Modulecontainers-0.7Haskell2010

Data.Map.Lazy

Finite Maps (lazy interface)

The Map k v type represents a finite map (sometimes called a dictionary) from keys of type k to values of type v. A Map is strict in its keys but lazy in its values.

The functions in Data.Map.Strict are careful to force values before installing them in a Map. This is usually more efficient in cases where laziness is not essential. The functions in this module do not do so.

When deciding if this is the correct data structure to use, consider:

If you are using Prelude.Int keys, you will get much better performance for most operations using Data.IntMap.Lazy.
If you don't care about ordering, consider using Data.HashMap.Lazy from the unordered-containers package instead.

For a walkthrough of the most commonly used functions see the maps introduction.

This module is intended to be imported qualified, to avoid name clashes with Prelude functions:

import qualified Data.Map.Lazy as Map

Note that the implementation is generally left-biased. Functions that take two maps as arguments and combine them, such as union and intersection, prefer the values in the first argument to those in the second.

Detailed performance information

The amortized running time is given for each operation, with n referring to the number of entries in the map.

Benchmarks comparing Data.Map.Lazy with other dictionary implementations can be found at https://github.com/haskell-perf/dictionaries.

Warning

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

Implementation

The implementation of Map is based on size balanced binary trees (or trees of bounded balance) as described by:

Stephen Adams, "Efficient sets: a balancing act", Journal of Functional Programming 3(4):553-562, October 1993, http://www.swiss.ai.mit.edu/~adams/BB/.
J. Nievergelt and E.M. Reingold, "Binary search trees of bounded balance", SIAM journal of computing 2(1), March 1973.

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

Guy Blelloch, Daniel Ferizovic, and Yihan Sun, "Just Join for Parallel Ordered Sets", https://arxiv.org/abs/1602.02120v3.

1 type
128 values

Packagecontainers-0.7
Exports129
LanguageHaskell2010
LicenceBSD-3-Clause
SourceLazy.hs

Map type

1 declaration

datadata Map k a

A Map from keys k to values a.

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

Instances22Bifoldable, Eq2, Ord2, Show2, Lift, Functor, …

Bifoldable MapDefined in containers-0.7 · Data.Map.Internal
Eq2 MapDefined in containers-0.7 · Data.Map.Internal
Ord2 MapDefined in containers-0.7 · Data.Map.Internal
Show2 MapDefined in containers-0.7 · Data.Map.Internal
(Lift k, Lift a) => Lift (Map k a)Defined in containers-0.7 · Data.Map.Internal
Functor (Map k)Defined in containers-0.7 · Data.Map.Internal
Foldable (Map k)Defined in containers-0.7 · Data.Map.Internal
Folds in order of increasing key.
Traversable (Map k)Defined in containers-0.7 · Data.Map.Internal
Traverses in order of increasing key.
Eq k => Eq1 (Map k)Defined in containers-0.7 · Data.Map.Internal
Ord k => Ord1 (Map k)Defined in containers-0.7 · Data.Map.Internal
(Ord k, Read k) => Read1 (Map k)Defined in containers-0.7 · Data.Map.Internal
Show k => Show1 (Map k)Defined in containers-0.7 · Data.Map.Internal
Ord k => IsList (Map k v)Defined in containers-0.7 · Data.Map.Internal
(Eq k, Eq a) => Eq (Map k a)Defined in containers-0.7 · Data.Map.Internal
(Data k, Data a, Ord k) => Data (Map k a)Defined in containers-0.7 · Data.Map.Internal
(Ord k, Ord v) => Ord (Map k v)Defined in containers-0.7 · Data.Map.Internal
(Ord k, Read k, Read e) => Read (Map k e)Defined in containers-0.7 · Data.Map.Internal
(Show k, Show a) => Show (Map k a)Defined in containers-0.7 · Data.Map.Internal
Ord k => Semigroup (Map k v)Defined in containers-0.7 · Data.Map.Internal
Ord k => Monoid (Map k v)Defined in containers-0.7 · Data.Map.Internal
(NFData k, NFData a) => NFData (Map k a)Defined in containers-0.7 · Data.Map.Internal
type Item (Map k v) = (k, v)Defined in containers-0.7 · Data.Map.Internal

Construction

4 declarations

valueempty :: Map k a

O(1). The empty map.

empty      == fromList []
size empty == 0

valuesingleton :: k -> a -> Map k a

O(1). A map with a single element.

singleton 1 'a'        == fromList [(1, 'a')]
size (singleton 1 'a') == 1

valuefromSet :: (k -> a) -> Set k -> Map k a

O(n). Build a map from a set of keys and a function which for each key computes its value.

fromSet (\k -> replicate k 'a') (Data.Set.fromList [3, 5]) == fromList [(5,"aaaaa"), (3,"aaa")]
fromSet undefined Data.Set.empty == empty

valuefromArgSet :: Set (Arg k a) -> Map k a

O(n). Build a map from a set of elements contained inside Args.

fromArgSet (Data.Set.fromList [Arg 3 "aaa", Arg 5 "aaaaa"]) == fromList [(5,"aaaaa"), (3,"aaa")]
fromArgSet Data.Set.empty == empty

From Unordered Lists

valuefromList :: Ord k => [(k, a)] -> Map k a

O(n \log n). Build a map from a list of key/value pairs. See also fromAscList. If the list contains more than one value for the same key, the last value for the key is retained.

If the keys of the list are ordered, a linear-time implementation is used.

fromList [] == empty
fromList [(5,"a"), (3,"b"), (5, "c")] == fromList [(5,"c"), (3,"b")]
fromList [(5,"c"), (3,"b"), (5, "a")] == fromList [(5,"a"), (3,"b")]

valuefromListWith :: Ord k => (a -> a -> a) -> [(k, a)] -> Map k a

O(n \log n). Build a map from a list of key/value pairs with a combining function. See also fromAscListWith.

