GHC.Data.Word64Map.Strict

ghc-lib-parser-9.10.1.20250103: The GHC API, decoupled from GHC versions

Copyright | (c) Daan Leijen 2002 (c) Andriy Palamarchuk 2008
License | BSD-style
Maintainer | libraries@haskell.org
Portability | portable
Safe Haskell | Ignore
Language | GHC2021

GHC.Data.Word64Map.Strict

Contents

- Map type
- Construction
  - From Unordered Lists
  - From Ascending Lists
- Insertion
- Deletion/Update
- Query
  - Lookup
  - Size
- Combine
  - Union
  - Difference
  - Intersection
  - Disjoint
  - Compose
  - Universal combining function
- Traversal
  - Map
- Folds
  - Strict folds
- Conversion
  - Lists
  - Ordered lists
- Filter
- Submap
- Min/Max

Description

# Finite Word64 Maps (strict interface)

The ``Word64Map` v` type represents a finite map (sometimes called a dictionary) from key of type `Word64` to values of type `v`.

Each function in this module is careful to force values before installing them in an `Word64Map`. This is usually more efficient when laziness is not necessary. When laziness is required, use the functions in Data.Word64Map.Lazy.

In particular, the functions in this module obey the following law:

- If all values stored in all maps in the arguments are in WHNF, then all values stored in all maps in the results will be in WHNF once those maps are evaluated.

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 Data.Word64Map.Strict (Word64Map)
    import qualified Data.Word64Map.Strict as Word64Map

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 and \(W\) referring to the number of bits in an `Word64` (64).

Benchmarks comparing Data.Word64Map.Strict with other dictionary implementations can be found at https://github.com/haskell-perf/dictionaries.

## Warning

The `Word64Map` type is shared between the lazy and strict modules, meaning that the same `Word64Map` value can be passed to functions in both modules. This means that the `Functor`, `Traversable` and `Data` instances are the same as for the Data.Word64Map.Lazy module, so if they are used the resulting map may contain suspended values (thunks).

## Implementation

The implementation is based on big-endian patricia trees. This data structure performs especially well on binary operations like `union` and `intersection`. Additionally, benchmarks show that it is also (much) faster on insertions and deletions when compared to a generic size-balanced map implementation (see Data.Map).

- Chris Okasaki and Andy Gill, "Fast Mergeable Integer Maps", Workshop on ML, September 1998, pages 77-86, http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.37.5452
- D.R. Morrison, "PATRICIA -- Practical Algorithm To Retrieve Information Coded In Alphanumeric", Journal of the ACM, 15(4), October 1968, pages 514-534.

