Module Base__.Map

type ('key, +'value, 'cmp) t
module Or_duplicate = Base__.Map_intf.Or_duplicate
module Continue_or_stop = Base__.Map_intf.Continue_or_stop
module Finished_or_unfinished : sig ... end
type ('k, 'cmp) comparator = (module Base.Comparator.S with type comparator_witness = 'cmp and type t = 'k)
val invariants : (_, _, _) t -> bool

Test if the invariants of the internal AVL search tree hold.

val comparator_s : ('a, _, 'cmp) t -> ('a, 'cmp) comparator

Returns a first-class module that can be used to build other map/set/etc. with the same notion of comparison.

val comparator : ('a, _, 'cmp) t -> ('a, 'cmp) Base.Comparator.t
val empty : ('a, 'cmp) comparator -> ('a, 'b, 'cmp) t

The empty map.

val singleton : ('a, 'cmp) comparator -> 'a -> 'b -> ('a, 'b, 'cmp) t

A map with one (key, data) pair.

val of_alist : ('a, 'cmp) comparator -> ('a * 'b) list -> [ `Ok of ('a, 'b, 'cmp) t | `Duplicate_key of 'a ]

Creates a map from an association list with unique keys.

val of_alist_or_error : ('a, 'cmp) comparator -> ('a * 'b) list -> ('a, 'b, 'cmp) t Base.Or_error.t

Creates a map from an association list with unique keys, returning an error if duplicate 'a keys are found.

val of_alist_exn : ('a, 'cmp) comparator -> ('a * 'b) list -> ('a, 'b, 'cmp) t

Creates a map from an association list with unique keys, raising an exception if duplicate 'a keys are found.

val of_alist_multi : ('a, 'cmp) comparator -> ('a * 'b) list -> ('a, 'b list, 'cmp) t

Creates a map from an association list 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.

val of_alist_fold : ('a, 'cmp) comparator -> ('a * 'b) list -> init:'c -> f:('c -> 'b -> 'c) -> ('a, 'c, 'cmp) t

Combines an association list into a map, folding together bound values with common keys.

val of_alist_reduce : ('a, 'cmp) comparator -> ('a * 'b) list -> f:('b -> 'b -> 'b) -> ('a, 'b, 'cmp) t

Combines an association list into a map, reducing together bound values with common keys.

val of_iteri : ('a, 'cmp) comparator -> iteri:(f:(key:'a -> data:'b -> unit) -> unit) -> [ `Ok of ('a, 'b, 'cmp) t | `Duplicate_key of 'a ]

of_iteri ~iteri behaves like of_alist, except that instead of taking a concrete data structure, 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.

val of_sorted_array : ('a, 'cmp) comparator -> ('a * 'b) array -> ('a, 'b, 'cmp) t Base.Or_error.t

Creates a map from a sorted array of key-data pairs. The input array must be sorted (either in ascending or descending order), as given by the relevant comparator, and must not contain duplicate keys. If either of these conditions does not hold, an error is returned.

val of_sorted_array_unchecked : ('a, 'cmp) comparator -> ('a * 'b) array -> ('a, 'b, 'cmp) t

Like of_sorted_array except that it returns a map with broken invariants when an Error would have been returned.

val of_increasing_iterator_unchecked : ('a, 'cmp) comparator -> len:int -> f:(int -> 'a * 'b) -> ('a, 'b, 'cmp) t

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.

val of_increasing_sequence : ('k, 'cmp) comparator -> ('k * 'v) Base.Sequence.t -> ('k, 'v, 'cmp) t Base.Or_error.t

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) Base.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.

val of_sequence_or_error : ('a, 'cmp) comparator -> ('a * 'b) Base.Sequence.t -> ('a, 'b, 'cmp) t Base.Or_error.t

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.

val of_sequence_exn : ('a, 'cmp) comparator -> ('a * 'b) Base.Sequence.t -> ('a, 'b, 'cmp) t

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.

val of_sequence_multi : ('a, 'cmp) comparator -> ('a * 'b) Base.Sequence.t -> ('a, 'b list, 'cmp) t

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_exn c (Sequence.to_list seq) but does not allocate the intermediate list.

val of_sequence_fold : ('a, 'cmp) comparator -> ('a * 'b) Base.Sequence.t -> init:'c -> f:('c -> 'b -> 'c) -> ('a, 'c, 'cmp) t

Combines 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) Base.Sequence.t -> f:('b -> 'b -> 'b) -> ('a, 'b, 'cmp) t

