Map is a functional data structure (balanced binary tree) implementing finite maps over a totally-ordered domain, called a "key".
For example:
let empty = Map.empty (module String)
let numbers =
Map.of_alist_exn (module String)
["three", Substr "three"; "four", Substr "four"]
Note that the functions in Map are polymorphic over the type of the key and of the data; you just need to pass in the first-class module for the key type (here, String).
Suppose you wanted to define a new module Foo to use in a map. You would write:
module Foo = struct
module T = struct
type t = int * int
let compare x y = Tuple2.compare Int.compare Int.compare
let sexp_of_t = Tuple2.sexp_of_t Int.sexp_of_t Int.sexp_of_t
end
include T
include Comparable.Make(T)
end
This gives you a module Foo with the appropriate comparator in it, and then this:
let m = Map.empty (module Foo)
lets you create a map keyed by Foo. The reason you need to write a sexp-converter and a comparison function for this to work is that maps both need comparison and the ability to serialize the key for generating useful errors. It's yet nicer to do this with the appropriate PPXs:
module Foo = struct
module T =
struct type t = int * int [@@deriving sexp_of, compare] end
include T
include Comparable.Make(T)
end
The interface
type ('key, +'value, 'cmp) t = ('key, 'value, 'cmp) Base.Map.tTest if invariants of internal AVL search tree hold.
val comparator_s : ('a, _, 'cmp) t -> ('a, 'cmp) comparatorval singleton : ('a, 'cmp) comparator -> 'a -> 'b -> ('a, 'b, 'cmp) tMap with one (key, data) pair.
val of_alist :
('a, 'cmp) comparator ->
('a * 'b) Base.List.t ->
[ `Ok of ('a, 'b, 'cmp) t | `Duplicate_key of 'a ]Creates map from an association list with unique keys.
Creates map from an association list with unique keys. Returns an error if duplicate 'a keys are found.
Creates map from an association list with unique keys. Raises an exception if duplicate 'a keys are found.
of_hashtbl_exn creates a map from bindings present in a hash table. of_hashtbl_exn raises if there are distinct keys a1 and a2 in the table with comparator.compare a1 a2 = 0, which is only possible if the hash-table comparison function is different than comparator.compare. In the common case, the comparison is the same, in which case of_hashtbl_exn does not raise, regardless of the keys present in the table.
Creates map from an association list with possibly repeated keys.
val of_alist_fold :
('a, 'cmp) comparator ->
('a * 'b) Base.List.t ->
init:'c ->
f:('c -> 'b -> 'c) ->
('a, 'c, 'cmp) tCombines an association list into a map, folding together bound values with common keys.
val of_alist_reduce :
('a, 'cmp) comparator ->
('a * 'b) Base.List.t ->
f:('b -> 'b -> 'b) ->
('a, 'b, 'cmp) tCombines an association list into a map, reducing together bound values with common keys.
of_iteri ~iteri behaves like of_alist, except that instead of taking a concrete datastruture, it takes an iteration function. For instance, to convert a string table into a map: of_iteri (module String) ~f:(Hashtbl.iteri table). It is faster than adding the elements one by one.
Trees
Parallel to the three kinds of map modules Map, Map.Poly, and Key.Map, there are also tree modules Map.Tree, Map.Poly.Tree, and Key.Map.Tree. A tree is a bare representation of a map, without the comparator. Thus tree operations need to obtain the comparator from somewhere. For Map.Poly.Tree and Key.Map.Tree, the comparator is implicit in the module name. For Map.Tree, the comparator must be passed to each operation.
The main advantages of trees over maps are slightly improved space usage (there is no outer container holding the comparator) and the ability to marshal trees, because a tree doesn't contain a closure, the way a map does.
The main disadvantages of using trees are needing to be more explicit about the comparator, and the possibility of accidentally using polymorphic equality on a tree (for which maps dynamically detect failure due to the presence of a closure in the data structure).
module Tree : sig ... endval to_tree : ('k, 'v, 'cmp) t -> ('k, 'v, 'cmp) Tree.tCreates a t from a Tree.t and a Comparator.t. This is an O(n) operation as it must discover the length of the Tree.t.