Synopsis

- data Word64Map a
- type Key = Word64
- empty :: Word64Map a
- singleton :: Key -> a -> Word64Map a
- fromSet :: (Key -> a) -> Word64Set -> Word64Map a
- fromList :: [(Key, a)] -> Word64Map a
- fromListWith :: (a -> a -> a) -> [(Key, a)] -> Word64Map a
- fromListWithKey :: (Key -> a -> a -> a) -> [(Key, a)] -> Word64Map a
- fromAscList :: [(Key, a)] -> Word64Map a
- fromAscListWith :: (a -> a -> a) -> [(Key, a)] -> Word64Map a
- fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key, a)] -> Word64Map a
- fromDistinctAscList :: [(Key, a)] -> Word64Map a
- insert :: Key -> a -> Word64Map a -> Word64Map a
- insertWith :: (a -> a -> a) -> Key -> a -> Word64Map a -> Word64Map a
- insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> Word64Map a -> Word64Map a
- insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> Word64Map a -> (Maybe a, Word64Map a)
- delete :: Key -> Word64Map a -> Word64Map a
- adjust :: (a -> a) -> Key -> Word64Map a -> Word64Map a
- adjustWithKey :: (Key -> a -> a) -> Key -> Word64Map a -> Word64Map a
- update :: (a -> Maybe a) -> Key -> Word64Map a -> Word64Map a
- updateWithKey :: (Key -> a -> Maybe a) -> Key -> Word64Map a -> Word64Map a
- updateLookupWithKey :: (Key -> a -> Maybe a) -> Key -> Word64Map a -> (Maybe a, Word64Map a)
- alter :: (Maybe a -> Maybe a) -> Key -> Word64Map a -> Word64Map a
- alterF :: Functor f => (Maybe a -> f (Maybe a)) -> Key -> Word64Map a -> f (Word64Map a)
- lookup :: Key -> Word64Map a -> Maybe a
- (!?) :: Word64Map a -> Key -> Maybe a
- (!) :: Word64Map a -> Key -> a
- findWithDefault :: a -> Key -> Word64Map a -> a
- member :: Key -> Word64Map a -> Bool
- notMember :: Key -> Word64Map a -> Bool
- lookupLT :: Key -> Word64Map a -> Maybe (Key, a)
- lookupGT :: Key -> Word64Map a -> Maybe (Key, a)
- lookupLE :: Key -> Word64Map a -> Maybe (Key, a)
- lookupGE :: Key -> Word64Map a -> Maybe (Key, a)
- null :: Word64Map a -> Bool
- size :: Word64Map a -> Int
- union :: Word64Map a -> Word64Map a -> Word64Map a
- unionWith :: (a -> a -> a) -> Word64Map a -> Word64Map a -> Word64Map a
- unionWithKey :: (Key -> a -> a -> a) -> Word64Map a -> Word64Map a -> Word64Map a
- unions :: Foldable f => f (Word64Map a) -> Word64Map a
- unionsWith :: Foldable f => (a -> a -> a) -> f (Word64Map a) -> Word64Map a
- difference :: Word64Map a -> Word64Map b -> Word64Map a
- (\\) :: Word64Map a -> Word64Map b -> Word64Map a
- differenceWith :: (a -> b -> Maybe a) -> Word64Map a -> Word64Map b -> Word64Map a
- differenceWithKey :: (Key -> a -> b -> Maybe a) -> Word64Map a -> Word64Map b -> Word64Map a
- intersection :: Word64Map a -> Word64Map b -> Word64Map a
- intersectionWith :: (a -> b -> c) -> Word64Map a -> Word64Map b -> Word64Map c
- intersectionWithKey :: (Key -> a -> b -> c) -> Word64Map a -> Word64Map b -> Word64Map c
- disjoint :: Word64Map a -> Word64Map b -> Bool
- compose :: Word64Map c -> Word64Map Word64 -> Word64Map c
- mergeWithKey :: (Key -> a -> b -> Maybe c) -> (Word64Map a -> Word64Map c) -> (Word64Map b -> Word64Map c) -> Word64Map a -> Word64Map b -> Word64Map c
- map :: (a -> b) -> Word64Map a -> Word64Map b
- mapWithKey :: (Key -> a -> b) -> Word64Map a -> Word64Map b
- traverseWithKey :: Applicative t => (Key -> a -> t b) -> Word64Map a -> t (Word64Map b)
- traverseMaybeWithKey :: Applicative f => (Key -> a -> f (Maybe b)) -> Word64Map a -> f (Word64Map b)
