| containers-0.2.0.1: Assorted concrete container types | Source code | Contents | Index
Data.Map |
Portability | portable
Stability | provisional
Maintainer | libraries@haskell.org
Contents
Map type Operators Query Construction Insertion Delete/Update Combine Union Difference Intersection Traversal Map Fold Conversion Lists Ordered lists Filter Submap Indexed Min/Max Debugging
Description
An efficient implementation of maps from keys to values (dictionaries). Since many function names (but not the type name) clash with Prelude names, this module is usually imported `qualified`, e.g.
      import Data.Map (Map)
      import qualified Data.Map as Map
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. Note that the implementation is left-biased -- the elements of a first argument are always preferred to the second, for example in `union` or `insert`. Operation comments contain the operation time complexity in the Big-O notation http://en.wikipedia.org/wiki/Big_O_notation.
Synopsis
data Map k a
(!) :: Ord k => Map k a -> k -> a
(\\) :: Ord k => Map k a -> Map k b -> Map k a
null :: Map k a -> Bool
size :: Map k a -> Int
member :: Ord k => k -> Map k a -> Bool
notMember :: Ord k => k -> Map k a -> Bool
lookup :: Ord k => k -> Map k a -> Maybe a
findWithDefault :: Ord k => a -> k -> Map k a -> a
empty :: Map k a
singleton :: k -> a -> Map k a
insert :: Ord k => k -> a -> Map k a -> Map k a
insertWith :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
insertLookupWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> (Maybe a, Map k a)
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
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
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 :: Ord k => [Map k a] -> Map k a
unionsWith :: Ord k => (a -> a -> a) -> [Map k a] -> Map k a
difference :: Ord k => Map k a -> Map k b -> Map k a
differenceWith :: Ord k => (a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a
differenceWithKey :: Ord k => (k -> a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a
intersection :: Ord k => Map k a -> Map k b -> Map k a
intersectionWith :: Ord k => (a -> b -> c) -> Map k a -> Map k b -> Map k c
intersectionWithKey :: Ord k => (k -> a -> b -> c) -> Map k a -> Map k b -> Map k c
map :: (a -> b) -> Map k a -> Map k b
mapWithKey :: (k -> a -> b) -> Map k a -> 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)
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
fold :: (a -> b -> b) -> b -> Map k a -> b
foldWithKey :: (k -> a -> b -> b) -> b -> Map k a -> b
elems :: Map k a -> [a]
keys :: Map k a -> [k]
keysSet :: Map k a -> Set k
assocs :: Map k a -> [(k, a)]
toList :: Map k a -> [(k, a)]
fromList :: Ord k => [(k, a)] -> Map k a
fromListWith :: Ord k => (a -> a -> a) -> [(k, a)] -> Map k a
fromListWithKey :: Ord k => (k -> a -> a -> a) -> [(k, a)] -> Map k a
toAscList :: Map k a -> [(k, a)]
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
filter :: Ord k => (a -> Bool) -> Map k a -> Map k a
filterWithKey :: Ord k => (k -> a -> Bool) -> Map k a -> Map k a
partition :: Ord k => (a -> Bool) -> Map k a -> (Map k a, Map k a)
partitionWithKey :: Ord k => (k -> a -> Bool) -> Map k a -> (Map k a, Map k a)
mapMaybe :: Ord k => (a -> Maybe b) -> Map k a -> Map k b
mapMaybeWithKey :: Ord k => (k -> a -> Maybe b) -> Map k a -> Map k b
mapEither :: Ord k => (a -> Either b c) -> Map k a -> (Map k b, Map k c)
mapEitherWithKey :: Ord k => (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)
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
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 :: (Show k, Show a) => Map k a -> String
showTreeWith :: (k -> a -> String) -> Bool -> Bool -> Map k a -> String
valid :: Ord k => Map k a -> Bool
Map type
data Map k a | Source
A Map from keys `k` to values `a`.
Instances
Typeable2 Map
Functor (Map k)
Traversable (Map k)
Foldable (Map k)
(Eq k, Eq a) => Eq (Map k a)
(Data k, Data a, Ord k) => Data (Map k a)
(Ord k, Ord v) => Ord (Map k v)
(Ord k, Read k, Read e) => Read (Map k e)
(Show k, Show a) => Show (Map k a)
Ord k => Monoid (Map k v)
Operators
(!) :: Ord k => Map k a -> k -> a | 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'
(\\) :: Ord k => Map k a -> Map k b -> Map k a | Source
Same as `difference`.
Query
null :: Map k a -> Bool | Source
O(1). Is the map empty?
