| 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
Description
Finite Maps (lazy interface)
The type represents a finite map (sometimes called a dictionary)
from keys of type Map k vk 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
Intkeys, you will get much better performance for most operations using Data.IntMap.Lazy. - If you don't care about ordering, consider using
Data.HashMap.Lazyfrom 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
A Map from keys k to values a.
Instances
| Eq2 Map # | Since: containers-0.5.9 |
| Ord2 Map # | Since: containers-0.5.9 |
Defined in Data.Map.Internal | |
| Show2 Map # | Since: containers-0.5.9 |
| Functor (Map k) # | |
| Foldable (Map k) # | |
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 # | |
| Traversable (Map k) # | |
| Eq k => Eq1 (Map k) # | Since: containers-0.5.9 |
| Ord k => Ord1 (Map k) # | Since: containers-0.5.9 |
Defined in Data.Map.Internal | |
| (Ord k, Read k) => Read1 (Map k) # | Since: containers-0.5.9 |
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 |
| Ord k => IsList (Map k v) # | Since: containers-0.5.6.2 |
| (Eq k, Eq a) => Eq (Map k a) # | |
| (Data k, Data a, Ord k) => Data (Map k a) # | |
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) # | |
Defined in Data.Map.Internal | |
| (Ord k, Read k, Read e) => Read (Map k e) # | |
| (Show k, Show a) => Show (Map k a) # | |
| Ord k => Semigroup (Map k v) # | |
| Ord k => Monoid (Map k v) # | |
| (NFData k, NFData a) => NFData (Map k a) # | |
Defined in Data.Map.Internal | |
| type Item (Map k v) # | |
Defined in Data.Map.Internal | |
Construction
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.
will insert the pair (key, value) into insertWith f key value mpmp 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.
will insert the pair (key, value) into insertWithKey f key value mpmp 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 ()
is a pair where the first element is equal to (insertLookupWithKey f k x map)
and the second element equal to (lookup k map).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 == emptyadjustWithKey :: 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 () updates the value update f k mapx
at k (if it is in the map). If (f x) is Nothing, the element is
deleted. If it is (), the key Just yk 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 () updates the
value updateWithKey f k mapx at k (if it is in the map). If (f k x) is Nothing,
the element is deleted. If it is (), the key Just yk 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 () alters the value alter f k mapx 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 () alters the value alterF f k mapx 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 (,
or Just value)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 ( returns
the value at key findWithDefault def k map)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
O(1). Is the map empty?
Data.Map.null (empty) == True Data.Map.null (singleton 1 'a') == False
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
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"
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 (), the element is updated with a new value Just yy.
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 (), the element is updated with a new value Just yy.
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
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 , a function combining two
mergeWithKey combine only1 only2Maps is created, such that
- if a key is present in both maps, it is passed with both corresponding
values to the
combinefunction. 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
only1and the output is added to the result; - a nonempty subtree present only in the second map is passed to
only2and 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 , but for example const empty,
map f, or filterWithKey f could be used for any mapMaybeWithKey ff.
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).
That is, behaves exactly like a regular traverseWithKey f m == fromList $ traverse ((k, v) -> (,) k $ f k v) (toList m)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).
is the map obtained by applying mapKeys f sf 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).
is the map obtained by applying mapKeysWith c f sf 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).
, but works only when mapKeysMonotonic f s == mapKeys f sf
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 sThis 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
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
foldMapWithKeyf =fold.mapWithKeyf
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
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 == []
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 == []
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) .toListtakeWhileAntitone 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) .toListdropWhileAntitone 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 = (takeWhileAntitonep xs,dropWhileAntitonep 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 () is a pair split k map(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 () splits a map just
like splitLookup k mapsplit 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 () returns isSubmapOfBy f t1 t2True 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 () returns isProperSubmapOfBy f m1 m2True 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.taken .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.dropn .toAscList
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
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 == NothingmaxView :: 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 == NothingminViewWithKey :: 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.