- mapAccum :: (a -> b -> (a, c)) -> a -> Word64Map b -> (a, Word64Map c)
- mapAccumWithKey :: (a -> Key -> b -> (a, c)) -> a -> Word64Map b -> (a, Word64Map c)
- mapAccumRWithKey :: (a -> Key -> b -> (a, c)) -> a -> Word64Map b -> (a, Word64Map c)
- mapKeys :: (Key -> Key) -> Word64Map a -> Word64Map a
- mapKeysWith :: (a -> a -> a) -> (Key -> Key) -> Word64Map a -> Word64Map a
- mapKeysMonotonic :: (Key -> Key) -> Word64Map a -> Word64Map a
- foldr :: (a -> b -> b) -> b -> Word64Map a -> b
- foldl :: (a -> b -> a) -> a -> Word64Map b -> a
- foldrWithKey :: (Key -> a -> b -> b) -> b -> Word64Map a -> b
- foldlWithKey :: (a -> Key -> b -> a) -> a -> Word64Map b -> a
- foldMapWithKey :: Monoid m => (Key -> a -> m) -> Word64Map a -> m
- foldr' :: (a -> b -> b) -> b -> Word64Map a -> b
- foldl' :: (a -> b -> a) -> a -> Word64Map b -> a
- foldrWithKey' :: (Key -> a -> b -> b) -> b -> Word64Map a -> b
- foldlWithKey' :: (a -> Key -> b -> a) -> a -> Word64Map b -> a
- elems :: Word64Map a -> [a]
- keys :: Word64Map a -> [Key]
- assocs :: Word64Map a -> [(Key, a)]
- keysSet :: Word64Map a -> Word64Set
- toList :: Word64Map a -> [(Key, a)]
- toAscList :: Word64Map a -> [(Key, a)]
- toDescList :: Word64Map a -> [(Key, a)]
- filter :: (a -> Bool) -> Word64Map a -> Word64Map a
- filterWithKey :: (Key -> a -> Bool) -> Word64Map a -> Word64Map a
- restrictKeys :: Word64Map a -> Word64Set -> Word64Map a
- withoutKeys :: Word64Map a -> Word64Set -> Word64Map a
- partition :: (a -> Bool) -> Word64Map a -> (Word64Map a, Word64Map a)
- partitionWithKey :: (Key -> a -> Bool) -> Word64Map a -> (Word64Map a, Word64Map a)
- takeWhileAntitone :: (Key -> Bool) -> Word64Map a -> Word64Map a
- dropWhileAntitone :: (Key -> Bool) -> Word64Map a -> Word64Map a
- spanAntitone :: (Key -> Bool) -> Word64Map a -> (Word64Map a, Word64Map a)
- mapMaybe :: (a -> Maybe b) -> Word64Map a -> Word64Map b
- mapMaybeWithKey :: (Key -> a -> Maybe b) -> Word64Map a -> Word64Map b
- mapEither :: (a -> Either b c) -> Word64Map a -> (Word64Map b, Word64Map c)
- mapEitherWithKey :: (Key -> a -> Either b c) -> Word64Map a -> (Word64Map b, Word64Map c)
- split :: Key -> Word64Map a -> (Word64Map a, Word64Map a)
- splitLookup :: Key -> Word64Map a -> (Word64Map a, Maybe a, Word64Map a)
- splitRoot :: Word64Map a -> [Word64Map a]
- isSubmapOf :: Eq a => Word64Map a -> Word64Map a -> Bool
- isSubmapOfBy :: (a -> b -> Bool) -> Word64Map a -> Word64Map b -> Bool
- isProperSubmapOf :: Eq a => Word64Map a -> Word64Map a -> Bool
- isProperSubmapOfBy :: (a -> b -> Bool) -> Word64Map a -> Word64Map b -> Bool
- lookupMin :: Word64Map a -> Maybe (Key, a)
- lookupMax :: Word64Map a -> Maybe (Key, a)
- findMin :: Word64Map a -> (Key, a)
- findMax :: Word64Map a -> (Key, a)
- deleteMin :: Word64Map a -> Word64Map a
- deleteMax :: Word64Map a -> Word64Map a
- deleteFindMin :: Word64Map a -> ((Key, a), Word64Map a)
- deleteFindMax :: Word64Map a -> ((Key, a), Word64Map a)
- updateMin :: (a -> Maybe a) -> Word64Map a -> Word64Map a
- updateMax :: (a -> Maybe a) -> Word64Map a -> Word64Map a
- updateMinWithKey :: (Key -> a -> Maybe a) -> Word64Map a -> Word64Map a
- updateMaxWithKey :: (Key -> a -> Maybe a) -> Word64Map a -> Word64Map a
- minView :: Word64Map a -> Maybe (a, Word64Map a)
- maxView :: Word64Map a -> Maybe (a, Word64Map a)
- minViewWithKey :: Word64Map a -> Maybe ((Key, a), Word64Map a)
- maxViewWithKey :: Word64Map a -> Maybe ((Key, a), Word64Map a)

