| Copyright | (c) Daan Leijen 2002 (c) Andriy Palamarchuk 2008 |
|---|---|
| License | BSD-style |
| Maintainer | libraries@haskell.org |
| Portability | portable |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
Data.Map.Strict.Internal
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
An efficient implementation of ordered maps from keys to values (dictionaries).
API of this module is strict in both the keys and the values.
If you need value-lazy maps, use Data.Map.Lazy instead.
The Map type is shared between the lazy and strict modules,
meaning that the same Map value can be passed to functions in
both modules (although that is rarely needed).
These modules are intended to be imported qualified, to avoid name clashes with Prelude functions, e.g.
import qualified Data.Map.Strict as Map
The implementation of Map is based on size balanced binary trees (or
trees of bounded balance) as described by:
- Stephen Adams, "Efficient sets: a balancing act", Journal of Functional Programming 3(4):553-562, October 1993, http://www.swiss.ai.mit.edu/~adams/BB/.
- J. Nievergelt and E.M. Reingold, "Binary search trees of bounded balance", SIAM journal of computing 2(1), March 1973.
Bounds for union, intersection, and difference are as given
by
- Guy Blelloch, Daniel Ferizovic, and Yihan Sun, "Just Join for Parallel Ordered Sets", https://arxiv.org/abs/1602.02120v3.
Note that the implementation is left-biased -- the elements of a
first argument are always preferred to the second, for example in
union or insert.
Warning: The size of the map must not exceed maxBound::Int. Violation of
this condition is not detected and if the size limit is exceeded, its
behaviour is undefined.
Operation comments contain the operation time complexity in the Big-O notation (http://en.wikipedia.org/wiki/Big_O_notation).
Be aware that the Functor, Traversable and Data instances
are the same as for the Data.Map.Lazy module, so if they are used
on strict maps, the resulting maps will be lazy.
Synopsis
- data Map k a
- type Size = Int
- (!) :: Ord k => Map k a -> k -> a
- (!?) :: Ord k => Map k a -> k -> Maybe a
- (\\) :: Ord k => Map k a -> Map k b -> Map k a
- null :: Map k a -> Bool
- size :: Map k a -> Int
- member :: Ord k => k -> Map k a -> Bool
- notMember :: Ord k => k -> Map k a -> Bool
- lookup :: Ord k => k -> Map k a -> Maybe a
- findWithDefault :: Ord k => a -> k -> Map k a -> a
- lookupLT :: Ord k => k -> Map k v -> Maybe (k, v)
- lookupGT :: Ord k => k -> Map k v -> Maybe (k, v)
- lookupLE :: Ord k => k -> Map k v -> Maybe (k, v)
- lookupGE :: Ord k => k -> Map k v -> Maybe (k, v)
- empty :: Map k a
- singleton :: k -> a -> Map k a
- insert :: Ord k => k -> a -> Map k a -> Map k a
- insertWith :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
- insertWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
- insertLookupWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> (Maybe a, Map k a)
- delete :: Ord k => k -> Map k a -> Map k a
- adjust :: Ord k => (a -> a) -> k -> Map k a -> Map k a
- adjustWithKey :: Ord k => (k -> a -> a) -> k -> Map k a -> Map k a
- update :: Ord k => (a -> Maybe a) -> k -> Map k a -> Map k a
- updateWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a
- updateLookupWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> (Maybe a, Map k a)
- alter :: Ord k => (Maybe a -> Maybe a) -> k -> Map k a -> Map k a
- alterF :: (Functor f, Ord k) => (Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a)
- union :: Ord k => Map k a -> Map k a -> Map k a
- unionWith :: Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a
- unionWithKey :: Ord k => (k -> a -> a -> a) -> Map k a -> Map k a -> Map k a
- unions :: (Foldable f, Ord k) => f (Map k a) -> Map k a
- unionsWith :: (Foldable f, Ord k) => (a -> a -> a) -> f (Map k a) -> Map k a
- difference :: Ord k => Map k a -> Map k b -> Map k a
- differenceWith :: Ord k => (a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a
- differenceWithKey :: Ord k => (k -> a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a
- intersection :: Ord k => Map k a -> Map k b -> Map k a
- intersectionWith :: Ord k => (a -> b -> c) -> Map k a -> Map k b -> Map k c
- intersectionWithKey :: Ord k => (k -> a -> b -> c) -> Map k a -> Map k b -> Map k c
- disjoint :: Ord k => Map k a -> Map k b -> Bool
- compose :: Ord b => Map b c -> Map a b -> Map a c
- type SimpleWhenMissing = WhenMissing Identity
- type SimpleWhenMatched = WhenMatched Identity
- merge :: Ord k => SimpleWhenMissing k a c -> SimpleWhenMissing k b c -> SimpleWhenMatched k a b c -> Map k a -> Map k b -> Map k c
- runWhenMatched :: WhenMatched f k x y z -> k -> x -> y -> f (Maybe z)
- runWhenMissing :: WhenMissing f k x y -> k -> x -> f (Maybe y)
- zipWithMaybeMatched :: Applicative f => (k -> x -> y -> Maybe z) -> WhenMatched f k x y z
- zipWithMatched :: Applicative f => (k -> x -> y -> z) -> WhenMatched f k x y z
- mapMaybeMissing :: Applicative f => (k -> x -> Maybe y) -> WhenMissing f k x y
- dropMissing :: Applicative f => WhenMissing f k x y
- preserveMissing :: Applicative f => WhenMissing f k x x
- preserveMissing' :: Applicative f => WhenMissing f k x x
- mapMissing :: Applicative f => (k -> x -> y) -> WhenMissing f k x y
- filterMissing :: Applicative f => (k -> x -> Bool) -> WhenMissing f k x x
- data WhenMissing f k x y = WhenMissing {
- missingSubtree :: Map k x -> f (Map k y)
- missingKey :: k -> x -> f (Maybe y)
- newtype WhenMatched f k x y z = WhenMatched {
- matchedKey :: k -> x -> y -> f (Maybe z)
- mergeA :: (Applicative f, Ord k) => WhenMissing f k a c -> WhenMissing f k b c -> WhenMatched f k a b c -> Map k a -> Map k b -> f (Map k c)
- zipWithMaybeAMatched :: Applicative f => (k -> x -> y -> f (Maybe z)) -> WhenMatched f k x y z
- zipWithAMatched :: Applicative f => (k -> x -> y -> f z) -> WhenMatched f k x y z
- traverseMaybeMissing :: Applicative f => (k -> x -> f (Maybe y)) -> WhenMissing f k x y
- traverseMissing :: Applicative f => (k -> x -> f y) -> WhenMissing f k x y
- filterAMissing :: Applicative f => (k -> x -> f Bool) -> WhenMissing f k x x
- mapWhenMissing :: Functor f => (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b
- mapWhenMatched :: Functor f => (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b
- mergeWithKey :: Ord k => (k -> a -> b -> Maybe c) -> (Map k a -> Map k c) -> (Map k b -> Map k c) -> Map k a -> Map k b -> Map k c
- map :: (a -> b) -> Map k a -> Map k b
- mapWithKey :: (k -> a -> b) -> Map k a -> Map k b
- traverseWithKey :: Applicative t => (k -> a -> t b) -> Map k a -> t (Map k b)
- traverseMaybeWithKey :: Applicative f => (k -> a -> f (Maybe b)) -> Map k a -> f (Map k b)
- mapAccum :: (a -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)
- mapAccumWithKey :: (a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)
- mapAccumRWithKey :: (a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)
- mapKeys :: Ord k2 => (k1 -> k2) -> Map k1 a -> Map k2 a
- mapKeysWith :: Ord k2 => (a -> a -> a) -> (k1 -> k2) -> Map k1 a -> Map k2 a
- mapKeysMonotonic :: (k1 -> k2) -> Map k1 a -> Map k2 a
- foldr :: (a -> b -> b) -> b -> Map k a -> b
- foldl :: (a -> b -> a) -> a -> Map k b -> a
- foldrWithKey :: (k -> a -> b -> b) -> b -> Map k a -> b
- foldlWithKey :: (a -> k -> b -> a) -> a -> Map k b -> a
- foldMapWithKey :: Monoid m => (k -> a -> m) -> Map k a -> m
- foldr' :: (a -> b -> b) -> b -> Map k a -> b
- foldl' :: (a -> b -> a) -> a -> Map k b -> a
- foldrWithKey' :: (k -> a -> b -> b) -> b -> Map k a -> b
- foldlWithKey' :: (a -> k -> b -> a) -> a -> Map k b -> a
- elems :: Map k a -> [a]
- keys :: Map k a -> [k]
- assocs :: Map k a -> [(k, a)]
- keysSet :: Map k a -> Set k
