). Build a map from an ascending list in linear time. The precondition (input list is ascending) is not checked.

    fromAscList [(3,"b"), (5,"a")]          == fromList [(3, "b"), (5, "a")]
    fromAscList [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "b")]
    valid (fromAscList [(3,"b"), (5,"a"), (5,"b")]) == True
    valid (fromAscList [(5,"a"), (3,"b"), (5,"b")]) == False

fromAscListWith :: Eq k => (a -> a -> a) -> [(k, a)] -> Map k a #

O(n). Build a map from an ascending list in linear time with a combining function for equal keys. The precondition (input list is ascending) is not checked.

    fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")]
    valid (fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")]) == True
    valid (fromAscListWith (++) [(5,"a"), (3,"b"), (5,"b")]) == False

fromAscListWithKey :: Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a #

O(n). Build a map from an ascending list in linear time with a combining function for equal keys. The precondition (input list is ascending) is not checked.

    let f k a1 a2 = (show k) ++ ":" ++ a1 ++ a2
    fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b"), (5,"b")] == fromList [(3, "b"), (5, "5:b5:ba")]
    valid (fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b"), (5,"b")]) == True
    valid (fromAscListWithKey f [(5,"a"), (3,"b"), (5,"b"), (5,"b")]) == False

fromDistinctAscList :: [(k, a)] -> Map k a #

O(n). Build a map from an ascending list of distinct elements in linear time. The precondition is not checked.

    fromDistinctAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")]
    valid (fromDistinctAscList [(3,"b"), (5,"a")])          == True
    valid (fromDistinctAscList [(3,"b"), (5,"a"), (5,"b")]) == False

## From Descending Lists

fromDescList :: Eq k => [(k, a)] -> Map k a #

O(n). Build a map from a descending list in linear time. The precondition (input list is descending) is not checked.

    fromDescList [(5,"a"), (3,"b")]          == fromList [(3, "b"), (5, "a")]
    fromDescList [(5,"a"), (5,"b"), (3,"b")] == fromList [(3, "b"), (5, "b")]
    valid (fromDescList [(5,"a"), (5,"b"), (3,"b")]) == True
    valid (fromDescList [(5,"a"), (3,"b"), (5,"b")]) == False

Since: containers-0.5.8

fromDescListWith :: Eq k => (a -> a -> a) -> [(k, a)] -> Map k a #

O(n). Build a map from a descending list in linear time with a combining function for equal keys. The precondition (input list is descending) is not checked.

    fromDescListWith (++) [(5,"a"), (5,"b"), (3,"b")] == fromList [(3, "b"), (5, "ba")]
    valid (fromDescListWith (++) [(5,"a"), (5,"b"), (3,"b")]) == True
    valid (fromDescListWith (++) [(5,"a"), (3,"b"), (5,"b")]) == False

Since: containers-0.5.8

fromDescListWithKey :: Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a #

O(n). Build a map from a descending list in linear time with a combining function for equal keys. The precondition (input list is descending) is not checked.

    let f k a1 a2 = (show k) ++ ":" ++ a1 ++ a2
    fromDescListWithKey f [(5,"a"), (5,"b"), (5,"b"), (3,"b")] == fromList [(3, "b"), (5, "5:b5:ba")]
    valid (fromDescListWithKey f [(5,"a"), (5,"b"), (5,"b"), (3,"b")]) == True
    valid (fromDescListWithKey f [(5,"a"), (3,"b"), (5,"b"), (5,"b")]) == False

fromDistinctDescList :: [(k, a)] -> Map k a #

O(n). Build a map from a descending list of distinct elements in linear time. The precondition is not checked.

    fromDistinctDescList [(5,"a"), (3,"b")] == fromList [(3, "b"), (5, "a")]
    valid (fromDistinctDescList [(5,"a"), (3,"b")])          == True
    valid (fromDistinctDescList [(5,"a"), (5,"b"), (3,"b")]) == False

Since: containers-0.5.8

# Insertion

insert :: Ord k => k -> a -> Map k a -> Map k a #

O(log n). Insert a new key and value in the map. If the key is already present in the map, the associated value is replaced with the supplied value. `insert` is equivalent to ``insertWith` `const``.

    insert 5 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'x')]
    insert 7 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'a'), (7, 'x')]
    insert 5 'x' empty                         == singleton 5 'x'

insertWith :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a #

O(log n). Insert with a function, combining new value and old value. ``insertWith` f key value mp` will insert the pair (key, value) into `mp` if key does not exist in the map. If the key does exist, the function will insert the pair `(key, f new_value old_value)`.

    insertWith (++) 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "xxxa")]
    insertWith (++) 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")]
    insertWith (++) 5 "xxx" empty                         == singleton 5 "xxx"

insertWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a #

O(log n). Insert with a function, combining key, new value and old value. ``insertWithKey` f key value mp` will insert the pair (key, value) into `mp` if key does not exist in the map. If the key does exist, the function will insert the pair `(key,f key new_value old_value)`. Note that the key passed to f is the same key passed to `insertWithKey`.

