rio-0.1.22.0: A standard library for Haskell

Safe Haskell | Safe-Inferred
Language | Haskell2010

RIO.Map

Contents

- Map type
- Operators
- Query
- Construction
  - Insertion
  - Delete/Update
- Combine
  - Union
  - Difference
  - Intersection
  - General combining functions
  - Deprecated general combining function
- Traversal
  - Map
- Folds
  - Strict folds
- Conversion
  - Lists
  - Ordered lists
- Filter
- Submap
- Indexed
- Min/Max
- Debugging

Description

Strict `Map`. Import as:

    import qualified RIO.Map as Map

This module does not export any partial or unchecked functions. For those, see RIO.Map.Partial and RIO.Map.Unchecked

Synopsis

- data Map k a
- (!?) :: Ord k => Map k a -> k -> Maybe a
- (\\) :: Ord k => Map k a -> Map k b -> Map k a
- null :: Map k a -> Bool
- size :: Map k a -> Int
- member :: Ord k => k -> Map k a -> Bool
- notMember :: Ord k => k -> Map k a -> Bool
- lookup :: Ord k => k -> Map k a -> Maybe a
- findWithDefault :: Ord k => a -> k -> Map k a -> a
- 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)
- empty :: Map k a
- singleton :: 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)
- 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
- 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
- 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
- fromSet :: (k -> a) -> Set k -> Map k a
- toList :: Map k a -> [(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
- 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
- elemAt :: Int -> Map k a -> (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)
- deleteMin :: Map k a -> Map k a
- deleteMax :: Map 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`.

The `Semigroup` operation for `Map` is `union`, which prefers values from the left operand. If `m1` maps a key `k` to a value `a1`, and `m2` maps the same key to a different value `a2`, then their union `m1 <> m2` maps `k` to `a1`.

#### Instances

Instances details

Bifoldable Map | Since: containers-0.6.3.1
Instance details Defined in Data.Map.Internal Methods bifold :: Monoid m => Map m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Map a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Map a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Map a b -> c #
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 #
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 #
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 # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Map a b] -> ShowS #
Hashable2 Map | Since: hashable-1.3.4.0
Instance details Defined in Data.Hashable.Class Methods liftHashWithSalt2 :: (Int -> a -> Int) -> (Int -> b -> Int) -> Int -> Map a b -> Int #
(Lift k, Lift a) => Lift (Map k a :: Type) | Since: containers-0.6.6
Instance details Defined in Data.Map.Internal Methods lift :: Quote m => Map k a -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Map k a -> Code m (Map k a) #
Foldable (Map k) | Folds in order of increasing key.
Instance details Defined in Data.Map.Internal Methods fold :: Monoid m => Map k m -> m # foldMap :: Monoid m => (a -> m) -> Map k a -> m # foldMap' :: Monoid m => (a -> m) -> Map k a -> m # foldr :: (a -> b -> b) -> b -> Map k a -> b # foldr' :: (a -> b -> b) -> b -> Map k a -> b # foldl :: (b -> a -> b) -> b -> Map k a -> b # foldl' :: (b -> a -> b) -> b -> Map k a -> b # foldr1 :: (a -> a -> a) -> Map k a -> a # foldl1 :: (a -> a -> a) -> Map k a -> a # toList :: Map k a -> [a] # null :: Map k a -> Bool # length :: Map k a -> Int # elem :: Eq a => a -> Map k a -> Bool # maximum :: Ord a => Map k a -> a # minimum :: Ord a => Map k a -> a # sum :: Num a => Map k a -> a # product :: Num a => Map k a -> a #
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 #
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 #
(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) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Map k a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Map k a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Map k a] #
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 # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Map k a] -> ShowS #
Traversable (Map k) | Traverses in order of increasing key.
Instance details Defined in Data.Map.Internal Methods traverse :: Applicative f => (a -> f b) -> Map k a -> f (Map k b) # sequenceA :: Applicative f => Map k (f a) -> f (Map k a) # mapM :: Monad m => (a -> m b) -> Map k a -> m (Map k b) # sequence :: Monad m => Map k (m a) -> m (Map k a) #
Functor (Map k) |
Instance details Defined in Data.Map.Internal Methods fmap :: (a -> b) -> Map k a -> Map k b # (<$) :: a -> Map k b -> Map k a #
Hashable k => Hashable1 (Map k) | Since: hashable-1.3.4.0
Instance details Defined in Data.Hashable.Class Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> Map k a -> Int #
(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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Map k a) # toConstr :: Map k a -> Constr # dataTypeOf :: Map k a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Map k a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Map k a)) # gmapT :: (forall b. Data b => b -> b) -> Map k a -> Map k a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Map k a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Map k a -> r # gmapQ :: (forall d. Data d => d -> u) -> Map k a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Map k a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) #
Ord k => Monoid (Map k v) |
Instance details Defined in Data.Map.Internal Methods mempty :: Map k v # mappend :: Map k v -> Map k v -> Map k v # mconcat :: [Map k v] -> Map k v #
Ord k => Semigroup (Map k v) |
Instance details Defined in Data.Map.Internal Methods (<>) :: Map k v -> Map k v -> Map k v # sconcat :: NonEmpty (Map k v) -> Map k v # stimes :: Integral b => b -> Map k v -> Map k v #
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) |
Instance details Defined in Data.Map.Internal type Item (Map k v) = (k, v)
Methods fromList :: [Item (Map k v)] -> Map k v # fromListN :: Int -> [Item (Map k v)] -> Map k v # toList :: Map k v -> [Item (Map k v)] #
(Ord k, Read k, Read e) => Read (Map k e) |
Instance details Defined in Data.Map.Internal Methods readsPrec :: Int -> ReadS (Map k e) # readList :: ReadS [Map k e] # readPrec :: ReadPrec (Map k e) # readListPrec :: ReadPrec [Map k e] #
(Show k, Show a) => Show (Map k a) |
Instance details Defined in Data.Map.Internal Methods showsPrec :: Int -> Map k a -> ShowS # show :: Map k a -> String # showList :: [Map k a] -> ShowS #
(NFData k, NFData a) => NFData (Map k a) |
Instance details Defined in Data.Map.Internal Methods rnf :: Map k a -> () #
(Eq k, Eq a) => Eq (Map k a) |
Instance details Defined in Data.Map.Internal Methods (==) :: Map k a -> Map k a -> Bool # (/=) :: Map k a -> Map k a -> Bool #
(Ord k, Ord v) => Ord (Map k v) |
Instance details Defined in Data.Map.Internal Methods compare :: Map k v -> Map k v -> Ordering # (<) :: Map k v -> Map k v -> Bool # (<=) :: Map k v -> Map k v -> Bool # (>) :: Map k v -> Map k v -> Bool # (>=) :: Map k v -> Map k v -> Bool # max :: Map k v -> Map k v -> Map k v # min :: Map k v -> Map k v -> Map k v #
(Hashable k, Hashable v) => Hashable (Map k v) | Since: hashable-1.3.4.0
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Map k v -> Int # hash :: Map k v -> Int #
type Item (Map k v) |
Instance details Defined in Data.Map.Internal type Item (Map k v) = (k, v)

