Data.IntMap.Internal

containers-0.6.4.1: Assorted concrete container types

Copyright | (c) Daan Leijen 2002 (c) Andriy Palamarchuk 2008 (c) wren romano 2016
License | BSD-style
Maintainer | libraries@haskell.org
Portability | portable
Safe Haskell | Trustworthy
Language | Haskell2010

Data.IntMap.Internal

Contents

- Map type
- Operators
- Query
- Construction
  - Insertion
  - Delete/Update
- Combine
  - Union
  - Difference
  - Intersection
  - Compose
  - General combining function
    - `WhenMatched` tactics
    - `WhenMissing` tactics
  - Applicative general combining function
    - `WhenMatched` tactics
    - `WhenMissing` tactics
  - Deprecated general combining function
- Traversal
  - Map
- Folds
  - Strict folds
- Conversion
  - Lists
  - Ordered lists
- Filter
- Submap
- Min/Max
- Debugging
- Internal types
- Utility
- Used by IntMap.Merge.Lazy and IntMap.Merge.Strict

Description

# WARNING

This module is considered internal.

The Package Versioning Policy does not apply.

The contents of this module may change in any way whatsoever and without any warning between minor versions of this package.

Authors importing this module are expected to track development closely.

# Description

This defines the data structures and core (hidden) manipulations on representations.