    let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
    insertWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:xxx|a")]
    insertWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")]
    insertWithKey f 5 "xxx" empty                         == singleton 5 "xxx"

insertLookupWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> (Maybe a, Map k a) #

O(log n). Combines insert operation with old value retrieval. The expression (``insertLookupWithKey` f k x map`) is a pair where the first element is equal to (``lookup` k map`) and the second element equal to (``insertWithKey` f k x map`).

    let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
    insertLookupWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:xxx|a")])
    insertLookupWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == (Nothing,  fromList [(3, "b"), (5, "a"), (7, "xxx")])
    insertLookupWithKey f 5 "xxx" empty                         == (Nothing,  singleton 5 "xxx")

This is how to define `insertLookup` using `insertLookupWithKey`:

    let insertLookup kx x t = insertLookupWithKey (\_ a _ -> a) kx x t
    insertLookup 5 "x" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "x")])
    insertLookup 7 "x" (fromList [(5,"a"), (3,"b")]) == (Nothing,  fromList [(3, "b"), (5, "a"), (7, "x")])

# Deletion/Update

delete :: Ord k => k -> Map k a -> Map k a #

O(log n). Delete a key and its value from the map. When the key is not a member of the map, the original map is returned.

    delete 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
    delete 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
    delete 5 empty                         == empty

adjust :: Ord k => (a -> a) -> k -> Map k a -> Map k a #

O(log n). Update a value at a specific key with the result of the provided function. When the key is not a member of the map, the original map is returned.

    adjust ("new " ++) 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")]
    adjust ("new " ++) 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
    adjust ("new " ++) 7 empty                         == empty

adjustWithKey :: Ord k => (k -> a -> a) -> k -> Map k a -> Map k a #

O(log n). Adjust a value at a specific key. When the key is not a member of the map, the original map is returned.

    let f key x = (show key) ++ ":new " ++ x
    adjustWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")]
    adjustWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
    adjustWithKey f 7 empty                         == empty

update :: Ord k => (a -> Maybe a) -> k -> Map k a -> Map k a #

O(log n). The expression (``update` f k map`) updates the value `x` at `k` (if it is in the map). If (`f x`) is `Nothing`, the element is deleted. If it is (``Just` y`), the key `k` is bound to the new value `y`.

    let f x = if x == "a" then Just "new a" else Nothing
    update f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")]
    update f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
    update f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"

updateWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a #

O(log n). The expression (``updateWithKey` f k map`) updates the value `x` at `k` (if it is in the map). If (`f k x`) is `Nothing`, the element is deleted. If it is (``Just` y`), the key `k` is bound to the new value `y`.

    let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing
    updateWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")]
    updateWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
    updateWithKey f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"

updateLookupWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> (Maybe a, Map k a) #

O(log n). Lookup and update. See also `updateWithKey`. The function returns changed value, if it is updated. Returns the original key value if the map entry is deleted.

    let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing
    updateLookupWithKey f 5 (fromList [(5,"a"), (3,"b")]) == (Just "5:new a", fromList [(3, "b"), (5, "5:new a")])
    updateLookupWithKey f 7 (fromList [(5,"a"), (3,"b")]) == (Nothing,  fromList [(3, "b"), (5, "a")])
    updateLookupWithKey f 3 (fromList [(5,"a"), (3,"b")]) == (Just "b", singleton 5 "a")

alter :: Ord k => (Maybe a -> Maybe a) -> k -> Map k a -> Map k a #

O(log n). The expression (``alter` f k map`) alters the value `x` at `k`, or absence thereof. `alter` can be used to insert, delete, or update a value in a `Map`. In short : ``lookup` k (`alter` f k m) = f (`lookup` k m)`.

    let f _ = Nothing
    alter f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
    alter f 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"

    let f _ = Just "c"
    alter f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "c")]
    alter f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "c")]

alterF :: (Functor f, Ord k) => (Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a) #

O(log n). The expression (``alterF` f k map`) alters the value `x` at `k`, or absence thereof. `alterF` can be used to inspect, insert, delete, or update a value in a `Map`. In short: ``lookup` k <$> `alterF` f k m = f (`lookup` k m)`.

Example:

    interactiveAlter :: Int -> Map Int String -> IO (Map Int String)
    interactiveAlter k m = alterF f k m where
      f Nothing -> do
         putStrLn $ show k ++
             " was not found in the map. Would you like to add it?"
         getUserResponse1 :: IO (Maybe String)
      f (Just old) -> do
         putStrLn "The key is currently bound to " ++ show old ++
             ". Would you like to change or delete it?"
         getUserresponse2 :: IO (Maybe String)

`alterF` is the most general operation for working with an individual key that may or may not be in a given map. When used with trivial functors like `Identity` and `Const`, it is often slightly slower than more specialized combinators like `lookup` and `insert`. However, when the functor is non-trivial and key comparison is not particularly cheap, it is the fastest way.