More interface
Creates map from a sorted array of key-data pairs. The input array must be sorted, as given by the relevant comparator (either in ascending or descending order), and must not contain any duplicate keys. If either of these conditions does not hold, an error is returned.
Like of_sorted_array except it returns a map with broken invariants when an Error would have been returned.
of_increasing_iterator_unchecked c ~len ~f behaves like of_sorted_array_unchecked c (Array.init len ~f), with the additional restriction that a decreasing order is not supported. The advantage is not requiring you to allocate an intermediate array. f will be called with 0, 1, ... len - 1, in order.
of_increasing_sequence c seq behaves like of_sorted_array c
(Sequence.to_array seq), but does not allocate the intermediate array.
The sequence will be folded over once, and the additional time complexity is O(n).
val of_sequence :
('k, 'cmp) comparator ->
('k * 'v) Sequence.t ->
[ `Ok of ('k, 'v, 'cmp) t | `Duplicate_key of 'k ]Creates a map from an association sequence with unique keys.
of_sequence c seq behaves like of_alist c (Sequence.to_list seq) but does not allocate the intermediate list.
If your sequence is increasing, use of_increasing_sequence for better performance.
Creates a map from an association sequence with unique keys, returning an error if duplicate 'a keys are found.
of_sequence_or_error c seq behaves like of_alist_or_error c (Sequence.to_list seq) but does not allocate the intermediate list.
Creates a map from an association sequence with unique keys, raising an exception if duplicate 'a keys are found.
of_sequence_exn c seq behaves like of_alist_exn c (Sequence.to_list seq) but does not allocate the intermediate list.
Creates a map from an association sequence with possibly repeated keys. The values in the map for a given key appear in the same order as they did in the association list.
of_sequence_multi c seq behaves like of_alist_multi c (Sequence.to_list seq) but does not allocate the intermediate list.
val of_sequence_fold :
('a, 'cmp) comparator ->
('a * 'b) Sequence.t ->
init:'c ->
f:('c -> 'b -> 'c) ->
('a, 'c, 'cmp) tCombines an association sequence into a map, folding together bound values with common keys.
of_sequence_fold c seq ~init ~f behaves like of_alist_fold c (Sequence.to_list seq) ~init ~f but does not allocate the intermediate list.
val of_sequence_reduce :
('a, 'cmp) comparator ->
('a * 'b) Sequence.t ->
f:('b -> 'b -> 'b) ->
('a, 'b, 'cmp) tCombines an association sequence into a map, reducing together bound values with common keys.
of_sequence_reduce c seq ~f behaves like of_alist_reduce c (Sequence.to_list seq) ~f but does not allocate the intermediate list.
Tests whether a map is empty or not.
length map returns number of elements in map. O(1), but Tree.length is O(n).
add_exn t ~key ~data returns t extended with key mapped to data, raising if mem key t.
val add_exn : ('k, 'v, 'cmp) t -> key:'k -> data:'v -> ('k, 'v, 'cmp) tval set : ('k, 'v, 'cmp) t -> key:'k -> data:'v -> ('k, 'v, 'cmp) tReturns a new map with the specified new binding; if the key was already bound, its previous binding disappears.
If key is not present then add a singleton list, otherwise, cons data onto the head of the existing list.
If k is present then remove its head element; if result is empty, remove the key.
find_multi t key returns t's values for key if key is present in the table, and returns the empty list otherwise.
change t key ~f returns a new map m that is the same as t on all keys except for key, and whose value for key is defined by f, i.e., find m key = f (find t
key).
val update :
('k, 'v, 'cmp) t ->
'k ->
f:('v Base.Option.t -> 'v) ->
('k, 'v, 'cmp) tupdate t key ~f is change t key ~f:(fun o -> Some (f o)).