Since: containers-0.5.9

Synopsis

- data IntMap a
  - = Bin !Prefix !Mask !(IntMap a) !(IntMap a)
  - | Tip !Key a
  - | Nil
- type Key = Int
- (!) :: IntMap a -> Key -> a
- (!?) :: IntMap a -> Key -> Maybe a
- (\\) :: IntMap a -> IntMap b -> IntMap a
- null :: IntMap a -> Bool
- size :: IntMap a -> Int
- member :: Key -> IntMap a -> Bool
- notMember :: Key -> IntMap a -> Bool
- lookup :: Key -> IntMap a -> Maybe a
- findWithDefault :: a -> Key -> IntMap a -> a
- lookupLT :: Key -> IntMap a -> Maybe (Key, a)
- lookupGT :: Key -> IntMap a -> Maybe (Key, a)
- lookupLE :: Key -> IntMap a -> Maybe (Key, a)
- lookupGE :: Key -> IntMap a -> Maybe (Key, a)
- disjoint :: IntMap a -> IntMap b -> Bool
- empty :: IntMap a
- singleton :: Key -> a -> IntMap a
- insert :: Key -> a -> IntMap a -> IntMap a
- insertWith :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
- insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
- insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a)
- delete :: Key -> IntMap a -> IntMap a
- adjust :: (a -> a) -> Key -> IntMap a -> IntMap a
- adjustWithKey :: (Key -> a -> a) -> Key -> IntMap a -> IntMap a
- update :: (a -> Maybe a) -> Key -> IntMap a -> IntMap a
- updateWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> IntMap a
- updateLookupWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> (Maybe a, IntMap a)
- alter :: (Maybe a -> Maybe a) -> Key -> IntMap a -> IntMap a
- alterF :: Functor f => (Maybe a -> f (Maybe a)) -> Key -> IntMap a -> f (IntMap a)
- union :: IntMap a -> IntMap a -> IntMap a
- unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
- unionWithKey :: (Key -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
- unions :: Foldable f => f (IntMap a) -> IntMap a
- unionsWith :: Foldable f => (a -> a -> a) -> f (IntMap a) -> IntMap a
- difference :: IntMap a -> IntMap b -> IntMap a
- differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
- differenceWithKey :: (Key -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
- intersection :: IntMap a -> IntMap b -> IntMap a
- intersectionWith :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
- intersectionWithKey :: (Key -> a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
- compose :: IntMap c -> IntMap Int -> IntMap c
- type SimpleWhenMissing = WhenMissing Identity
- type SimpleWhenMatched = WhenMatched Identity
- runWhenMatched :: WhenMatched f x y z -> Key -> x -> y -> f (Maybe z)
- runWhenMissing :: WhenMissing f x y -> Key -> x -> f (Maybe y)
- merge :: SimpleWhenMissing a c -> SimpleWhenMissing b c -> SimpleWhenMatched a b c -> IntMap a -> IntMap b -> IntMap c
- zipWithMaybeMatched :: Applicative f => (Key -> x -> y -> Maybe z) -> WhenMatched f x y z
- zipWithMatched :: Applicative f => (Key -> x -> y -> z) -> WhenMatched f x y z
- mapMaybeMissing :: Applicative f => (Key -> x -> Maybe y) -> WhenMissing f x y
- dropMissing :: Applicative f => WhenMissing f x y
- preserveMissing :: Applicative f => WhenMissing f x x
- mapMissing :: Applicative f => (Key -> x -> y) -> WhenMissing f x y
- filterMissing :: Applicative f => (Key -> x -> Bool) -> WhenMissing f x x
- data WhenMissing f x y = WhenMissing {
  - missingSubtree :: IntMap x -> f (IntMap y)
  - missingKey :: Key -> x -> f (Maybe y)
  }
- newtype WhenMatched f x y z = WhenMatched {
  - matchedKey :: Key -> x -> y -> f (Maybe z)
  }
- mergeA :: Applicative f => WhenMissing f a c -> WhenMissing f b c -> WhenMatched f a b c -> IntMap a -> IntMap b -> f (IntMap c)
- zipWithMaybeAMatched :: (Key -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
- zipWithAMatched :: Applicative f => (Key -> x -> y -> f z) -> WhenMatched f x y z
- traverseMaybeMissing :: Applicative f => (Key -> x -> f (Maybe y)) -> WhenMissing f x y
- traverseMissing :: Applicative f => (Key -> x -> f y) -> WhenMissing f x y
- filterAMissing :: Applicative f => (Key -> x -> f Bool) -> WhenMissing f x x
- mergeWithKey :: (Key -> a -> b -> Maybe c) -> (IntMap a -> IntMap c) -> (IntMap b -> IntMap c) -> IntMap a -> IntMap b -> IntMap c
- mergeWithKey' :: (Prefix -> Mask -> IntMap c -> IntMap c -> IntMap c) -> (IntMap a -> IntMap b -> IntMap c) -> (IntMap a -> IntMap c) -> (IntMap b -> IntMap c) -> IntMap a -> IntMap b -> IntMap c
- map :: (a -> b) -> IntMap a -> IntMap b
- mapWithKey :: (Key -> a -> b) -> IntMap a -> IntMap b
- traverseWithKey :: Applicative t => (Key -> a -> t b) -> IntMap a -> t (IntMap b)
- traverseMaybeWithKey :: Applicative f => (Key -> a -> f (Maybe b)) -> IntMap a -> f (IntMap b)
- mapAccum :: (a -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
- mapAccumWithKey :: (a -> Key -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