Note on rewrite rules:

This module includes GHC rewrite rules to optimize `alterF` for the `Const` and `Identity` functors. In general, these rules improve performance. The sole exception is that when using `Identity`, deleting a key that is already absent takes longer than it would without the rules. If you expect this to occur a very large fraction of the time, you might consider using a private copy of the `Identity` type.

Note: `alterF` is a flipped version of the `at` combinator from `At`.

Since: containers-0.5.8

# Query

## Lookup

lookup :: Ord k => k -> Map k a -> Maybe a #

O(log n). Lookup the value at a key in the map.

The function will return the corresponding value as `(`Just` value)`, or `Nothing` if the key isn't in the map.

An example of using `lookup`:

    import Prelude hiding (lookup)
    import Data.Map

    employeeDept = fromList([("John","Sales"), ("Bob","IT")])
    deptCountry = fromList([("IT","USA"), ("Sales","France")])
    countryCurrency = fromList([("USA", "Dollar"), ("France", "Euro")])

    employeeCurrency :: String -> Maybe String
    employeeCurrency name = do
        dept <- lookup name employeeDept
        country <- lookup dept deptCountry
        lookup country countryCurrency

    main = do
        putStrLn $ "John's currency: " ++ (show (employeeCurrency "John"))
        putStrLn $ "Pete's currency: " ++ (show (employeeCurrency "Pete"))

The output of this program:

      John's currency: Just "Euro"
      Pete's currency: Nothing

(!?) :: Ord k => Map k a -> k -> Maybe a infixl 9 #

O(log n). Find the value at a key. Returns `Nothing` when the element can not be found.

    fromList [(5, 'a'), (3, 'b')] !? 1 == Nothing

    fromList [(5, 'a'), (3, 'b')] !? 5 == Just 'a'

Since: containers-0.5.9

(!) :: Ord k => Map k a -> k -> a infixl 9 #

O(log n). Find the value at a key. Calls `error` when the element can not be found.

    fromList [(5,'a'), (3,'b')] ! 1    Error: element not in the map
    fromList [(5,'a'), (3,'b')] ! 5 == 'a'

findWithDefault :: Ord k => a -> k -> Map k a -> a #

O(log n). The expression `(`findWithDefault` def k map)` returns the value at key `k` or returns default value `def` when the key is not in the map.

    findWithDefault 'x' 1 (fromList [(5,'a'), (3,'b')]) == 'x'
    findWithDefault 'x' 5 (fromList [(5,'a'), (3,'b')]) == 'a'

member :: Ord k => k -> Map k a -> Bool #

O(log n). Is the key a member of the map? See also `notMember`.

    member 5 (fromList [(5,'a'), (3,'b')]) == True
    member 1 (fromList [(5,'a'), (3,'b')]) == False

notMember :: Ord k => k -> Map k a -> Bool #

O(log n). Is the key not a member of the map? See also `member`.

    notMember 5 (fromList [(5,'a'), (3,'b')]) == False
    notMember 1 (fromList [(5,'a'), (3,'b')]) == True

lookupLT :: Ord k => k -> Map k v -> Maybe (k, v) #

O(log n). Find largest key smaller than the given one and return the corresponding (key, value) pair.

    lookupLT 3 (fromList [(3,'a'), (5,'b')]) == Nothing
    lookupLT 4 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a')

lookupGT :: Ord k => k -> Map k v -> Maybe (k, v) #

O(log n). Find smallest key greater than the given one and return the corresponding (key, value) pair.

    lookupGT 4 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b')
    lookupGT 5 (fromList [(3,'a'), (5,'b')]) == Nothing

lookupLE :: Ord k => k -> Map k v -> Maybe (k, v) #

O(log n). Find largest key smaller or equal to the given one and return the corresponding (key, value) pair.

    lookupLE 2 (fromList [(3,'a'), (5,'b')]) == Nothing
    lookupLE 4 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a')
    lookupLE 5 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b')

lookupGE :: Ord k => k -> Map k v -> Maybe (k, v) #

O(log n). Find smallest key greater or equal to the given one and return the corresponding (key, value) pair.

    lookupGE 3 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a')
    lookupGE 4 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b')
    lookupGE 6 (fromList [(3,'a'), (5,'b')]) == Nothing

## Size

null :: Map k a -> Bool #

O(1). Is the map empty?

    Data.Map.null (empty)           == True
    Data.Map.null (singleton 1 'a') == False

size :: Map k a -> Int #

O(1). The number of elements in the map.

    size empty                                   == 0
    size (singleton 1 'a')                       == 1
    size (fromList([(1,'a'), (2,'c'), (3,'b')])) == 3

# Combine

## Union

union :: Ord k => Map k a -> Map k a -> Map k a #

O(m*log(n/m + 1)), m <= n. The expression (``union` t1 t2`) takes the left-biased union of `t1` and `t2`. It prefers `t1` when duplicate keys are encountered, i.e. (``union` == `unionWith` `const``).

    union (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "a"), (7, "C")]

unionWith :: Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a #

O(m*log(n/m + 1)), m <= n. Union with a combining function.

    unionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "aA"), (7, "C")]

unionWithKey :: Ord k => (k -> a -> a -> a) -> Map k a -> Map k a -> Map k a #

O(m*log(n/m + 1)), m <= n. Union with a combining function.

    let f key left_value right_value = (show key) ++ ":" ++ left_value ++ "|" ++ right_value
    unionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "5:a|A"), (7, "C")]

unions :: (Foldable f, Ord k) => f (Map k a) -> Map k a #

The union of a list of maps: (``unions` == `foldl` `union` `empty``).

    unions [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])]
        == fromList [(3, "b"), (5, "a"), (7, "C")]
    unions [(fromList [(5, "A3"), (3, "B3")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "a"), (3, "b")])]
        == fromList [(3, "B3"), (5, "A3"), (7, "C")]

unionsWith :: (Foldable f, Ord k) => (a -> a -> a) -> f (Map k a) -> Map k a #

The union of a list of maps, with a combining operation: (``unionsWith` f == `foldl` (`unionWith` f) `empty``).

    unionsWith (++) [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])]
        == fromList [(3, "bB3"), (5, "aAA3"), (7, "C")]

## Difference

difference :: Ord k => Map k a -> Map k b -> Map k a #

O(m*log(n/m + 1)), m <= n. Difference of two maps. Return elements of the first map not existing in the second map.

    difference (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 3 "b"

(\\) :: Ord k => Map k a -> Map k b -> Map k a infixl 9 #

Same as `difference`.

differenceWith :: Ord k => (a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a #

O(n+m). Difference with a combining function. When two equal keys are encountered, the combining function is applied to the values of these keys. If it returns `Nothing`, the element is discarded (proper set difference). If it returns (``Just` y`), the element is updated with a new value `y`.

    let f al ar = if al == "b" then Just (al ++ ":" ++ ar) else Nothing
    differenceWith f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (7, "C")])
        == singleton 3 "b:B"

differenceWithKey :: Ord k => (k -> a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a #

O(n+m). Difference with a combining function. When two equal keys are encountered, the combining function is applied to the key and both values. If it returns `Nothing`, the element is discarded (proper set difference). If it returns (``Just` y`), the element is updated with a new value `y`.

    let f k al ar = if al == "b" then Just ((show k) ++ ":" ++ al ++ "|" ++ ar) else Nothing
    differenceWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (10, "C")])
        == singleton 3 "3:b|B"

## Intersection

intersection :: Ord k => Map k a -> Map k b -> Map k a #

O(m*log(n/m + 1)), m <= n. Intersection of two maps. Return data in the first map for the keys existing in both maps. (``intersection` m1 m2 == `intersectionWith` `const` m1 m2`).

    intersection (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "a"

intersectionWith :: Ord k => (a -> b -> c) -> Map k a -> Map k b -> Map k c #

O(m*log(n/m + 1)), m <= n. Intersection with a combining function.

    intersectionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "aA"

intersectionWithKey :: Ord k => (k -> a -> b -> c) -> Map k a -> Map k b -> Map k c #

O(m*log(n/m + 1)), m <= n. Intersection with a combining function.

    let f k al ar = (show k) ++ ":" ++ al ++ "|" ++ ar
    intersectionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "5:a|A"

## General combining functions

See Data.Map.Merge.Lazy

## Unsafe general combining function

mergeWithKey :: Ord k => (k -> a -> b -> Maybe c) -> (Map k a -> Map k c) -> (Map k b -> Map k c) -> Map k a -> Map k b -> Map k c #

O(n+m). An unsafe general combining function.

WARNING: This function can produce corrupt maps and its results may depend on the internal structures of its inputs. Users should prefer `merge` or `mergeA`.

When `mergeWithKey` is given three arguments, it is inlined to the call site. You should therefore use `mergeWithKey` only to define custom combining functions. For example, you could define `unionWithKey`, `differenceWithKey` and `intersectionWithKey` as

    myUnionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) id id m1 m2
    myDifferenceWithKey f m1 m2 = mergeWithKey f id (const empty) m1 m2
    myIntersectionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) (const empty) (const empty) m1 m2

When calling ``mergeWithKey` combine only1 only2`, a function combining two `Map`s is created, such that

- if a key is present in both maps, it is passed with both corresponding values to the `combine` function. Depending on the result, the key is either present in the result with specified value, or is left out;
- a nonempty subtree present only in the first map is passed to `only1` and the output is added to the result;
- a nonempty subtree present only in the second map is passed to `only2` and the output is added to the result.

The `only1` and `only2` methods must return a map with a subset (possibly empty) of the keys of the given map. The values can be modified arbitrarily. Most common variants of `only1` and `only2` are `id` and ``const` `empty``, but for example ``map` f`, ``filterWithKey` f`, or ``mapMaybeWithKey` f` could be used for any `f`.

# Traversal

## Map

map :: (a -> b) -> Map k a -> Map k b #

O(n). Map a function over all values in the map.