# Map type

data Word64Map a #

A map of integers to values `a`.

#### Instances

Instances details

Eq1 Word64Map # | Since: 0.5.9
Instance details Defined in GHC.Data.Word64Map.Internal Methods liftEq :: (a -> b -> Bool) -> Word64Map a -> Word64Map b -> Bool #
Ord1 Word64Map # | Since: 0.5.9
Instance details Defined in GHC.Data.Word64Map.Internal Methods liftCompare :: (a -> b -> Ordering) -> Word64Map a -> Word64Map b -> Ordering #
Read1 Word64Map # | Since: 0.5.9
Instance details Defined in GHC.Data.Word64Map.Internal Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Word64Map a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Word64Map a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Word64Map a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Word64Map a] #
Show1 Word64Map # | Since: 0.5.9
Instance details Defined in GHC.Data.Word64Map.Internal Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Word64Map a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Word64Map a] -> ShowS #
Functor Word64Map # |
Instance details Defined in GHC.Data.Word64Map.Internal Methods fmap :: (a -> b) -> Word64Map a -> Word64Map b # (<$) :: a -> Word64Map b -> Word64Map a #
Foldable Word64Map # | Folds in order of increasing key.
Instance details Defined in GHC.Data.Word64Map.Internal Methods fold :: Monoid m => Word64Map m -> m # foldMap :: Monoid m => (a -> m) -> Word64Map a -> m # foldMap' :: Monoid m => (a -> m) -> Word64Map a -> m # foldr :: (a -> b -> b) -> b -> Word64Map a -> b # foldr' :: (a -> b -> b) -> b -> Word64Map a -> b # foldl :: (b -> a -> b) -> b -> Word64Map a -> b # foldl' :: (b -> a -> b) -> b -> Word64Map a -> b # foldr1 :: (a -> a -> a) -> Word64Map a -> a # foldl1 :: (a -> a -> a) -> Word64Map a -> a # toList :: Word64Map a -> [a] # null :: Word64Map a -> Bool # length :: Word64Map a -> Int # elem :: Eq a => a -> Word64Map a -> Bool # maximum :: Ord a => Word64Map a -> a # minimum :: Ord a => Word64Map a -> a # sum :: Num a => Word64Map a -> a # product :: Num a => Word64Map a -> a #
Traversable Word64Map # | Traverses in order of increasing key.
Instance details Defined in GHC.Data.Word64Map.Internal Methods traverse :: Applicative f => (a -> f b) -> Word64Map a -> f (Word64Map b) # sequenceA :: Applicative f => Word64Map (f a) -> f (Word64Map a) # mapM :: Monad m => (a -> m b) -> Word64Map a -> m (Word64Map b) # sequence :: Monad m => Word64Map (m a) -> m (Word64Map a) #
NFData a => NFData (Word64Map a) # |
Instance details Defined in GHC.Data.Word64Map.Internal Methods rnf :: Word64Map a -> () #
Monoid (Word64Map a) # |
Instance details Defined in GHC.Data.Word64Map.Internal Methods mempty :: Word64Map a # mappend :: Word64Map a -> Word64Map a -> Word64Map a # mconcat :: [Word64Map a] -> Word64Map a #
Semigroup (Word64Map a) # | Since: 0.5.7
Instance details Defined in GHC.Data.Word64Map.Internal Methods (<>) :: Word64Map a -> Word64Map a -> Word64Map a # sconcat :: NonEmpty (Word64Map a) -> Word64Map a # stimes :: Integral b => b -> Word64Map a -> Word64Map a #
Data a => Data (Word64Map a) # |
Instance details Defined in GHC.Data.Word64Map.Internal Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Word64Map a -> c (Word64Map a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Word64Map a) # toConstr :: Word64Map a -> Constr # dataTypeOf :: Word64Map a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Word64Map a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Word64Map a)) # gmapT :: (forall b. Data b => b -> b) -> Word64Map a -> Word64Map a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Word64Map a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Word64Map a -> r # gmapQ :: (forall d. Data d => d -> u) -> Word64Map a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Word64Map a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Word64Map a -> m (Word64Map a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Word64Map a -> m (Word64Map a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Word64Map a -> m (Word64Map a) #
IsList (Word64Map a) # | Since: 0.5.6.2
Instance details Defined in GHC.Data.Word64Map.Internal Associated Types
type Item (Word64Map a) |
Instance details Defined in GHC.Data.Word64Map.Internal type Item (Word64Map a) = (Key, a)
Methods fromList :: [Item (Word64Map a)] -> Word64Map a # fromListN :: Int -> [Item (Word64Map a)] -> Word64Map a # toList :: Word64Map a -> [Item (Word64Map a)] #
Read e => Read (Word64Map e) # |
Instance details Defined in GHC.Data.Word64Map.Internal Methods readsPrec :: Int -> ReadS (Word64Map e) # readList :: ReadS [Word64Map e] # readPrec :: ReadPrec (Word64Map e) # readListPrec :: ReadPrec [Word64Map e] #
Show a => Show (Word64Map a) # |
Instance details Defined in GHC.Data.Word64Map.Internal Methods showsPrec :: Int -> Word64Map a -> ShowS # show :: Word64Map a -> String # showList :: [Word64Map a] -> ShowS #
Eq a => Eq (Word64Map a) # |
Instance details Defined in GHC.Data.Word64Map.Internal Methods (==) :: Word64Map a -> Word64Map a -> Bool # (/=) :: Word64Map a -> Word64Map a -> Bool #
Ord a => Ord (Word64Map a) # |
Instance details Defined in GHC.Data.Word64Map.Internal Methods compare :: Word64Map a -> Word64Map a -> Ordering # (<) :: Word64Map a -> Word64Map a -> Bool # (<=) :: Word64Map a -> Word64Map a -> Bool # (>) :: Word64Map a -> Word64Map a -> Bool # (>=) :: Word64Map a -> Word64Map a -> Bool # max :: Word64Map a -> Word64Map a -> Word64Map a # min :: Word64Map a -> Word64Map a -> Word64Map a #
type Item (Word64Map a) # |
Instance details Defined in GHC.Data.Word64Map.Internal type Item (Word64Map a) = (Key, a)

type Key = Word64 #

# Construction

empty :: Word64Map a #

\(O(1)\). The empty map.

    empty      == fromList []
    size empty == 0

singleton :: Key -> a -> Word64Map a #

\(O(1)\). A map of one element.

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

fromSet :: (Key -> a) -> Word64Set -> Word64Map 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.Word64Set.fromList [3, 5]) == fromList [(5,"aaaaa"), (3,"aaa")]
    fromSet undefined Data.Word64Set.empty == empty

## From Unordered Lists

fromList :: [(Key, a)] -> Word64Map a #

\(O(n \min(n,W))\). Create a map from a list of key/value pairs.

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

fromListWith :: (a -> a -> a) -> [(Key, a)] -> Word64Map a #

\(O(n \min(n,W))\). Create a map from a list of key/value pairs with a combining function. See also `fromAscListWith`.

    fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"a")] == fromList [(3, "ab"), (5, "aba")]
    fromListWith (++) [] == empty

fromListWithKey :: (Key -> a -> a -> a) -> [(Key, a)] -> Word64Map a #

\(O(n \min(n,W))\). 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

## From Ascending Lists

fromAscList :: [(Key, a)] -> Word64Map a #

\(O(n)\). Build a map from a list of key/value pairs where the keys are in ascending order.

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

fromAscListWith :: (a -> a -> a) -> [(Key, a)] -> Word64Map a #

\(O(n)\). Build a map from a list of key/value pairs where the keys are in ascending order, with a combining function on equal keys. The precondition (input list is ascending) is not checked.

