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| Data.Map | | Portability | portable | | Stability | provisional | | Maintainer | libraries@haskell.org |
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| Description |
An efficient implementation of maps from keys to values (dictionaries).
This module is intended to be imported qualified, to avoid name
clashes with Prelude functions. eg.
import Data.Map 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.
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| Synopsis |
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| data Map k a | | | (!) :: Ord k => Map k a -> k -> 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 | | | lookup :: (Monad m, Ord k) => k -> Map k a -> m a | | | findWithDefault :: Ord k => a -> k -> Map k a -> a | | | 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) | | | 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 :: Ord k => [Map k a] -> Map k a | | | unionsWith :: Ord k => (a -> a -> a) -> [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 | | | map :: (a -> b) -> Map k a -> Map k b | | | mapWithKey :: (k -> a -> b) -> Map k a -> 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) | | | 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 | | | fold :: (a -> b -> b) -> b -> Map k a -> b | | | foldWithKey :: (k -> a -> b -> b) -> b -> Map k a -> b | | | elems :: Map k a -> [a] | | | keys :: Map k a -> [k] | | | keysSet :: Map k a -> Set k | | | assocs :: Map k a -> [(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)] | | | 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 | | | filter :: Ord k => (a -> Bool) -> Map k a -> Map k a | | | filterWithKey :: Ord k => (k -> a -> Bool) -> Map k a -> Map k a | | | partition :: Ord k => (a -> Bool) -> Map k a -> (Map k a, Map k a) | | | partitionWithKey :: Ord k => (k -> a -> Bool) -> Map k a -> (Map k a, Map k a) | | | 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) | | | 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 :: (Monad m, Ord k) => k -> Map k a -> m 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 | | | 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 | | | showTree :: (Show k, Show a) => Map k a -> String | | | showTreeWith :: (k -> a -> String) -> Bool -> Bool -> Map k a -> String | | | valid :: Ord k => Map k a -> Bool |
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| Map type
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| data Map k a |
| A Map from keys k to values a.
|  Instances | |
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| Operators
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| (!) :: Ord k => Map k a -> k -> a |
| O(log n). Find the value at a key.
Calls error when the element can not be found.
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| (\\) :: Ord k => Map k a -> Map k b -> Map k a |
| O(n+m). See difference.
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| Query
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| null :: Map k a -> Bool |
| O(1). Is the map empty?
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| size :: Map k a -> Int |
| O(1). The number of elements in the map.
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| member :: Ord k => k -> Map k a -> Bool |
| O(log n). Is the key a member of the map?
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| lookup :: (Monad m, Ord k) => k -> Map k a -> m a |
| O(log n). Lookup the value at a key in the map.
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| findWithDefault :: Ord k => a -> k -> Map k a -> a |
| O(log n). The expression (findWithDefault def k map) returns
the value at key k or returns def when the key is not in the map.
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| Construction
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| empty :: Map k a |
| O(1). The empty map.
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| singleton :: k -> a -> Map k a |
| O(1). A map with a single element.
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| Insertion
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| insert :: Ord k => k -> a -> Map k a -> Map k a |
| O(log n). Insert a new key and value in the map.
If the key is already present in the map, the associated value is
replaced with the supplied value, i.e. insert is equivalent to
insertWith const.
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| insertWith :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a |
| O(log n). Insert with a combining function.
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| insertWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a |
| O(log n). Insert with a combining function.
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| insertLookupWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> (Maybe a, Map k a) |
| O(log n). 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).
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| Delete/Update
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| delete :: Ord k => k -> Map k a -> Map k a |
| O(log n). Delete a key and its value from the map. When the key is not
a member of the map, the original map is returned.
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| adjust :: Ord k => (a -> a) -> k -> Map k a -> Map k a |
| O(log n). Adjust a value at a specific key. When the key is not
a member of the map, the original map is returned.
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| adjustWithKey :: Ord k => (k -> a -> a) -> k -> Map k a -> Map k a |
| O(log n). Adjust a value at a specific key. When the key is not
a member of the map, the original map is returned.
