Data.Map.Strict Copyright (c) Daan Leijen 2002(c) Andriy Palamarchuk 2008 License BSD-style Maintainer yhernandez@example.org Portability portable Safe Haskell Safe Language Haskell98 Contents Map type Construction From Unordered Lists From Ascending Lists From Descending Lists Insertion Deletion/Update Query Lookup Size Combine Union Difference Intersection Disjoint General combining functions Deprecated general combining function TraversalMap FoldsStrict folds Conversion Lists Ordered lists Filter Submap Indexed Min/Max Debugging Description Finite Maps (strict interface) The Map k v type represents a finite map (sometimes called a dictionary) from keys of type k to values of type v. Each function in this module is careful to force values before installing them in a Map. This is usually more efficient when laziness is not necessary. When laziness is required, use the functions in Data.Map.Lazy. In particular, the functions in this module obey the following law: If all values stored in all maps in the arguments are in WHNF, then all values stored in all maps in the results will be in WHNF once those maps are evaluated. When deciding if this is the correct data structure to use, consider: If you are using Int keys, you will get much better performance for most operations using Data.IntMap.Strict. If you don't care about ordering, consider use Data.HashMap.Strict from the unordered-containers package instead. For a walkthrough of the most commonly used functions see the maps introduction. This module is intended to be imported qualified, to avoid name clashes with Prelude functions: import qualified Data.Map.Strict 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.Strict with other dictionary implementations can be found at https://github.com/haskell-perf/dictionaries. Warning The size of a Map must not exceed maxBoun8b7c:f320:99b9:690f:4595:cd17:293a:c069Int. Violation of this condition is not detected and if the size limit is exceeded, its behaviour is undefined. The Map type is shared between the lazy and strict modules, meaning that the same Map value can be passed to functions in both modules. This means that the Functor, Traversable and Data instances are the same as for the Data.Map.Lazy module, so if they are used the resulting maps may contain suspended values (thunks). 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. Map typedata Map k a Source 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 Eq2 Map Since: containers-0.5.9 Instance detailsDefined in Data.Map.Internal Methods liftEq2 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> b -> Bool) -> (c -> d -> Bool) -> Map a c -> Map b d -> Bool Source Ord2 Map Since: containers-0.5.9 Instance detailsDefined in Data.Map.Internal Methods liftCompare2 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> b -> Ordering) -> (c -> d -> Ordering) -> Map a c -> Map b d -> Ordering Source Show2 Map Since: containers-0.5.9 Instance detailsDefined in Data.Map.Internal Methods liftShowsPrec2 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Map a b -> ShowS Source liftShowList2 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Map a b] -> ShowS Source Functor (Map k) Instance detailsDefined in Data.Map.Internal Methods fmap 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> b) -> Map k a -> Map k b Source (<$) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 a -> Map k b -> Map k a Source Foldable (Map k) Folds in order of increasing key. Instance detailsDefined in Data.Map.Internal Methods fold 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Monoid m => Map k m -> m Source foldMap 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Monoid m => (a -> m) -> Map k a -> m Source foldMap' 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Monoid m => (a -> m) -> Map k a -> m Source foldr 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> b -> b) -> b -> Map k a -> b Source foldr' 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> b -> b) -> b -> Map k a -> b Source foldl 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (b -> a -> b) -> b -> Map k a -> b Source foldl' 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (b -> a -> b) -> b -> Map k a -> b Source foldr1 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> a -> a) -> Map k a -> a Source foldl1 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> a -> a) -> Map k a -> a Source toList 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a -> [a] Source null 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a -> Bool Source length 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a -> Int Source elem 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Eq a => a -> Map k a -> Bool Source maximum 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord a => Map k a -> a Source minimum 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord a => Map k a -> a Source sum 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Num a => Map k a -> a Source product 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Num a => Map k a -> a Source Traversable (Map k) Traverses in order of increasing key. Instance detailsDefined in Data.Map.Internal Methods traverse 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Applicative f => (a -> f b) -> Map k a -> f (Map k b) Source sequenceA 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Applicative f => Map k (f a) -> f (Map k a) Source mapM 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Monad m => (a -> m b) -> Map k a -> m (Map k b) Source sequence 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Monad m => Map k (m a) -> m (Map k a) Source Eq k => Eq1 (Map k) Since: containers-0.5.9 Instance detailsDefined in Data.Map.Internal Methods liftEq 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> b -> Bool) -> Map k a -> Map k b -> Bool Source Ord k => Ord1 (Map k) Since: containers-0.5.9 Instance detailsDefined in Data.Map.Internal Methods liftCompare 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> b -> Ordering) -> Map k a -> Map k b -> Ordering Source (Ord k, Read k) => Read1 (Map k) Since: containers-0.5.9 Instance detailsDefined in Data.Map.Internal Methods liftReadsPrec 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Map k a) Source liftReadList 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (Int -> ReadS a) -> ReadS [a] -> ReadS [Map k a] Source liftReadPrec 8b7c:f320:99b9:690f:4595:cd17:293a:c069 ReadPrec a -> ReadPrec [a] -> ReadPrec (Map k a) Source liftReadListPrec 8b7c:f320:99b9:690f:4595:cd17:293a:c069 