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

fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key, a)] -> Word64Map a #

\(O(n)\). Build a map from a list of key/value pairs where the keys are in ascending order, with a combining function on equal keys. The precondition (input list is ascending) is not checked.

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

fromDistinctAscList :: [(Key, a)] -> Word64Map a #

\(O(n)\). Build a map from a list of key/value pairs where the keys are in ascending order and all distinct. The precondition (input list is strictly ascending) is not checked.

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

# Insertion

insert :: Key -> a -> Word64Map a -> Word64Map a #

\(O(\min(n,W))\). Insert a new key/value pair in the map. If the key is already present in the map, the associated value is replaced with the supplied value, i.e. `insert` is equivalent to ``insertWith` `const``.

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

insertWith :: (a -> a -> a) -> Key -> a -> Word64Map a -> Word64Map a #

\(O(\min(n,W))\). Insert with a combining function. ``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 `f new_value old_value`.

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

insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> Word64Map a -> Word64Map a #

\(O(\min(n,W))\). Insert with a combining function. ``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 `f key new_value old_value`.

    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"

If the key exists in the map, this function is lazy in `value` but strict in the result of `f`.

insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> Word64Map a -> (Maybe a, Word64Map a) #

\(O(\min(n,W))\). The expression (``insertLookupWithKey` f k x map`) is a pair where the first element is equal to (``lookup` k map`) and the second element equal to (``insertWithKey` f k x map`).

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

This is how to define `insertLookup` using `insertLookupWithKey`:

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

# Deletion/Update

delete :: Key -> Word64Map a -> Word64Map a #

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

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

adjust :: (a -> a) -> Key -> Word64Map a -> Word64Map a #

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

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

adjustWithKey :: (Key -> a -> a) -> Key -> Word64Map a -> Word64Map a #

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

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

update :: (a -> Maybe a) -> Key -> Word64Map a -> Word64Map a #

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

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

updateWithKey :: (Key -> a -> Maybe a) -> Key -> Word64Map a -> Word64Map a #

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

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

updateLookupWithKey :: (Key -> a -> Maybe a) -> Key -> Word64Map a -> (Maybe a, Word64Map a) #

\(O(\min(n,W))\). Lookup and update. The function returns original value, if it is updated. This is different behavior than `updateLookupWithKey`. 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 "a", fromList [(3, "b"), (5, "5:new a")])
    updateLookupWithKey f 7 (fromList [(5,"a"), (3,"b")]) == (Nothing,  fromList [(3, "b"), (5, "a")])
    updateLookupWithKey f 3 (fromList [(5,"a"), (3,"b")]) == (Just "b", singleton 5 "a")

alter :: (Maybe a -> Maybe a) -> Key -> Word64Map a -> Word64Map a #

\(O(\min(n,W))\). 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 an `Word64Map`. In short : ``lookup` k (`alter` f k m) = f (`lookup` k m)`.

alterF :: Functor f => (Maybe a -> f (Maybe a)) -> Key -> Word64Map a -> f (Word64Map 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 an `Word64Map`. In short : ``lookup` k $ `alterF` f k m = f (`lookup` k m)`.

Example:

    interactiveAlter :: Int -> Word64Map String -> IO (Word64Map 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.

# Query

## Lookup

lookup :: Key -> Word64Map a -> Maybe a #

\(O(\min(n,W))\). Lookup the value at a key in the map. See also `lookup`.

(!?) :: Word64Map a -> Key -> Maybe a infixl 9 #

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

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

Since: 0.5.11

(!) :: Word64Map a -> Key -> a #

\(O(\min(n,W))\). Find the value at a key. Calls `error` when the element can not be found.

    fromList [(5,'a'), (3,'b')] ! 1    Error: element not in the map
    fromList [(5,'a'), (3,'b')] ! 5 == 'a'

findWithDefault :: a -> Key -> Word64Map a -> a #

\(O(\min(n,W))\). The expression `(`findWithDefault` def k map)` returns the value at key `k` or returns `def` when the key is not an element of the map.

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

member :: Key -> Word64Map a -> Bool #

\(O(\min(n,W))\). Is the key a member of the map?

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

notMember :: Key -> Word64Map a -> Bool #

\(O(\min(n,W))\). Is the key not a member of the map?

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

lookupLT :: Key -> Word64Map a -> Maybe (Key, a) #

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

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

lookupGT :: Key -> Word64Map a -> Maybe (Key, a) #

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

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

lookupLE :: Key -> Word64Map a -> Maybe (Key, a) #

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

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

lookupGE :: Key -> Word64Map a -> Maybe (Key, a) #

\(O(\min(n,W))\). 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

null :: Word64Map a -> Bool #

\(O(1)\). Is the map empty?

    Data.Word64Map.null (empty)           == True
    Data.Word64Map.null (singleton 1 'a') == False

size :: Word64Map a -> Int #

\(O(n)\). Number of elements in the map.