     Data.Map.null (empty)           == True
     Data.Map.null (singleton 1 'a') == False
size :: 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
member :: 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 :: 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
lookup :: 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 :: String -> Maybe String
     employeeCurrency name = do
         dept <- lookup name employeeDept
         country <- lookup dept deptCountry
         lookup country countryCurrency

     main = do
         putStrLn $ "John's currency: " ++ (show (employeeCurrency "John"))
         putStrLn $ "Pete's currency: " ++ (show (employeeCurrency "Pete"))
The output of this program:
       John's currency: Just "Euro"
       Pete's currency: Nothing
findWithDefault :: Ord k => a -> k -> Map k a -> a | 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'
Construction
empty :: Map k a | Source
O(1). The empty map.
     empty      == fromList []
     size empty == 0
singleton :: 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
Insertion
insert :: 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 :: 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 :: 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 :: 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")])
insertWith' :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a | Source
Same as `insertWith`, but the combining function is applied strictly.
insertWithKey' :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a | Source
Same as `insertWithKey`, but the combining function is applied strictly.
Delete/Update
delete :: 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 :: 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 :: 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 :: 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 :: 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 :: 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 :: 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")]
Combine
Union
union :: Ord k => Map k a -> Map k a -> Map k a | Source
O(n+m). 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``). The implementation uses the efficient hedge-union algorithm. Hedge-union is more efficient on (bigset ``union`` smallset).
     union (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "a"), (7, "C")]
unionWith :: Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a | Source
O(n+m). Union with a combining function. The implementation uses the efficient hedge-union algorithm.
     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 | Source
O(n+m). Union with a combining function. The implementation uses the efficient hedge-union algorithm. Hedge-union is more efficient on (bigset ``union`` smallset).
     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 :: Ord k => [Map k a] -> Map k a | Source
The union of a list of maps: (``unions` == Prelude.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 :: Ord k => (a -> a -> a) -> [Map k a] -> Map k a | Source
The union of a list of maps, with a combining operation: (``unionsWith` f == Prelude.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 | Source
O(n+m). Difference of two maps. Return elements of the first map not existing in the second map. The implementation uses an efficient hedge algorithm comparable with hedge-union.
     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 | 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`. The implementation uses an efficient hedge algorithm comparable with hedge-union.
     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 | 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`. The implementation uses an efficient hedge algorithm comparable with hedge-union.
     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 | Source
O(n+m). 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 | Source
O(n+m). 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 | Source
O(n+m). Intersection with a combining function. Intersection is more efficient on (bigset ``intersection`` smallset).
     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"
Traversal
Map
map :: (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 :: (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")]
mapAccum :: (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 :: (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")])
mapKeys :: 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 smallest of these 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 | 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`.
     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 | 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
Fold
fold :: (a -> b -> b) -> b -> Map k a -> b | Source
O(n). Fold the values in the map, such that ``fold` f z == Prelude.foldr f z . `elems``. For example,
     elems map = fold (:) [] map
     let f a len = len + (length a)
     fold f 0 (fromList [(5,"a"), (3,"bbb")]) == 4
foldWithKey :: (k -> a -> b -> b) -> b -> Map k a -> b | Source
O(n). Fold the keys and values in the map, such that ``foldWithKey` f z == Prelude.foldr (`uncurry` f) z . `toAscList``. For example,
     keys map = foldWithKey (\k x ks -> k:ks) [] map
     let f k a result = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")"
     foldWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (5:a)(3:b)"
Conversion
elems :: Map k a -> [a] | Source
O(n). Return all elements of the map in the ascending order of their keys.
     elems (fromList [(5,"a"), (3,"b")]) == ["b","a"]
     elems empty == []
keys :: Map k a -> [k] | Source
O(n). Return all keys of the map in ascending order.
     keys (fromList [(5,"a"), (3,"b")]) == [3,5]
     keys empty == []
keysSet :: 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
assocs :: Map k a -> [(k, a)] | Source
O(n). Return all key/value pairs in the map in ascending key order.
     assocs (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
     assocs empty == []
Lists
toList :: Map k a -> [(k, a)] | Source
O(n). Convert to a list of key/value pairs.
     toList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
     toList empty == []
fromList :: 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.
     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 | 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 :: 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
Ordered lists
toAscList :: Map k a -> [(k, a)] | Source
O(n). Convert to an ascending list.
     toAscList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
fromAscList :: 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 :: 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 :: 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 :: [(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
Filter
filter :: Ord k => (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 :: Ord k => (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"
partition :: Ord 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`.
     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 :: Ord k => (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")])
mapMaybe :: Ord k => (a -> Maybe b) -> Map k a -> Map k b | Source
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 :: Ord k => (k -> a -> Maybe b) -> Map k a -> Map k b | Source
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 :: Ord k => (a -> Either b c) -> Map k a -> (Map k b, Map k c) | Source
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 :: Ord k => (k -> a -> Either b c) -> Map k a -> (Map k b, Map k c) | Source
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) | Source
O(log n). The expression (``split` k map`) is a pair `(map1,map2)` where the keys in `map1` are smaller than `k` and the keys in `map2` larger than `k`. Any key equal to `k` is found in neither `map1` nor `map2`.
     split 2 (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3,"b"), (5,"a")])
     split 3 (fromList [(5,"a"), (3,"b")]) == (empty, singleton 5 "a")
     split 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a")
     split 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", empty)
     split 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], empty)
splitLookup :: Ord k => k -> Map k a -> (Map k a, Maybe a, Map k a) | Source
O(log n). The expression (``splitLookup` k map`) splits a map just like `split` but also returns ``lookup` k map`.