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

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

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

Performance

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

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

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

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

because they evaluate as, respectively:

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

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

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

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

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

valuefromListWithKey :: Ord k => (k -> a -> a -> a) -> [(k, a)] -> Map k a

O(n \log n). Build a map from a list of key/value pairs with a combining function. See also fromAscListWithKey.

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

Also see the performance note on fromListWith.

From Ascending Lists

valuefromAscList :: Eq k => [(k, a)] -> Map k a

O(n). Build a map from an ascending list in linear time. The precondition (input list is ascending) is not checked.

fromAscList [(3,"b"), (5,"a")]          == fromList [(3, "b"), (5, "a")]
fromAscList [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "b")]
valid (fromAscList [(3,"b"), (5,"a"), (5,"b")]) == True
valid (fromAscList [(5,"a"), (3,"b"), (5,"b")]) == False

valuefromAscListWith :: Eq k => (a -> a -> a) -> [(k, a)] -> Map k a

O(n). Build a map from an ascending list in linear time with a combining function for equal keys. The precondition (input list is ascending) is not checked.

fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")]
valid (fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")]) == True
valid (fromAscListWith (++) [(5,"a"), (3,"b"), (5,"b")]) == False

valuefromAscListWithKey :: Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a

O(n). Build a map from an ascending list in linear time with a combining function for equal keys. The precondition (input list is ascending) is not checked.

let f k a1 a2 = (show k) ++ ":" ++ a1 ++ a2
fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b"), (5,"b")] == fromList [(3, "b"), (5, "5:b5:ba")]
valid (fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b"), (5,"b")]) == True
valid (fromAscListWithKey f [(5,"a"), (3,"b"), (5,"b"), (5,"b")]) == False

Also see the performance note on fromListWith.

valuefromDistinctAscList :: [(k, a)] -> Map k a

O(n). Build a map from an ascending list of distinct elements in linear time. The precondition is not checked.

fromDistinctAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")]
valid (fromDistinctAscList [(3,"b"), (5,"a")])          == True
valid (fromDistinctAscList [(3,"b"), (5,"a"), (5,"b")]) == False

From Descending Lists

valuefromDescList :: Eq k => [(k, a)] -> Map k a

O(n). Build a map from a descending list in linear time. The precondition (input list is descending) is not checked.

fromDescList [(5,"a"), (3,"b")]          == fromList [(3, "b"), (5, "a")]
fromDescList [(5,"a"), (5,"b"), (3,"b")] == fromList [(3, "b"), (5, "b")]
valid (fromDescList [(5,"a"), (5,"b"), (3,"b")]) == True
valid (fromDescList [(5,"a"), (3,"b"), (5,"b")]) == False

valuefromDescListWith :: Eq k => (a -> a -> a) -> [(k, a)] -> Map k a

O(n). Build a map from a descending list in linear time with a combining function for equal keys. The precondition (input list is descending) is not checked.

fromDescListWith (++) [(5,"a"), (5,"b"), (3,"b")] == fromList [(3, "b"), (5, "ba")]
valid (fromDescListWith (++) [(5,"a"), (5,"b"), (3,"b")]) == True
valid (fromDescListWith (++) [(5,"a"), (3,"b"), (5,"b")]) == False

Also see the performance note on fromListWith.

valuefromDescListWithKey :: Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a

O(n). Build a map from a descending list in linear time with a combining function for equal keys. The precondition (input list is descending) is not checked.

let f k a1 a2 = (show k) ++ ":" ++ a1 ++ a2
fromDescListWithKey f [(5,"a"), (5,"b"), (5,"b"), (3,"b")] == fromList [(3, "b"), (5, "5:b5:ba")]
valid (fromDescListWithKey f [(5,"a"), (5,"b"), (5,"b"), (3,"b")]) == True
valid (fromDescListWithKey f [(5,"a"), (3,"b"), (5,"b"), (5,"b")]) == False

Also see the performance note on fromListWith.

valuefromDistinctDescList :: [(k, a)] -> Map k a

O(n). Build a map from a descending list of distinct elements in linear time. The precondition is not checked.

fromDistinctDescList [(5,"a"), (3,"b")] == fromList [(3, "b"), (5, "a")]
valid (fromDistinctDescList [(5,"a"), (3,"b")])          == True
valid (fromDistinctDescList [(5,"a"), (5,"b"), (3,"b")]) == False

Insertion

4 declarations

valueinsert :: Ord k => k -> a -> Map k a -> Map k a

O(\log n). Insert a new key and value in the map. If the key is already present in the map, the associated value is replaced with the supplied value. insert is equivalent to insertWith const.

insert 5 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'x')]
insert 7 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'a'), (7, 'x')]
insert 5 'x' empty                         == singleton 5 'x'

valueinsertWith :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a

O(\log n). Insert with a function, combining new value and old value. insertWith f key value mp will insert the pair (key, value) into mp if key does not exist in the map. If the key does exist, the function will insert the pair (key, f new_value old_value).

insertWith (++) 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "xxxa")]
insertWith (++) 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")]
insertWith (++) 5 "xxx" empty                         == singleton 5 "xxx"

Also see the performance note on fromListWith.

valueinsertWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a

O(\log n). Insert with a function, combining key, new value and old value. insertWithKey f key value mp will insert the pair (key, value) into mp if key does not exist in the map. If the key does exist, the function will insert the pair (key,f key new_value old_value). Note that the key passed to f is the same key passed to insertWithKey.

let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
insertWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:xxx|a")]
insertWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")]
insertWithKey f 5 "xxx" empty                         == singleton 5 "xxx"

Also see the performance note on fromListWith.

valueinsertLookupWithKey

:: Ord k
=> k -> a -> a -> a
-> k
-> a
-> Map k a
-> (Maybe a, Map k a)

O(\log n). Combines insert operation with old value retrieval. The expression (insertLookupWithKey f k x map) is a pair where the first element is equal to (lookup k map) and the second element equal to (insertWithKey f k x map).

let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
insertLookupWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:xxx|a")])
insertLookupWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == (Nothing,  fromList [(3, "b"), (5, "a"), (7, "xxx")])
insertLookupWithKey f 5 "xxx" empty                         == (Nothing,  singleton 5 "xxx")

This is how to define insertLookup using insertLookupWithKey:

let insertLookup kx x t = insertLookupWithKey (\_ a _ -> a) kx x t
insertLookup 5 "x" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "x")])
insertLookup 7 "x" (fromList [(5,"a"), (3,"b")]) == (Nothing,  fromList [(3, "b"), (5, "a"), (7, "x")])

Also see the performance note on fromListWith.