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

# Combine

## Union

union :: Word64Map a -> Word64Map a -> Word64Map a #

\(O(n+m)\). The (left-biased) union of two maps. It prefers the first map when duplicate keys are encountered, i.e. (``union` == `unionWith` `const``).

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

unionWith :: (a -> a -> a) -> Word64Map a -> Word64Map a -> Word64Map a #

\(O(n+m)\). The union with a combining function.

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

unionWithKey :: (Key -> a -> a -> a) -> Word64Map a -> Word64Map a -> Word64Map a #

\(O(n+m)\). The union with a combining function.

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

unions :: Foldable f => f (Word64Map a) -> Word64Map a #

The union of a list of maps.

    unions [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])]
        == fromList [(3, "b"), (5, "a"), (7, "C")]
    unions [(fromList [(5, "A3"), (3, "B3")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "a"), (3, "b")])]
        == fromList [(3, "B3"), (5, "A3"), (7, "C")]

unionsWith :: Foldable f => (a -> a -> a) -> f (Word64Map a) -> Word64Map a #

The union of a list of maps, with a combining operation.

    unionsWith (++) [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])]
        == fromList [(3, "bB3"), (5, "aAA3"), (7, "C")]

## Difference

difference :: Word64Map a -> Word64Map b -> Word64Map a #

\(O(n+m)\). Difference between two maps (based on keys).

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

(\\) :: Word64Map a -> Word64Map b -> Word64Map a infixl 9 #

Same as `difference`.

differenceWith :: (a -> b -> Maybe a) -> Word64Map a -> Word64Map b -> Word64Map a #

\(O(n+m)\). Difference with a combining function.

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

differenceWithKey :: (Key -> a -> b -> Maybe a) -> Word64Map a -> Word64Map b -> Word64Map 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

intersection :: Word64Map a -> Word64Map b -> Word64Map a #

\(O(n+m)\). The (left-biased) intersection of two maps (based on keys).

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

intersectionWith :: (a -> b -> c) -> Word64Map a -> Word64Map b -> Word64Map c #

\(O(n+m)\). The intersection with a combining function.

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

intersectionWithKey :: (Key -> a -> b -> c) -> Word64Map a -> Word64Map b -> Word64Map c #

\(O(n+m)\). The 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

disjoint :: Word64Map a -> Word64Map b -> Bool #

\(O(n+m)\). 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

    disjoint a b == null (intersection a b)

Since: 0.6.2.1

## Compose

compose :: Word64Map c -> Word64Map Word64 -> Word64Map 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: \( O(n * \min(m,W)) \), 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.Word64Map.Strict exposed a version of `compose` that forced the values of the output `Word64Map`. This version does not force these values.

Since: 0.6.3.1

## Universal combining function

mergeWithKey :: (Key -> a -> b -> Maybe c) -> (Word64Map a -> Word64Map c) -> (Word64Map b -> Word64Map c) -> Word64Map a -> Word64Map b -> Word64Map c #

\(O(n+m)\). A high-performance universal combining function. Using `mergeWithKey`, all combining functions can be defined without any loss of efficiency (with exception of `union`, `difference` and `intersection`, where sharing of some nodes is lost with `mergeWithKey`).

Please make sure you know what is going on when using `mergeWithKey`, otherwise you can be surprised by unexpected code growth or even corruption of the data structure.

When `mergeWithKey` is given three arguments, it is inlined to the call site. You should therefore use `mergeWithKey` only to define your 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 `Word64Map`s is created, such that

- if a key is present in both maps, it is passed with both corresponding values to the `combine` function. Depending on the result, the key is either present in the result with specified value, or is left out;
- a nonempty subtree present only in the first map is passed to `only1` and the output is added to the result;
- a nonempty subtree present only in the second map is passed to `only2` and the output is added to the result.

The `only1` and `only2` methods must return a map with a subset (possibly empty) of the keys of the given map. The values can be modified arbitrarily. Most common variants of `only1` and `only2` are `id` and ``const` `empty``, but for example ``map` f` or ``filterWithKey` f` could be used for any `f`.

# Traversal

## Map

map :: (a -> b) -> Word64Map a -> Word64Map b #

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

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

mapWithKey :: (Key -> a -> b) -> Word64Map a -> Word64Map 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")]

traverseWithKey :: Applicative t => (Key -> a -> t b) -> Word64Map a -> t (Word64Map b) #

\(O(n)\). ``traverseWithKey` f s == `fromList` $ `traverse` ((k, v) -> (,) k $ f k v) (`toList` m)` That is, behaves exactly like a regular `traverse` except that the traversing function also has access to the key associated with a value.

    traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(1, 'a'), (5, 'e')]) == Just (fromList [(1, 'b'), (5, 'f')])
    traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(2, 'c')])           == Nothing

traverseMaybeWithKey :: Applicative f => (Key -> a -> f (Maybe b)) -> Word64Map a -> f (Word64Map b) #

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

Since: 0.6.4

mapAccum :: (a -> b -> (a, c)) -> a -> Word64Map b -> (a, Word64Map 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")])

mapAccumWithKey :: (a -> Key -> b -> (a, c)) -> a -> Word64Map b -> (a, Word64Map 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")])

mapAccumRWithKey :: (a -> Key -> b -> (a, c)) -> a -> Word64Map b -> (a, Word64Map c) #

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

mapKeys :: (Key -> Key) -> Word64Map a -> Word64Map a #

\(O(n \min(n,W))\). ``mapKeys` f s` is the map obtained by applying `f` to each key of `s`.