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

mapWithKey :: (k -> a -> b) -> Map k a -> Map k b #

O(n). 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")]

traverseWithKey :: Applicative t => (k -> a -> t b) -> Map k a -> t (Map k b) #

O(n). ``traverseWithKey` f m == `fromList` $ `traverse` ((k, v) -> (,) k $ f k v) (`toList` m)` That is, behaves exactly like a regular `traverse` except that the traversing function also has access to the key associated with a value.

    traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(1, 'a'), (5, 'e')]) == Just (fromList [(1, 'b'), (5, 'f')])
    traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(2, 'c')])           == Nothing

traverseMaybeWithKey :: Applicative f => (k -> a -> f (Maybe b)) -> Map k a -> f (Map k b) #

O(n). Traverse keys/values and collect the `Just` results.

Since: containers-0.5.8

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

O(n). 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")])

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

O(n). 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")])

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

O(n). The function `mapAccumR` threads an accumulating argument through the map in descending order of keys.

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

O(n*log n). ``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"

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

O(n*log n). ``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"

mapKeysMonotonic :: (k1 -> k2) -> Map k1 a -> Map k2 a #

O(n). ``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

# Folds

foldr :: (a -> b -> b) -> b -> Map k a -> b #

O(n). Fold the values in the map using the given right-associative binary operator, such that ``foldr` f z == `foldr` f z . `elems``.

For example,

    elems map = foldr (:) [] map

    let f a len = len + (length a)
    foldr f 0 (fromList [(5,"a"), (3,"bbb")]) == 4

foldl :: (a -> b -> a) -> a -> Map k b -> a #

O(n). Fold the values in the map using the given left-associative binary operator, such that ``foldl` f z == `foldl` f z . `elems``.

For example,

    elems = reverse . foldl (flip (:)) []

    let f len a = len + (length a)
    foldl f 0 (fromList [(5,"a"), (3,"bbb")]) == 4

foldrWithKey :: (k -> a -> b -> b) -> b -> Map k a -> b #

O(n). Fold the keys and values in the map using the given right-associative binary operator, such that ``foldrWithKey` f z == `foldr` (`uncurry` f) z . `toAscList``.

For example,

    keys map = foldrWithKey (\k x ks -> k:ks) [] map

    let f k a result = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")"
    foldrWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (5:a)(3:b)"

foldlWithKey :: (a -> k -> b -> a) -> a -> Map k b -> a #

O(n). Fold the keys and values in the map using the given left-associative binary operator, such that ``foldlWithKey` f z == `foldl` (\z' (kx, x) -> f z' kx x) z . `toAscList``.

For example,

    keys = reverse . foldlWithKey (\ks k x -> k:ks) []

    let f result k a = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")"
    foldlWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (3:b)(5:a)"

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

O(n). 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.

Since: containers-0.5.4

## Strict folds

foldr' :: (a -> b -> b) -> b -> Map k a -> b #

O(n). A strict version of `foldr`. Each application of the operator is evaluated before using the result in the next application. This function is strict in the starting value.

foldl' :: (a -> b -> a) -> a -> Map k b -> a #

O(n). A strict version of `foldl`. Each application of the operator is evaluated before using the result in the next application. This function is strict in the starting value.

foldrWithKey' :: (k -> a -> b -> b) -> b -> Map k a -> b #

O(n). A strict version of `foldrWithKey`. Each application of the operator is evaluated before using the result in the next application. This function is strict in the starting value.

foldlWithKey' :: (a -> k -> b -> a) -> a -> Map k b -> a #

O(n). A strict version of `foldlWithKey`. Each application of the operator is evaluated before using the result in the next application. This function is strict in the starting value.

# Conversion

elems :: Map k a -> [a] #

O(n). Return all elements of the map in the ascending order of their keys. Subject to list fusion.

    elems (fromList [(5,"a"), (3,"b")]) == ["b","a"]
    elems empty == []

keys :: Map k a -> [k] #

O(n). Return all keys of the map in ascending order. Subject to list fusion.

    keys (fromList [(5,"a"), (3,"b")]) == [3,5]
    keys empty == []

assocs :: Map k a -> [(k, a)] #

O(n). An alias for `toAscList`. Return all key/value pairs in the map in ascending key order. Subject to list fusion.

    assocs (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
    assocs empty == []

keysSet :: Map k a -> Set k #

O(n). The set of all keys of the map.

    keysSet (fromList [(5,"a"), (3,"b")]) == Data.Set.fromList [3,5]
    keysSet empty == Data.Set.empty

## Lists

toList :: Map k a -> [(k, a)] #

O(n). Convert the map to a list of key/value pairs. Subject to list fusion.

    toList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
    toList empty == []

## Ordered lists

toAscList :: Map k a -> [(k, a)] #

O(n). Convert the map to a list of key/value pairs where the keys are in ascending order. Subject to list fusion.

    toAscList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]

toDescList :: Map k a -> [(k, a)] #

O(n). Convert the map to a list of key/value pairs where the keys are in descending order. Subject to list fusion.

    toDescList (fromList [(5,"a"), (3,"b")]) == [(5,"a"), (3,"b")]

# Filter

filter :: (a -> Bool) -> Map k a -> Map k a #

O(n). Filter all values that satisfy the predicate.