Deletion/Update

8 declarations

valuedelete :: Ord k => k -> Map k a -> Map k a

O(\log n). Delete a key and its value from the map. When the key is not a member of the map, the original map is returned.

delete 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
delete 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
delete 5 empty                         == empty

valueadjust :: Ord k => (a -> a) -> k -> Map k a -> Map k a

O(\log n). Update a value at a specific key with the result of the provided function. When the key is not a member of the map, the original map is returned.

adjust ("new " ++) 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")]
adjust ("new " ++) 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
adjust ("new " ++) 7 empty                         == empty

valueadjustWithKey :: Ord k => (k -> a -> a) -> k -> Map k a -> Map k a

O(\log n). Adjust a value at a specific key. When the key is not a member of the map, the original map is returned.

let f key x = (show key) ++ ":new " ++ x
adjustWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")]
adjustWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
adjustWithKey f 7 empty                         == empty

valueupdate :: Ord k => (a -> Maybe a) -> k -> Map k a -> Map k a

O(\log n). The expression (update f k map) updates the value x at k (if it is in the map). If (f x) is Nothing, the element is deleted. If it is (Just y), the key k is bound to the new value y.

let f x = if x == "a" then Just "new a" else Nothing
update f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")]
update f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
update f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"

valueupdateWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a

O(\log n). The expression (updateWithKey f k map) updates the value x at k (if it is in the map). If (f k x) is Nothing, the element is deleted. If it is (Just y), the key k is bound to the new value y.

let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing
updateWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")]
updateWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
updateWithKey f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"

valueupdateLookupWithKey

:: Ord k
=> k -> a -> Maybe a
-> k
-> Map k a
-> (Maybe a, Map k a)

O(\log n). Lookup and update. See also updateWithKey. The function returns changed value, if it is updated. Returns the original key value if the map entry is deleted.

let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing
updateLookupWithKey f 5 (fromList [(5,"a"), (3,"b")]) == (Just "5:new a", fromList [(3, "b"), (5, "5:new a")])
updateLookupWithKey f 7 (fromList [(5,"a"), (3,"b")]) == (Nothing,  fromList [(3, "b"), (5, "a")])
updateLookupWithKey f 3 (fromList [(5,"a"), (3,"b")]) == (Just "b", singleton 5 "a")

valuealter :: Ord k => (Maybe a -> Maybe a) -> k -> Map k a -> Map k a

O(\log n). The expression (alter f k map) alters the value x at k, or absence thereof. alter can be used to insert, delete, or update a value in a Map. In short : lookup k (alter f k m) = f (lookup k m).

let f _ = Nothing
alter f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
alter f 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"

let f _ = Just "c"
alter f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "c")]
alter f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "c")]

Note that adjust = alter . fmap.

valuealterF

:: (Functor f, Ord k)
=> Maybe a -> f (Maybe a)
-> k
-> Map k a
-> f (Map k a)

O(\log n). The expression (alterF f k map) alters the value x at k, or absence thereof. alterF can be used to inspect, insert, delete, or update a value in a Map. In short: lookup k <$> alterF f k m = f (lookup k m).

Example:

interactiveAlter :: Int -> Map Int String -> IO (Map Int String)
interactiveAlter k m = alterF f k m where
  f Nothing = do
     putStrLn $ show k ++
         " was not found in the map. Would you like to add it?"
     getUserResponse1 :: IO (Maybe String)
  f (Just old) = do
     putStrLn $ "The key is currently bound to " ++ show old ++
         ". Would you like to change or delete it?"
     getUserResponse2 :: IO (Maybe String)

alterF is the most general operation for working with an individual key that may or may not be in a given map. When used with trivial functors like Identity and Const, it is often slightly slower than more specialized combinators like lookup and insert. However, when the functor is non-trivial and key comparison is not particularly cheap, it is the fastest way.

Note on rewrite rules:

This module includes GHC rewrite rules to optimize alterF for the Const and Identity functors. In general, these rules improve performance. The sole exception is that when using Identity, deleting a key that is already absent takes longer than it would without the rules. If you expect this to occur a very large fraction of the time, you might consider using a private copy of the Identity type.

Note: alterF is a flipped version of the at combinator from Control.Lens.At.

Query

0 declarations

Lookup

valuelookup :: Ord k => k -> Map k a -> Maybe a

O(\log n). Lookup the value at a key in the map.

The function will return the corresponding value as (Just value), or Nothing if the key isn't in the map.

An example of using lookup:

import Prelude hiding (lookup)
import Data.Map

employeeDept = fromList([("John","Sales"), ("Bob","IT")])
deptCountry = fromList([("IT","USA"), ("Sales","France")])
countryCurrency = fromList([("USA", "Dollar"), ("France", "Euro")])

employeeCurrency :: String -> Maybe String
employeeCurrency name = do
    dept <- lookup name employeeDept
    country <- lookup dept deptCountry
    lookup country countryCurrency

main = do
    putStrLn $ "John's currency: " ++ (show (employeeCurrency "John"))
    putStrLn $ "Pete's currency: " ++ (show (employeeCurrency "Pete"))

The output of this program:

  John's currency: Just "Euro"
  Pete's currency: Nothing

value(!?) :: Ord k => Map k a -> k -> Maybe a

O(\log n). Find the value at a key. Returns Nothing when the element can not be found.

