containers-0.5.8.1: Assorted concrete container types

Data.Map.Lazy

Description

An efficient implementation of ordered maps from keys to values (dictionaries).

API of this module is strict in the keys, but lazy in the values. If you need value-strict maps, use Data.Map.Strict instead. The Map type itself is shared between the lazy and strict modules, meaning that the same Map value can be passed to functions in both modules (although that is rarely needed).

These modules are intended to be imported qualified, to avoid name clashes with Prelude functions, e.g.

 import qualified Data.Map.Lazy 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.

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

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.

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

Operation comments contain the operation time complexity in the Big-O notation (http://en.wikipedia.org/wiki/Big_O_notation).

Synopsis

# Strictness properties

This module satisfies the following strictness property:

• Key arguments are evaluated to WHNF

Here are some examples that illustrate the property:

insertWith (\ new old -> old) undefined v m  ==  undefined
insertWith (\ new old -> old) k undefined m  ==  OK
delete undefined m  ==  undefined

# Map type

data Map k a Source #

A Map from keys k to values a.

Instances

 Functor (Map k) Source # Methodsfmap :: (a -> b) -> Map k a -> Map k b #(<$) :: a -> Map k b -> Map k a # Foldable (Map k) Source # Methodsfold :: Monoid m => Map k m -> m #foldMap :: Monoid m => (a -> m) -> Map k a -> m #foldr :: (a -> b -> b) -> b -> Map k a -> b #foldr' :: (a -> b -> b) -> b -> Map k a -> b #foldl :: (b -> a -> b) -> b -> Map k a -> b #foldl' :: (b -> a -> b) -> b -> Map k a -> b #foldr1 :: (a -> a -> a) -> Map k a -> a #foldl1 :: (a -> a -> a) -> Map k a -> a #toList :: Map k a -> [a] #null :: Map k a -> Bool #length :: Map k a -> Int #elem :: Eq a => a -> Map k a -> Bool #maximum :: Ord a => Map k a -> a #minimum :: Ord a => Map k a -> a #sum :: Num a => Map k a -> a #product :: Num a => Map k a -> a # Source # Methodstraverse :: Applicative f => (a -> f b) -> Map k a -> f (Map k b) #sequenceA :: Applicative f => Map k (f a) -> f (Map k a) #mapM :: Monad m => (a -> m b) -> Map k a -> m (Map k b) #sequence :: Monad m => Map k (m a) -> m (Map k a) # Ord k => IsList (Map k v) Source # Associated Typestype Item (Map k v) :: * # MethodsfromList :: [Item (Map k v)] -> Map k v #fromListN :: Int -> [Item (Map k v)] -> Map k v #toList :: Map k v -> [Item (Map k v)] # (Eq k, Eq a) => Eq (Map k a) Source # Methods(==) :: Map k a -> Map k a -> Bool #(/=) :: Map k a -> Map k a -> Bool # (Data k, Data a, Ord k) => Data (Map k a) Source # Methodsgfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Map k a -> c (Map k a) #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Map k a) #toConstr :: Map k a -> Constr #dataTypeOf :: Map k a -> DataType #dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Map k a)) #dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Map k a)) #gmapT :: (forall b. Data b => b -> b) -> Map k a -> Map k a #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Map k a -> r #gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Map k a -> r #gmapQ :: (forall d. Data d => d -> u) -> Map k a -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> Map k a -> u #gmapM :: Monad m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) # (Ord k, Ord v) => Ord (Map k v) Source # Methodscompare :: Map k v -> Map k v -> Ordering #(<) :: Map k v -> Map k v -> Bool #(<=) :: Map k v -> Map k v -> Bool #(>) :: Map k v -> Map k v -> Bool #(>=) :: Map k v -> Map k v -> Bool #max :: Map k v -> Map k v -> Map k v #min :: Map k v -> Map k v -> Map k v # (Ord k, Read k, Read e) => Read (Map k e) Source # MethodsreadsPrec :: Int -> ReadS (Map k e) #readList :: ReadS [Map k e] #readPrec :: ReadPrec (Map k e) #readListPrec :: ReadPrec [Map k e] # (Show k, Show a) => Show (Map k a) Source # MethodsshowsPrec :: Int -> Map k a -> ShowS #show :: Map k a -> String #showList :: [Map k a] -> ShowS # Ord k => Semigroup (Map k v) Source # Methods(<>) :: Map k v -> Map k v -> Map k v #sconcat :: NonEmpty (Map k v) -> Map k v #stimes :: Integral b => b -> Map k v -> Map k v # Ord k => Monoid (Map k v) Source # Methodsmempty :: Map k v #mappend :: Map k v -> Map k v -> Map k v #mconcat :: [Map k v] -> Map k v # (NFData k, NFData a) => NFData (Map k a) Source # Methodsrnf :: Map k a -> () # type Item (Map k v) Source # type Item (Map k v) = (k, v) # Operators (!) :: 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' (\\) :: Ord k => Map k a -> Map k b -> Map k a infixl 9 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' lookupLT :: 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 :: 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 :: 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 :: 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 # 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")]) ## 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")] alterF :: (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 :: Int -> Map Int String -> IO (Map Int String)