- argSet :: Map k a -> Set (Arg k a)
- fromSet :: (k -> a) -> Set k -> Map k a
- fromArgSet :: Set (Arg k a) -> Map k a
- toList :: Map k a -> [(k, a)]
- fromList :: Ord k => [(k, a)] -> Map k a
- fromListWith :: Ord k => (a -> a -> a) -> [(k, a)] -> Map k a
- fromListWithKey :: Ord k => (k -> a -> a -> a) -> [(k, a)] -> Map k a
- toAscList :: Map k a -> [(k, a)]
- toDescList :: Map k a -> [(k, a)]
- fromAscList :: Eq k => [(k, a)] -> Map k a
- fromAscListWith :: Eq k => (a -> a -> a) -> [(k, a)] -> Map k a
- fromAscListWithKey :: Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a
- fromDistinctAscList :: [(k, a)] -> Map k a
- fromDescList :: Eq k => [(k, a)] -> Map k a
- fromDescListWith :: Eq k => (a -> a -> a) -> [(k, a)] -> Map k a
- fromDescListWithKey :: Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a
- fromDistinctDescList :: [(k, a)] -> Map k a
- filter :: (a -> Bool) -> Map k a -> Map k a
- filterWithKey :: (k -> a -> Bool) -> Map k a -> Map k a
- restrictKeys :: Ord k => Map k a -> Set k -> Map k a
- withoutKeys :: Ord k => Map k a -> Set k -> Map k a
- partition :: (a -> Bool) -> Map k a -> (Map k a, Map k a)
- partitionWithKey :: (k -> a -> Bool) -> Map k a -> (Map k a, Map k a)
- takeWhileAntitone :: (k -> Bool) -> Map k a -> Map k a
- dropWhileAntitone :: (k -> Bool) -> Map k a -> Map k a
- spanAntitone :: (k -> Bool) -> Map k a -> (Map k a, Map k a)
- mapMaybe :: (a -> Maybe b) -> Map k a -> Map k b
- mapMaybeWithKey :: (k -> a -> Maybe b) -> Map k a -> Map k b
- mapEither :: (a -> Either b c) -> Map k a -> (Map k b, Map k c)
- mapEitherWithKey :: (k -> a -> Either b c) -> Map k a -> (Map k b, Map k c)
- split :: Ord k => k -> Map k a -> (Map k a, Map k a)
- splitLookup :: Ord k => k -> Map k a -> (Map k a, Maybe a, Map k a)
- splitRoot :: Map k b -> [Map k b]
- isSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Bool
- isSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool
- isProperSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Bool
- isProperSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool
- lookupIndex :: Ord k => k -> Map k a -> Maybe Int
- findIndex :: Ord k => k -> Map k a -> Int
- elemAt :: Int -> Map k a -> (k, a)
- updateAt :: (k -> a -> Maybe a) -> Int -> Map k a -> Map k a
- deleteAt :: Int -> Map k a -> Map k a
- take :: Int -> Map k a -> Map k a
- drop :: Int -> Map k a -> Map k a
- splitAt :: Int -> Map k a -> (Map k a, Map k a)
- lookupMin :: Map k a -> Maybe (k, a)
- lookupMax :: Map k a -> Maybe (k, a)
- findMin :: Map k a -> (k, a)
- findMax :: Map k a -> (k, a)
- deleteMin :: Map k a -> Map k a
- deleteMax :: Map k a -> Map k a
- deleteFindMin :: Map k a -> ((k, a), Map k a)
- deleteFindMax :: Map k a -> ((k, a), Map k a)
- updateMin :: (a -> Maybe a) -> Map k a -> Map k a
- updateMax :: (a -> Maybe a) -> Map k a -> Map k a
- updateMinWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a
- updateMaxWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a
- minView :: Map k a -> Maybe (a, Map k a)
- maxView :: Map k a -> Maybe (a, Map k a)
- minViewWithKey :: Map k a -> Maybe ((k, a), Map k a)
- maxViewWithKey :: Map k a -> Maybe ((k, a), Map k a)
- showTree :: Whoops "showTree has moved to Data.Map.Internal.Debug.showTree." => Map k a -> String
- showTreeWith :: Whoops "showTreeWith has moved to Data.Map.Internal.Debug.showTreeWith." => (k -> a -> String) -> Bool -> Bool -> Map k a -> String
- valid :: Ord k => Map k a -> Bool
Strictness properties
This module satisfies the following strictness properties:
- Key arguments are evaluated to WHNF;
- Keys and values are evaluated to WHNF before they are stored in the map.
Here's an example illustrating the first property:
delete undefined m == undefined
Here are some examples that illustrate the second property:
map (\ v -> undefined) m == undefined -- m is not empty mapKeys (\ k -> undefined) m == undefined -- m is not empty
Map type
A Map from keys k to values a.
The Semigroup operation for Map is union, which prefers
values from the left operand. If m1 maps a key k to a value
a1, and m2 maps the same key to a different value a2, then
their union m1 <> m2 maps k to a1.
Instances
| Bifoldable Map Source # | Since: containers-0.6.3.1 |
| Eq2 Map Source # | Since: containers-0.5.9 |
| Ord2 Map Source # | Since: containers-0.5.9 |
Defined in Data.Map.Internal | |
| Show2 Map Source # | Since: containers-0.5.9 |
| (Lift k, Lift a) => Lift (Map k a :: Type) Source # | Since: containers-0.6.6 |
| Foldable (Map k) Source # | Folds in order of increasing key. |
Defined in Data.Map.Internal Methods fold :: Monoid m => Map k m -> m Source # foldMap :: Monoid m => (a -> m) -> Map k a -> m Source # foldMap' :: Monoid m => (a -> m) -> Map k a -> m Source # foldr :: (a -> b -> b) -> b -> Map k a -> b Source # foldr' :: (a -> b -> b) -> b -> Map k a -> b Source # foldl :: (b -> a -> b) -> b -> Map k a -> b Source # foldl' :: (b -> a -> b) -> b -> Map k a -> b Source # foldr1 :: (a -> a -> a) -> Map k a -> a Source # foldl1 :: (a -> a -> a) -> Map k a -> a Source # toList :: Map k a -> [a] Source # null :: Map k a -> Bool Source # length :: Map k a -> Int Source # elem :: Eq a => a -> Map k a -> Bool Source # maximum :: Ord a => Map k a -> a Source # minimum :: Ord a => Map k a -> a Source # | |
| Eq k => Eq1 (Map k) Source # | Since: containers-0.5.9 |
| Ord k => Ord1 (Map k) Source # | Since: containers-0.5.9 |
Defined in Data.Map.Internal | |
| (Ord k, Read k) => Read1 (Map k) Source # | Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Map k a) Source # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Map k a] Source # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Map k a) Source # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Map k a] Source # | |
| Show k => Show1 (Map k) Source # | Since: containers-0.5.9 |
| Traversable (Map k) Source # | Traverses in order of increasing key. |
| Functor (Map k) Source # | |
| (Data k, Data a, Ord k) => Data (Map k a) Source # | |
Defined in Data.Map.Internal Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Map k a -> c (Map k a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Map k a) Source # toConstr :: Map k a -> Constr Source # dataTypeOf :: Map k a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Map k a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Map k a)) Source # gmapT :: (forall b. Data b => b -> b) -> Map k a -> Map k a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Map k a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Map k a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Map k a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Map k a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) Source # | |
| Ord k => Monoid (Map k v) Source # | |
| Ord k => Semigroup (Map k v) Source # | |
| Ord k => IsList (Map k v) Source # | Since: containers-0.5.6.2 |
| (Ord k, Read k, Read e) => Read (Map k e) Source # | |
| (Show k, Show a) => Show (Map k a) Source # | |
| (NFData k, NFData a) => NFData (Map k a) Source # | |
Defined in Data.Map.Internal | |
| (Eq k, Eq a) => Eq (Map k a) Source # | |
| (Ord k, Ord v) => Ord (Map k v) Source # | |
| type Item (Map k v) Source # | |
Defined in Data.Map.Internal | |
Operators
(!) :: Ord k => Map k a -> k -> a infixl 9 Source #
\(O(\log n)\). Find the value at a key.
Calls error when the element can not be found.
fromList [(5,'a'), (3,'b')] ! 1 Error: element not in the map fromList [(5,'a'), (3,'b')] ! 5 == 'a'
(!?) :: Ord k => Map k a -> k -> Maybe a infixl 9 Source #
\(O(\log n)\). 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-0.5.9
Query
null :: Map k a -> Bool Source #
\(O(1)\). Is the map empty?