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

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

mapKeysWith :: (a -> a -> a) -> (Key -> Key) -> Word64Map a -> Word64Map 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`.

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

mapKeysMonotonic :: (Key -> Key) -> Word64Map a -> Word64Map a #

\(O(n \min(n,W))\). ``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 slightly better performance than `mapKeys`.

    mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")]) == fromList [(6, "b"), (10, "a")]

# Folds

foldr :: (a -> b -> b) -> b -> Word64Map 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

foldl :: (a -> b -> a) -> a -> Word64Map 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

foldrWithKey :: (Key -> a -> b -> b) -> b -> Word64Map a -> b #

\(O(n)\). Fold the keys and values in the map using the given right-associative binary operator, such that ``foldrWithKey` f z == `foldr` (`uncurry` f) z . `toAscList``.

For example,

    keys map = foldrWithKey (\k x ks -> k:ks) [] map

    let f k a result = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")"
    foldrWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (5:a)(3:b)"

foldlWithKey :: (a -> Key -> b -> a) -> a -> Word64Map b -> a #

\(O(n)\). Fold the keys and values in the map using the given left-associative binary operator, such that ``foldlWithKey` f z == `foldl` (\z' (kx, x) -> f z' kx x) z . `toAscList``.

For example,

    keys = reverse . foldlWithKey (\ks k x -> k:ks) []

    let f result k a = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")"
    foldlWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (3:b)(5:a)"

foldMapWithKey :: Monoid m => (Key -> a -> m) -> Word64Map a -> m #

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

    foldMapWithKey f = fold . mapWithKey f

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

Since: 0.5.4

## Strict folds

foldr' :: (a -> b -> b) -> b -> Word64Map 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.

foldl' :: (a -> b -> a) -> a -> Word64Map 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.

foldrWithKey' :: (Key -> a -> b -> b) -> b -> Word64Map 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.

foldlWithKey' :: (a -> Key -> b -> a) -> a -> Word64Map 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

elems :: Word64Map 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 == []

keys :: Word64Map a -> [Key] #

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

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

assocs :: Word64Map a -> [(Key, a)] #

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

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

keysSet :: Word64Map a -> Word64Set #

\(O(n \min(n,W))\). The set of all keys of the map.

    keysSet (fromList [(5,"a"), (3,"b")]) == Data.Word64Set.fromList [3,5]
    keysSet empty == Data.Word64Set.empty

## Lists

toList :: Word64Map a -> [(Key, 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

toAscList :: Word64Map a -> [(Key, 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")]

toDescList :: Word64Map a -> [(Key, 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

filter :: (a -> Bool) -> Word64Map a -> Word64Map a #

\(O(n)\). Filter all values that satisfy some predicate.

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

filterWithKey :: (Key -> a -> Bool) -> Word64Map a -> Word64Map a #

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

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

restrictKeys :: Word64Map a -> Word64Set -> Word64Map a #

\(O(n+m)\). The restriction of a map to the keys in a set.

    m `restrictKeys` s = filterWithKey (\k _ -> k `member` s) m

Since: 0.5.8

withoutKeys :: Word64Map a -> Word64Set -> Word64Map a #

\(O(n+m)\). Remove all the keys in a given set from a map.

    m `withoutKeys` s = filterWithKey (\k _ -> k `notMember` s) m

Since: 0.5.8

partition :: (a -> Bool) -> Word64Map a -> (Word64Map a, Word64Map a) #

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

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

partitionWithKey :: (Key -> a -> Bool) -> Word64Map a -> (Word64Map a, Word64Map a) #

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

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

takeWhileAntitone :: (Key -> Bool) -> Word64Map a -> Word64Map a #

\(O(\min(n,W))\). Take while a predicate on the keys holds. The user is responsible for ensuring that for all `Int`s, `j < k ==> p j >= p k`. See note at `spanAntitone`.

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

Since: 0.6.7

dropWhileAntitone :: (Key -> Bool) -> Word64Map a -> Word64Map a #

\(O(\min(n,W))\). Drop while a predicate on the keys holds. The user is responsible for ensuring that for all `Int`s, `j < k ==> p j >= p k`. See note at `spanAntitone`.