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| update :: Ord k => (a -> Maybe a) -> k -> Map k a -> Map k a |
| O(log n). The expression (update f k map) updates the value x
at k (if it is in the map). If (f x) is Nothing, the element is
deleted. If it is (Just y), the key k is bound to the new value y.
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| updateWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a |
| O(log n). The expression (updateWithKey f k map) updates the
value x at k (if it is in the map). If (f k x) is Nothing,
the element is deleted. If it is (Just y), the key k is bound
to the new value y.
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| updateLookupWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> (Maybe a, Map k a) |
| O(log n). Lookup and update.
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| Combine
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| Union
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| union :: Ord k => Map k a -> Map k a -> Map k a |
| O(n+m).
The expression (union t1 t2) takes the left-biased union of t1 and t2.
It prefers t1 when duplicate keys are encountered,
i.e. (union == unionWith const).
The implementation uses the efficient hedge-union algorithm.
Hedge-union is more efficient on (bigset union smallset)?
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| unionWith :: Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a |
| O(n+m). Union with a combining function. The implementation uses the efficient hedge-union algorithm.
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| unionWithKey :: Ord k => (k -> a -> a -> a) -> Map k a -> Map k a -> Map k a |
| O(n+m).
Union with a combining function. The implementation uses the efficient hedge-union algorithm.
Hedge-union is more efficient on (bigset union smallset).
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| unions :: Ord k => [Map k a] -> Map k a |
| The union of a list of maps:
(unions == foldl union empty).
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| unionsWith :: Ord k => (a -> a -> a) -> [Map k a] -> Map k a |
| The union of a list of maps, with a combining operation:
(unionsWith f == foldl (unionWith f) empty).
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| Difference
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| difference :: Ord k => Map k a -> Map k b -> Map k a |
| O(n+m). Difference of two maps.
The implementation uses an efficient hedge algorithm comparable with hedge-union.
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| differenceWith :: Ord k => (a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a |
| O(n+m). Difference with a combining function.
The implementation uses an efficient hedge algorithm comparable with hedge-union.
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| differenceWithKey :: Ord k => (k -> a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a |
| O(n+m). Difference with a combining function. When two equal keys are
encountered, the combining function is applied to the key and both values.
If it returns Nothing, the element is discarded (proper set difference). If
it returns (Just y), the element is updated with a new value y.
The implementation uses an efficient hedge algorithm comparable with hedge-union.
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| Intersection
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| intersection :: Ord k => Map k a -> Map k b -> Map k a |
| O(n+m). Intersection of two maps. The values in the first
map are returned, i.e. (intersection m1 m2 == intersectionWith const m1 m2).
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| intersectionWith :: Ord k => (a -> b -> c) -> Map k a -> Map k b -> Map k c |
| O(n+m). Intersection with a combining function.
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| intersectionWithKey :: Ord k => (k -> a -> b -> c) -> Map k a -> Map k b -> Map k c |
| O(n+m). Intersection with a combining function.
Intersection is more efficient on (bigset intersection smallset)
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| Traversal
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| Map
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| map :: (a -> b) -> Map k a -> Map k b |
| O(n). Map a function over all values in the map.
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| mapWithKey :: (k -> a -> b) -> Map k a -> Map k b |
| O(n). Map a function over all values in the map.
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| mapAccum :: (a -> b -> (a, c)) -> a -> Map k b -> (a, Map k c) |
| O(n). The function mapAccum threads an accumulating
argument through the map in ascending order of keys.
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| mapAccumWithKey :: (a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c) |
| O(n). The function mapAccumWithKey threads an accumulating
argument through the map in ascending order of keys.
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| mapKeys :: Ord k2 => (k1 -> k2) -> Map k1 a -> Map k2 a |
O(n*log n).
mapKeys f s is the map obtained by applying f to each key of s.
The size of the result may be smaller if f maps two or more distinct
keys to the same new key. In this case the value at the smallest of
these keys is retained.