Data.Map.null (empty) == True Data.Map.null (singleton 1 'a') == False
size :: Map k a -> Int Source #
\(O(1)\). The number of elements in the map.
size empty == 0 size (singleton 1 'a') == 1 size (fromList([(1,'a'), (2,'c'), (3,'b')])) == 3
member :: Ord k => k -> Map k a -> Bool Source #
\(O(\log n)\). Is the key a member of the map? See also notMember.
member 5 (fromList [(5,'a'), (3,'b')]) == True member 1 (fromList [(5,'a'), (3,'b')]) == False
notMember :: Ord k => k -> Map k a -> Bool Source #
\(O(\log n)\). Is the key not a member of the map? See also member.
notMember 5 (fromList [(5,'a'), (3,'b')]) == False notMember 1 (fromList [(5,'a'), (3,'b')]) == True
lookup :: Ord k => k -> Map k a -> Maybe a Source #
\(O(\log n)\). Lookup the value at a key in the map.
The function will return the corresponding value as (,
or Just value)Nothing if the key isn't in the map.
An example of using lookup:
import Prelude hiding (lookup)
import Data.Map
employeeDept = fromList([("John","Sales"), ("Bob","IT")])
deptCountry = fromList([("IT","USA"), ("Sales","France")])
countryCurrency = fromList([("USA", "Dollar"), ("France", "Euro")])
employeeCurrency :: String -> Maybe String
employeeCurrency name = do
dept <- lookup name employeeDept
country <- lookup dept deptCountry
lookup country countryCurrency
main = do
putStrLn $ "John's currency: " ++ (show (employeeCurrency "John"))
putStrLn $ "Pete's currency: " ++ (show (employeeCurrency "Pete"))The output of this program:
John's currency: Just "Euro" Pete's currency: Nothing
findWithDefault :: Ord k => a -> k -> Map k a -> a Source #
\(O(\log n)\). The expression ( returns
the value at key findWithDefault def k map)k or returns default value def
when the key is not in the map.
findWithDefault 'x' 1 (fromList [(5,'a'), (3,'b')]) == 'x' findWithDefault 'x' 5 (fromList [(5,'a'), (3,'b')]) == 'a'
lookupLT :: Ord k => k -> Map k v -> Maybe (k, v) Source #
\(O(\log n)\). Find largest key smaller than the given one and return the corresponding (key, value) pair.
lookupLT 3 (fromList [(3,'a'), (5,'b')]) == Nothing lookupLT 4 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a')
lookupGT :: Ord k => k -> Map k v -> Maybe (k, v) Source #
\(O(\log n)\). Find smallest key greater than the given one and return the corresponding (key, value) pair.
lookupGT 4 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b') lookupGT 5 (fromList [(3,'a'), (5,'b')]) == Nothing
lookupLE :: Ord k => k -> Map k v -> Maybe (k, v) Source #
\(O(\log n)\). Find largest key smaller or equal to the given one and return the corresponding (key, value) pair.
lookupLE 2 (fromList [(3,'a'), (5,'b')]) == Nothing lookupLE 4 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a') lookupLE 5 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b')
lookupGE :: Ord k => k -> Map k v -> Maybe (k, v) Source #
\(O(\log n)\). Find smallest key greater or equal to the given one and return the corresponding (key, value) pair.
lookupGE 3 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a') lookupGE 4 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b') lookupGE 6 (fromList [(3,'a'), (5,'b')]) == Nothing
Construction
singleton :: k -> a -> Map k a Source #
\(O(1)\). A map with a single element.
singleton 1 'a' == fromList [(1, 'a')] size (singleton 1 'a') == 1
Insertion
insert :: Ord k => k -> a -> Map k a -> Map k a Source #
\(O(\log n)\). Insert a new key and value in the map.
If the key is already present in the map, the associated value is
replaced with the supplied value. insert is equivalent to
.insertWith const
insert 5 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'x')] insert 7 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'a'), (7, 'x')] insert 5 'x' empty == singleton 5 'x'
insertWith :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a Source #
\(O(\log n)\). Insert with a function, combining new value and old value.
will insert the pair (key, value) into insertWith f key value mpmp if key does
not exist in the map. If the key does exist, the function will
insert the pair (key, f new_value old_value).
insertWith (++) 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "xxxa")] insertWith (++) 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")] insertWith (++) 5 "xxx" empty == singleton 5 "xxx"
insertWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a Source #
\(O(\log n)\). Insert with a function, combining key, new value and old value.
will insert the pair (key, value) into insertWithKey f key value mpmp if key does
not exist in the map. If the key does exist, the function will
insert the pair (key,f key new_value old_value).
Note that the key passed to f is the same key passed to insertWithKey.
let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value insertWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:xxx|a")] insertWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")] insertWithKey f 5 "xxx" empty == singleton 5 "xxx"
insertLookupWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> (Maybe a, Map k a) Source #
\(O(\log n)\). Combines insert operation with old value retrieval.
The expression ()
is a pair where the first element is equal to (insertLookupWithKey f k x map)
and the second element equal to (lookup k map).insertWithKey f k x map
let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value insertLookupWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:xxx|a")]) insertLookupWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "xxx")]) insertLookupWithKey f 5 "xxx" empty == (Nothing, singleton 5 "xxx")
This is how to define insertLookup using insertLookupWithKey:
let insertLookup kx x t = insertLookupWithKey (\_ a _ -> a) kx x t insertLookup 5 "x" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "x")]) insertLookup 7 "x" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "x")])
Delete/Update
delete :: Ord k => k -> Map k a -> Map k a Source #
\(O(\log n)\). Delete a key and its value from the map. When the key is not a member of the map, the original map is returned.
delete 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" delete 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] delete 5 empty == empty
adjust :: Ord k => (a -> a) -> k -> Map k a -> Map k a Source #
\(O(\log n)\). Update a value at a specific key with the result of the provided function. When the key is not a member of the map, the original map is returned.
adjust ("new " ++) 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")]
adjust ("new " ++) 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
adjust ("new " ++) 7 empty == emptyadjustWithKey :: Ord k => (k -> a -> a) -> k -> Map k a -> Map k a Source #
\(O(\log n)\). Adjust a value at a specific key. When the key is not a member of the map, the original map is returned.
let f key x = (show key) ++ ":new " ++ x adjustWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")] adjustWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] adjustWithKey f 7 empty == empty
update :: Ord k => (a -> Maybe a) -> k -> Map k a -> Map k a Source #
\(O(\log n)\). The expression () updates the value update f k mapx
at k (if it is in the map). If (f x) is Nothing, the element is
deleted. If it is (), the key Just yk is bound to the new value y.
let f x = if x == "a" then Just "new a" else Nothing update f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")] update f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] update f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
updateWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a Source #
\(O(\log n)\). The expression () updates the
value updateWithKey f k mapx at k (if it is in the map). If (f k x) is Nothing,
the element is deleted. If it is (), the key Just yk is bound
to the new value y.
let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing updateWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")] updateWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] updateWithKey f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
updateLookupWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> (Maybe a, Map k a) Source #
\(O(\log n)\). Lookup and update. See also updateWithKey.
The function returns changed value, if it is updated.
Returns the original key value if the map entry is deleted.
let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing updateLookupWithKey f 5 (fromList [(5,"a"), (3,"b")]) == (Just "5:new a", fromList [(3, "b"), (5, "5:new a")]) updateLookupWithKey f 7 (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a")]) updateLookupWithKey f 3 (fromList [(5,"a"), (3,"b")]) == (Just "b", singleton 5 "a")
alter :: Ord k => (Maybe a -> Maybe a) -> k -> Map k a -> Map k a Source #
\(O(\log n)\). The expression () alters the value alter f k mapx at k, or absence thereof.
alter can be used to insert, delete, or update a value in a Map.
In short : .lookup k (alter f k m) = f (lookup k m)
let f _ = Nothing alter f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] alter f 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" let f _ = Just "c" alter f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "c")] alter f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "c")]
Note that .adjust = alter . fmap
alterF :: (Functor f, Ord k) => (Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a) Source #
\(O(\log n)\). The expression () alters the value alterF f k mapx at k, or absence thereof.
alterF can be used to inspect, insert, delete, or update a value in a Map.
In short: .lookup k <$> alterF f k m = f (lookup k m)
Example:
interactiveAlter :: Int -> Map Int String -> IO (Map Int String)
interactiveAlter k m = alterF f k m where
f Nothing = do
putStrLn $ show k ++
" was not found in the map. Would you like to add it?"
getUserResponse1 :: IO (Maybe String)
f (Just old) = do
putStrLn $ "The key is currently bound to " ++ show old ++
". Would you like to change or delete it?"
getUserResponse2 :: IO (Maybe String)
alterF is the most general operation for working with an individual
key that may or may not be in a given map. When used with trivial
functors like Identity and Const, it is often slightly slower than
more specialized combinators like lookup and insert. However, when
the functor is non-trivial and key comparison is not particularly cheap,
it is the fastest way.
Note on rewrite rules:
This module includes GHC rewrite rules to optimize alterF for
the Const and Identity functors. In general, these rules
improve performance. The sole exception is that when using
Identity, deleting a key that is already absent takes longer
than it would without the rules. If you expect this to occur
a very large fraction of the time, you might consider using a
private copy of the Identity type.
Note: alterF is a flipped version of the at combinator from
Control.Lens.At.