Returns the value bound to the given key if it exists, and None otherwise.
val find_exn : ('k, 'v, 'cmp) t -> 'k -> 'vReturns the value bound to the given key, raising Caml.Not_found or Not_found_s if none exists.
val find_or_error : ('k, 'v, 'cmp) t -> 'k -> 'v Or_error.tval remove : ('k, 'v, 'cmp) t -> 'k -> ('k, 'v, 'cmp) tReturns a new map with any binding for the key in question removed.
mem map key tests whether map contains a binding for key.
Iterates until f returns Stop. If f returns Stop, the final result is Unfinished. Otherwise, the final result is Finished.
val iter2 :
('k, 'v1, 'cmp) t ->
('k, 'v2, 'cmp) t ->
f:
(key:'k ->
data:[ `Left of 'v1 | `Right of 'v2 | `Both of 'v1 * 'v2 ] ->
Base.Unit.t) ->
Base.Unit.tIterates two maps side by side. The complexity of this function is O(M+N). If two inputs are [(0, a); (1, a)] and [(1, b); (2, b)], f will be called with [(0, `Left a); (1, `Both (a, b)); (2, `Right b)]
val map : ('k, 'v1, 'cmp) t -> f:('v1 -> 'v2) -> ('k, 'v2, 'cmp) tReturns new map with bound values replaced by the result of f applied to them.
val mapi :
('k, 'v1, 'cmp) t ->
f:(key:'k -> data:'v1 -> 'v2) ->
('k, 'v2, 'cmp) tLike map, but f takes both key and data as arguments.
val fold : ('k, 'v, _) t -> init:'a -> f:(key:'k -> data:'v -> 'a -> 'a) -> 'aFolds over keys and data in map in increasing order of key.
val fold_right :
('k, 'v, _) t ->
init:'a ->
f:(key:'k -> data:'v -> 'a -> 'a) ->
'aFolds over keys and data in map in decreasing order of key.
val fold2 :
('k, 'v1, 'cmp) t ->
('k, 'v2, 'cmp) t ->
init:'a ->
f:
(key:'k ->
data:[ `Left of 'v1 | `Right of 'v2 | `Both of 'v1 * 'v2 ] ->
'a ->
'a) ->
'aFolds over two maps side by side, like iter2.
filter, filteri, filter_keys, filter_map, and filter_mapi run in O(n * lg n) time; they simply accumulate each key & data retained by f into a new map using add.
val filter_keys : ('k, 'v, 'cmp) t -> f:('k -> Base.Bool.t) -> ('k, 'v, 'cmp) tval filter : ('k, 'v, 'cmp) t -> f:('v -> Base.Bool.t) -> ('k, 'v, 'cmp) tval filteri :
('k, 'v, 'cmp) t ->
f:(key:'k -> data:'v -> Base.Bool.t) ->
('k, 'v, 'cmp) tval filter_map :
('k, 'v1, 'cmp) t ->
f:('v1 -> 'v2 Base.Option.t) ->
('k, 'v2, 'cmp) tReturns new map with bound values filtered by the result of f applied to them.
val filter_mapi :
('k, 'v1, 'cmp) t ->
f:(key:'k -> data:'v1 -> 'v2 Base.Option.t) ->
('k, 'v2, 'cmp) tLike filter_map, but function takes both key and data as arguments.
val partition_mapi :
('k, 'v1, 'cmp) t ->
f:(key:'k -> data:'v1 -> [ `Fst of 'v2 | `Snd of 'v3 ]) ->
('k, 'v2, 'cmp) t * ('k, 'v3, 'cmp) tpartition_mapi t ~f returns two new ts, with each key in t appearing in exactly one of the result maps depending on its mapping in f.