# Operators

(!?) :: 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 -> Map k b -> Map k a infixl 9 #

Same as `difference`.

# Query

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

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

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

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'

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

# 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

## 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"

Also see the performance note on `fromListWith`.

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"

Also see the performance note on `fromListWith`.

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")])

Also see the performance note on `fromListWith`.

## Delete/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")]

Note that ``adjust` = alter . fmap`.

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 `Control.Lens.At`.

Since: containers-0.5.8

# Combine

## Union

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

\(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). 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 #

\(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). Union with a combining function.

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

Also see the performance note on `fromListWith`.

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

\(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). 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")]

Also see the performance note on `fromListWith`.

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 #

\(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). 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"

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 #

\(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). 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 #

\(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). 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 #

\(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). 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.Strict

## Deprecated 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 universal 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` or ``filterWithKey` 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) -> (v' -> v' `seq` (k,v')) <$> f k v) (`toList` m)` That is, it behaves much like a regular `traverse` except that the traversing function also has access to the key associated with a value and the values are forced before they are installed in the result map.

    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 `mapAccumRWithKey` 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"

Also see the performance note on `fromListWith`.

# 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

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

## 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 == []

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, a linear-time implementation is used.

    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,"x"), (5,"c")] == fromList [(3, "x"), (5, "cba")]
    fromListWith (++) [] == empty

Note the reverse ordering of `"cba"` in the example.

The symmetric combining function `f` is applied in a left-fold over the list, as `f new old`.

### Performance

You should ensure that the given `f` is fast with this order of arguments.

Symmetric functions may be slow in one order, and fast in another. For the common case of collecting values of matching keys in a list, as above:

The complexity of `(++) a b` is \(O(a)\), so it is fast when given a short list as its first argument. Thus:

    fromListWith       (++)  (replicate 1000000 (3, "x"))   -- O(n),  fast
    fromListWith (flip (++)) (replicate 1000000 (3, "x"))   -- O(n²), extremely slow

because they evaluate as, respectively:

    fromList [(3, "x" ++ ("x" ++ "xxxxx..xxxxx"))]   -- O(n)
    fromList [(3, ("xxxxx..xxxxx" ++ "x") ++ "x")]   -- O(n²)

Thus, to get good performance with an operation like `(++)` while also preserving the same order as in the input list, reverse the input:

    fromListWith (++) (reverse [(5,"a"), (5,"b"), (5,"c")]) == fromList [(5, "abc")]

and it is always fast to combine singleton-list values `[v]` with `fromListWith (++)`, as in:

    fromListWith (++) $ reverse $ map (\(k, v) -> (k, [v])) someListOfTuples

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 key new_value old_value = show key ++ ":" ++ new_value ++ "|" ++ old_value
    fromListWithKey f [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"c")] == fromList [(3, "3:a|b"), (5, "5:c|5:b|a")]
    fromListWithKey f [] == empty

Also see the performance note on `fromListWith`.

## 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 #

\(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). Restrict a `Map` to only those keys found in a `Set`.

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

Since: containers-0.5.8

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

\(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). 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 = partitionWithKey (\k _ -> p k) 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 #

\(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). This function is defined as (``isSubmapOf` = `isSubmapOfBy` (==)`).

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

\(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). 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)])

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

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

\(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). 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 #

\(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). 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)])

# 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

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

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 #

\(O(\log n)\). 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 #

\(O(\log n)\). 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")
    lookupMin 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

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

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