Since: containers-0.5.8
Combine
Union
union :: Ord k => Map k a -> Map k a -> Map k a Source #
\(O\bigl(m \log\bigl(\frac{n+1}{m+1}\bigr)\bigr), \; m \leq n\).
The expression () takes the left-biased union of union t1 t2t1 and t2.
It prefers t1 when duplicate keys are encountered,
i.e. ().union == unionWith const
union (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "a"), (7, "C")]
unionWith :: Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a Source #
\(O\bigl(m \log\bigl(\frac{n+1}{m+1}\bigr)\bigr), \; m \leq n\). Union with a combining function.
unionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "aA"), (7, "C")]
unionWithKey :: Ord k => (k -> a -> a -> a) -> Map k a -> Map k a -> Map k a Source #
\(O\bigl(m \log\bigl(\frac{n+1}{m+1}\bigr)\bigr), \; m \leq n\). Union with a combining function.
let f key left_value right_value = (show key) ++ ":" ++ left_value ++ "|" ++ right_value unionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "5:a|A"), (7, "C")]
unions :: (Foldable f, Ord k) => f (Map k a) -> Map k a Source #
The union of a list of maps:
().unions == foldl union empty
unions [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])]
== fromList [(3, "b"), (5, "a"), (7, "C")]
unions [(fromList [(5, "A3"), (3, "B3")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "a"), (3, "b")])]
== fromList [(3, "B3"), (5, "A3"), (7, "C")]unionsWith :: (Foldable f, Ord k) => (a -> a -> a) -> f (Map k a) -> Map k a Source #
The union of a list of maps, with a combining operation:
().unionsWith f == foldl (unionWith f) empty
unionsWith (++) [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])]
== fromList [(3, "bB3"), (5, "aAA3"), (7, "C")]Difference
difference :: Ord k => Map k a -> Map k b -> Map k a Source #
\(O\bigl(m \log\bigl(\frac{n+1}{m+1}\bigr)\bigr), \; m \leq n\). Difference of two maps. Return elements of the first map not existing in the second map.
difference (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 3 "b"
differenceWith :: Ord k => (a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a Source #
\(O(n+m)\). Difference with a combining function.
When two equal keys are
encountered, the combining function is applied to the values of these keys.
If it returns Nothing, the element is discarded (proper set difference). If
it returns (), the element is updated with a new value Just yy.
let f al ar = if al == "b" then Just (al ++ ":" ++ ar) else Nothing
differenceWith f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (7, "C")])
== singleton 3 "b:B"differenceWithKey :: Ord k => (k -> a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a Source #
\(O(n+m)\). Difference with a combining function. When two equal keys are
encountered, the combining function is applied to the key and both values.
If it returns Nothing, the element is discarded (proper set difference). If
it returns (), the element is updated with a new value Just yy.
let f k al ar = if al == "b" then Just ((show k) ++ ":" ++ al ++ "|" ++ ar) else Nothing
differenceWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (10, "C")])
== singleton 3 "3:b|B"Intersection
intersection :: Ord k => Map k a -> Map k b -> Map k a Source #
\(O\bigl(m \log\bigl(\frac{n+1}{m+1}\bigr)\bigr), \; m \leq n\). Intersection of two maps.
Return data in the first map for the keys existing in both maps.
().intersection m1 m2 == intersectionWith const m1 m2
intersection (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "a"
intersectionWith :: Ord k => (a -> b -> c) -> Map k a -> Map k b -> Map k c Source #
\(O\bigl(m \log\bigl(\frac{n+1}{m+1}\bigr)\bigr), \; m \leq n\). Intersection with a combining function.
intersectionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "aA"
intersectionWithKey :: Ord k => (k -> a -> b -> c) -> Map k a -> Map k b -> Map k c Source #
\(O\bigl(m \log\bigl(\frac{n+1}{m+1}\bigr)\bigr), \; m \leq n\). Intersection with a combining function.
let f k al ar = (show k) ++ ":" ++ al ++ "|" ++ ar intersectionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "5:a|A"
Disjoint
disjoint :: Ord k => Map k a -> Map k b -> Bool Source #
\(O\bigl(m \log\bigl(\frac{n+1}{m+1}\bigr)\bigr), \; m \leq n\). Check whether the key sets of two
maps are disjoint (i.e., their intersection is empty).
disjoint (fromList [(2,'a')]) (fromList [(1,()), (3,())]) == True disjoint (fromList [(2,'a')]) (fromList [(1,'a'), (2,'b')]) == False disjoint (fromList []) (fromList []) == True
xs`disjoint`ys = null (xs`intersection`ys)
Since: containers-0.6.2.1
Compose
compose :: Ord b => Map b c -> Map a b -> Map a c Source #
Relate the keys of one map to the values of the other, by using the values of the former as keys for lookups in the latter.
Complexity: \( O (n * \log(m)) \), where \(m\) is the size of the first argument
compose (fromList [('a', "A"), ('b', "B")]) (fromList [(1,'a'),(2,'b'),(3,'z')]) = fromList [(1,"A"),(2,"B")](composebc ab!?) = (bc!?) <=< (ab!?)
Note: Prior to v0.6.4, Data.Map.Strict exposed a version of
compose that forced the values of the output Map. This version does not
force these values.
Since: containers-0.6.3.1
General combining function
type SimpleWhenMissing = WhenMissing Identity Source #
A tactic for dealing with keys present in one map but not the other in
merge.
A tactic of type SimpleWhenMissing k x z is an abstract representation
of a function of type k -> x -> Maybe z .
Since: containers-0.5.9
type SimpleWhenMatched = WhenMatched Identity Source #
A tactic for dealing with keys present in both maps in merge.
A tactic of type SimpleWhenMatched k x y z is an abstract representation
of a function of type k -> x -> y -> Maybe z .
Since: containers-0.5.9
Arguments
| :: Ord k | |
| => SimpleWhenMissing k a c | What to do with keys in |
| -> SimpleWhenMissing k b c | What to do with keys in |
| -> SimpleWhenMatched k a b c | What to do with keys in both |
| -> Map k a | Map |
| -> Map k b | Map |
| -> Map k 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,
dropMissingdrops all the keys.preserveMissingleaves 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 preserveMissing dropMissing (zipWithMatched f)
symmetricDifference = merge preserveMissing preserveMissing (zipWithMaybeMatched $ \ _ _ _ -> Nothing)
mapEachPiece f g h = merge (mapMissing f) (mapMissing g) (zipWithMatched h)
Since: containers-0.5.9
runWhenMatched :: WhenMatched f k x y z -> k -> x -> y -> f (Maybe z) Source #
Along with zipWithMaybeAMatched, witnesses the isomorphism between
WhenMatched f k x y z and k -> x -> y -> f (Maybe z).
Since: containers-0.5.9
runWhenMissing :: WhenMissing f k x y -> k -> x -> f (Maybe y) Source #
Along with traverseMaybeMissing, witnesses the isomorphism between
WhenMissing f k x y and k -> x -> f (Maybe y).
Since: containers-0.5.9
WhenMatched tactics
zipWithMaybeMatched :: Applicative f => (k -> x -> y -> Maybe z) -> WhenMatched f k x y z Source #
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 :: (k -> x -> y -> Maybe z)
-> SimpleWhenMatched k x y z
zipWithMatched :: Applicative f => (k -> x -> y -> z) -> WhenMatched f k x y z Source #
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 :: (k -> x -> y -> z)
-> SimpleWhenMatched k x y z
WhenMissing tactics
mapMaybeMissing :: Applicative f => (k -> x -> Maybe y) -> WhenMissing f k x y Source #
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 :: (k -> x -> Maybe y) -> SimpleWhenMissing k x y
mapMaybeMissing f = traverseMaybeMissing (\k x -> pure (f k x))
but mapMaybeMissing uses fewer unnecessary Applicative operations.
dropMissing :: Applicative f => WhenMissing f k x y Source #
Drop all the entries whose keys are missing from the other map.
dropMissing :: SimpleWhenMissing k x y
dropMissing = mapMaybeMissing (\_ _ -> Nothing)
but dropMissing is much faster.
Since: containers-0.5.9
preserveMissing :: Applicative f => WhenMissing f k x x Source #
Preserve, unchanged, the entries whose keys are missing from the other map.
preserveMissing :: SimpleWhenMissing k x x
preserveMissing = Merge.Lazy.mapMaybeMissing (\_ x -> Just x)
but preserveMissing is much faster.
Since: containers-0.5.9
preserveMissing' :: Applicative f => WhenMissing f k x x Source #
Force the entries whose keys are missing from the other map and otherwise preserve them unchanged.
preserveMissing' :: SimpleWhenMissing k x x
preserveMissing' = Merge.Lazy.mapMaybeMissing (\_ x -> Just $! x)
but preserveMissing' is quite a bit faster.