interactiveAlter k m = alterF f k m where
f Nothing -> do
putStrLn $show k ++ " was not found in the map. Would you like to add it?" getUserResponse1 :: IO (Maybe String) f (Just old) -> do putStrLn "The key is currently bound to " ++ show old ++ ". Would you like to change or delete it?" getUserresponse2 :: IO (Maybe String)  alterF is the most general operation for working with an individual key that may or may not be in a given map. When used with trivial functors like Identity and Const, it is often slightly slower than more specialized combinators like lookup and insert. However, when the functor is non-trivial and key comparison is not particularly cheap, it is the fastest way. Note on rewrite rules: This module includes GHC rewrite rules to optimize alterF for the Const and Identity functors. In general, these rules improve performance. The sole exception is that when using Identity, deleting a key that is already absent takes longer than it would without the rules. If you expect this to occur a very large fraction of the time, you might consider using a private copy of the Identity type. Note: alterF is a flipped version of the at combinator from At. Since: 0.5.8 # Combine ## Union union :: 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 :: 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 :: 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 :: Ord k => [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 :: 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 == 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(m*log(n/m + 1)), m <= n. Difference of two maps. Return elements of the first map not existing in the second map. difference (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 3 "b" differenceWith :: Ord k => (a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a 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 :: 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" ## Intersection intersection :: 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 :: 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 :: 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" ## General combining functions ## Unsafe general combining function mergeWithKey :: Ord k => (k -> a -> b -> Maybe c) -> (Map k a -> Map k c) -> (Map k b -> Map k c) -> Map k a -> Map k b -> Map k c Source # O(n+m). An unsafe general combining function. WARNING: This function can produce corrupt maps and its results may depend on the internal structures of its inputs. Users should prefer merge or mergeA. When mergeWithKey is given three arguments, it is inlined to the call site. You should therefore use mergeWithKey only to define custom combining functions. For example, you could define unionWithKey, differenceWithKey and intersectionWithKey as myUnionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) id id m1 m2 myDifferenceWithKey f m1 m2 = mergeWithKey f id (const empty) m1 m2 myIntersectionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) (const empty) (const empty) m1 m2 When calling mergeWithKey combine only1 only2, a function combining two 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, filterWithKey f, or mapMaybeWithKey f could be used for any f. # 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")] traverseWithKey :: Applicative t => (k -> a -> t b) -> Map k a -> t (Map k b) Source # O(n). traverseWithKey f m == fromList$ traverse ((k, v) -> (,) k $f k v) (toList m) That is, behaves exactly like a regular traverse except that the traversing function also has access to the key associated with a value. traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(1, 'a'), (5, 'e')]) == Just (fromList [(1, 'b'), (5, 'f')]) traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(2, 'c')]) == Nothing traverseMaybeWithKey :: Applicative f => (k -> a -> f (Maybe b)) -> Map k a -> f (Map k b) Source # O(n). Traverse keys/values and collect the Just results. 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")]) mapAccumRWithKey :: (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 :: 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 :: 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 # Folds foldr :: (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 :: (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 :: (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 :: (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 :: 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. ## Strict folds foldr' :: (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' :: (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' :: (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' :: (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. # Conversion elems :: 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 :: 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 :: 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 :: 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 