Data.Dependent.Map

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.

O(log n). Insert with a function, combining new value and old value. insertWith f key value mp will insert the entry key :=> value into mp if key does not exist in the map. If the key does exist, the function will insert the entry key :=> f new_value old_value.

Same as insertWith, but the combining function is applied strictly. This is often the most desirable behavior.

O(log n). Insert with a function, combining key, new value and old value. insertWithKey f key value mp will insert the entry key :=> value into mp if key does not exist in the map. If the key does exist, the function will insert the entry key :=> f key new_value old_value. Note that the key passed to f is the same key passed to insertWithKey.

Same as insertWithKey, but the combining function is applied strictly.

O(log n). Combines insert operation with old value retrieval. The expression (insertLookupWithKey f k x map) is a pair where the first element is equal to (lookup k map) and the second element equal to (insertWithKey f k x map).

O(log n). A strict version of insertLookupWithKey.

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.

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.

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.

O(log n). A strict version of adjustWithKey.

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.

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.

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.

O(log n). The expression (alter f k map) alters the value x at k, or absence thereof. alter can be used to insert, delete, or update a value in a Map. In short : lookup k (alter f k m) = f (lookup k m).

Works the same as alter except the new value is returned in some Functor f. In short : (v' -> alter (const v') k dm) $ f (lookup k dm)

O(m*log(n/m + 1)), m <= n. The expression (union t1 t2) takes the left-biased union of t1 and t2. It prefers t1 when duplicate keys are encountered, i.e. (union == unionWith const).

O(n+m). Union with a combining function.

The union of a list of maps: (unions == foldl union empty).

The union of a list of maps, with a combining operation: (unionsWithKey f == foldl (unionWithKey f) empty).

O(m * log (n/m + 1)), m <= n. Difference of two maps. Return elements of the first map not existing in the second map.

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.

O(m * log (n/m + 1), m <= 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).

O(m * log (n/m + 1), m <= n. Intersection with a combining function.

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

O(n). ffor == flip map except we cannot actually use flip because of the lack of impredicative types.

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

O(n). fforWithKey == flip mapWithKey except we cannot actually use flip because of the lack of impredicative types.

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

O(n). forWithKey == flip traverseWithKey except we cannot actually use flip because of the lack of impredicative types.

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

O(n). forWithKey == flip traverseWithKey except we cannot actually use flip because of the lack of impredicative types.

O(n). The function mapAccumLWithKey threads an accumulating argument through the map in ascending order of keys.

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

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.

O(n). mapKeysMonotonic f s == mapKeys f s, but works only when f is strictly monotonic. That is, for any values x and y, if x < y then f x < f y. The precondition is not checked. Semi-formally, we have:

and [x < y ==> f x < f y | x <- ls, y <- ls]
                    ==> mapKeysMonotonic f s == mapKeys f s
    where ls = keys s

This means that f maps distinct original keys to distinct resulting keys. This function has better performance than mapKeys.

O(n). Fold the keys and values in the map, such that foldWithKey f z == foldr (uncurry f) z . toAscList.

This is identical to foldrWithKey, and you should use that one instead of this one. This name is kept for backward compatibility.

O(n). Post-order fold. The function will be applied from the lowest value to the highest.

O(n). Pre-order fold. The function will be applied from the highest value to the lowest.

O(n). Convert to a list of key/value pairs.

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.

O(n*log n). Build a map from a list of key/value pairs with a combining function. See also fromAscListWithKey.

O(n). Convert to an ascending list.

O(n). Convert to a descending list.

O(n). Build a map from an ascending list in linear time. The precondition (input list is ascending) is not checked.

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.

O(n). Build a map from an ascending list of distinct elements in linear time. The precondition is not checked.