- mapAccumRWithKey :: (a -> Key -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
- mapKeys :: (Key -> Key) -> IntMap a -> IntMap a
- mapKeysWith :: (a -> a -> a) -> (Key -> Key) -> IntMap a -> IntMap a
- mapKeysMonotonic :: (Key -> Key) -> IntMap a -> IntMap a
- foldr :: (a -> b -> b) -> b -> IntMap a -> b
- foldl :: (a -> b -> a) -> a -> IntMap b -> a
- foldrWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b
- foldlWithKey :: (a -> Key -> b -> a) -> a -> IntMap b -> a
- foldMapWithKey :: Monoid m => (Key -> a -> m) -> IntMap a -> m
- foldr' :: (a -> b -> b) -> b -> IntMap a -> b
- foldl' :: (a -> b -> a) -> a -> IntMap b -> a
- foldrWithKey' :: (Key -> a -> b -> b) -> b -> IntMap a -> b
- foldlWithKey' :: (a -> Key -> b -> a) -> a -> IntMap b -> a
- elems :: IntMap a -> [a]
- keys :: IntMap a -> [Key]
- assocs :: IntMap a -> [(Key, a)]
- keysSet :: IntMap a -> IntSet
- fromSet :: (Key -> a) -> IntSet -> IntMap a
- toList :: IntMap a -> [(Key, a)]
- fromList :: [(Key, a)] -> IntMap a
- fromListWith :: (a -> a -> a) -> [(Key, a)] -> IntMap a
- fromListWithKey :: (Key -> a -> a -> a) -> [(Key, a)] -> IntMap a
- toAscList :: IntMap a -> [(Key, a)]
- toDescList :: IntMap a -> [(Key, a)]
- fromAscList :: [(Key, a)] -> IntMap a
- fromAscListWith :: (a -> a -> a) -> [(Key, a)] -> IntMap a
- fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key, a)] -> IntMap a
- fromDistinctAscList :: [(Key, a)] -> IntMap a
- filter :: (a -> Bool) -> IntMap a -> IntMap a
- filterWithKey :: (Key -> a -> Bool) -> IntMap a -> IntMap a
- restrictKeys :: IntMap a -> IntSet -> IntMap a
- withoutKeys :: IntMap a -> IntSet -> IntMap a
- partition :: (a -> Bool) -> IntMap a -> (IntMap a, IntMap a)
- partitionWithKey :: (Key -> a -> Bool) -> IntMap a -> (IntMap a, IntMap a)
- mapMaybe :: (a -> Maybe b) -> IntMap a -> IntMap b
- mapMaybeWithKey :: (Key -> a -> Maybe b) -> IntMap a -> IntMap b
- mapEither :: (a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
- mapEitherWithKey :: (Key -> a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
- split :: Key -> IntMap a -> (IntMap a, IntMap a)
- splitLookup :: Key -> IntMap a -> (IntMap a, Maybe a, IntMap a)
- splitRoot :: IntMap a -> [IntMap a]
- isSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
- isSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
- isProperSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
- isProperSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
- lookupMin :: IntMap a -> Maybe (Key, a)
- lookupMax :: IntMap a -> Maybe (Key, a)
- findMin :: IntMap a -> (Key, a)
- findMax :: IntMap a -> (Key, a)
- deleteMin :: IntMap a -> IntMap a
- deleteMax :: IntMap a -> IntMap a
- deleteFindMin :: IntMap a -> ((Key, a), IntMap a)
- deleteFindMax :: IntMap a -> ((Key, a), IntMap a)
- updateMin :: (a -> Maybe a) -> IntMap a -> IntMap a
- updateMax :: (a -> Maybe a) -> IntMap a -> IntMap a
- updateMinWithKey :: (Key -> a -> Maybe a) -> IntMap a -> IntMap a
- updateMaxWithKey :: (Key -> a -> Maybe a) -> IntMap a -> IntMap a
- minView :: IntMap a -> Maybe (a, IntMap a)
- maxView :: IntMap a -> Maybe (a, IntMap a)
- minViewWithKey :: IntMap a -> Maybe ((Key, a), IntMap a)
- maxViewWithKey :: IntMap a -> Maybe ((Key, a), IntMap a)
- showTree :: Show a => IntMap a -> String
- showTreeWith :: Show a => Bool -> Bool -> IntMap a -> String
- type Mask = Int
- type Prefix = Int
- type Nat = Word
- natFromInt :: Key -> Nat
- intFromNat :: Nat -> Key
- link :: Prefix -> IntMap a -> Prefix -> IntMap a -> IntMap a
- linkWithMask :: Mask -> Prefix -> IntMap a -> IntMap a -> IntMap a
- bin :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a
- binCheckLeft :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a
- binCheckRight :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a
- zero :: Key -> Mask -> Bool
- nomatch :: Key -> Prefix -> Mask -> Bool
- match :: Key -> Prefix -> Mask -> Bool
- mask :: Key -> Mask -> Prefix
- maskW :: Nat -> Nat -> Prefix
- shorter :: Mask -> Mask -> Bool
- branchMask :: Prefix -> Prefix -> Mask
- highestBitMask :: Word -> Word
- mapWhenMissing :: (Applicative f, Monad f) => (a -> b) -> WhenMissing f x a -> WhenMissing f x b
- mapWhenMatched :: Functor f => (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b
- lmapWhenMissing :: (b -> a) -> WhenMissing f a x -> WhenMissing f b x
- contramapFirstWhenMatched :: (b -> a) -> WhenMatched f a y z -> WhenMatched f b y z
- contramapSecondWhenMatched :: (b -> a) -> WhenMatched f x a z -> WhenMatched f x b z
- mapGentlyWhenMissing :: Functor f => (a -> b) -> WhenMissing f x a -> WhenMissing f x b
- mapGentlyWhenMatched :: Functor f => (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b