fromSet :: (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 ## Lists toList :: 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 == [] 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. If the keys of the list are ordered, linear-time implementation is used, with the performance equal to fromDistinctAscList. fromList [] == empty fromList [(5,"a"), (3,"b"), (5, "c")] == fromList [(5,"c"), (3,"b")] fromList [(5,"c"), (3,"b"), (5, "a")] == fromList [(5,"a"), (3,"b")] fromListWith :: Ord k => (a -> a -> a) -> [(k, a)] -> Map k a 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 the map to a list of key/value pairs where the keys are in ascending order. Subject to list fusion. toAscList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")] toDescList :: Map k a -> [(k, a)] 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")] 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 fromDescList :: 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,"b")] == fromList [(3, "b"), (5, "b")] valid (fromDescList [(5,"a"), (5,"b"), (3,"b")]) == True valid (fromDescList [(5,"a"), (3,"b"), (5,"b")]) == False fromDescListWith :: 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 :: 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 :: [(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"), (5,"b"), (3,"b")]) == False # Filter filter :: (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 :: (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 :: Ord k => Map k a -> Set k -> Map k a Source # O(m*log(nm + 1)), m <= n/. Restrict a Map to only those keys found in a Set. m restrictKeys s = filterWithKey (k _ -> k member' s) m  Since: 0.5.8 withoutKeys :: Ord k => Map k a -> Set k -> Map k a Source # O(m*log(nm + 1)), m <= n/. Remove all keys in a Set from a Map. m withoutKeys s = filterWithKey (k _ -> k notMember' s) m  Since: 0.5.8 partition :: (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 :: (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 :: (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 note at spanAntitone. takeWhileAntitone p = fromDistinctAscList . takeWhile (p . fst) . toList takeWhileAntitone p = filterWithKey (k _ -> p k)  dropWhileAntitone :: (k -> Bool) -> Map k a -> Map k a Source # O(log n). Drop while a predicate on the keys holds. The user is responsible for ensuring that for all keys j and k in the map, j < k ==> p j >= p k. See note at spanAntitone. dropWhileAntitone p = fromDistinctAscList . dropWhile (p . fst) . toList dropWhileAntitone p = filterWithKey (k -> not (p k))  spanAntitone :: (k -> Bool) -> Map k a -> (Map k a, Map k a) Source # O(log n). Divide a map at the point where a predicate on the keys stops holding. The user is responsible for ensuring that for all keys j and k in the map, j < k ==> p j >= p k. spanAntitone p xs = (takeWhileAntitone p xs, dropWhileAntitone p xs) spanAntitone p xs = partition p xs  Note: if p is not actually antitone, then spanAntitone will split the map at some unspecified point where the predicate switches from holding to not holding (where the predicate is seen to hold before the first key and to fail after the last key). mapMaybe :: (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 :: (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 :: (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 :: (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) splitRoot :: Map k b -> [Map k b] Source # O(1). Decompose a map into pieces based on the structure of the underlying tree. This function is useful for consuming a map in parallel. No guarantee is made as to the sizes of the pieces; an internal, but deterministic process determines this. However, it is guaranteed that the pieces returned will be in ascending order (all elements in the first submap less than all elements in the second, and so on). Examples: splitRoot (fromList (zip [1..6] ['a'..])) == [fromList [(1,'a'),(2,'b'),(3,'c')],fromList [(4,'d')],fromList [(5,'e'),(6,'f')]] splitRoot empty == [] Note that the current implementation does not return more than three submaps, but you should not depend on this behaviour because it can change in the future without notice. # Submap isSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Bool Source # O(m*log(nm + 1)), m <= n/. This function is defined as (isSubmapOf = isSubmapOfBy (==)). isSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool Source # O(m*log(nm + 1)), m <= n/. The expression (isSubmapOfBy f t1 t2) returns True if all keys in t1 are in tree t2, and when f returns True when applied to their respective values. For example, the following expressions are all True: isSubmapOfBy (==) (fromList [('a',1)]) (fromList [('a',1),('b',2)]) isSubmapOfBy (<=) (fromList [('a',1)]) (fromList [('a',1),('b',2)]) isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1),('b',2)]) But the following are all False: isSubmapOfBy (==) (fromList [('a',2)]) (fromList [('a',1),('b',2)]) isSubmapOfBy (<) (fromList [('a',1)]) (fromList [('a',1),('b',2)]) isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1)]) isProperSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Bool Source # O(m*log(nm + 1)), m <= n/. Is this a proper submap? (ie. a submap but not equal). Defined as (isProperSubmapOf = isProperSubmapOfBy (==)). isProperSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool Source # O(m*log(nm + 1)), m <= n/. Is this a proper submap? (ie. a submap but not equal). The expression (isProperSubmapOfBy f m1 m2) returns True when m1 and m2 are not equal, all keys in m1 are in m2, and when f returns True when applied to their respective values. For example, the following expressions are all True: isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) But the following are all False: isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)]) isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)]) isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) # Indexed lookupIndex :: Ord k => k -> Map k a -> Maybe Int Source # O(log n). Lookup the index of a key, which is its zero-based index in the sequence sorted by keys. The index is a number from 0 up to, but not including, the size of the map. isJust (lookupIndex 2 (fromList [(5,"a"), (3,"b")])) == False fromJust (lookupIndex 3 (fromList [(5,"a"), (3,"b")])) == 0 fromJust (lookupIndex 5 (fromList [(5,"a"), (3,"b")])) == 1 isJust (lookupIndex 6 (fromList [(5,"a"), (3,"b")])) == False findIndex :: Ord k => k -> Map k a -> Int Source # O(log n). Return the index of a key, which is its zero-based index in the sequence sorted by keys. The index is a number from 0 up to, but not including, the size of the map. Calls error when the key is not a member of the map. findIndex 2 (fromList [(5,"a"), (3,"b")]) Error: element is not in the map findIndex 3 (fromList [(5,"a"), (3,"b")]) == 0 findIndex 5 (fromList [(5,"a"), (3,"b")]) == 1 findIndex 6 (fromList [(5,"a"), (3,"b")]) Error: element is not in the map elemAt :: Int -> Map k a -> (k, a) Source # O(log n). Retrieve an element by its index, i.e. by its zero-based index in the sequence sorted by keys. If the index is out of range (less than zero, greater or equal to size of the map), error is called. elemAt 0 (fromList [(5,"a"), (3,"b")]) == (3,"b") elemAt 1 (fromList [(5,"a"), (3,"b")]) == (5, "a") elemAt 2 (fromList [(5,"a"), (3,"b")]) Error: index out of range updateAt :: (k -> a -> Maybe a) -> Int -> Map k a -> Map k a Source # O(log n). Update the element at index, i.e. by its zero-based index in the sequence sorted by keys. If the index is out of range (less than zero, greater or equal to size of the map), error is called. updateAt (\ _ _ -> Just "x") 0 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "x"), (5, "a")] updateAt (\ _ _ -> Just "x") 1 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "x")] updateAt (\ _ _ -> Just "x") 2 (fromList [(5,"a"), (3,"b")]) Error: index out of range updateAt (\ _ _ -> Just "x") (-1) (fromList [(5,"a"), (3,"b")]) Error: index out of range updateAt (\_ _ -> Nothing) 0 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" updateAt (\_ _ -> Nothing) 1 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" updateAt (\_ _ -> Nothing) 2 (fromList [(5,"a"), (3,"b")]) Error: index out of range updateAt (\_ _ -> Nothing) (-1) (fromList [(5,"a"), (3,"b")]) Error: index out of range deleteAt :: Int -> Map k a -> Map k a Source # O(log n). Delete the element at index, i.e. by its zero-based index in the sequence sorted by keys. If the index is out of range (less than zero, greater or equal to size of the map), error is called. deleteAt 0 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" deleteAt 1 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" deleteAt 2 (fromList [(5,"a"), (3,"b")]) Error: index out of range deleteAt (-1) (fromList [(5,"a"), (3,"b")]) Error: index out of range take :: Int -> Map k a -> Map k a Source # Take a given number of entries in key order, beginning with the smallest keys. take n = fromDistinctAscList . take n . toAscList  drop :: Int -> Map k a -> Map k a Source # Drop a given number of entries in key order, beginning with the smallest keys. drop n = fromDistinctAscList . drop n . toAscList  splitAt :: Int -> Map k a -> (Map k a, Map k a) Source # O(log n). Split a map at a particular index. splitAt !n !xs = (take n xs, drop n xs)  # Min/Max findMin :: Map k a -> (k, a) Source # O(log n). The minimal key of the map. Calls error if the map is empty. findMin (fromList [(5,"a"), (3,"b")]) == (3,"b") findMin empty Error: empty map has no minimal element findMax :: Map k a -> (k, a) Source # O(log n). The maximal key of the map. Calls error if 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 empty map. maxView (fromList [(5,"a"), (3,"b")]) == Just ("a", singleton 3 "b") maxView empty == Nothing minViewWithKey :: Map k a -> Maybe ((k, a), Map k a) 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 # Deprecated: This function is being removed from the public API. 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 # Deprecated: This function is being removed from the public API. 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