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| mapKeysWith :: Ord k2 => (a -> a -> a) -> (k1 -> k2) -> Map k1 a -> Map k2 a |
O(n*log n).
mapKeysWith c f s is the map obtained by applying f to each key of s.
The size of the result may be smaller if f maps two or more distinct
keys to the same new key. In this case the associated values will be
combined using c.
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| mapKeysMonotonic :: (k1 -> k2) -> Map k1 a -> Map k2 a |
O(n).
mapKeysMonotonic f s == mapKeys f s, but works only when f
is strictly monotonic.
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
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| Fold
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| fold :: (a -> b -> b) -> b -> Map k a -> b |
O(n). Fold the values in the map, such that
fold f z == foldr f z . elems.
For example,
elems map = fold (:) [] map
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| foldWithKey :: (k -> a -> b -> b) -> b -> Map k a -> b |
O(n). Fold the keys and values in the map, such that
foldWithKey f z == foldr (uncurry f) z . toAscList.
For example,
keys map = foldWithKey (\k x ks -> k:ks) [] map
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| Conversion
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| elems :: Map k a -> [a] |
| O(n).
Return all elements of the map in the ascending order of their keys.
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| keys :: Map k a -> [k] |
| O(n). Return all keys of the map in ascending order.
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| keysSet :: Map k a -> Set k |
| O(n). The set of all keys of the map.
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| assocs :: Map k a -> [(k, a)] |
| O(n). Return all key/value pairs in the map in ascending key order.
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| Lists
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| toList :: Map k a -> [(k, a)] |
| O(n). Convert to a list of key/value pairs.
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| fromList :: Ord k => [(k, a)] -> Map k a |
| O(n*log n). Build a map from a list of key/value pairs. See also fromAscList.
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| fromListWith :: Ord k => (a -> a -> a) -> [(k, a)] -> Map k a |
| O(n*log n). Build a map from a list of key/value pairs with a combining function. See also fromAscListWith.
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| fromListWithKey :: Ord k => (k -> a -> a -> a) -> [(k, a)] -> Map k a |
| O(n*log n). Build a map from a list of key/value pairs with a combining function. See also fromAscListWithKey.
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| Ordered lists
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| toAscList :: Map k a -> [(k, a)] |
| O(n). Convert to an ascending list.
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| fromAscList :: Eq k => [(k, a)] -> Map k a |
| O(n). Build a map from an ascending list in linear time.
The precondition (input list is ascending) is not checked.
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| fromAscListWith :: Eq k => (a -> a -> a) -> [(k, a)] -> Map k a |
| O(n). Build a map from an ascending list in linear time with a combining function for equal keys.
The precondition (input list is ascending) is not checked.
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| fromAscListWithKey :: Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a |
| O(n). Build a map from an ascending list in linear time with a
combining function for equal keys.
The precondition (input list is ascending) is not checked.
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| fromDistinctAscList :: [(k, a)] -> Map k a |
| O(n). Build a map from an ascending list of distinct elements in linear time.
The precondition is not checked.
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| Filter
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| filter :: Ord k => (a -> Bool) -> Map k a -> Map k a |
| O(n). Filter all values that satisfy the predicate.
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| filterWithKey :: Ord k => (k -> a -> Bool) -> Map k a -> Map k a |
| O(n). Filter all keys/values that satisfy the predicate.
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| partition :: Ord k => (a -> Bool) -> Map k a -> (Map k a, Map k a) |
| O(n). partition the map according to a predicate. The first
map contains all elements that satisfy the predicate, the second all
elements that fail the predicate. See also split.
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| partitionWithKey :: Ord k => (k -> a -> Bool) -> Map k a -> (Map k a, Map k a) |
| O(n). partition the map according to a predicate. The first
map contains all elements that satisfy the predicate, the second all
elements that fail the predicate. See also split.