val partition_map :
('k, 'v1, 'cmp) t ->
f:('v1 -> [ `Fst of 'v2 | `Snd of 'v3 ]) ->
('k, 'v2, 'cmp) t * ('k, 'v3, 'cmp) tpartition_map t ~f = partition_mapi t ~f:(fun ~key:_ ~data -> f data)
val partitioni_tf :
('k, 'v, 'cmp) t ->
f:(key:'k -> data:'v -> Base.Bool.t) ->
('k, 'v, 'cmp) t * ('k, 'v, 'cmp) tpartitioni_tf t ~f
=
partition_mapi t ~f:(fun ~key ~data ->
if f ~key ~data
then `Fst data
else `Snd data)
val partition_tf :
('k, 'v, 'cmp) t ->
f:('v -> Base.Bool.t) ->
('k, 'v, 'cmp) t * ('k, 'v, 'cmp) tpartition_tf t ~f = partitioni_tf t ~f:(fun ~key:_ ~data -> f data)
Total ordering between maps. The first argument is a total ordering used to compare data associated with equal keys in the two maps.
Hash function: a building block to use when hashing data structures containing maps in them. hash_fold_direct hash_fold_key is compatible with compare_direct iff hash_fold_key is compatible with (comparator m).compare of the map m being hashed.
equal cmp m1 m2 tests whether the maps m1 and m2 are equal, that is, contain equal keys and associate them with equal data. cmp is the equality predicate used to compare the data associated with the keys.
Returns list of keys in map.
Returns list of data in map.
val to_alist :
?key_order:[ `Increasing | `Decreasing ] ->
('k, 'v, _) t ->
('k * 'v) Base.List.tCreates association list from map.
Additional operations on maps
val merge :
('k, 'v1, 'cmp) t ->
('k, 'v2, 'cmp) t ->
f:
(key:'k ->
[ `Left of 'v1 | `Right of 'v2 | `Both of 'v1 * 'v2 ] ->
'v3 Base.Option.t) ->
('k, 'v3, 'cmp) tMerges two maps. The runtime is O(length(t1) + length(t2)). In particular, you shouldn't use this function to merge a list of maps. Consider using merge_skewed instead.
val merge_skewed :
('k, 'v, 'cmp) t ->
('k, 'v, 'cmp) t ->
combine:(key:'k -> 'v -> 'v -> 'v) ->
('k, 'v, 'cmp) tA special case of merge, merge_skewed t1 t2 is a map containing all the bindings of t1 and t2. Bindings that appear in both t1 and t2 are merged using the combine function. In a call combine ~key v1 v2 the value v1 comes from t1 and v2 from t2.
The runtime of merge_skewed is O(l1 * log(l2)), where l1 is the length of the smaller map and l2 the length of the larger map. This is likely to be faster than merge when one of the maps is a lot smaller, or when you merge a list of maps.
symmetric_diff t1 t2 ~data_equal returns a list of changes between t1 and t2. It is intended to be efficient in the case where t1 and t2 share a large amount of structure. The keys in the output sequence will be in sorted order.
fold_symmetric_diff t1 t2 ~data_equal folds across an implicit sequence of changes between t1 and t2, in sorted order by keys. Equivalent to Sequence.fold (symmetric_diff t1 t2 ~data_equal), and more efficient.
min_elt map returns Some (key, data) pair corresponding to the minimum key in map, None if map is empty.
val min_elt_exn : ('k, 'v, _) t -> 'k * 'vmax_elt map returns Some (key, data) pair corresponding to the maximum key in map, and None if map is empty.
val max_elt_exn : ('k, 'v, _) t -> 'k * 'vThe following functions have the same semantics as similar functions in Core_kernel.List.
val split :
('k, 'v, 'cmp) t ->
'k ->
('k, 'v, 'cmp) t * ('k * 'v) Base.Option.t * ('k, 'v, 'cmp) tsplit t key returns a map of keys strictly less than key, the mapping of key if any, and a map of keys strictly greater than key.
Runtime is O(m + log n) where n is the size of the input map, and m is the size of the smaller of the two output maps. The O(m) term is due to the need to calculate the length of the output maps. *
val append :
lower_part:('k, 'v, 'cmp) t ->
upper_part:('k, 'v, 'cmp) t ->
[ `Ok of ('k, 'v, 'cmp) t | `Overlapping_key_ranges ]append ~lower_part ~upper_part returns `Ok map where map contains all the (key,
value) pairs from the two input maps if all the keys from lower_part are less than all the keys from upper_part. Otherwise it returns `Overlapping_key_ranges.
