Rebase.Data.Map.Lazy · rebase-1.21.2

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 == []

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.

Instances45Bifoldable, Eq2, Ord2, Show2, Hashable2, FoldableWithIndex, …

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
Hashable2 MapDefined in hashable-1.4.7.0 · Data.Hashable.Class
FoldableWithIndex k (Map k)Defined in indexed-traversable-0.1.4 · WithIndex
FunctorWithIndex k (Map k)Defined in indexed-traversable-0.1.4 · WithIndex
TraversableWithIndex k (Map k)Defined in indexed-traversable-0.1.4 · WithIndex
(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
Hashable k => Hashable1 (Map k)Defined in hashable-1.4.7.0 · Data.Hashable.Class
Ord k => Alt (Map k)Defined in semigroupoids-6.0.1 · Data.Functor.Alt
Ord k => Apply (Map k)Defined in semigroupoids-6.0.1 · Data.Functor.Bind.Class
A 'Map k' is not Applicative, but it is an instance of Apply
Ord k => Bind (Map k)Defined in semigroupoids-6.0.1 · Data.Functor.Bind.Class
A 'Map k' is not a Monad, but it is an instance of Bind
Ord k => Plus (Map k)Defined in semigroupoids-6.0.1 · Data.Functor.Plus
Invariant (Map k)Defined in invariant-0.6.4 · Data.Functor.Invariant
from the containers package
Ord k => Adjustable (Map k)Defined in keys-3.12.3 · Data.Key
FoldableWithKey (Map k)Defined in keys-3.12.3 · Data.Key
Ord k => Indexable (Map k)Defined in keys-3.12.3 · Data.Key
Keyed (Map k)Defined in keys-3.12.3 · Data.Key
Ord k => Lookup (Map k)Defined in keys-3.12.3 · Data.Key
TraversableWithKey (Map k)Defined in keys-3.12.3 · Data.Key
Ord k => Zip (Map k)Defined in keys-3.12.3 · Data.Key
Ord k => ZipWithKey (Map k)Defined in keys-3.12.3 · Data.Key
Default k => Pointed (Map k)Defined in pointed-5.0.4 · Data.Pointed
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
(Binary k, Binary e) => Binary (Map k e)Defined in binary-0.8.9.3 · Data.Binary.Class
(Hashable k, Hashable v) => Hashable (Map k v)Defined in hashable-1.4.7.0 · Data.Hashable.Class
Default (Map k v)Defined in data-default-0.8.0.1 · Data.Default.Internal
type Item (Map k v) = (k, v)Defined in containers-0.7 · Data.Map.Internal
type Key (Map k) = kDefined in keys-3.12.3 · Data.Key

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 == []

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

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). 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.

valueempty :: Map k a

#

O(1). The empty map.

empty      == fromList []
size empty == 0

valuenull :: Map k a -> Bool

#

O(1). Is the map empty?

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

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")]

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'

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)

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

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

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 == []

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.

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

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

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.

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

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

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")])

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)

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")]

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'

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"

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"

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")]

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

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"

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)

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"

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'

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.

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)"

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.

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)"

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.

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"

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.

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

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"

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

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")]

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

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.

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"

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.

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.

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"

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

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.

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"

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

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

#

Same as difference.

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

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 == []

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

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

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

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

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))

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

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

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

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

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.

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.

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)])

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

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')

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')

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

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

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")])

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.

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")])

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")])

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

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.

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

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

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.

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

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

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

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")])

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

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).

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.

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)

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")]

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.

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")]

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")

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"

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"

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"

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"

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"

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

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.

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

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

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

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

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

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

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

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