ReadPrec a -> ReadPrec [a] -> ReadPrec [Map k a] Source Show k => Show1 (Map k) Since: containers-0.5.9 Instance detailsDefined in Data.Map.Internal Methods liftShowsPrec 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Map k a -> ShowS Source liftShowList 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Map k a] -> ShowS Source Ord k => IsList (Map k v) Since: containers-289-452-1278 Instance detailsDefined in Data.Map.Internal Associated Types type Item (Map k v) Source Methods fromList 8b7c:f320:99b9:690f:4595:cd17:293a:c069 [Item (Map k v)] -> Map k v Source fromListN 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Int -> [Item (Map k v)] -> Map k v Source toList 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k v -> [Item (Map k v)] Source (Eq k, Eq a) => Eq (Map k a) Instance detailsDefined in Data.Map.Internal Methods (==) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a -> Map k a -> Bool (/=) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a -> Map k a -> Bool (Data k, Data a, Ord k) => Data (Map k a) Instance detailsDefined in Data.Map.Internal Methods gfoldl 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Map k a) Source toConstr 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a -> Constr Source dataTypeOf 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a -> DataType Source dataCast1 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Map k a)) Source dataCast2 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Map k a)) Source gmapT 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (forall b. Data b => b -> b) -> Map k a -> Map k a Source gmapQl 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Map k a -> r Source gmapQr 8b7c:f320:99b9:690f:4595:cd17:293a:c069 forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Map k a -> r Source gmapQ 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (forall d. Data d => d -> u) -> Map k a -> [u] Source gmapQi 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Int -> (forall d. Data d => d -> u) -> Map k a -> u Source gmapM 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Monad m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) Source gmapMp 8b7c:f320:99b9:690f:4595:cd17:293a:c069 MonadPlus m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) Source gmapMo 8b7c:f320:99b9:690f:4595:cd17:293a:c069 MonadPlus m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) Source (Ord k, Ord v) => Ord (Map k v) Instance detailsDefined in Data.Map.Internal Methods compare 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k v -> Map k v -> Ordering (<) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k v -> Map k v -> Bool (<=) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k v -> Map k v -> Bool (>) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k v -> Map k v -> Bool (>=) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k v -> Map k v -> Bool max 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k v -> Map k v -> Map k v min 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k v -> Map k v -> Map k v (Ord k, Read k, Read e) => Read (Map k e) Instance detailsDefined in Data.Map.Internal Methods readsPrec 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Int -> ReadS (Map k e) Source readList 8b7c:f320:99b9:690f:4595:cd17:293a:c069 ReadS [Map k e] Source readPrec 8b7c:f320:99b9:690f:4595:cd17:293a:c069 ReadPrec (Map k e) Source readListPrec 8b7c:f320:99b9:690f:4595:cd17:293a:c069 ReadPrec [Map k e] Source (Show k, Show a) => Show (Map k a) Instance detailsDefined in Data.Map.Internal Methods showsPrec 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Int -> Map k a -> ShowS Source show 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a -> String Source showList 8b7c:f320:99b9:690f:4595:cd17:293a:c069 [Map k a] -> ShowS Source Ord k => Semigroup (Map k v) Instance detailsDefined in Data.Map.Internal Methods (<>) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k v -> Map k v -> Map k v Source sconcat 8b7c:f320:99b9:690f:4595:cd17:293a:c069 NonEmpty (Map k v) -> Map k v Source stimes 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Integral b => b -> Map k v -> Map k v Source Ord k => Monoid (Map k v) Instance detailsDefined in Data.Map.Internal Methods mempty 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k v Source mappend 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k v -> Map k v -> Map k v Source mconcat 8b7c:f320:99b9:690f:4595:cd17:293a:c069 [Map k v] -> Map k v Source (NFData k, NFData a) => NFData (Map k a) Instance detailsDefined in Data.Map.Internal Methods rnf 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a -> () Source type Item (Map k v) Instance detailsDefined in Data.Map.Internal type Item (Map k v) = (k, v) Constructionempty 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a Source O(1). The empty map. empty == fromList [] size empty == 0 singleton 8b7c:f320:99b9:690f:4595:cd17:293a:c069 k -> a -> Map k a Source O(1). A map with a single element. singleton 1 'a' == fromList [(1, 'a')] size (singleton 1 'a') == 1 fromSet 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (k -> a) -> Set k -> Map k a Source 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 ListsfromList 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => [(k, a)] -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => (a -> a -> a) -> [(k, a)] -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => (k -> a -> a -> a) -> [(k, a)] -> Map k a Source 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 ListsfromAscList 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Eq k => [(k, a)] -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Eq k => (a -> a -> a) -> [(k, a)] -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 [(k, a)] -> Map k a Source 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 ListsfromDescList 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Eq k => [(k, a)] -> Map k a Source 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,"a")] == fromList [(3, "b"), (5, "b")] valid (fromDescList [(5,"a"), (5,"b"), (3,"b")]) == True valid (fromDescList [(5,"a"), (3,"b"), (5,"b")]) == False fromDescListWith 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Eq k => (a -> a -> a) -> [(k, a)] -> Map k a Source 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 fromDescListWithKey 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 [(k, a)] -> Map k a Source 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"), (3,"b"), (3,"a")]) == False