# Map type

data IntMap a #

A map of integers to values `a`.

Constructors

Bin !Prefix !Mask !(IntMap a) !(IntMap a) |
Tip !Key a |
Nil |

#### Instances

Instances details

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

type Key = Int #

# Operators

(!) :: IntMap 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'

(!?) :: IntMap 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: containers-0.5.11

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

Same as `difference`.

# Query

null :: IntMap a -> Bool #

O(1). Is the map empty?

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

size :: IntMap 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

member :: Key -> IntMap 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 -> IntMap 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

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

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

findWithDefault :: a -> Key -> IntMap 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'

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

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

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

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

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

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

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

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

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

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

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

disjoint :: IntMap a -> IntMap 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: containers-0.6.2.1

# Construction

empty :: IntMap a #

O(1). The empty map.

    empty      == fromList []
    size empty == 0

singleton :: Key -> a -> IntMap a #

O(1). A map of one element.

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

## Insertion

insert :: Key -> a -> IntMap a -> IntMap 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 -> IntMap a -> IntMap 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 -> IntMap a -> IntMap 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"

insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap 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")])

## Delete/Update

delete :: Key -> IntMap a -> IntMap 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 -> IntMap a -> IntMap 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 -> IntMap a -> IntMap 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 -> IntMap a -> IntMap 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 -> IntMap a -> IntMap 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 -> IntMap a -> (Maybe a, IntMap 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 -> IntMap a -> IntMap 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 `IntMap`. In short : ``lookup` k (`alter` f k m) = f (`lookup` k m)`.

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

Example:

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

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

Since: containers-0.5.8

# Combine

## Union

union :: IntMap a -> IntMap a -> IntMap 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) -> IntMap a -> IntMap a -> IntMap 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) -> IntMap a -> IntMap a -> IntMap 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 (IntMap a) -> IntMap 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 (IntMap a) -> IntMap 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 :: IntMap a -> IntMap b -> IntMap 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"

differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap 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) -> IntMap a -> IntMap b -> IntMap 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 :: IntMap a -> IntMap b -> IntMap 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) -> IntMap a -> IntMap b -> IntMap 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) -> IntMap a -> IntMap b -> IntMap 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"

## Compose

compose :: IntMap c -> IntMap Int -> IntMap 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.IntMap.Strict exposed a version of `compose` that forced the values of the output `IntMap`. This version does not force these values.

Since: containers-0.6.3.1

## General combining function

type SimpleWhenMissing = WhenMissing Identity #

A tactic for dealing with keys present in one map but not the other in `merge`.

A tactic of type `SimpleWhenMissing x z` is an abstract representation of a function of type `Key -> x -> Maybe z`.

Since: containers-0.5.9

type SimpleWhenMatched = WhenMatched Identity #

A tactic for dealing with keys present in both maps in `merge`.

A tactic of type `SimpleWhenMatched x y z` is an abstract representation of a function of type `Key -> x -> y -> Maybe z`.

Since: containers-0.5.9

runWhenMatched :: WhenMatched f x y z -> Key -> x -> y -> f (Maybe z) #

Along with zipWithMaybeAMatched, witnesses the isomorphism between `WhenMatched f x y z` and `Key -> x -> y -> f (Maybe z)`.

Since: containers-0.5.9

runWhenMissing :: WhenMissing f x y -> Key -> x -> f (Maybe y) #

Along with traverseMaybeMissing, witnesses the isomorphism between `WhenMissing f x y` and `Key -> x -> f (Maybe y)`.

Since: containers-0.5.9

merge #

Arguments

:: SimpleWhenMissing a c | What to do with keys in `m1` but not `m2`
-> SimpleWhenMissing b c | What to do with keys in `m2` but not `m1`
-> SimpleWhenMatched a b c | What to do with keys in both `m1` and `m2`
-> IntMap a | Map `m1`
-> IntMap b | Map `m2`
-> IntMap c |

Merge two maps.

`merge` takes two `WhenMissing` tactics, a `WhenMatched` tactic and two maps. It uses the tactics to merge the maps. Its behavior is best understood via its fundamental tactics, `mapMaybeMissing` and `zipWithMaybeMatched`.

Consider

    merge (mapMaybeMissing g1)
                 (mapMaybeMissing g2)
                 (zipWithMaybeMatched f)
                 m1 m2

Take, for example,

    m1 = [(0, 'a'), (1, 'b'), (3, 'c'), (4, 'd')]
    m2 = [(1, "one"), (2, "two"), (4, "three")]

`merge` will first "align" these maps by key:

    m1 = [(0, 'a'), (1, 'b'),               (3, 'c'), (4, 'd')]
    m2 =           [(1, "one"), (2, "two"),           (4, "three")]

It will then pass the individual entries and pairs of entries to `g1`, `g2`, or `f` as appropriate:

    maybes = [g1 0 'a', f 1 'b' "one", g2 2 "two", g1 3 'c', f 4 'd' "three"]

This produces a `Maybe` for each key:

    keys =     0        1          2           3        4
    results = [Nothing, Just True, Just False, Nothing, Just True]

Finally, the `Just` results are collected into a map:

    return value = [(1, True), (2, False), (4, True)]

The other tactics below are optimizations or simplifications of `mapMaybeMissing` for special cases. Most importantly,

- `dropMissing` drops all the keys.
- `preserveMissing` leaves all the entries alone.