Runtime is O(log n) where n is the size of the larger input map. This can be significantly faster than Map.merge or repeated Map.add.
assert (match Map.append ~lower_part ~upper_part with
| `Ok whole_map ->
whole_map
= Map.(of_alist_exn (List.append (to_alist lower_part) (to_alist upper_part)))
| `Overlapping_key_ranges -> true);
subrange t ~lower_bound ~upper_bound returns a map containing all the entries from t whose keys lie inside the interval indicated by ~lower_bound and ~upper_bound. If this interval is empty, an empty map is returned.
Runtime is O(m + log n) where n is the size of the input map, and m is the size of the output map. The O(m) term is due to the need to calculate the length of the output map.
val fold_range_inclusive :
('k, 'v, 'cmp) t ->
min:'k ->
max:'k ->
init:'a ->
f:(key:'k -> data:'v -> 'a -> 'a) ->
'afold_range_inclusive t ~min ~max ~init ~f folds f (with initial value ~init) over all keys (and their associated values) that are in the range [min, max] (inclusive).
val range_to_alist :
('k, 'v, 'cmp) t ->
min:'k ->
max:'k ->
('k * 'v) Base.List.trange_to_alist t ~min ~max returns an associative list of the elements whose keys lie in [min, max] (inclusive), with the smallest key being at the head of the list.
val closest_key :
('k, 'v, 'cmp) t ->
[ `Greater_or_equal_to | `Greater_than | `Less_or_equal_to | `Less_than ] ->
'k ->
('k * 'v) Base.Option.tclosest_key t dir k returns the (key, value) pair in t with key closest to k, which satisfies the given inequality bound.
For example, closest_key t `Less_than k would be the pair with the closest key to k where key < k.
to_sequence can be used to get the same results as closest_key. It is less efficient for individual lookups but more efficient for finding many elements starting at some value.
nth t n finds the (key, value) pair of rank n (i.e., such that there are exactly n keys strictly less than the found key), if one exists. O(log(length t) + n) time.
rank t k if k is in t, returns the number of keys strictly less than k in t, otherwise None.
val to_sequence :
?order:[ `Increasing_key | `Decreasing_key ] ->
?keys_greater_or_equal_to:'k ->
?keys_less_or_equal_to:'k ->
('k, 'v, 'cmp) t ->
('k * 'v) Sequence.tto_sequence ?order ?keys_greater_or_equal_to ?keys_less_or_equal_to t gives a sequence of key-value pairs between keys_less_or_equal_to and keys_greater_or_equal_to inclusive, presented in order. If keys_greater_or_equal_to > keys_less_or_equal_to, the sequence is empty. Cost is O(log n) up front and amortized O(1) to produce each element.
val binary_search :
('k, 'v, 'cmp) t ->
compare:(key:'k -> data:'v -> 'key -> Base.Int.t) ->
[ `Last_strictly_less_than
| `Last_less_than_or_equal_to
| `Last_equal_to
| `First_equal_to
| `First_greater_than_or_equal_to
| `First_strictly_greater_than ] ->
'key ->
('k * 'v) Base.Option.tbinary_search t ~compare which elt returns the (key, value) pair in t specified by compare and which, if one exists.
t must be sorted in increasing order according to compare, where compare and elt divide t into three (possibly empty) segments:
| < elt | = elt | > elt |
binary_search returns an element on the boundary of segments as specified by which. See the diagram below next to the which variants.
binary_search does not check that compare orders t, and behavior is unspecified if compare doesn't order t. Behavior is also unspecified if compare mutates t.
val binary_search_segmented :
('k, 'v, 'cmp) t ->
segment_of:(key:'k -> data:'v -> [ `Left | `Right ]) ->
[ `Last_on_left | `First_on_right ] ->
('k * 'v) Base.Option.tbinary_search_segmented t ~segment_of which takes a segment_of function that divides t into two (possibly empty) segments:
| segment_of elt = `Left | segment_of elt = `Right |
binary_search_segmented returns the (key, value) pair on the boundary of the segments as specified by which: `Last_on_left yields the last element of the left segment, while `First_on_right yields the first element of the right segment. It returns None if the segment is empty.