Property

prop> fromList [(5, 'a'), (3, 'b')] !? 1 == Nothing

Property

prop> fromList [(5, 'a'), (3, 'b')] !? 5 == Just 'a'

value(!) :: Ord k => Map k a -> k -> a

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'

valuefindWithDefault :: Ord k => a -> k -> Map k a -> a

O(\log n). The expression (findWithDefault def k map) returns the value at key k or returns default value def when the key is not in the map.

findWithDefault 'x' 1 (fromList [(5,'a'), (3,'b')]) == 'x'
findWithDefault 'x' 5 (fromList [(5,'a'), (3,'b')]) == 'a'

valuemember :: Ord k => k -> Map k a -> Bool

O(\log n). Is the key a member of the map? See also notMember.

member 5 (fromList [(5,'a'), (3,'b')]) == True
member 1 (fromList [(5,'a'), (3,'b')]) == False

valuenotMember :: Ord k => k -> Map k a -> Bool

O(\log n). Is the key not a member of the map? See also member.

notMember 5 (fromList [(5,'a'), (3,'b')]) == False
notMember 1 (fromList [(5,'a'), (3,'b')]) == True

valuelookupLT :: Ord k => k -> Map k v -> Maybe (k, v)

O(\log n). Find largest key smaller than the given one and return the corresponding (key, value) pair.

lookupLT 3 (fromList [(3,'a'), (5,'b')]) == Nothing
lookupLT 4 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a')

valuelookupGT :: Ord k => k -> Map k v -> Maybe (k, v)

O(\log n). Find smallest key greater than the given one and return the corresponding (key, value) pair.

lookupGT 4 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b')
lookupGT 5 (fromList [(3,'a'), (5,'b')]) == Nothing

valuelookupLE :: Ord k => k -> Map k v -> Maybe (k, v)

O(\log n). Find largest key smaller or equal to the given one and return the corresponding (key, value) pair.

lookupLE 2 (fromList [(3,'a'), (5,'b')]) == Nothing
lookupLE 4 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a')
lookupLE 5 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b')

valuelookupGE :: Ord k => k -> Map k v -> Maybe (k, v)

O(\log n). Find smallest key greater or equal to the given one and return the corresponding (key, value) pair.

lookupGE 3 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a')
lookupGE 4 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b')
lookupGE 6 (fromList [(3,'a'), (5,'b')]) == Nothing

Size

valuenull :: Map k a -> Bool

O(1). Is the map empty?

Data.Map.null (empty)           == True
Data.Map.null (singleton 1 'a') == False

valuesize :: Map k a -> Int

O(1). The number of elements in the map.

size empty                                   == 0
size (singleton 1 'a')                       == 1
size (fromList([(1,'a'), (2,'c'), (3,'b')])) == 3

Combine

0 declarations

Union

valueunion :: Ord k => Map k a -> Map k a -> Map k a

O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n. The expression (union t1 t2) takes the left-biased union of t1 and t2. It prefers t1 when duplicate keys are encountered, i.e. (union == unionWith const).

union (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "a"), (7, "C")]

valueunionWith :: Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a

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

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

Also see the performance note on fromListWith.

valueunionWithKey :: Ord k => (k -> a -> a -> a) -> Map k a -> Map k a -> Map k a

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

let f key left_value right_value = (show key) ++ ":" ++ left_value ++ "|" ++ right_value
unionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "5:a|A"), (7, "C")]

Also see the performance note on fromListWith.

valueunions :: (Foldable f, Ord k) => f (Map k a) -> Map k a

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")]

valueunionsWith :: (Foldable f, Ord k) => (a -> a -> a) -> f (Map k a) -> Map k a

The union of a list of maps, with a combining operation: (unionsWith f == 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

valuedifference :: Ord k => Map k a -> Map k b -> Map k a

O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n. Difference of two maps. Return elements of the first map not existing in the second map.

difference (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 3 "b"

value(\\) :: Ord k => Map k a -> Map k b -> Map k a

Same as difference.

valuedifferenceWith

:: Ord k
=> a -> b -> Maybe a
-> Map k a
-> Map k b
-> Map k a

O(n+m). Difference with a combining function. When two equal keys are encountered, the combining function is applied to the values of these keys. If it returns Nothing, the element is discarded (proper set difference). If it returns (Just y), the element is updated with a new value y.

let f al ar = if al == "b" then Just (al ++ ":" ++ ar) else Nothing
differenceWith f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (7, "C")])
    == singleton 3 "b:B"

valuedifferenceWithKey

:: Ord k
=> k -> a -> b -> Maybe a
-> Map k a
-> Map k b
-> Map k a

O(n+m). Difference with a combining function. When two equal keys are encountered, the combining function is applied to the key and both values. If it returns Nothing, the element is discarded (proper set difference). If it returns (Just y), the element is updated with a new value y.

let f k al ar = if al == "b" then Just ((show k) ++ ":" ++ al ++ "|" ++ ar) else Nothing
differenceWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (10, "C")])
    == singleton 3 "3:b|B"

Intersection

valueintersection :: Ord k => Map k a -> Map k b -> Map k a

O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n. Intersection of two maps. Return data in the first map for the keys existing in both maps. (intersection m1 m2 == intersectionWith const m1 m2).

intersection (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "a"

valueintersectionWith :: Ord k => (a -> b -> c) -> Map k a -> Map k b -> Map k c

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

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

valueintersectionWithKey

:: Ord k
=> k -> a -> b -> c
-> Map k a
-> Map k b
-> Map k c

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

let f k al ar = (show k) ++ ":" ++ al ++ "|" ++ ar
intersectionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "5:a|A"

Disjoint

valuedisjoint :: Ord k => Map k a -> Map k b -> Bool

O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n. Check whether the key sets of two maps are disjoint (i.e., their intersection is empty).

disjoint (fromList [(2,'a')]) (fromList [(1,()), (3,())])   == True
disjoint (fromList [(2,'a')]) (fromList [(1,'a'), (2,'b')]) == False
disjoint (fromList [])        (fromList [])                 == True

xs `disjoint` ys = null (xs `intersection` ys)

Compose

valuecompose :: Ord b => Map b c -> Map a b -> Map a c

Relate the keys of one map to the values of the other, by using the values of the former as keys for lookups in the latter.