When `merge` is given three arguments, it is inlined at the call site. To prevent excessive inlining, you should typically use `merge` to define your custom combining functions.

Examples:

    unionWithKey f = merge preserveMissing preserveMissing (zipWithMatched f)

    intersectionWithKey f = merge dropMissing dropMissing (zipWithMatched f)

    differenceWith f = merge diffPreserve diffDrop f

    symmetricDifference = merge diffPreserve diffPreserve (\ _ _ _ -> Nothing)

    mapEachPiece f g h = merge (diffMapWithKey f) (diffMapWithKey g)

Since: containers-0.5.9

### `WhenMatched` tactics

zipWithMaybeMatched :: Applicative f => (Key -> x -> y -> Maybe z) -> WhenMatched f x y z #

When a key is found in both maps, apply a function to the key and values and maybe use the result in the merged map.

    zipWithMaybeMatched
      :: (Key -> x -> y -> Maybe z)
      -> SimpleWhenMatched x y z

Since: containers-0.5.9

zipWithMatched :: Applicative f => (Key -> x -> y -> z) -> WhenMatched f x y z #

When a key is found in both maps, apply a function to the key and values and use the result in the merged map.

    zipWithMatched
      :: (Key -> x -> y -> z)
      -> SimpleWhenMatched x y z

Since: containers-0.5.9

### `WhenMissing` tactics

mapMaybeMissing :: Applicative f => (Key -> x -> Maybe y) -> WhenMissing f x y #

Map over the entries whose keys are missing from the other map, optionally removing some. This is the most powerful `SimpleWhenMissing` tactic, but others are usually more efficient.

    mapMaybeMissing :: (Key -> x -> Maybe y) -> SimpleWhenMissing x y

    mapMaybeMissing f = traverseMaybeMissing (\k x -> pure (f k x))

but `mapMaybeMissing` uses fewer unnecessary `Applicative` operations.

Since: containers-0.5.9

dropMissing :: Applicative f => WhenMissing f x y #

Drop all the entries whose keys are missing from the other map.

    dropMissing :: SimpleWhenMissing x y

    dropMissing = mapMaybeMissing (\_ _ -> Nothing)

but `dropMissing` is much faster.

Since: containers-0.5.9

preserveMissing :: Applicative f => WhenMissing f x x #

Preserve, unchanged, the entries whose keys are missing from the other map.

    preserveMissing :: SimpleWhenMissing x x

    preserveMissing = Merge.Lazy.mapMaybeMissing (\_ x -> Just x)

but `preserveMissing` is much faster.

Since: containers-0.5.9

mapMissing :: Applicative f => (Key -> x -> y) -> WhenMissing f x y #

Map over the entries whose keys are missing from the other map.

    mapMissing :: (k -> x -> y) -> SimpleWhenMissing x y

    mapMissing f = mapMaybeMissing (\k x -> Just $ f k x)

but `mapMissing` is somewhat faster.

Since: containers-0.5.9

filterMissing :: Applicative f => (Key -> x -> Bool) -> WhenMissing f x x #

Filter the entries whose keys are missing from the other map.

    filterMissing :: (k -> x -> Bool) -> SimpleWhenMissing x x

    filterMissing f = Merge.Lazy.mapMaybeMissing $ \k x -> guard (f k x) *> Just x

but this should be a little faster.

Since: containers-0.5.9

## Applicative general combining function

data WhenMissing f x y #

A tactic for dealing with keys present in one map but not the other in `merge` or `mergeA`.

A tactic of type `WhenMissing f k x z` is an abstract representation of a function of type `Key -> x -> f (Maybe z)`.