Since: containers-0.5.9
mapMissing :: Applicative f => (k -> x -> y) -> WhenMissing f k x y Source #
Map over the entries whose keys are missing from the other map.
mapMissing :: (k -> x -> y) -> SimpleWhenMissing k x y
mapMissing f = mapMaybeMissing (\k x -> Just $ f k x)
but mapMissing is somewhat faster.
filterMissing :: Applicative f => (k -> x -> Bool) -> WhenMissing f k x x Source #
Filter the entries whose keys are missing from the other map.
filterMissing :: (k -> x -> Bool) -> SimpleWhenMissing k 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 k x y Source #
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 k -> x -> f (Maybe z) .
Since: containers-0.5.9
Constructors
| WhenMissing | |
Fields
| |
Instances
| (Applicative f, Monad f) => Category (WhenMissing f k :: Type -> Type -> Type) Source # | Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods id :: forall (a :: k0). WhenMissing f k a a Source # (.) :: forall (b :: k0) (c :: k0) (a :: k0). WhenMissing f k b c -> WhenMissing f k a b -> WhenMissing f k a c Source # | |
| (Applicative f, Monad f) => Applicative (WhenMissing f k x) Source # | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods pure :: a -> WhenMissing f k x a Source # (<*>) :: WhenMissing f k x (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b Source # liftA2 :: (a -> b -> c) -> WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x c Source # (*>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b Source # (<*) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x a Source # | |
| (Applicative f, Monad f) => Functor (WhenMissing f k x) Source # | Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods fmap :: (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b Source # (<$) :: a -> WhenMissing f k x b -> WhenMissing f k x a Source # | |
| (Applicative f, Monad f) => Monad (WhenMissing f k x) Source # | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods (>>=) :: WhenMissing f k x a -> (a -> WhenMissing f k x b) -> WhenMissing f k x b Source # (>>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b Source # return :: a -> WhenMissing f k x a Source # | |
newtype WhenMatched f k x y z Source #
A tactic for dealing with keys present in both
maps in merge or mergeA.
A tactic of type WhenMatched f k x y z is an abstract representation
of a function of type k -> x -> y -> f (Maybe z) .
Since: containers-0.5.9
Constructors
| WhenMatched | |
Fields
| |
Instances
| (Monad f, Applicative f) => Category (WhenMatched f k x :: Type -> Type -> Type) Source # | Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods id :: forall (a :: k0). WhenMatched f k x a a Source # (.) :: forall (b :: k0) (c :: k0) (a :: k0). WhenMatched f k x b c -> WhenMatched f k x a b -> WhenMatched f k x a c Source # | |
| (Monad f, Applicative f) => Applicative (WhenMatched f k x y) Source # | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods pure :: a -> WhenMatched f k x y a Source # (<*>) :: WhenMatched f k x y (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b Source # liftA2 :: (a -> b -> c) -> WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y c Source # (*>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b Source # (<*) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y a Source # | |
| Functor f => Functor (WhenMatched f k x y) Source # | Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods fmap :: (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b Source # (<$) :: a -> WhenMatched f k x y b -> WhenMatched f k x y a Source # | |
| (Monad f, Applicative f) => Monad (WhenMatched f k x y) Source # | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods (>>=) :: WhenMatched f k x y a -> (a -> WhenMatched f k x y b) -> WhenMatched f k x y b Source # (>>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b Source # return :: a -> WhenMatched f k x y a Source # | |
Arguments
| :: (Applicative f, Ord k) | |
| => WhenMissing f k a c | What to do with keys in |
| -> WhenMissing f k b c | What to do with keys in |
| -> WhenMatched f k a b c | What to do with keys in both |
| -> Map k a | Map |
| -> Map k b | Map |
| -> f (Map k 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,
dropMissingdrops all the keys.preserveMissingleaves all the entries alone.mapMaybeMissingdoes not use theApplicativecontext.
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
zipWithMaybeAMatched :: Applicative f => (k -> x -> y -> f (Maybe z)) -> WhenMatched f k x y z Source #
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.
zipWithAMatched :: Applicative f => (k -> x -> y -> f z) -> WhenMatched f k x y z Source #
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.
WhenMissing tactics
traverseMaybeMissing :: Applicative f => (k -> x -> f (Maybe y)) -> WhenMissing f k x y Source #
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.
traverseMissing :: Applicative f => (k -> x -> f y) -> WhenMissing f k x y Source #
Traverse over the entries whose keys are missing from the other map.
filterAMissing :: Applicative f => (k -> x -> f Bool) -> WhenMissing f k x x Source #
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
Covariant maps for tactics
mapWhenMissing :: Functor f => (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b Source #
Map covariantly over a .WhenMissing f k x
mapWhenMatched :: Functor f => (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b Source #
Map covariantly over a .WhenMatched f k x y
Deprecated general combining function
mergeWithKey :: Ord k => (k -> a -> b -> Maybe c) -> (Map k a -> Map k c) -> (Map k b -> Map k c) -> Map k a -> Map k b -> Map k c Source #
\(O(n+m)\). An unsafe universal combining function.
WARNING: This function can produce corrupt maps and its results
may depend on the internal structures of its inputs. Users should
prefer merge or
mergeA.
When mergeWithKey is given three arguments, it is inlined to the call
site. You should therefore use mergeWithKey only to define custom
combining functions. For example, you could define unionWithKey,
differenceWithKey and intersectionWithKey as
myUnionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) id id m1 m2 myDifferenceWithKey f m1 m2 = mergeWithKey f id (const empty) m1 m2 myIntersectionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) (const empty) (const empty) m1 m2
When calling , a function combining two
mergeWithKey combine only1 only2Maps is created, such that
- if a key is present in both maps, it is passed with both corresponding
values to the
combinefunction. 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
only1and the output is added to the result; - a nonempty subtree present only in the second map is passed to
only2and 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 , but for example const empty or
map f could be used for any filterWithKey ff.
Traversal
Map
map :: (a -> b) -> Map k a -> Map k b Source #
\(O(n)\). Map a function over all values in the map.
map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]
mapWithKey :: (k -> a -> b) -> Map k a -> Map k b Source #
\(O(n)\). Map a function over all values in the map.
let f key x = (show key) ++ ":" ++ x mapWithKey f (fromList [(5,"a"), (3,"b")]) == fromList [(3, "3:b"), (5, "5:a")]
traverseWithKey :: Applicative t => (k -> a -> t b) -> Map k a -> t (Map k b) Source #
\(O(n)\).
That is, it behaves much like a regular traverseWithKey f m == fromList <$> traverse (\(k, v) -> (v' -> v' `seq` (k,v')) <$> f k v) (toList m)traverse except that the traversing
function also has access to the key associated with a value and the values are
forced before they are installed in the result map.
traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(1, 'a'), (5, 'e')]) == Just (fromList [(1, 'b'), (5, 'f')]) traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(2, 'c')]) == Nothing
traverseMaybeWithKey :: Applicative f => (k -> a -> f (Maybe b)) -> Map k a -> f (Map k b) Source #
\(O(n)\). Traverse keys/values and collect the Just results.
Since: containers-0.5.8
mapAccum :: (a -> b -> (a, c)) -> a -> Map k b -> (a, Map k c) Source #
\(O(n)\). The function mapAccum threads an accumulating
argument through the map in ascending order of keys.
let f a b = (a ++ b, b ++ "X")
mapAccum f "Everything: " (fromList [(5,"a"), (3,"b")]) == ("Everything: ba", fromList [(3, "bX"), (5, "aX")])mapAccumWithKey :: (a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c) Source #
\(O(n)\). The function mapAccumWithKey threads an accumulating
argument through the map in ascending order of keys.
let f a k b = (a ++ " " ++ (show k) ++ "-" ++ b, b ++ "X")
mapAccumWithKey f "Everything:" (fromList [(5,"a"), (3,"b")]) == ("Everything: 3-b 5-a", fromList [(3, "bX"), (5, "aX")])mapAccumRWithKey :: (a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c) Source #
\(O(n)\). The function mapAccumRWithKey threads an accumulating
argument through the map in descending order of keys.
mapKeys :: Ord k2 => (k1 -> k2) -> Map k1 a -> Map k2 a Source #
\(O(n \log n)\).
is the map obtained by applying mapKeys f sf to each key of s.
The size of the result may be smaller if f maps two or more distinct
keys to the same new key. In this case the value at the greatest of the
original keys is retained.
mapKeys (+ 1) (fromList [(5,"a"), (3,"b")]) == fromList [(4, "b"), (6, "a")] mapKeys (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "c" mapKeys (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "c"
mapKeysWith :: Ord k2 => (a -> a -> a) -> (k1 -> k2) -> Map k1 a -> Map k2 a Source #
\(O(n \log n)\).
is the map obtained by applying mapKeysWith c f sf to each key of s.