    filter (> "a") (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
    filter (> "x") (fromList [(5,"a"), (3,"b")]) == empty
    filter (< "a") (fromList [(5,"a"), (3,"b")]) == empty

filterWithKey :: (k -> a -> Bool) -> Map k a -> Map k a #

O(n). Filter all keys/values that satisfy the predicate.

    filterWithKey (\k _ -> k > 4) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"

restrictKeys :: Ord k => Map k a -> Set k -> Map k a #

O(m*log(n/m + 1)), m <= n. Restrict a `Map` to only those keys found in a `Set`.

    m `restrictKeys` s = filterWithKey (k _ -> k `member` s) m
    m `restrictKeys` s = m `intersect` fromSet (const ()) s

Since: containers-0.5.8

withoutKeys :: Ord k => Map k a -> Set k -> Map k a #

O(m*log(n/m + 1)), m <= n. Remove all keys in a `Set` from a `Map`.

    m `withoutKeys` s = filterWithKey (k _ -> k `notMember` s) m
    m `withoutKeys` s = m `difference` fromSet (const ()) s

Since: containers-0.5.8

partition :: (a -> Bool) -> Map k a -> (Map k a, Map k a) #

O(n). Partition the map according to a predicate. The first map contains all elements that satisfy the predicate, the second all elements that fail the predicate. See also `split`.

    partition (> "a") (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a")
    partition (< "x") (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty)
    partition (> "x") (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")])

partitionWithKey :: (k -> a -> Bool) -> Map k a -> (Map k a, Map k a) #

O(n). Partition the map according to a predicate. The first map contains all elements that satisfy the predicate, the second all elements that fail the predicate. See also `split`.

    partitionWithKey (\ k _ -> k > 3) (fromList [(5,"a"), (3,"b")]) == (singleton 5 "a", singleton 3 "b")
    partitionWithKey (\ k _ -> k < 7) (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty)
    partitionWithKey (\ k _ -> k > 7) (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")])

takeWhileAntitone :: (k -> Bool) -> Map k a -> Map k a #

O(log n). Take while a predicate on the keys holds. The user is responsible for ensuring that for all keys `j` and `k` in the map, `j < k ==> p j >= p k`. See note at `spanAntitone`.

    takeWhileAntitone p = fromDistinctAscList . takeWhile (p . fst) . toList
    takeWhileAntitone p = filterWithKey (k _ -> p k)

Since: containers-0.5.8

dropWhileAntitone :: (k -> Bool) -> Map k a -> Map k a #

O(log n). Drop while a predicate on the keys holds. The user is responsible for ensuring that for all keys `j` and `k` in the map, `j < k ==> p j >= p k`. See note at `spanAntitone`.

    dropWhileAntitone p = fromDistinctAscList . dropWhile (p . fst) . toList
    dropWhileAntitone p = filterWithKey (k -> not (p k))

Since: containers-0.5.8

spanAntitone :: (k -> Bool) -> Map k a -> (Map k a, Map k a) #

O(log n). Divide a map at the point where a predicate on the keys stops holding. The user is responsible for ensuring that for all keys `j` and `k` in the map, `j < k ==> p j >= p k`.

    spanAntitone p xs = (takeWhileAntitone p xs, dropWhileAntitone p xs)
    spanAntitone p xs = partition p xs

Note: if `p` is not actually antitone, then `spanAntitone` will split the map at some unspecified point where the predicate switches from holding to not holding (where the predicate is seen to hold before the first key and to fail after the last key).

Since: containers-0.5.8

mapMaybe :: (a -> Maybe b) -> Map k a -> Map k b #

O(n). 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"

mapMaybeWithKey :: (k -> a -> Maybe b) -> Map k a -> Map k b #

O(n). 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"

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

O(n). 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")])

mapEitherWithKey :: (k -> a -> Either b c) -> Map k a -> (Map k b, Map k c) #

O(n). Map keys/values and separate the `Left` and `Right` results.

    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")])

split :: Ord k => k -> Map k a -> (Map k a, Map k a) #

O(log n). The expression (``split` k map`) is a pair `(map1,map2)` where the keys in `map1` are smaller than `k` and the keys in `map2` larger than `k`. Any key equal to `k` is found in neither `map1` nor `map2`.

    split 2 (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3,"b"), (5,"a")])
    split 3 (fromList [(5,"a"), (3,"b")]) == (empty, singleton 5 "a")
    split 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a")
    split 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", empty)
    split 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], empty)

splitLookup :: Ord k => k -> Map k a -> (Map k a, Maybe a, Map k a) #

O(log n). The expression (``splitLookup` k map`) splits a map just like `split` but also returns ``lookup` k map`.

    splitLookup 2 (fromList [(5,"a"), (3,"b")]) == (empty, Nothing, fromList [(3,"b"), (5,"a")])
    splitLookup 3 (fromList [(5,"a"), (3,"b")]) == (empty, Just "b", singleton 5 "a")
    splitLookup 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Nothing, singleton 5 "a")
    splitLookup 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Just "a", empty)
    splitLookup 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], Nothing, empty)

splitRoot :: Map k b -> [Map k b] #

O(1). Decompose a map into pieces based on the structure of the underlying tree. This function is useful for consuming a map in parallel.