binary_search_segmented does not check that segment_of segments t as in the diagram, and behavior is unspecified if segment_of doesn't segment t. Behavior is also unspecified if segment_of mutates t.
val of_key_set :
('key, 'cmp) Base.Set.t ->
f:('key -> 'data) ->
('key, 'data, 'cmp) tConvert a set to a map. Runs in O(length t) time plus a call to f for each key to compute the associated data.
val key_set : ('key, _, 'cmp) t -> ('key, 'cmp) Base.Set.tConverts a map to a set of its keys. Runs in O(length t) time.
This shrinker and the other shrinkers for maps and trees produce a shrunk value by dropping a key-value pair, shrinking a key or shrinking a value. A shrunk key will override an existing key's value.
Which Map module should you use?
The map types and operations appear in three places:
- Map: polymorphic map operations
- Map.Poly: maps that use polymorphic comparison to order keys
- Key.Map: maps with a fixed key type that use
Key.compare to order keys
where Key is any module defining values that can be used as keys of a map, like Int, String, etc. To add this functionality to an arbitrary module, use the Comparable.Make functor.
You should use Map for functions that access existing maps, like find, mem, add, fold, iter, and to_alist. For functions that create maps, like empty, singleton, and of_alist, strive to use the corresponding Key.Map function, which will use the comparison function specifically for Key. As a last resort, if you don't have easy access to a comparison function for the keys in your map, use Map.Poly to create the map. This will use OCaml's built-in polymorphic comparison to compare keys, with all the usual performance and robustness problems that entails.
Interface design details
An instance of the map type is determined by the types of the map's keys and values, and the comparison function used to order the keys:
type ('key, 'value, 'cmp) Map.t
'cmp is a phantom type uniquely identifying the comparison function, as generated by Comparator.Make.
Map.Poly supports arbitrary key and value types, but enforces that the comparison function used to order the keys is polymorphic comparison. Key.Map has a fixed key type and comparison function, and supports arbitrary values.
type ('key, 'value) Map.Poly.t = ('key , 'value, Comparator.Poly.t ) Map.t
type 'value Key.Map.t = (Key.t, 'value, Key.comparator_witness) Map.t
The same map operations exist in Map, Map.Poly, and Key.Map, albeit with different types. For example:
val Map.length : (_, _, _) Map.t -> int
val Map.Poly.length : (_, _) Map.Poly.t -> int
val Key.Map.length : _ Key.Map.t -> int
Because Map.Poly.t and Key.Map.t are exposed as instances of the more general Map.t type, one can use Map.length on any map. The same is true for all of the functions that access an existing map, such as add, change, find, fold, iter, map, to_alist, etc.
Depending on the number of type variables N, the type of accessor (resp. creator) functions is defined in the module type AccessorsN (CreatorsN) in Map_intf. Also for creators, when the comparison function is not fixed, i.e., the 'cmp variable of Map.t is free, we need to pass a comparator to the function creating the map. The module type is called Creators3_with_comparator. There is also a module type Accessors3_with_comparator in addition to Accessors3 which used for trees since the comparator is not known.
module Poly : sig ... endinclude For_deriving with type ('a, 'b, 'c) t := ('a, 'b, 'c) t
val compare_m__t :
(module Compare_m) ->
('v -> 'v -> int) ->
('k, 'v, 'cmp) t ->
('k, 'v, 'cmp) t ->
intval equal_m__t :
(module Equal_m) ->
('v -> 'v -> bool) ->
('k, 'v, 'cmp) t ->
('k, 'v, 'cmp) t ->
boolmodule M (K : sig ... end) : sig ... endThe following *bin* functions support bin-io on base-style maps, e.g.:
The following functors may be used to define stable modules