insert key f map modifies or insert an element of the map; f takes None if the value was not previously bound, and Some old where old is the previously bound value otherwise. The function preserves physical equality when possible. O(log(n)) complexity. Preserves physical equality if the new value is physically equal to the old.
update key f map modifies, insert, or remove an element from the map; f takes None if the value was not previously bound, and Some old where old is the previously bound value otherwise. The function preserves physical equality when possible. It returns None if the element should be removed O(log(n)) complexity. Preserves physical equality if the new value is physically equal to the old.
Unconditionally adds a value in the map (independently from whether the old value existed). O(log(n)) complexity. Preserves physical equality if the new value is physically equal to the old.
Returns true if the predicate holds on all map bindings. Short-circuiting
In the following, the *no_share function allows taking arguments of different types (but cannot share subtrees of the map), while the default functions attempt to preserve and benefit from sharing the subtrees (using physical equality to detect sharing).
map f m returns a map where the value bound to each key is replaced by f value. The subtrees for which the returned value is physically the same (i.e. f key value == value for all the keys in the subtree) are guaranteed to be physically equal to the original subtree. O(n) complexity. f is called in increasing order of keys.
mapi f m returns a map where the value bound to each key is replaced by f key value. The subtrees for which the returned value is physically the same (i.e. f key value == value for all the keys in the subtree) are guaranteed to be physically equal to the original subtree. O(n) complexity. f is called in increasing order of keys.
mapi_no_share f m returns a map where the value bound to each key is replaced by f key value. O(n) complexity. f is called in increasing order of keys.
filter_map m f returns a map where the value bound to each key is removed (if f key value returns None), or is replaced by v ((if f key value returns Some v). The subtrees for which the returned value is physically the same (i.e. f key value = Some v with value == v for all the keys in the subtree) are guaranteed to be physically equal to the original subtree. O(n) complexity. f is called in increasing order of keys.
filter_map m f returns a map where the value bound to each key is removed (if f key value returns None), or is replaced by v ((if f key value returns Some v). O(n) complexity. f is called in increasing order of keys.
Operations on pairs of maps
The following functions combine two maps. It is key for the performance, when we have large maps who share common subtrees, not to visit the nodes in these subtrees. Hence, we have specialized versions of these functions that assume properties of the function parameter (reflexive relation, idempotent operation, etc.)
When we cannot enjoy these properties, our functions explicitly say so (with a nonreflexive or nonidempotent prefix). The names are a bit long, but having these names avoids using an ineffective code by default, by forcing to know and choose between the fast and slow version.
It is also important to not visit a subtree when there merging this subtree with Empty; hence we provide union and inter operations.
reflexive_same_domain_for_all2 f map1 map2 returns true if map1 and map2 have the same keys, and f key value1 value2 returns true for each mapping pair of keys. We assume that f is reflexive (i.e. f key value value returns true) to avoid visiting physically equal subtrees of map1 and map2. The complexity is O(log(n)*Delta) where Delta is the number of different keys between map1 and map2.
nonreflexive_same_domain_for_all2 f map1 map2 returns true if map1 and map2 have the same keys, and f key value1 value2 returns true for each mapping pair of keys. The complexity is O(min(|map1|,|map2|)).
reflexive_subset_domain_for_all2 f map1 map2 returns true if all the keys of map1 also are in map2, and f key (find map1 key) (find map2 key) returns true when both keys are present in the map. We assume that f is reflexive (i.e. f key value value returns true) to avoid visiting physically equal subtrees of map1 and map2. The complexity is O(log(n)*Delta) where Delta is the number of different keys between map1 and map2.
idempotent_union f map1 map2 returns a map whose keys is the union of the keys of map1 and map2. f is used to combine the values a key is mapped in both maps. We assume that f is idempotent (i.e. f key value value == value) to avoid visiting physically equal subtrees of map1 and map2, and also to preserve physical equality of the subtreess in that case. The complexity is O(log(n)*Delta) where Delta is the number of different keys between map1 and map2. f is called in increasing order of keys. f is never called on physically equal values.
idempotent_inter f map1 map2 returns a map whose keys is the intersection of the keys of map1 and map2. f is used to combine the values a key is mapped in both maps. We assume that f is idempotent (i.e. f key value value == value) to avoid visiting physically equal subtrees of map1 and map2, and also to preserve physical equality of the subtrees in that case. The complexity is O(log(n)*Delta) where Delta is the number of different keys between map1 and map2. f is called in increasing order of keys. f is never called on physically equal values.
nonidempotent_inter_no_share f map1 map2 returns a map whose keys is the intersection of the keys of map1 and map2. f is used to combine the values a key is mapped in both maps. f does not need to be idempotent, which imply that we have to visit physically equal subtrees of map1 and map2. The complexity is O(log(n)*min(|map1|,|map2|)). f is called in increasing order of keys. f is called on every shared binding.
idempotent_inter_filter f m1 m2 is like idempotent_inter f m1 m2 (assuming idempotence, using and preserving physically equal subtrees), but it also removes the key->value bindings for which f returns None.
slow_merge f m1 m2 returns a map whose keys are a subset of the keys of m1 and m2. The f function is used to combine keys, similarly to the Map.merge function. This funcion has to traverse all the bindings in m1 and m2; its complexity is O(|m1|+|m2|). Use one of faster functions above if you can.