No guarantee is made as to the sizes of the pieces; an internal, but deterministic process determines this. However, it is guaranteed that the pieces returned will be in ascending order (all elements in the first submap less than all elements in the second, and so on).

Examples:

    splitRoot (fromList (zip [1..6] ['a'..])) ==
      [fromList [(1,'a'),(2,'b'),(3,'c')],fromList [(4,'d')],fromList [(5,'e'),(6,'f')]]

    splitRoot empty == []

Note that the current implementation does not return more than three submaps, but you should not depend on this behaviour because it can change in the future without notice.

Since: containers-0.5.4

# Submap

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

O(m*log(n/m + 1)), m <= n. This function is defined as (``isSubmapOf` = `isSubmapOfBy` (==)`).

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

O(m*log(n/m + 1)), m <= n. 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)])

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

O(m*log(n/m + 1)), m <= n. Is this a proper submap? (ie. a submap but not equal). Defined as (``isProperSubmapOf` = `isProperSubmapOfBy` (==)`).

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

O(m*log(n/m + 1)), m <= n. Is this a proper submap? (ie. a submap but not equal). The expression (``isProperSubmapOfBy` f m1 m2`) returns `True` when `m1` and `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)])

# Indexed

lookupIndex :: Ord k => k -> Map k a -> Maybe Int #

O(log n). Lookup the index of a key, which is its zero-based index in the sequence sorted by keys. The index is a number from 0 up to, but not including, the `size` of the map.

    isJust (lookupIndex 2 (fromList [(5,"a"), (3,"b")]))   == False
    fromJust (lookupIndex 3 (fromList [(5,"a"), (3,"b")])) == 0
    fromJust (lookupIndex 5 (fromList [(5,"a"), (3,"b")])) == 1
    isJust (lookupIndex 6 (fromList [(5,"a"), (3,"b")]))   == False

findIndex :: Ord k => k -> Map k a -> Int #

O(log n). Return the index of a key, which is its zero-based index in the sequence sorted by keys. The index is a number from 0 up to, but not including, the `size` of the map. Calls `error` when the key is not a `member` of the map.

    findIndex 2 (fromList [(5,"a"), (3,"b")])    Error: element is not in the map
    findIndex 3 (fromList [(5,"a"), (3,"b")]) == 0
    findIndex 5 (fromList [(5,"a"), (3,"b")]) == 1
    findIndex 6 (fromList [(5,"a"), (3,"b")])    Error: element is not in the map

elemAt :: Int -> Map k a -> (k, a) #

O(log n). Retrieve an element by its index, i.e. by its zero-based index in the sequence sorted by keys. If the index is out of range (less than zero, greater or equal to `size` of the map), `error` is called.

    elemAt 0 (fromList [(5,"a"), (3,"b")]) == (3,"b")
    elemAt 1 (fromList [(5,"a"), (3,"b")]) == (5, "a")
    elemAt 2 (fromList [(5,"a"), (3,"b")])    Error: index out of range

updateAt :: (k -> a -> Maybe a) -> Int -> Map k a -> Map k a #

O(log n). Update the element at index, i.e. by its zero-based index in the sequence sorted by keys. If the index is out of range (less than zero, greater or equal to `size` of the map), `error` is called.

    updateAt (\ _ _ -> Just "x") 0    (fromList [(5,"a"), (3,"b")]) == fromList [(3, "x"), (5, "a")]
    updateAt (\ _ _ -> Just "x") 1    (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "x")]
    updateAt (\ _ _ -> Just "x") 2    (fromList [(5,"a"), (3,"b")])    Error: index out of range
    updateAt (\ _ _ -> Just "x") (-1) (fromList [(5,"a"), (3,"b")])    Error: index out of range
    updateAt (\_ _  -> Nothing)  0    (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
    updateAt (\_ _  -> Nothing)  1    (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
    updateAt (\_ _  -> Nothing)  2    (fromList [(5,"a"), (3,"b")])    Error: index out of range
    updateAt (\_ _  -> Nothing)  (-1) (fromList [(5,"a"), (3,"b")])    Error: index out of range

deleteAt :: Int -> Map k a -> Map k a #

O(log n). Delete the element at index, i.e. by its zero-based index in the sequence sorted by keys. If the index is out of range (less than zero, greater or equal to `size` of the map), `error` is called.

    deleteAt 0  (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
    deleteAt 1  (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
    deleteAt 2 (fromList [(5,"a"), (3,"b")])     Error: index out of range
    deleteAt (-1) (fromList [(5,"a"), (3,"b")])  Error: index out of range

take :: Int -> Map k a -> Map k a #

Take a given number of entries in key order, beginning with the smallest keys.

    take n = fromDistinctAscList . take n . toAscList

Since: containers-0.5.8

drop :: Int -> Map k a -> Map k a #

Drop a given number of entries in key order, beginning with the smallest keys.