Complexity: O (n * \log(m)) , where m is the size of the first argument

compose (fromList [('a', "A"), ('b', "B")]) (fromList [(1,'a'),(2,'b'),(3,'z')]) = fromList [(1,"A"),(2,"B")]

(compose bc ab !?) = (bc !?) <=< (ab !?)

Note: Prior to v0.6.4, Data.Map.Strict exposed a version of compose that forced the values of the output Map. This version does not force these values.

General combining functions

See Data.Map.Merge.Lazy

Unsafe general combining function

valuemergeWithKey

:: Ord k
=> k -> a -> b -> Maybe c
-> Map k a -> Map k c
-> Map k b -> Map k c
-> Map k a
-> Map k b
-> Map k c

O(n+m). An unsafe general combining function.

WARNING: This function can produce corrupt maps and its results may depend on the internal structures of its inputs. Users should prefer merge or mergeA.

When mergeWithKey is given three arguments, it is inlined to the call site. You should therefore use mergeWithKey only to define custom combining functions. For example, you could define unionWithKey, differenceWithKey and intersectionWithKey as

myUnionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) id id m1 m2
myDifferenceWithKey f m1 m2 = mergeWithKey f id (const empty) m1 m2
myIntersectionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) (const empty) (const empty) m1 m2

When calling 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

0 declarations

Map

valuemap :: (a -> b) -> Map k a -> Map k b

O(n). Map a function over all values in the map.

map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]

valuemapWithKey :: (k -> a -> b) -> Map k a -> Map k b

O(n). Map a function over all values in the map.

let f key x = (show key) ++ ":" ++ x
mapWithKey f (fromList [(5,"a"), (3,"b")]) == fromList [(3, "3:b"), (5, "5:a")]

valuetraverseWithKey

:: Applicative t
=> k -> a -> t b
-> Map k a
-> t (Map k b)

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

valuetraverseMaybeWithKey

:: Applicative f
=> k -> a -> f (Maybe b)
-> Map k a
-> f (Map k b)

O(n). Traverse keys/values and collect the Just results.

valuemapAccum :: (a -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)

O(n). The function mapAccum threads an accumulating argument through the map in ascending order of keys.

let f a b = (a ++ b, b ++ "X")
mapAccum f "Everything: " (fromList [(5,"a"), (3,"b")]) == ("Everything: ba", fromList [(3, "bX"), (5, "aX")])

valuemapAccumWithKey :: (a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)

O(n). The function mapAccumWithKey threads an accumulating argument through the map in ascending order of keys.

let f a k b = (a ++ " " ++ (show k) ++ "-" ++ b, b ++ "X")
mapAccumWithKey f "Everything:" (fromList [(5,"a"), (3,"b")]) == ("Everything: 3-b 5-a", fromList [(3, "bX"), (5, "aX")])

valuemapAccumRWithKey :: (a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)

O(n). The function mapAccumRWithKey threads an accumulating argument through the map in descending order of keys.

valuemapKeys :: Ord k2 => (k1 -> k2) -> Map k1 a -> Map k2 a

O(n \log n). mapKeys f s is the map obtained by applying f to each key of s.

The size of the result may be smaller if f maps two or more distinct keys to the same new key. In this case the value at the greatest of the original keys is retained.

mapKeys (+ 1) (fromList [(5,"a"), (3,"b")])                        == fromList [(4, "b"), (6, "a")]
mapKeys (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "c"
mapKeys (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "c"

valuemapKeysWith :: Ord k2 => (a -> a -> a) -> (k1 -> k2) -> Map k1 a -> Map k2 a

O(n \log n). mapKeysWith c f s is the map obtained by applying f to each key of s.

The size of the result may be smaller if f maps two or more distinct keys to the same new key. In this case the associated values will be combined using c. The value at the greater of the two original keys is used as the first argument to c.

mapKeysWith (++) (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "cdab"
mapKeysWith (++) (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "cdab"

Also see the performance note on fromListWith.

valuemapKeysMonotonic :: (k1 -> k2) -> Map k1 a -> Map k2 a

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

5 declarations

valuefoldr :: (a -> b -> b) -> b -> Map k a -> b

O(n). Fold the values in the map using the given right-associative binary operator, such that foldr f z == foldr f z . elems.

For example,

elems map = foldr (:) [] map

let f a len = len + (length a)
foldr f 0 (fromList [(5,"a"), (3,"bbb")]) == 4

valuefoldl :: (a -> b -> a) -> a -> Map k b -> a

O(n). Fold the values in the map using the given left-associative binary operator, such that foldl f z == foldl f z . elems.

For example,

elems = reverse . foldl (flip (:)) []

let f len a = len + (length a)
foldl f 0 (fromList [(5,"a"), (3,"bbb")]) == 4

valuefoldrWithKey :: (k -> a -> b -> b) -> b -> Map k a -> b

O(n). Fold the keys and values in the map using the given right-associative binary operator, such that foldrWithKey f z == Prelude.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)"

valuefoldlWithKey :: (a -> k -> b -> a) -> a -> Map k b -> a

O(n). Fold the keys and values in the map using the given left-associative binary operator, such that foldlWithKey f z == Prelude.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)"

valuefoldMapWithKey :: Monoid m => (k -> a -> m) -> Map k a -> m

O(n). Fold the keys and values in the map using the given monoid, such that

foldMapWithKey f = Prelude.fold . mapWithKey f

This can be an asymptotically faster than foldrWithKey or foldlWithKey for some monoids.

Strict folds

valuefoldr' :: (a -> b -> b) -> b -> Map k a -> b

O(n). A strict version of foldr. Each application of the operator is evaluated before using the result in the next application. This function is strict in the starting value.

valuefoldl' :: (a -> b -> a) -> a -> Map k b -> a

O(n). A strict version of foldl. Each application of the operator is evaluated before using the result in the next application. This function is strict in the starting value.

valuefoldrWithKey' :: (k -> a -> b -> b) -> b -> Map k a -> b

O(n). A strict version of foldrWithKey. Each application of the operator is evaluated before using the result in the next application. This function is strict in the starting value.

valuefoldlWithKey' :: (a -> k -> b -> a) -> a -> Map k b -> a

O(n). A strict version of foldlWithKey. Each application of the operator is evaluated before using the result in the next application. This function is strict in the starting value.