     splitLookup 2 (fromList [(5,"a"), (3,"b")]) == (empty, Nothing, fromList [(3,"b"), (5,"a")])
     splitLookup 3 (fromList [(5,"a"), (3,"b")]) == (empty, Just "b", singleton 5 "a")
     splitLookup 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Nothing, singleton 5 "a")
     splitLookup 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Just "a", empty)
     splitLookup 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], Nothing, empty)
Submap
isSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Bool | Source
O(n+m). This function is defined as (``isSubmapOf` = `isSubmapOfBy` (==)`).
isSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool | Source
O(n+m). The expression (``isSubmapOfBy` f t1 t2`) returns `True` if all keys in `t1` are in tree `t2`, and when `f` returns `True` when applied to their respective values. For example, the following expressions are all `True`:
     isSubmapOfBy (==) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
     isSubmapOfBy (<=) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
     isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1),('b',2)])
But the following are all `False`:
     isSubmapOfBy (==) (fromList [('a',2)]) (fromList [('a',1),('b',2)])
     isSubmapOfBy (<)  (fromList [('a',1)]) (fromList [('a',1),('b',2)])
     isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1)])
isProperSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Bool | Source
O(n+m). 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 | Source
O(n+m). Is this a proper submap? (ie. a submap but not equal). The expression (``isProperSubmapOfBy` f m1 m2`) returns `True` when `m1` and `m2` are not equal, all keys in `m1` are in `m2`, and when `f` returns `True` when applied to their respective values. For example, the following expressions are all `True`:
     isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
     isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
But the following are all `False`:
     isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
     isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
     isProperSubmapOfBy (<)  (fromList [(1,1)])       (fromList [(1,1),(2,2)])
Indexed
lookupIndex :: Ord k => k -> Map k a -> Maybe Int | Source
O(log n). Lookup the index of a key. 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 | Source
O(log n). Return the index of a key. 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) | Source
O(log n). Retrieve an element by index. Calls `error` when an invalid index is used.
     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 | Source
O(log n). Update the element at index. Calls `error` when an invalid index is used.
     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 | Source
O(log n). Delete the element at index. Defined as (``deleteAt` i map = `updateAt` (k x -> `Nothing`) i map`).
     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
Min/Max
findMin :: Map k a -> (k, a) | Source
O(log n). The minimal key of the map. Calls `error` is the map is empty.
     findMin (fromList [(5,"a"), (3,"b")]) == (3,"b")
     findMin empty                            Error: empty map has no minimal element
findMax :: Map k a -> (k, a) | Source
O(log n). The maximal key of the map. Calls `error` is the map is empty.
     findMax (fromList [(5,"a"), (3,"b")]) == (5,"a")
     findMax empty                            Error: empty map has no maximal element
deleteMin :: Map k a -> Map k a | Source
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 | Source
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) | Source
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) | Source
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 | Source
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 | Source
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 | Source
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 | Source
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) | Source
O(log n). Retrieves the value associated with minimal key of the map, and the map stripped of that element, or `Nothing` if passed an empty map.
     minView (fromList [(5,"a"), (3,"b")]) == Just ("b", singleton 5 "a")
     minView empty == Nothing
maxView :: Map k a -> Maybe (a, Map k a) | Source
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
     maxView (fromList [(5,"a"), (3,"b")]) == Just ("a", singleton 3 "b")
     maxView empty == Nothing
minViewWithKey :: Map k a -> Maybe ((k, a), Map k a) | Source
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) | Source
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 :: (Show k, Show a) => Map k a -> String | Source
O(n). Show the tree that implements the map. The tree is shown in a compressed, hanging format. See `showTreeWith`.
showTreeWith :: (k -> a -> String) -> Bool -> Bool -> Map k a -> String | Source
O(n). The expression (``showTreeWith` showelem hang wide map`) shows the tree that implements the map. Elements are shown using the `showElem` function. If `hang` is `True`, a hanging tree is shown otherwise a rotated tree is shown. If `wide` is `True`, an extra wide version is shown.
      Map> let t = fromDistinctAscList [(x,()) | x <- [1..5]]
      Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True False t
      (4,())
      +--(2,())
      |  +--(1,())
      |  +--(3,())
      +--(5,())

      Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True True t
      (4,())
      |
      +--(2,())
      |  |
      |  +--(1,())
      |  |
      |  +--(3,())
      |
      +--(5,())

      Map> putStrLn $ showTreeWith (\k x -> show (k,x)) False True t
      +--(5,())
      |
      (4,())
      |
      |  +--(3,())
      |  |
      +--(2,())
         |
         +--(1,())
valid :: Ord k => Map k a -> Bool | Source
O(n). Test if the internal map structure is valid.
     valid (fromAscList [(3,"b"), (5,"a")]) == True
     valid (fromAscList [(5,"a"), (3,"b")]) == False
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