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| split :: Ord k => k -> Map k a -> (Map k a, Map k a) |
| O(log n). The expression (split k map) is a pair (map1,map2) where
the keys in map1 are smaller than k and the keys in map2 larger than k. Any key equal to k is found in neither map1 nor map2.
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| splitLookup :: Ord k => k -> Map k a -> (Map k a, Maybe a, Map k a) |
| O(log n). The expression (splitLookup k map) splits a map just
like split but also returns lookup k map.
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| Submap
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| isSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Bool |
| O(n+m).
This function is defined as (isSubmapOf = isSubmapOfBy (==)).
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| isSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool |
O(n+m).
The expression (isSubmapOfBy f t1 t2) returns True if
all keys in t1 are in tree t2, and when f returns True when
applied to their respective values. For example, the following
expressions are all True:
isSubmapOfBy (==) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (<=) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1),('b',2)])
But the following are all False:
isSubmapOfBy (==) (fromList [('a',2)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (<) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1)])
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| isProperSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Bool |
| O(n+m). Is this a proper submap? (ie. a submap but not equal).
Defined as (isProperSubmapOf = isProperSubmapOfBy (==)).
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| isProperSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k 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
m1 and 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)])
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| Indexed
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| lookupIndex :: (Monad m, Ord k) => k -> Map k a -> m Int |
| O(log n). Lookup the index of a key. The index is a number from
0 up to, but not including, the size of the map.
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| findIndex :: Ord k => k -> Map k a -> Int |
| O(log n). Return the index of a key. 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.
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| elemAt :: Int -> Map k a -> (k, a) |
| O(log n). Retrieve an element by index. Calls error when an
invalid index is used.
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| updateAt :: (k -> a -> Maybe a) -> Int -> Map k a -> Map k a |
| O(log n). Update the element at index. Calls error when an
invalid index is used.
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| deleteAt :: Int -> Map k a -> Map k a |
| O(log n). Delete the element at index.
Defined as (deleteAt i map = updateAt (k x -> Nothing) i map).
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| Min/Max
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| findMin :: Map k a -> (k, a) |
| O(log n). The minimal key of the map.
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| findMax :: Map k a -> (k, a) |
| O(log n). The maximal key of the map.
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| deleteMin :: Map k a -> Map k a |
| O(log n). Delete the minimal key.
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| deleteMax :: Map k a -> Map k a |
| O(log n). Delete the maximal key.
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| deleteFindMin :: Map k a -> ((k, a), Map k a) |
| O(log n). Delete and find the minimal element.
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| deleteFindMax :: Map k a -> ((k, a), Map k a) |
| O(log n). Delete and find the maximal element.
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| updateMin :: (a -> Maybe a) -> Map k a -> Map k a |
| O(log n). Update the value at the minimal key.
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| updateMax :: (a -> Maybe a) -> Map k a -> Map k a |
| O(log n). Update the value at the maximal key.
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| updateMinWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a |
| O(log n). Update the value at the minimal key.
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| updateMaxWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a |
| O(log n). Update the value at the maximal key.
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| Debugging
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| showTree :: (Show k, Show a) => Map k a -> String |
| O(n). Show the tree that implements the map. The tree is shown
in a compressed, hanging format.
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| showTreeWith :: (k -> a -> String) -> Bool -> Bool -> Map k a -> String |
O(n). The expression (showTreeWith showelem hang wide map) shows
the tree that implements the map. Elements are shown using the showElem function. 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.
Map> let t = fromDistinctAscList [(x,()) | x <- [1..5]]
Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True False t
(4,())
+--(2,())
| +--(1,())
| +--(3,())
+--(5,())
Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True True t
(4,())
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+--(2,())
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| +--(1,())
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| +--(3,())
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+--(5,())
Map> putStrLn $ showTreeWith (\k x -> show (k,x)) False True t
+--(5,())
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(4,())
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| +--(3,())
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+--(2,())
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+--(1,())
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| valid :: Ord k => Map k a -> Bool |
| O(n). Test if the internal map structure is valid.
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| Produced by Haddock version 0.7 |