Conversion

5 declarations

valueelems :: Map k a -> [a]

O(n). Return all elements of the map in the ascending order of their keys. Subject to list fusion.

elems (fromList [(5,"a"), (3,"b")]) == ["b","a"]
elems empty == []

valuekeys :: Map k a -> [k]

O(n). Return all keys of the map in ascending order. Subject to list fusion.

keys (fromList [(5,"a"), (3,"b")]) == [3,5]
keys empty == []

valueassocs :: Map k a -> [(k, a)]

O(n). An alias for toAscList. Return all key/value pairs in the map in ascending key order. Subject to list fusion.

assocs (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
assocs empty == []

valuekeysSet :: Map k a -> Set k

O(n). The set of all keys of the map.

keysSet (fromList [(5,"a"), (3,"b")]) == Data.Set.fromList [3,5]
keysSet empty == Data.Set.empty

valueargSet :: Map k a -> Set (Arg k a)

O(n). The set of all elements of the map contained in Args.

argSet (fromList [(5,"a"), (3,"b")]) == Data.Set.fromList [Arg 3 "b",Arg 5 "a"]
argSet empty == Data.Set.empty

Lists

valuetoList :: Map k a -> [(k, a)]

O(n). Convert the map to a list of key/value pairs. Subject to list fusion.

toList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
toList empty == []

Ordered lists

valuetoAscList :: Map k a -> [(k, a)]

O(n). Convert the map to a list of key/value pairs where the keys are in ascending order. Subject to list fusion.

toAscList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]

valuetoDescList :: Map k a -> [(k, a)]

O(n). Convert the map to a list of key/value pairs where the keys are in descending order. Subject to list fusion.

toDescList (fromList [(5,"a"), (3,"b")]) == [(5,"a"), (3,"b")]

Filter

16 declarations

valuefilter :: (a -> Bool) -> Map k a -> Map k a

O(n). Filter all values that satisfy the predicate.

filter (> "a") (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
filter (> "x") (fromList [(5,"a"), (3,"b")]) == empty
filter (< "a") (fromList [(5,"a"), (3,"b")]) == empty

valuefilterWithKey :: (k -> a -> Bool) -> Map k a -> Map k a

O(n). Filter all keys/values that satisfy the predicate.

filterWithKey (\k _ -> k > 4) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"

valuerestrictKeys :: Ord k => Map k a -> Set k -> Map k a

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

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

valuewithoutKeys :: Ord k => Map k a -> Set k -> Map k a

O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n. Remove all keys in a Set from a Map.

m `withoutKeys` s = filterWithKey (\k _ -> k `Set.notMember` s) m
m `withoutKeys` s = m `difference` fromSet (const ()) s

valuepartition :: (a -> Bool) -> Map k a -> (Map k a, Map k a)

O(n). Partition the map according to a predicate. The first map contains all elements that satisfy the predicate, the second all elements that fail the predicate. See also split.

partition (> "a") (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a")
partition (< "x") (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty)
partition (> "x") (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")])

valuepartitionWithKey :: (k -> a -> Bool) -> Map k a -> (Map k a, Map k a)

O(n). Partition the map according to a predicate. The first map contains all elements that satisfy the predicate, the second all elements that fail the predicate. See also split.

partitionWithKey (\ k _ -> k > 3) (fromList [(5,"a"), (3,"b")]) == (singleton 5 "a", singleton 3 "b")
partitionWithKey (\ k _ -> k < 7) (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty)
partitionWithKey (\ k _ -> k > 7) (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")])

valuetakeWhileAntitone :: (k -> Bool) -> Map k a -> Map k a

O(\log n). Take while a predicate on the keys holds. The user is responsible for ensuring that for all keys j and k in the map, j < k ==> p j >= p k. See note at spanAntitone.

takeWhileAntitone p = fromDistinctAscList . takeWhile (p . fst) . toList
takeWhileAntitone p = filterWithKey (k _ -> p k)

valuedropWhileAntitone :: (k -> Bool) -> Map k a -> Map k a

O(\log n). Drop while a predicate on the keys holds. The user is responsible for ensuring that for all keys j and k in the map, j < k ==> p j >= p k. See note at spanAntitone.

dropWhileAntitone p = fromDistinctAscList . dropWhile (p . fst) . toList
dropWhileAntitone p = filterWithKey (\k _ -> not (p k))

valuespanAntitone :: (k -> Bool) -> Map k a -> (Map k a, Map k a)

O(\log n). Divide a map at the point where a predicate on the keys stops holding. The user is responsible for ensuring that for all keys j and k in the map, j < k ==> p j >= p k.

spanAntitone p xs = (takeWhileAntitone p xs, dropWhileAntitone p xs)
spanAntitone p xs = partitionWithKey (\k _ -> p k) xs

Note: if p is not actually antitone, then spanAntitone will split the map at some unspecified point where the predicate switches from holding to not holding (where the predicate is seen to hold before the first key and to fail after the last key).

valuemapMaybe :: (a -> Maybe b) -> Map k a -> Map k b

O(n). Map values and collect the Just results.

let f x = if x == "a" then Just "new a" else Nothing
mapMaybe f (fromList [(5,"a"), (3,"b")]) == singleton 5 "new a"

valuemapMaybeWithKey :: (k -> a -> Maybe b) -> Map k a -> Map k b

O(n). Map keys/values and collect the Just results.

let f k _ = if k < 5 then Just ("key : " ++ (show k)) else Nothing
mapMaybeWithKey f (fromList [(5,"a"), (3,"b")]) == singleton 3 "key : 3"

valuemapEither :: (a -> Either b c) -> Map k a -> (Map k b, Map k c)

O(n). Map values and separate the Left and Right results.