The size of the result may be smaller if f maps two or more distinct
keys to the same new key. In this case the associated values will be
combined using c. The value at the greater of the two original keys
is used as the first argument to c.
mapKeysWith (++) (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "cdab" mapKeysWith (++) (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "cdab"
mapKeysMonotonic :: (k1 -> k2) -> Map k1 a -> Map k2 a Source #
\(O(n)\).
, but works only when mapKeysMonotonic f s == mapKeys f sf
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 sThis means that f maps distinct original keys to distinct resulting keys.
This function has better performance than mapKeys.
mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")]) == fromList [(6, "b"), (10, "a")] valid (mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")])) == True valid (mapKeysMonotonic (\ _ -> 1) (fromList [(5,"a"), (3,"b")])) == False
Folds
foldrWithKey :: (k -> a -> b -> b) -> b -> Map k a -> b Source #
\(O(n)\). Fold the keys and values in the map using the given right-associative
binary operator, such that
.foldrWithKey f z == foldr (uncurry f) z . toAscList
For example,
keys map = foldrWithKey (\k x ks -> k:ks) [] map
let f k a result = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")"
foldrWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (5:a)(3:b)"foldlWithKey :: (a -> k -> b -> a) -> a -> Map k b -> a Source #
\(O(n)\). Fold the keys and values in the map using the given left-associative
binary operator, such that
.foldlWithKey f z == foldl (\z' (kx, x) -> f z' kx x) z . toAscList
For example,
keys = reverse . foldlWithKey (\ks k x -> k:ks) []
let f result k a = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")"
foldlWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (3:b)(5:a)"foldMapWithKey :: Monoid m => (k -> a -> m) -> Map k a -> m Source #
\(O(n)\). Fold the keys and values in the map using the given monoid, such that
foldMapWithKeyf =fold.mapWithKeyf
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 -> Map k a -> b Source #
\(O(n)\). A strict version of foldr. Each application of the operator is
evaluated before using the result in the next application. This
function is strict in the starting value.
foldl' :: (a -> b -> a) -> a -> Map k b -> a Source #
\(O(n)\). A strict version of foldl. Each application of the operator is
evaluated before using the result in the next application. This
function is strict in the starting value.
foldrWithKey' :: (k -> a -> b -> b) -> b -> Map k a -> b Source #
\(O(n)\). A strict version of foldrWithKey. Each application of the operator is
evaluated before using the result in the next application. This
function is strict in the starting value.
foldlWithKey' :: (a -> k -> b -> a) -> a -> Map k b -> a Source #
\(O(n)\). A strict version of foldlWithKey. Each application of the operator is
evaluated before using the result in the next application. This
function is strict in the starting value.
Conversion
elems :: Map k a -> [a] Source #
\(O(n)\). Return all elements of the map in the ascending order of their keys. Subject to list fusion.
elems (fromList [(5,"a"), (3,"b")]) == ["b","a"] elems empty == []
keys :: Map k a -> [k] Source #
\(O(n)\). Return all keys of the map in ascending order. Subject to list fusion.
keys (fromList [(5,"a"), (3,"b")]) == [3,5] keys empty == []
assocs :: Map k a -> [(k, a)] Source #
\(O(n)\). An alias for toAscList. Return all key/value pairs in the map
in ascending key order. Subject to list fusion.
assocs (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")] assocs empty == []
keysSet :: Map k a -> Set k Source #
\(O(n)\). The set of all keys of the map.
keysSet (fromList [(5,"a"), (3,"b")]) == Data.Set.fromList [3,5] keysSet empty == Data.Set.empty
argSet :: Map k a -> Set (Arg k a) Source #
\(O(n)\). The set of all elements of the map contained in Args.
argSet (fromList [(5,"a"), (3,"b")]) == Data.Set.fromList [Arg 3 "b",Arg 5 "a"] argSet empty == Data.Set.empty
fromSet :: (k -> a) -> Set k -> Map k a Source #
\(O(n)\). Build a map from a set of keys and a function which for each key computes its value.
fromSet (\k -> replicate k 'a') (Data.Set.fromList [3, 5]) == fromList [(5,"aaaaa"), (3,"aaa")] fromSet undefined Data.Set.empty == empty
fromArgSet :: Set (Arg k a) -> Map k a Source #
\(O(n)\). Build a map from a set of elements contained inside Args.
fromArgSet (Data.Set.fromList [Arg 3 "aaa", Arg 5 "aaaaa"]) == fromList [(5,"aaaaa"), (3,"aaa")] fromArgSet Data.Set.empty == empty
Lists
toList :: Map k a -> [(k, a)] Source #
\(O(n)\). Convert the map to a list of key/value pairs. Subject to list fusion.
toList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")] toList empty == []
fromList :: Ord k => [(k, a)] -> Map k a Source #
\(O(n \log n)\). Build a map from a list of key/value pairs. See also fromAscList.
If the list contains more than one value for the same key, the last value
for the key is retained.
If the keys of the list are ordered, linear-time implementation is used,
with the performance equal to fromDistinctAscList.
fromList [] == empty fromList [(5,"a"), (3,"b"), (5, "c")] == fromList [(5,"c"), (3,"b")] fromList [(5,"c"), (3,"b"), (5, "a")] == fromList [(5,"a"), (3,"b")]
fromListWith :: Ord k => (a -> a -> a) -> [(k, a)] -> Map k a Source #
\(O(n \log n)\). Build a map from a list of key/value pairs with a combining function. See also fromAscListWith.
fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"a")] == fromList [(3, "ab"), (5, "aba")] fromListWith (++) [] == empty
fromListWithKey :: Ord k => (k -> a -> a -> a) -> [(k, a)] -> Map k a Source #
\(O(n \log n)\). Build a map from a list of key/value pairs with a combining function. See also fromAscListWithKey.
let f 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 :: Map k a -> [(k, a)] Source #
\(O(n)\). Convert the map to a list of key/value pairs where the keys are in ascending order. Subject to list fusion.
toAscList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
toDescList :: Map k a -> [(k, a)] Source #
\(O(n)\). Convert the map to a list of key/value pairs where the keys are in descending order. Subject to list fusion.
toDescList (fromList [(5,"a"), (3,"b")]) == [(5,"a"), (3,"b")]
fromAscList :: Eq k => [(k, a)] -> Map k a Source #
\(O(n)\). Build a map from an ascending list in linear time. The precondition (input list is ascending) is not checked.
fromAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")] fromAscList [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "b")] valid (fromAscList [(3,"b"), (5,"a"), (5,"b")]) == True valid (fromAscList [(5,"a"), (3,"b"), (5,"b")]) == False
fromAscListWith :: Eq k => (a -> a -> a) -> [(k, a)] -> Map k a Source #
\(O(n)\). Build a map from an ascending list in linear time with a combining function for equal keys. The precondition (input list is ascending) is not checked.
fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")] valid (fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")]) == True valid (fromAscListWith (++) [(5,"a"), (3,"b"), (5,"b")]) == False
fromAscListWithKey :: Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a Source #
\(O(n)\). Build a map from an ascending list in linear time with a combining function for equal keys. The precondition (input list is ascending) is not checked.
let f k a1 a2 = (show k) ++ ":" ++ a1 ++ a2 fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b"), (5,"b")] == fromList [(3, "b"), (5, "5:b5:ba")] valid (fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b"), (5,"b")]) == True valid (fromAscListWithKey f [(5,"a"), (3,"b"), (5,"b"), (5,"b")]) == False
fromDistinctAscList :: [(k, a)] -> Map k a Source #
\(O(n)\). Build a map from an ascending list of distinct elements in linear time. The precondition is not checked.
fromDistinctAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")] valid (fromDistinctAscList [(3,"b"), (5,"a")]) == True valid (fromDistinctAscList [(3,"b"), (5,"a"), (5,"b")]) == False
fromDescList :: Eq k => [(k, a)] -> Map k a Source #
\(O(n)\). Build a map from a descending list in linear time. The precondition (input list is descending) is not checked.
fromDescList [(5,"a"), (3,"b")] == fromList [(3, "b"), (5, "a")] fromDescList [(5,"a"), (5,"b"), (3,"a")] == fromList [(3, "b"), (5, "b")] valid (fromDescList [(5,"a"), (5,"b"), (3,"b")]) == True valid (fromDescList [(5,"a"), (3,"b"), (5,"b")]) == False
fromDescListWith :: Eq k => (a -> a -> a) -> [(k, a)] -> Map k a Source #
\(O(n)\). Build a map from a descending list in linear time with a combining function for equal keys. The precondition (input list is descending) is not checked.
fromDescListWith (++) [(5,"a"), (5,"b"), (3,"b")] == fromList [(3, "b"), (5, "ba")] valid (fromDescListWith (++) [(5,"a"), (5,"b"), (3,"b")]) == True valid (fromDescListWith (++) [(5,"a"), (3,"b"), (5,"b")]) == False
fromDescListWithKey :: Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a Source #
\(O(n)\). Build a map from a descending list in linear time with a combining function for equal keys. The precondition (input list is descending) is not checked.