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

Since: 0.6.7

spanAntitone :: (Key -> Bool) -> Word64Map a -> (Word64Map a, Word64Map a) #

\(O(\min(n,W))\). Divide a map at the point where a predicate on the keys stops holding. The user is responsible for ensuring that for all `Int`s, `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.

Since: 0.6.7

mapMaybe :: (a -> Maybe b) -> Word64Map a -> Word64Map 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"

mapMaybeWithKey :: (Key -> a -> Maybe b) -> Word64Map a -> Word64Map 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"

mapEither :: (a -> Either b c) -> Word64Map a -> (Word64Map b, Word64Map 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")])

mapEitherWithKey :: (Key -> a -> Either b c) -> Word64Map a -> (Word64Map b, Word64Map 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")])

split :: Key -> Word64Map a -> (Word64Map a, Word64Map a) #

\(O(\min(n,W))\). The expression (``split` k map`) is a pair `(map1,map2)` where all keys in `map1` are lower than `k` and all keys in `map2` larger than `k`. Any key equal to `k` is found in neither `map1` nor `map2`.

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

splitLookup :: Key -> Word64Map a -> (Word64Map a, Maybe a, Word64Map a) #

\(O(\min(n,W))\). Performs a `split` but also returns whether the pivot key was found in the original map.

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

splitRoot :: Word64Map a -> [Word64Map a] #

\(O(1)\). 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::Int] ['a'..])) ==
      [fromList [(1,'a'),(2,'b'),(3,'c')],fromList [(4,'d'),(5,'e'),(6,'f')]]

    splitRoot empty == []

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

# Submap

isSubmapOf :: Eq a => Word64Map a -> Word64Map a -> Bool #

\(O(n+m)\). Is this a submap? Defined as (``isSubmapOf` = `isSubmapOfBy` (==)`).

isSubmapOfBy :: (a -> b -> Bool) -> Word64Map a -> Word64Map b -> Bool #

\(O(n+m)\). The expression (``isSubmapOfBy` f m1 m2`) returns `True` if 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`:

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

But the following are all `False`:

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

isProperSubmapOf :: Eq a => Word64Map a -> Word64Map a -> Bool #

\(O(n+m)\). Is this a proper submap? (ie. a submap but not equal). Defined as (``isProperSubmapOf` = `isProperSubmapOfBy` (==)`).

isProperSubmapOfBy :: (a -> b -> Bool) -> Word64Map a -> Word64Map b -> Bool #

\(O(n+m)\). 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)])

# Min/Max

lookupMin :: Word64Map a -> Maybe (Key, a) #

\(O(\min(n,W))\). The minimal key of the map. Returns `Nothing` if the map is empty.

lookupMax :: Word64Map a -> Maybe (Key, a) #

\(O(\min(n,W))\). The maximal key of the map. Returns `Nothing` if the map is empty.

findMin :: Word64Map a -> (Key, a) #

\(O(\min(n,W))\). The minimal key of the map. Calls `error` if the map is empty. Use `minViewWithKey` if the map may be empty.

findMax :: Word64Map a -> (Key, a) #

\(O(\min(n,W))\). The maximal key of the map. Calls `error` if the map is empty. Use `maxViewWithKey` if the map may be empty.

deleteMin :: Word64Map a -> Word64Map a #

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

Note that this is a change of behaviour for consistency with `Map` – versions prior to 0.5 threw an error if the `Word64Map` was already empty.

deleteMax :: Word64Map a -> Word64Map a #

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

Note that this is a change of behaviour for consistency with `Map` – versions prior to 0.5 threw an error if the `Word64Map` was already empty.

deleteFindMin :: Word64Map a -> ((Key, a), Word64Map a) #

\(O(\min(n,W))\). Delete and find the minimal element. This function throws an error if the map is empty. Use `minViewWithKey` if the map may be empty.

deleteFindMax :: Word64Map a -> ((Key, a), Word64Map a) #

\(O(\min(n,W))\). Delete and find the maximal element. This function throws an error if the map is empty. Use `maxViewWithKey` if the map may be empty.

updateMin :: (a -> Maybe a) -> Word64Map a -> Word64Map 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"

updateMax :: (a -> Maybe a) -> Word64Map a -> Word64Map 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"

updateMinWithKey :: (Key -> a -> Maybe a) -> Word64Map a -> Word64Map 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"

updateMaxWithKey :: (Key -> a -> Maybe a) -> Word64Map a -> Word64Map 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"

minView :: Word64Map a -> Maybe (a, Word64Map a) #

\(O(\min(n,W))\). Retrieves the minimal key of the map, and the map stripped of that element, or `Nothing` if passed an empty map.

maxView :: Word64Map a -> Maybe (a, Word64Map a) #

\(O(\min(n,W))\). Retrieves the maximal key of the map, and the map stripped of that element, or `Nothing` if passed an empty map.

minViewWithKey :: Word64Map a -> Maybe ((Key, a), Word64Map a) #

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

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

maxViewWithKey :: Word64Map a -> Maybe ((Key, a), Word64Map a) #

\(O(\min(n,W))\). 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