let f a = if a < "c" then Left a else Right a
mapEither f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
    == (fromList [(3,"b"), (5,"a")], fromList [(1,"x"), (7,"z")])

mapEither (\ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
    == (empty, fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])

valuemapEitherWithKey :: (k -> a -> Either b c) -> Map k a -> (Map k b, Map k c)

O(n). Map keys/values and separate the Left and Right results.

let f k a = if k < 5 then Left (k * 2) else Right (a ++ a)
mapEitherWithKey f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
    == (fromList [(1,2), (3,6)], fromList [(5,"aa"), (7,"zz")])

mapEitherWithKey (\_ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
    == (empty, fromList [(1,"x"), (3,"b"), (5,"a"), (7,"z")])

valuesplit :: Ord k => k -> Map k a -> (Map k a, Map k a)

O(\log n). The expression (split k map) is a pair (map1,map2) where the keys in map1 are smaller than k and the keys in map2 larger than k. Any key equal to k is found in neither map1 nor map2.

split 2 (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3,"b"), (5,"a")])
split 3 (fromList [(5,"a"), (3,"b")]) == (empty, singleton 5 "a")
split 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a")
split 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", empty)
split 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], empty)

valuesplitLookup :: Ord k => k -> Map k a -> (Map k a, Maybe a, Map k a)

O(\log n). The expression (splitLookup k map) splits a map just like split but also returns lookup k map.

splitLookup 2 (fromList [(5,"a"), (3,"b")]) == (empty, Nothing, fromList [(3,"b"), (5,"a")])
splitLookup 3 (fromList [(5,"a"), (3,"b")]) == (empty, Just "b", singleton 5 "a")
splitLookup 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Nothing, singleton 5 "a")
splitLookup 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Just "a", empty)
splitLookup 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], Nothing, empty)

valuesplitRoot :: Map k b -> [Map k b]

O(1). Decompose a map into pieces based on the structure of the underlying tree. This function is useful for consuming a map in parallel.

No guarantee is made as to the sizes of the pieces; an internal, but deterministic process determines this. However, it is guaranteed that the pieces returned will be in ascending order (all elements in the first submap less than all elements in the second, and so on).

Examples:

splitRoot (fromList (zip [1..6] ['a'..])) ==
  [fromList [(1,'a'),(2,'b'),(3,'c')],fromList [(4,'d')],fromList [(5,'e'),(6,'f')]]

splitRoot empty == []

Note that the current implementation does not return more than three submaps, but you should not depend on this behaviour because it can change in the future without notice.

Submap

4 declarations

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

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

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

O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n. The expression (isSubmapOfBy f t1 t2) returns True if all keys in t1 are in tree t2, and when f returns True when applied to their respective values. For example, the following expressions are all True:

isSubmapOfBy (==) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (<=) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1),('b',2)])

But the following are all False:

isSubmapOfBy (==) (fromList [('a',2)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (<)  (fromList [('a',1)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1)])

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

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

O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n. Is this a proper submap? (ie. a submap but not equal). Defined as (isProperSubmapOf = isProperSubmapOfBy (==)).

valueisProperSubmapOfBy

:: Ord k
=> a -> b -> Bool
-> Map k a
-> Map k b
-> Bool

O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n. Is this a proper submap? (ie. a submap but not equal). The expression (isProperSubmapOfBy f m1 m2) returns True when keys m1 and keys m2 are not equal, all keys in m1 are in m2, and when f returns True when applied to their respective values. For example, the following expressions are all True:

isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])

But the following are all False:

isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
isProperSubmapOfBy (<)  (fromList [(1,1)])       (fromList [(1,1),(2,2)])

Indexed

8 declarations

valuelookupIndex :: Ord k => k -> Map k a -> Maybe Int

O(\log n). Lookup the index of a key, which is its zero-based index in the sequence sorted by keys. The index is a number from 0 up to, but not including, the size of the map.

isJust (lookupIndex 2 (fromList [(5,"a"), (3,"b")]))   == False
fromJust (lookupIndex 3 (fromList [(5,"a"), (3,"b")])) == 0
fromJust (lookupIndex 5 (fromList [(5,"a"), (3,"b")])) == 1
isJust (lookupIndex 6 (fromList [(5,"a"), (3,"b")]))   == False

valuefindIndex :: Ord k => k -> Map k a -> Int

O(\log n). Return the index of a key, which is its zero-based index in the sequence sorted by keys. The index is a number from 0 up to, but not including, the size of the map. Calls error when the key is not a member of the map.

findIndex 2 (fromList [(5,"a"), (3,"b")])    Error: element is not in the map
findIndex 3 (fromList [(5,"a"), (3,"b")]) == 0
findIndex 5 (fromList [(5,"a"), (3,"b")]) == 1
findIndex 6 (fromList [(5,"a"), (3,"b")])    Error: element is not in the map

valueelemAt :: Int -> Map k a -> (k, a)

O(\log n). Retrieve an element by its index, i.e. by its zero-based index in the sequence sorted by keys. If the index is out of range (less than zero, greater or equal to size of the map), error is called.

elemAt 0 (fromList [(5,"a"), (3,"b")]) == (3,"b")
elemAt 1 (fromList [(5,"a"), (3,"b")]) == (5, "a")
elemAt 2 (fromList [(5,"a"), (3,"b")])    Error: index out of range

valueupdateAt :: (k -> a -> Maybe a) -> Int -> Map k a -> Map k a

O(\log n). Update the element at index, i.e. by its zero-based index in the sequence sorted by keys. If the index is out of range (less than zero, greater or equal to size of the map), error is called.

updateAt (\ _ _ -> Just "x") 0    (fromList [(5,"a"), (3,"b")]) == fromList [(3, "x"), (5, "a")]
updateAt (\ _ _ -> Just "x") 1    (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "x")]
updateAt (\ _ _ -> Just "x") 2    (fromList [(5,"a"), (3,"b")])    Error: index out of range
updateAt (\ _ _ -> Just "x") (-1) (fromList [(5,"a"), (3,"b")])    Error: index out of range
updateAt (\_ _  -> Nothing)  0    (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
updateAt (\_ _  -> Nothing)  1    (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
updateAt (\_ _  -> Nothing)  2    (fromList [(5,"a"), (3,"b")])    Error: index out of range
updateAt (\_ _  -> Nothing)  (-1) (fromList [(5,"a"), (3,"b")])    Error: index out of range

valuedeleteAt :: Int -> Map k a -> Map k a

O(\log n). Delete the element at index, i.e. by its zero-based index in the sequence sorted by keys. If the index is out of range (less than zero, greater or equal to size of the map), error is called.