Since: containers-0.5.9

Constructors

WhenMissing |
Fields missingSubtree :: IntMap x -> f (IntMap y) missingKey :: Key -> x -> f (Maybe y)

#### Instances

Instances details

(Applicative f, Monad f) => Category (WhenMissing f :: Type -> Type -> Type) # | Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods id :: forall (a :: k). WhenMissing f a a Source # (.) :: forall (b :: k) (c :: k) (a :: k). WhenMissing f b c -> WhenMissing f a b -> WhenMissing f a c Source #
(Applicative f, Monad f) => Applicative (WhenMissing f x) # | Equivalent to `ReaderT k (ReaderT x (MaybeT f))`. Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods pure :: a -> WhenMissing f x a Source # (<*>) :: WhenMissing f x (a -> b) -> WhenMissing f x a -> WhenMissing f x b Source # liftA2 :: (a -> b -> c) -> WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x c Source # (*>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b Source # (<*) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x a Source #
(Applicative f, Monad f) => Functor (WhenMissing f x) # | Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> WhenMissing f x a -> WhenMissing f x b Source # (<$) :: a -> WhenMissing f x b -> WhenMissing f x a Source #
(Applicative f, Monad f) => Monad (WhenMissing f x) # | Equivalent to `ReaderT k (ReaderT x (MaybeT f))`. Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods (>>=) :: WhenMissing f x a -> (a -> WhenMissing f x b) -> WhenMissing f x b Source # (>>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b Source # return :: a -> WhenMissing f x a Source #

newtype WhenMatched f x y z #

A tactic for dealing with keys present in both maps in `merge` or `mergeA`.

A tactic of type `WhenMatched f x y z` is an abstract representation of a function of type `Key -> x -> y -> f (Maybe z)`.

Since: containers-0.5.9

Constructors

WhenMatched |
Fields matchedKey :: Key -> x -> y -> f (Maybe z)

#### Instances

Instances details

(Monad f, Applicative f) => Category (WhenMatched f x :: Type -> Type -> Type) # | Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods id :: forall (a :: k). WhenMatched f x a a Source # (.) :: forall (b :: k) (c :: k) (a :: k). WhenMatched f x b c -> WhenMatched f x a b -> WhenMatched f x a c Source #
(Monad f, Applicative f) => Applicative (WhenMatched f x y) # | Equivalent to `ReaderT Key (ReaderT x (ReaderT y (MaybeT f)))` Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods pure :: a -> WhenMatched f x y a Source # (<*>) :: WhenMatched f x y (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b Source # liftA2 :: (a -> b -> c) -> WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y c Source # (*>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b Source # (<*) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y a Source #
Functor f => Functor (WhenMatched f x y) # | Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b Source # (<$) :: a -> WhenMatched f x y b -> WhenMatched f x y a Source #
(Monad f, Applicative f) => Monad (WhenMatched f x y) # | Equivalent to `ReaderT Key (ReaderT x (ReaderT y (MaybeT f)))` Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods (>>=) :: WhenMatched f x y a -> (a -> WhenMatched f x y b) -> WhenMatched f x y b Source # (>>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b Source # return :: a -> WhenMatched f x y a Source #

mergeA #

Arguments

:: Applicative f |
=> WhenMissing f a c | What to do with keys in `m1` but not `m2`
-> WhenMissing f b c | What to do with keys in `m2` but not `m1`
-> WhenMatched f a b c | What to do with keys in both `m1` and `m2`
-> IntMap a | Map `m1`
-> IntMap b | Map `m2`
-> f (IntMap c) |

An applicative version of `merge`.

`mergeA` takes two `WhenMissing` tactics, a `WhenMatched` tactic and two maps. It uses the tactics to merge the maps. Its behavior is best understood via its fundamental tactics, `traverseMaybeMissing` and `zipWithMaybeAMatched`.

Consider

    mergeA (traverseMaybeMissing g1)
                  (traverseMaybeMissing g2)
                  (zipWithMaybeAMatched f)
                  m1 m2

Take, for example,

    m1 = [(0, 'a'), (1, 'b'), (3,'c'), (4, 'd')]
    m2 = [(1, "one"), (2, "two"), (4, "three")]

`mergeA` will first "align" these maps by key:

    m1 = [(0, 'a'), (1, 'b'),               (3, 'c'), (4, 'd')]
    m2 =           [(1, "one"), (2, "two"),           (4, "three")]

It will then pass the individual entries and pairs of entries to `g1`, `g2`, or `f` as appropriate:

    actions = [g1 0 'a', f 1 'b' "one", g2 2 "two", g1 3 'c', f 4 'd' "three"]

Next, it will perform the actions in the `actions` list in order from left to right.

    keys =     0        1          2           3        4
    results = [Nothing, Just True, Just False, Nothing, Just True]

Finally, the `Just` results are collected into a map:

    return value = [(1, True), (2, False), (4, True)]

The other tactics below are optimizations or simplifications of `traverseMaybeMissing` for special cases. Most importantly,

- `dropMissing` drops all the keys.
- `preserveMissing` leaves all the entries alone.
- `mapMaybeMissing` does not use the `Applicative` context.