Insertioninsert 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => k -> a -> Map k a -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a Source O(log n). Insert with a function, combining new value and old value. insertWith f key value mp will insert the pair (key, value) into mp if key does not exist in the map. If the key does exist, the function will insert the pair (key, f new_value old_value). insertWith (++) 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "xxxa")] insertWith (++) 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")] insertWith (++) 5 "xxx" empty == singleton 5 "xxx" insertWithKey 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a Source O(log n). Insert with a function, combining key, new value and old value. insertWithKey f key value mp will insert the pair (key, value) into mp if key does not exist in the map. If the key does exist, the function will insert the pair (key,f key new_value old_value). Note that the key passed to f is the same key passed to insertWithKey. let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value insertWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:xxx|a")] insertWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")] insertWithKey f 5 "xxx" empty == singleton 5 "xxx" insertLookupWithKey 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> (Maybe a, Map k a) Source O(log n). Combines insert operation with old value retrieval. The expression (insertLookupWithKey f k x map) is a pair where the first element is equal to (lookup k map) and the second element equal to (insertWithKey f k x map). let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value insertLookupWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:xxx|a")]) insertLookupWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "xxx")]) insertLookupWithKey f 5 "xxx" empty == (Nothing, singleton 5 "xxx") This is how to define insertLookup using insertLookupWithKey: let insertLookup kx x t = insertLookupWithKey (\_ a _ -> a) kx x t insertLookup 5 "x" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "x")]) insertLookup 7 "x" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "x")]) Deletion/Updatedelete 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => k -> Map k a -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => (a -> a) -> k -> Map k a -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => (k -> a -> a) -> k -> Map k a -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => (a -> Maybe a) -> k -> Map k a -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => (k -> a -> Maybe a) -> k -> Map k a -> (Maybe a, Map k a) Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => (Maybe a -> Maybe a) -> k -> Map k a -> Map k a Source O(log n). The expression (alter f k map) alters the value x at k, or absence thereof. alter can be used to insert, delete, or update a value in a Map. In short : lookup k (alter f k m) = f (lookup k m). let f _ = Nothing alter f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] alter f 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" let f _ = Just "c" alter f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "c")] alter f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "c")] alterF 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (Functor f, Ord k) => (Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a) Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 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. QueryLookuplookup 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => k -> Map k a -> Maybe a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 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 (!?) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => Map k a -> k -> Maybe a infixl 9 Source 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 (!) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => Map k a -> k -> a infixl 9 Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => a -> k -> Map k a -> a Source O(log n). The expression (findWithDefault def k map) returns the value at key k or returns default value def when the key is not in the map. findWithDefault 'x' 1 (fromList [(5,'a'), (3,'b')]) == 'x' findWithDefault 'x' 5 (fromList [(5,'a'), (3,'b')]) == 'a' member 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => k -> Map k a -> Bool Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => k -> Map k a -> Bool Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => k -> Map k v -> Maybe (k, v) Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => k -> Map k v -> Maybe (k, v) Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => k -> Map k v -> Maybe (k, v) Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => k -> Map k v -> Maybe (k, v) Source 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 Sizenull 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a -> Bool Source O(1). Is the map empty? Data.Map.null (empty) == True Data.Map.null (singleton 1 'a') == False size 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a -> Int Source 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 CombineUnionunion 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => Map k a -> Map k a -> Map k a Source O(m*log(n/m + 1)), m <= n. The expression (union t1 t2) takes the left-biased union of t1 and t2. It prefers t1 when duplicate keys are encountered, i.e. (union == unionWith const). union (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "a"), (7, "C")] unionWith 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => (k -> a -> a -> a) -> Map k a -> Map k a -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (Foldable f, Ord k) => f (Map k a) -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (Foldable f, Ord k) => (a -> a -> a) -> f (Map k a) -> Map k a Source 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")] Differencedifference 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => Map k a -> Map k b -> Map k a Source 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" (\\) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => Map k a -> Map k b -> Map k a infixl 9 Source Same as difference. differenceWith 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => (a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => (k -> a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a Source 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" Intersectionintersection 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => Map k a -> Map k b -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => (a -> b -> c) -> Map k a -> Map k b -> Map k c Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => (k -> a -> b -> c) -> Map k a -> Map k b -> Map k c Source 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" Disjointdisjoint 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => Map k a -> Map k b -> Bool Source O(m*log(n/m + 1)), m <= n. Check whether the key sets of two maps are disjoint (i.e., their intersection is empty). disjoint (fromList [(2,'a')]) (fromList [(1,()), (3,())]) == True disjoint (fromList [(2,'a')]) (fromList [(1,'a'), (2,'b')]) == False disjoint (fromList []) (fromList []) == True xs `disjoint` ys = null (xs `intersection` ys) Since: containers-289-452-1278 General combining functionsSee Data.Map.Merge.Strict Deprecated general combining functionmergeWithKey 8b7c:f320:99b9:690f:4595:cd17:293a:c069 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 Source 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 Maps 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. TraversalMapmap 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> b) -> Map k a -> Map k b Source O(n). Map a function over all values in the map. map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")] mapWithKey 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (k -> a -> b) -> Map k a -> Map k b Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Applicative t => (k -> a -> t b) -> Map k a -> t (Map k b) Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Applicative f => (k -> a -> f (Maybe b)) -> Map k a -> f (Map k b) Source O(n). Traverse keys/values and collect the Just results. Since: containers-0.5.8 mapAccum 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> b -> (a, c)) -> a -> Map k b -> (a, Map k c) Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c) Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c) Source O(n). The function mapAccumR threads an accumulating argument through the map in descending order of keys. mapKeys 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k2 => (k1 -> k2) -> Map k1 a -> Map k2 a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k2 => (a -> a -> a) -> (k1 -> k2) -> Map k1 a -> Map k2 a Source O(n*log n). mapKeysWith c f s is the map obtained by applying f to each key of s. The size of the result may be smaller if f maps two or more distinct keys to the same new key. In this case the associated values will be combined using c. The value at the greater of the two original keys is used as the first argument to c. mapKeysWith (++) (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "cdab" mapKeysWith (++) (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "cdab" mapKeysMonotonic 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (k1 -> k2) -> Map k1 a -> Map k2 a Source O(n). mapKeysMonotonic f s == mapKeys f s, but works only when f is strictly monotonic. That is, for any values x and y, if x < y then f x < f y. The precondition is not checked. Semi-formally, we have: and [x < y ==> f x < f y | x <- ls, y <- ls] ==> mapKeysMonotonic f s == mapKeys f s where ls = keys s This means that f maps distinct original keys to distinct resulting keys. This function has better performance than mapKeys. mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")]) == fromList [(6, "b"), (10, "a")] valid (mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")])) == True valid (mapKeysMonotonic (\ _ -> 1) (fromList [(5,"a"), (3,"b")])) == False Foldsfoldr 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> b -> b) -> b -> Map k a -> b Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> b -> a) -> a -> Map k b -> a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (k -> a -> b -> b) -> b -> Map k a -> b Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> k -> b -> a) -> a -> Map k b -> a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Monoid m => (k -> a -> m) -> Map k a -> m Source 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 foldsfoldr' 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> b -> b) -> b -> Map k a -> b Source 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' 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> b -> a) -> a -> Map k b -> a Source 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' 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (k -> a -> b -> b) -> b -> Map k a -> b Source 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' 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> k -> b -> a) -> a -> Map k b -> a Source 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. Conversionelems 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a -> [a] Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a -> [k] Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a -> [(k, a)] Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a -> Set k Source 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 ListstoList 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a -> [(k, a)] Source 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 liststoAscList 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a -> [(k, a)] Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Map k a -> [(k, a)] Source 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")] Filterfilter 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> Bool) -> Map k a -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (k -> a -> Bool) -> Map k a -> Map k a Source O(n). Filter all keys/values that satisfy the predicate. filterWithKey (\k _ -> k > 4) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" restrictKeys 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => Map k a -> Set k -> Map k a Source 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 `intersection` fromSet (const ()) s Since: containers-0.5.8 withoutKeys 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord k => Map k a -> Set k -> Map k a Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> Bool) -> Map k a -> (Map k a, Map k a) Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (k -> a -> Bool) -> Map k a -> (Map k a, Map k a) Source 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (k -> Bool) -> Map k a -> Map k a Source 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 yhernandez@example.org. takeWhileAntitone p = fromDistinctAscList . takeWhile (p . fst) . toList takeWhileAntitone p = filterWithKey (k _ -> p k) Since: containers-0.5.8 dropWhileAntitone
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