deleteAt 0  (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
deleteAt 1  (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
deleteAt 2 (fromList [(5,"a"), (3,"b")])     Error: index out of range
deleteAt (-1) (fromList [(5,"a"), (3,"b")])  Error: index out of range

valuetake :: Int -> Map k a -> Map k a

O(\log n). Take a given number of entries in key order, beginning with the smallest keys.

take n = fromDistinctAscList . Prelude.take n . toAscList

valuedrop :: Int -> Map k a -> Map k a

O(\log n). Drop a given number of entries in key order, beginning with the smallest keys.

drop n = fromDistinctAscList . Prelude.drop n . toAscList

valuesplitAt :: Int -> Map k a -> (Map k a, Map k a)

O(\log n). Split a map at a particular index.

splitAt !n !xs = (take n xs, drop n xs)

Min/Max

16 declarations

valuelookupMin :: Map k a -> Maybe (k, a)

O(\log n). The minimal key of the map. Returns Nothing if the map is empty.

lookupMin (fromList [(5,"a"), (3,"b")]) == Just (3,"b")
lookupMin empty = Nothing

valuelookupMax :: Map k a -> Maybe (k, a)

O(\log n). The maximal key of the map. Returns Nothing if the map is empty.

lookupMax (fromList [(5,"a"), (3,"b")]) == Just (5,"a")
lookupMax empty = Nothing

valuefindMin :: Map k a -> (k, a)

O(\log n). The minimal key of the map. Calls error if the map is empty.

findMin (fromList [(5,"a"), (3,"b")]) == (3,"b")
findMin empty                            Error: empty map has no minimal element

valuefindMax :: Map k a -> (k, a)

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

valuedeleteMin :: Map k a -> Map k a

O(\log n). Delete the minimal key. Returns an empty map if the map is empty.

deleteMin (fromList [(5,"a"), (3,"b"), (7,"c")]) == fromList [(5,"a"), (7,"c")]
deleteMin empty == empty

valuedeleteMax :: Map k a -> Map k a

O(\log n). Delete the maximal key. Returns an empty map if the map is empty.

deleteMax (fromList [(5,"a"), (3,"b"), (7,"c")]) == fromList [(3,"b"), (5,"a")]
deleteMax empty == empty

valuedeleteFindMin :: Map k a -> ((k, a), Map k a)

O(\log n). Delete and find the minimal element.

deleteFindMin (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((3,"b"), fromList[(5,"a"), (10,"c")])
deleteFindMin empty                                      Error: can not return the minimal element of an empty map

valuedeleteFindMax :: Map k a -> ((k, a), Map k a)

O(\log n). Delete and find the maximal element.

deleteFindMax (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((10,"c"), fromList [(3,"b"), (5,"a")])
deleteFindMax empty                                      Error: can not return the maximal element of an empty map

valueupdateMin :: (a -> Maybe a) -> Map k a -> Map k a

O(\log n). Update the value at the minimal key.

updateMin (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "Xb"), (5, "a")]
updateMin (\ _ -> Nothing)         (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"

valueupdateMax :: (a -> Maybe a) -> Map k a -> Map k a

O(\log n). Update the value at the maximal key.

updateMax (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "Xa")]
updateMax (\ _ -> Nothing)         (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"

valueupdateMinWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a

O(\log n). Update the value at the minimal key.

updateMinWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"3:b"), (5,"a")]
updateMinWithKey (\ _ _ -> Nothing)                     (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"

valueupdateMaxWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a

O(\log n). Update the value at the maximal key.

updateMaxWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"b"), (5,"5:a")]
updateMaxWithKey (\ _ _ -> Nothing)                     (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"

valueminView :: Map k a -> Maybe (a, Map k a)

O(\log n). Retrieves the value associated with minimal key of the map, and the map stripped of that element, or Nothing if passed an empty map.

minView (fromList [(5,"a"), (3,"b")]) == Just ("b", singleton 5 "a")
minView empty == Nothing

valuemaxView :: Map k a -> Maybe (a, Map k a)

O(\log n). Retrieves the value associated with maximal key of the map, and the map stripped of that element, or Nothing if passed an empty map.

maxView (fromList [(5,"a"), (3,"b")]) == Just ("a", singleton 3 "b")
maxView empty == Nothing

valueminViewWithKey :: Map k a -> Maybe ((k, a), Map k a)

O(\log n). Retrieves the minimal (key,value) pair of the map, and the map stripped of that element, or Nothing if passed an empty map.

minViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((3,"b"), singleton 5 "a")
minViewWithKey empty == Nothing

valuemaxViewWithKey :: Map k a -> Maybe ((k, a), Map k a)

O(\log n). Retrieves the maximal (key,value) pair of the map, and the map stripped of that element, or Nothing if passed an empty map.

maxViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((5,"a"), singleton 3 "b")
maxViewWithKey empty == Nothing

Debugging

3 declarations

valueshowTree

:: Whoops "showTree has moved to Data.Map.Internal.Debug.showTree."
=> Map k a
-> String

This function has moved to showTree.

valueshowTreeWith

:: Whoops "showTreeWith has moved to Data.Map.Internal.Debug.showTreeWith."
=> k -> a -> String
-> Bool
-> Bool
-> Map k a
-> String

This function has moved to showTreeWith.

valuevalid :: Ord k => Map k a -> Bool

O(n). Test if the internal map structure is valid.

valid (fromAscList [(3,"b"), (5,"a")]) == True
valid (fromAscList [(5,"a"), (3,"b")]) == False