When `mergeA` is given three arguments, it is inlined at the call site. To prevent excessive inlining, you should generally only use `mergeA` to define custom combining functions.

Since: containers-0.5.9

### `WhenMatched` tactics

The tactics described for `merge` work for `mergeA` as well. Furthermore, the following are available.

zipWithMaybeAMatched :: (Key -> x -> y -> f (Maybe z)) -> WhenMatched f x y z #

When a key is found in both maps, apply a function to the key and values, perform the resulting action, and maybe use the result in the merged map.

This is the fundamental `WhenMatched` tactic.

Since: containers-0.5.9

zipWithAMatched :: Applicative f => (Key -> x -> y -> f z) -> WhenMatched f x y z #

When a key is found in both maps, apply a function to the key and values to produce an action and use its result in the merged map.

Since: containers-0.5.9

### `WhenMissing` tactics

The tactics described for `merge` work for `mergeA` as well. Furthermore, the following are available.

traverseMaybeMissing :: Applicative f => (Key -> x -> f (Maybe y)) -> WhenMissing f x y #

Traverse over the entries whose keys are missing from the other map, optionally producing values to put in the result. This is the most powerful `WhenMissing` tactic, but others are usually more efficient.

Since: containers-0.5.9

traverseMissing :: Applicative f => (Key -> x -> f y) -> WhenMissing f x y #

Traverse over the entries whose keys are missing from the other map.

Since: containers-0.5.9

filterAMissing :: Applicative f => (Key -> x -> f Bool) -> WhenMissing f x x #

Filter the entries whose keys are missing from the other map using some `Applicative` action.

    filterAMissing f = Merge.Lazy.traverseMaybeMissing $
      \k x -> (\b -> guard b *> Just x) <$> f k x

but this should be a little faster.

Since: containers-0.5.9

## Deprecated general combining function

mergeWithKey :: (Key -> a -> b -> Maybe c) -> (IntMap a -> IntMap c) -> (IntMap b -> IntMap c) -> IntMap a -> IntMap b -> IntMap 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 `IntMap`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`.

mergeWithKey' :: (Prefix -> Mask -> IntMap c -> IntMap c -> IntMap c) -> (IntMap a -> IntMap b -> IntMap c) -> (IntMap a -> IntMap c) -> (IntMap b -> IntMap c) -> IntMap a -> IntMap b -> IntMap c #

# Traversal

## Map

map :: (a -> b) -> IntMap a -> IntMap 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) -> IntMap a -> IntMap 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) -> IntMap a -> t (IntMap 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)) -> IntMap a -> f (IntMap b) #

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

Since: containers-0.6.4

mapAccum :: (a -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap 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 -> IntMap b -> (a, IntMap 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 -> IntMap b -> (a, IntMap c) #

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

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

O(n*min(n,W)). ``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) -> IntMap a -> IntMap 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 -> IntMap 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 -> IntMap 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 -> IntMap 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 -> IntMap 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) -> IntMap 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: containers-0.5.4

## Strict folds

foldr' :: (a -> b -> b) -> b -> IntMap 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 -> IntMap 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 -> IntMap 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 -> IntMap 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 :: IntMap 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 :: IntMap 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 :: IntMap 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 :: IntMap a -> IntSet #

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

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

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

## Lists

toList :: IntMap 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 == []

fromList :: [(Key, a)] -> IntMap 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)] -> IntMap 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,"c")] == fromList [(3, "ab"), (5, "cba")]
    fromListWith (++) [] == empty

fromListWithKey :: (Key -> a -> a -> a) -> [(Key, a)] -> IntMap 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

## Ordered lists

toAscList :: IntMap 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 :: IntMap 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")]

fromAscList :: [(Key, a)] -> IntMap 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)] -> IntMap 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)] -> IntMap 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.