let f k a1 a2 = (show k) ++ ":" ++ a1 ++ a2 fromDescListWithKey f [(5,"a"), (5,"b"), (5,"b"), (3,"b")] == fromList [(3, "b"), (5, "5:b5:ba")] valid (fromDescListWithKey f [(5,"a"), (5,"b"), (5,"b"), (3,"b")]) == True valid (fromDescListWithKey f [(5,"a"), (3,"b"), (5,"b"), (5,"b")]) == False
fromDistinctDescList :: [(k, a)] -> Map k a Source #
\(O(n)\). Build a map from a descending list of distinct elements in linear time. The precondition is not checked.
fromDistinctDescList [(5,"a"), (3,"b")] == fromList [(3, "b"), (5, "a")] valid (fromDistinctDescList [(5,"a"), (3,"b")]) == True valid (fromDistinctDescList [(5,"a"), (3,"b"), (3,"a")]) == False
Filter
filter :: (a -> Bool) -> Map k a -> Map k a Source #
\(O(n)\). Filter all values that satisfy the predicate.
filter (> "a") (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" filter (> "x") (fromList [(5,"a"), (3,"b")]) == empty filter (< "a") (fromList [(5,"a"), (3,"b")]) == empty
filterWithKey :: (k -> a -> Bool) -> Map k a -> Map k a Source #
\(O(n)\). Filter all keys/values that satisfy the predicate.
filterWithKey (\k _ -> k > 4) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
restrictKeys :: Ord k => Map k a -> Set k -> Map k a Source #
\(O\bigl(m \log\bigl(\frac{n+1}{m+1}\bigr)\bigr), \; m \leq n\). Restrict a Map to only those keys
found in a Set.
m `restrictKeys` s =filterWithKey(\k _ -> k`member`s) m m `restrictKeys` s = m`intersection`fromSet(const ()) s
Since: containers-0.5.8
withoutKeys :: Ord k => Map k a -> Set k -> Map k a Source #
\(O\bigl(m \log\bigl(\frac{n+1}{m+1}\bigr)\bigr), \; m \leq n\). Remove all keys in a Set from a Map.
m `withoutKeys` s =filterWithKey(\k _ -> k`notMember`s) m m `withoutKeys` s = m`difference`fromSet(const ()) s
Since: containers-0.5.8
partition :: (a -> Bool) -> Map k a -> (Map k a, Map k a) Source #
\(O(n)\). Partition the map according to a predicate. The first
map contains all elements that satisfy the predicate, the second all
elements that fail the predicate. See also split.
partition (> "a") (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a") partition (< "x") (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty) partition (> "x") (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")])
partitionWithKey :: (k -> a -> Bool) -> Map k a -> (Map k a, Map k a) Source #
\(O(n)\). Partition the map according to a predicate. The first
map contains all elements that satisfy the predicate, the second all
elements that fail the predicate. See also split.
partitionWithKey (\ k _ -> k > 3) (fromList [(5,"a"), (3,"b")]) == (singleton 5 "a", singleton 3 "b") partitionWithKey (\ k _ -> k < 7) (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty) partitionWithKey (\ k _ -> k > 7) (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")])
takeWhileAntitone :: (k -> Bool) -> Map k a -> Map k a Source #
\(O(\log n)\). Take while a predicate on the keys holds.
The user is responsible for ensuring that for all keys j and k in the map,
j < k ==> p j >= p k. See note at spanAntitone.
takeWhileAntitone p =fromDistinctAscList.takeWhile(p . fst) .toListtakeWhileAntitone p =filterWithKey(k _ -> p k)
Since: containers-0.5.8
dropWhileAntitone :: (k -> Bool) -> Map k a -> Map k a Source #
\(O(\log n)\). Drop while a predicate on the keys holds.
The user is responsible for ensuring that for all keys j and k in the map,
j < k ==> p j >= p k. See note at spanAntitone.
dropWhileAntitone p =fromDistinctAscList.dropWhile(p . fst) .toListdropWhileAntitone p =filterWithKey(\k _ -> not (p k))
Since: containers-0.5.8
spanAntitone :: (k -> Bool) -> Map k a -> (Map k a, Map k a) Source #
\(O(\log n)\). Divide a map at the point where a predicate on the keys stops holding.
The user is responsible for ensuring that for all keys j and k in the map,
j < k ==> p j >= p k.
spanAntitone p xs = (takeWhileAntitonep xs,dropWhileAntitonep xs) spanAntitone p xs = partitionWithKey (\k _ -> p k) xs
Note: if p is not actually antitone, then spanAntitone will split the map
at some unspecified point where the predicate switches from holding to not
holding (where the predicate is seen to hold before the first key and to fail
after the last key).
Since: containers-0.5.8
mapMaybe :: (a -> Maybe b) -> Map k a -> Map k b Source #
\(O(n)\). Map values and collect the Just results.
let f x = if x == "a" then Just "new a" else Nothing mapMaybe f (fromList [(5,"a"), (3,"b")]) == singleton 5 "new a"
mapMaybeWithKey :: (k -> a -> Maybe b) -> Map k a -> Map k b Source #
\(O(n)\). Map keys/values and collect the Just results.
let f k _ = if k < 5 then Just ("key : " ++ (show k)) else Nothing
mapMaybeWithKey f (fromList [(5,"a"), (3,"b")]) == singleton 3 "key : 3"mapEither :: (a -> Either b c) -> Map k a -> (Map k b, Map k c) Source #
\(O(n)\). Map values and separate the Left and Right results.
let f a = if a < "c" then Left a else Right a
mapEither f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
== (fromList [(3,"b"), (5,"a")], fromList [(1,"x"), (7,"z")])
mapEither (\ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
== (empty, fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])mapEitherWithKey :: (k -> a -> Either b c) -> Map k a -> (Map k b, Map k c) Source #
\(O(n)\). Map keys/values and separate the Left and Right results.
let f k a = if k < 5 then Left (k * 2) else Right (a ++ a)
mapEitherWithKey f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
== (fromList [(1,2), (3,6)], fromList [(5,"aa"), (7,"zz")])
mapEitherWithKey (\_ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
== (empty, fromList [(1,"x"), (3,"b"), (5,"a"), (7,"z")])split :: Ord k => k -> Map k a -> (Map k a, Map k a) Source #
\(O(\log n)\). The expression () is a pair split k map(map1,map2) where
the keys in map1 are smaller than k and the keys in map2 larger than k.
Any key equal to k is found in neither map1 nor map2.
split 2 (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3,"b"), (5,"a")]) split 3 (fromList [(5,"a"), (3,"b")]) == (empty, singleton 5 "a") split 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a") split 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", empty) split 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], empty)
splitLookup :: Ord k => k -> Map k a -> (Map k a, Maybe a, Map k a) Source #
\(O(\log n)\). The expression () splits a map just
like splitLookup k mapsplit but also returns .lookup k map
splitLookup 2 (fromList [(5,"a"), (3,"b")]) == (empty, Nothing, fromList [(3,"b"), (5,"a")]) splitLookup 3 (fromList [(5,"a"), (3,"b")]) == (empty, Just "b", singleton 5 "a") splitLookup 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Nothing, singleton 5 "a") splitLookup 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Just "a", empty) splitLookup 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], Nothing, empty)
splitRoot :: Map k b -> [Map k b] Source #
\(O(1)\). Decompose a map into pieces based on the structure of the underlying tree. This function is useful for consuming a map in parallel.
No guarantee is made as to the sizes of the pieces; an internal, but deterministic process determines this. However, it is guaranteed that the pieces returned will be in ascending order (all elements in the first submap less than all elements in the second, and so on).
Examples:
splitRoot (fromList (zip [1..6] ['a'..])) == [fromList [(1,'a'),(2,'b'),(3,'c')],fromList [(4,'d')],fromList [(5,'e'),(6,'f')]]
splitRoot empty == []
Note that the current implementation does not return more than three submaps, but you should not depend on this behaviour because it can change in the future without notice.
Since: containers-0.5.4
Submap
isSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Bool Source #
\(O\bigl(m \log\bigl(\frac{n+1}{m+1}\bigr)\bigr), \; m \leq n\).
This function is defined as ().isSubmapOf = isSubmapOfBy (==)
isSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool Source #
\(O\bigl(m \log\bigl(\frac{n+1}{m+1}\bigr)\bigr), \; m \leq n\).
The expression () returns isSubmapOfBy f t1 t2True if
all keys in t1 are in tree t2, and when f returns True when
applied to their respective values. For example, the following
expressions are all True:
isSubmapOfBy (==) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (<=) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1),('b',2)])But the following are all False:
isSubmapOfBy (==) (fromList [('a',2)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (<) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1)])Note that isSubmapOfBy (_ _ -> True) m1 m2 tests whether all the keys
in m1 are also keys in m2.
isProperSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Bool Source #
\(O\bigl(m \log\bigl(\frac{n+1}{m+1}\bigr)\bigr), \; m \leq n\). Is this a proper submap? (ie. a submap but not equal).