    drop n = fromDistinctAscList . drop n . toAscList

Since: containers-0.5.8

splitAt :: Int -> Map k a -> (Map k a, Map k a) #

O(log n). Split a map at a particular index.

    splitAt !n !xs = (take n xs, drop n xs)

Since: containers-0.5.8

# Min/Max

lookupMin :: Map k a -> Maybe (k, a) #

O(log n). The minimal key of the map. Returns `Nothing` if the map is empty.

    lookupMin (fromList [(5,"a"), (3,"b")]) == Just (3,"b")
    findMin empty = Nothing

Since: containers-0.5.9

lookupMax :: Map k a -> Maybe (k, a) #

O(log n). The maximal key of the map. Returns `Nothing` if the map is empty.

    lookupMax (fromList [(5,"a"), (3,"b")]) == Just (5,"a")
    lookupMax empty = Nothing

Since: containers-0.5.9

findMin :: Map k a -> (k, a) #

O(log n). The minimal key of the map. Calls `error` if the map is empty.

    findMin (fromList [(5,"a"), (3,"b")]) == (3,"b")
    findMin empty                            Error: empty map has no minimal element

findMax :: Map k a -> (k, a) #

deleteMin :: Map k a -> Map k a #

O(log n). Delete the minimal key. Returns an empty map if the map is empty.

    deleteMin (fromList [(5,"a"), (3,"b"), (7,"c")]) == fromList [(5,"a"), (7,"c")]
    deleteMin empty == empty

deleteMax :: Map k a -> Map k a #

O(log n). Delete the maximal key. Returns an empty map if the map is empty.

    deleteMax (fromList [(5,"a"), (3,"b"), (7,"c")]) == fromList [(3,"b"), (5,"a")]
    deleteMax empty == empty

deleteFindMin :: Map k a -> ((k, a), Map k a) #

O(log n). Delete and find the minimal element.

    deleteFindMin (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((3,"b"), fromList[(5,"a"), (10,"c")])
    deleteFindMin                                            Error: can not return the minimal element of an empty map

deleteFindMax :: Map k a -> ((k, a), Map k a) #

O(log n). Delete and find the maximal element.

    deleteFindMax (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((10,"c"), fromList [(3,"b"), (5,"a")])
    deleteFindMax empty                                      Error: can not return the maximal element of an empty map

updateMin :: (a -> Maybe a) -> Map k a -> Map k a #

O(log n). Update the value at the minimal key.

    updateMin (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "Xb"), (5, "a")]
    updateMin (\ _ -> Nothing)         (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"

updateMax :: (a -> Maybe a) -> Map k a -> Map k a #

O(log n). Update the value at the maximal key.

    updateMax (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "Xa")]
    updateMax (\ _ -> Nothing)         (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"

updateMinWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a #

O(log n). Update the value at the minimal key.

    updateMinWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"3:b"), (5,"a")]
    updateMinWithKey (\ _ _ -> Nothing)                     (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"

updateMaxWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a #

O(log n). Update the value at the maximal key.

    updateMaxWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"b"), (5,"5:a")]
    updateMaxWithKey (\ _ _ -> Nothing)                     (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"

minView :: Map k a -> Maybe (a, Map k a) #

O(log n). Retrieves the value associated with minimal key of the map, and the map stripped of that element, or `Nothing` if passed an empty map.

    minView (fromList [(5,"a"), (3,"b")]) == Just ("b", singleton 5 "a")
    minView empty == Nothing

maxView :: Map k a -> Maybe (a, Map k a) #

O(log n). Retrieves the value associated with maximal key of the map, and the map stripped of that element, or `Nothing` if passed an empty map.

    maxView (fromList [(5,"a"), (3,"b")]) == Just ("a", singleton 3 "b")
    maxView empty == Nothing

minViewWithKey :: Map k a -> Maybe ((k, a), Map k a) #

O(log n). Retrieves the minimal (key,value) pair of the map, and the map stripped of that element, or `Nothing` if passed an empty map.

    minViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((3,"b"), singleton 5 "a")
    minViewWithKey empty == Nothing

maxViewWithKey :: Map k a -> Maybe ((k, a), Map k a) #

O(log n). Retrieves the maximal (key,value) pair of the map, and the map stripped of that element, or `Nothing` if passed an empty map.

    maxViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((5,"a"), singleton 3 "b")
    maxViewWithKey empty == Nothing

# Debugging

showTree :: Whoops "showTree has moved to Data.Map.Internal.Debug.showTree." => Map k a -> String #

This function has moved to `showTree`.

showTreeWith :: Whoops "showTreeWith has moved to Data.Map.Internal.Debug.showTreeWith." => (k -> a -> String) -> Bool -> Bool -> Map k a -> String #

This function has moved to `showTreeWith`.

valid :: Ord k => Map k a -> Bool #

O(n). Test if the internal map structure is valid.

    valid (fromAscList [(3,"b"), (5,"a")]) == True
    valid (fromAscList [(5,"a"), (3,"b")]) == False