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

fromDistinctAscList :: [(Key, a)] -> IntMap 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")]

# Filter

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

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

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

restrictKeys :: IntMap a -> IntSet -> IntMap 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: containers-0.5.8

withoutKeys :: IntMap a -> IntSet -> IntMap 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: containers-0.5.8

partition :: (a -> Bool) -> IntMap a -> (IntMap a, IntMap 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) -> IntMap a -> (IntMap a, IntMap 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")])

mapMaybe :: (a -> Maybe b) -> IntMap a -> IntMap 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) -> IntMap a -> IntMap 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) -> IntMap a -> (IntMap b, IntMap 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) -> IntMap a -> (IntMap b, IntMap 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 -> IntMap a -> (IntMap a, IntMap 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 -> IntMap a -> (IntMap a, Maybe a, IntMap 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 :: IntMap a -> [IntMap 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 => IntMap a -> IntMap a -> Bool #

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

isSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap 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 => IntMap a -> IntMap a -> Bool #

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

isProperSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap 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 :: IntMap a -> Maybe (Key, a) #

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

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

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

findMin :: IntMap 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 :: IntMap 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 :: IntMap a -> IntMap 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 `IntMap` was already empty.

deleteMax :: IntMap a -> IntMap 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 `IntMap` was already empty.

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

O(min(n,W)). 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) -> IntMap a -> IntMap a #

O(min(n,W)). 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) -> IntMap a -> IntMap a #

O(min(n,W)). 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) -> IntMap a -> IntMap a #

O(min(n,W)). 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 :: IntMap a -> Maybe (a, IntMap 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 :: IntMap a -> Maybe (a, IntMap 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 :: IntMap a -> Maybe ((Key, a), IntMap 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 :: IntMap a -> Maybe ((Key, a), IntMap 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

# Debugging

showTree :: Show a => IntMap a -> String #

O(n). Show the tree that implements the map. The tree is shown in a compressed, hanging format.

showTreeWith :: Show a => Bool -> Bool -> IntMap a -> String #

O(n). The expression (``showTreeWith` hang wide map`) shows the tree that implements the map. If `hang` is `True`, a hanging tree is shown otherwise a rotated tree is shown. If `wide` is `True`, an extra wide version is shown.

# Internal types

type Mask = Int #

type Prefix = Int #

type Nat = Word #

# Utility

natFromInt :: Key -> Nat #

intFromNat :: Nat -> Key #

link :: Prefix -> IntMap a -> Prefix -> IntMap a -> IntMap a #

linkWithMask :: Mask -> Prefix -> IntMap a -> IntMap a -> IntMap a #

bin :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a #

binCheckLeft :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a #

binCheckRight :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a #

zero :: Key -> Mask -> Bool #

Should this key follow the left subtree of a `Bin` with switching bit `m`? N.B., the answer is only valid when `match i p m` is true.

nomatch :: Key -> Prefix -> Mask -> Bool #

Does the key `i` differ from the prefix `p` before getting to the switching bit `m`?

match :: Key -> Prefix -> Mask -> Bool #

Does the key `i` match the prefix `p` (up to but not including bit `m`)?

mask :: Key -> Mask -> Prefix #

The prefix of key `i` up to (but not including) the switching bit `m`.

maskW :: Nat -> Nat -> Prefix #

The prefix of key `i` up to (but not including) the switching bit `m`.

shorter :: Mask -> Mask -> Bool #

Does the left switching bit specify a shorter prefix?

branchMask :: Prefix -> Prefix -> Mask #

The first switching bit where the two prefixes disagree.

highestBitMask :: Word -> Word #

Return a word where only the highest bit is set.

# Used by IntMap.Merge.Lazy and IntMap.Merge.Strict

mapWhenMissing :: (Applicative f, Monad f) => (a -> b) -> WhenMissing f x a -> WhenMissing f x b #

Map covariantly over a ``WhenMissing` f x`.

Since: containers-0.5.9

mapWhenMatched :: Functor f => (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b #

Map covariantly over a ``WhenMatched` f x y`.

Since: containers-0.5.9

lmapWhenMissing :: (b -> a) -> WhenMissing f a x -> WhenMissing f b x #

Map contravariantly over a ``WhenMissing` f _ x`.

Since: containers-0.5.9

contramapFirstWhenMatched :: (b -> a) -> WhenMatched f a y z -> WhenMatched f b y z #

Map contravariantly over a ``WhenMatched` f _ y z`.

Since: containers-0.5.9

contramapSecondWhenMatched :: (b -> a) -> WhenMatched f x a z -> WhenMatched f x b z #

Map contravariantly over a ``WhenMatched` f x _ z`.

Since: containers-0.5.9

mapGentlyWhenMissing :: Functor f => (a -> b) -> WhenMissing f x a -> WhenMissing f x b #

Map covariantly over a ``WhenMissing` f x`, using only a 'Functor f' constraint.

mapGentlyWhenMatched :: Functor f => (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b #

Map covariantly over a ``WhenMatched` f k x`, using only a 'Functor f' constraint.