Defined as ().isProperSubmapOf = isProperSubmapOfBy (==)
isProperSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool Source #
\(O\bigl(m \log\bigl(\frac{n+1}{m+1}\bigr)\bigr), \; m \leq n\). Is this a proper submap? (ie. a submap but not equal).
The expression () returns isProperSubmapOfBy f m1 m2True when
keys m1 and keys m2 are not equal,
all keys in m1 are in m2, and when f returns True when
applied to their respective values. For example, the following
expressions are all True:
isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
But the following are all False:
isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)]) isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)]) isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
Indexed
lookupIndex :: Ord k => k -> Map k a -> Maybe Int Source #
\(O(\log n)\). Lookup the index of a key, which is its zero-based index in
the sequence sorted by keys. The index is a number from 0 up to, but not
including, the size of the map.
isJust (lookupIndex 2 (fromList [(5,"a"), (3,"b")])) == False fromJust (lookupIndex 3 (fromList [(5,"a"), (3,"b")])) == 0 fromJust (lookupIndex 5 (fromList [(5,"a"), (3,"b")])) == 1 isJust (lookupIndex 6 (fromList [(5,"a"), (3,"b")])) == False
findIndex :: Ord k => k -> Map k a -> Int Source #
\(O(\log n)\). Return the index of a key, which is its zero-based index in
the sequence sorted by keys. The index is a number from 0 up to, but not
including, the size of the map. Calls error when the key is not
a member of the map.
findIndex 2 (fromList [(5,"a"), (3,"b")]) Error: element is not in the map findIndex 3 (fromList [(5,"a"), (3,"b")]) == 0 findIndex 5 (fromList [(5,"a"), (3,"b")]) == 1 findIndex 6 (fromList [(5,"a"), (3,"b")]) Error: element is not in the map
elemAt :: Int -> Map k a -> (k, a) Source #
\(O(\log n)\). Retrieve an element by its index, i.e. by its zero-based
index in the sequence sorted by keys. If the index is out of range (less
than zero, greater or equal to size of the map), error is called.
elemAt 0 (fromList [(5,"a"), (3,"b")]) == (3,"b") elemAt 1 (fromList [(5,"a"), (3,"b")]) == (5, "a") elemAt 2 (fromList [(5,"a"), (3,"b")]) Error: index out of range
updateAt :: (k -> a -> Maybe a) -> Int -> Map k a -> Map k a Source #
\(O(\log n)\). Update the element at index. Calls error when an
invalid index is used.
updateAt (\ _ _ -> Just "x") 0 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "x"), (5, "a")] updateAt (\ _ _ -> Just "x") 1 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "x")] updateAt (\ _ _ -> Just "x") 2 (fromList [(5,"a"), (3,"b")]) Error: index out of range updateAt (\ _ _ -> Just "x") (-1) (fromList [(5,"a"), (3,"b")]) Error: index out of range updateAt (\_ _ -> Nothing) 0 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" updateAt (\_ _ -> Nothing) 1 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" updateAt (\_ _ -> Nothing) 2 (fromList [(5,"a"), (3,"b")]) Error: index out of range updateAt (\_ _ -> Nothing) (-1) (fromList [(5,"a"), (3,"b")]) Error: index out of range
deleteAt :: Int -> Map k a -> Map k a Source #
\(O(\log n)\). Delete the element at index, i.e. by its zero-based index in
the sequence sorted by keys. If the index is out of range (less than zero,
greater or equal to size of the map), error is called.
deleteAt 0 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" deleteAt 1 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" deleteAt 2 (fromList [(5,"a"), (3,"b")]) Error: index out of range deleteAt (-1) (fromList [(5,"a"), (3,"b")]) Error: index out of range
take :: Int -> Map k a -> Map k a Source #
\(O(\log n)\). Take a given number of entries in key order, beginning with the smallest keys.
take n =fromDistinctAscList.taken .toAscList
Since: containers-0.5.8
drop :: Int -> Map k a -> Map k a Source #
\(O(\log n)\). Drop a given number of entries in key order, beginning with the smallest keys.
drop n =fromDistinctAscList.dropn .toAscList
Since: containers-0.5.8
Min/Max
lookupMin :: Map k a -> Maybe (k, a) Source #
\(O(\log n)\). The minimal key of the map. Returns Nothing if the map is empty.
lookupMin (fromList [(5,"a"), (3,"b")]) == Just (3,"b") lookupMin empty = Nothing
Since: containers-0.5.9
lookupMax :: Map k a -> Maybe (k, a) Source #
\(O(\log n)\). The maximal key of the map. Returns Nothing if the map is empty.
lookupMax (fromList [(5,"a"), (3,"b")]) == Just (5,"a") lookupMax empty = Nothing
Since: containers-0.5.9
findMin :: Map k a -> (k, a) Source #
\(O(\log n)\). The minimal key of the map. Calls error if the map is empty.
findMin (fromList [(5,"a"), (3,"b")]) == (3,"b") findMin empty Error: empty map has no minimal element
findMax :: Map k a -> (k, a) Source #
\(O(\log n)\). The maximal key of the map. Calls error if the map is empty.
findMax (fromList [(5,"a"), (3,"b")]) == (5,"a") findMax empty Error: empty map has no maximal element
deleteMin :: Map k a -> Map k a Source #
\(O(\log n)\). Delete the minimal key. Returns an empty map if the map is empty.
deleteMin (fromList [(5,"a"), (3,"b"), (7,"c")]) == fromList [(5,"a"), (7,"c")] deleteMin empty == empty
deleteMax :: Map k a -> Map k a Source #
\(O(\log n)\). Delete the maximal key. Returns an empty map if the map is empty.
deleteMax (fromList [(5,"a"), (3,"b"), (7,"c")]) == fromList [(3,"b"), (5,"a")] deleteMax empty == empty
deleteFindMin :: Map k a -> ((k, a), Map k a) Source #
\(O(\log n)\). Delete and find the minimal element.
deleteFindMin (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((3,"b"), fromList[(5,"a"), (10,"c")]) deleteFindMin empty Error: can not return the minimal element of an empty map
deleteFindMax :: Map k a -> ((k, a), Map k a) Source #
\(O(\log n)\). Delete and find the maximal element.
deleteFindMax (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((10,"c"), fromList [(3,"b"), (5,"a")]) deleteFindMax empty Error: can not return the maximal element of an empty map
updateMin :: (a -> Maybe a) -> Map k a -> Map k a Source #
\(O(\log n)\). Update the value at the minimal key.
updateMin (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "Xb"), (5, "a")]
updateMin (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"updateMax :: (a -> Maybe a) -> Map k a -> Map k a Source #
\(O(\log n)\). Update the value at the maximal key.
updateMax (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "Xa")]
updateMax (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"updateMinWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a Source #
\(O(\log n)\). Update the value at the minimal key.
updateMinWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"3:b"), (5,"a")] updateMinWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
updateMaxWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a Source #
\(O(\log n)\). Update the value at the maximal key.
updateMaxWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"b"), (5,"5:a")] updateMaxWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
minView :: Map k a -> Maybe (a, Map k a) Source #
\(O(\log n)\). Retrieves the value associated with minimal key of the
map, and the map stripped of that element, or Nothing if passed an
empty map.
minView (fromList [(5,"a"), (3,"b")]) == Just ("b", singleton 5 "a")
minView empty == NothingmaxView :: Map k a -> Maybe (a, Map k a) Source #
\(O(\log n)\). Retrieves the value associated with maximal key of the
map, and the map stripped of that element, or Nothing if passed an
empty map.
maxView (fromList [(5,"a"), (3,"b")]) == Just ("a", singleton 3 "b")
maxView empty == NothingminViewWithKey :: Map k a -> Maybe ((k, a), Map k a) Source #
\(O(\log n)\). Retrieves the minimal (key,value) pair of the map, and
the map stripped of that element, or Nothing if passed an empty map.
minViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((3,"b"), singleton 5 "a") minViewWithKey empty == Nothing
maxViewWithKey :: Map k a -> Maybe ((k, a), Map k a) Source #
\(O(\log n)\). Retrieves the maximal (key,value) pair of the map, and
the map stripped of that element, or Nothing if passed an empty map.
maxViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((5,"a"), singleton 3 "b") maxViewWithKey empty == Nothing
Debugging
showTree :: Whoops "showTree has moved to Data.Map.Internal.Debug.showTree." => Map k a -> String Source #
This function has moved to showTree.
showTreeWith :: Whoops "showTreeWith has moved to Data.Map.Internal.Debug.showTreeWith." => (k -> a -> String) -> Bool -> Bool -> Map k a -> String Source #
This function has moved to showTreeWith.