Combines 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.

val is_empty : (_, _, _) t -> bool

Tests whether a map is empty.

val length : (_, _, _) t -> int

length map returns the number of elements in map. O(1), but Tree.length is O(n).

val set : ('k, 'v, 'cmp) t -> key:'k -> data:'v -> ('k, 'v, 'cmp) t

Returns a new map with the specified new binding; if the key was already bound, its previous binding disappears.

val add : ('k, 'v, 'cmp) t -> key:'k -> data:'v -> ('k, 'v, 'cmp) t Or_duplicate.t

add t ~key ~data adds a new entry to t mapping key to data and returns `Ok with the new map, or if key is already present in t, returns `Duplicate.

val add_exn : ('k, 'v, 'cmp) t -> key:'k -> data:'v -> ('k, 'v, 'cmp) t
val add_multi : ('k, 'v list, 'cmp) t -> key:'k -> data:'v -> ('k, 'v list, 'cmp) t

If key is not present then add a singleton list, otherwise, cons data onto the head of the existing list.

val remove_multi : ('k, 'v list, 'cmp) t -> 'k -> ('k, 'v list, 'cmp) t

If the key is present, then remove its head element; if the result is empty, remove the key.

val find_multi : ('k, 'v list, 'cmp) t -> 'k -> 'v list

Returns the value bound to the given key, or the empty list if there is none.

val change : ('k, 'v, 'cmp) t -> 'k -> f:('v option -> 'v option) -> ('k, 'v, 'cmp) t

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 option -> 'v) -> ('k, 'v, 'cmp) t

update t key ~f is change t key ~f:(fun o -> Some (f o)).

val find : ('k, 'v, 'cmp) t -> 'k -> 'v option

Returns Some value bound to the given key, or None if none exists.

val find_exn : ('k, 'v, 'cmp) t -> 'k -> 'v

Returns the value bound to the given key, raising Caml.Not_found or Not_found_s if none exists.

val remove : ('k, 'v, 'cmp) t -> 'k -> ('k, 'v, 'cmp) t

Returns a new map with any binding for the key in question removed.

val mem : ('k, _, 'cmp) t -> 'k -> bool

mem map key tests whether map contains a binding for key.

val iter_keys : ('k, _, _) t -> f:('k -> unit) -> unit
val iter : (_, 'v, _) t -> f:('v -> unit) -> unit
val iteri : ('k, 'v, _) t -> f:(key:'k -> data:'v -> unit) -> unit
val iteri_until : ('k, 'v, _) t -> f:(key:'k -> data:'v -> Continue_or_stop.t) -> Finished_or_unfinished.t

Iterates until the first time 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 ] -> unit) -> unit

Iterates 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) t

Returns a new map with bound values replaced by f applied to the bound values.

val mapi : ('k, 'v1, 'cmp) t -> f:(key:'k -> data:'v1 -> 'v2) -> ('k, 'v2, 'cmp) t

Like map, but the passed function takes both key and data as arguments.

val fold : ('k, 'v, _) t -> init:'a -> f:(key:'k -> data:'v -> 'a -> 'a) -> 'a

Folds over keys and data in the map in increasing order of key.

val fold_right : ('k, 'v, _) t -> init:'a -> f:(key:'k -> data:'v -> 'a -> 'a) -> 'a

Folds over keys and data in the 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) -> 'a

Folds over two maps side by side, like iter2.

val filter_keys : ('k, 'v, 'cmp) t -> f:('k -> bool) -> ('k, 'v, 'cmp) t

filter, filteri, filter_keys, filter_map, and filter_mapi run in O(n * lg n) time; they simply accumulate each key & data pair retained by f into a new map using add.

val filter : ('k, 'v, 'cmp) t -> f:('v -> bool) -> ('k, 'v, 'cmp) t
val filteri : ('k, 'v, 'cmp) t -> f:(key:'k -> data:'v -> bool) -> ('k, 'v, 'cmp) t
val filter_map : ('k, 'v1, 'cmp) t -> f:('v1 -> 'v2 option) -> ('k, 'v2, 'cmp) t

Returns a new map with bound values filtered by f applied to the bound values.

val filter_mapi : ('k, 'v1, 'cmp) t -> f:(key:'k -> data:'v1 -> 'v2 option) -> ('k, 'v2, 'cmp) t

Like filter_map, but the passed 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) t

partition_mapi t ~f returns two new ts, with each key in t appearing in exactly one of the resulting 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) t

partition_map t ~f = partition_mapi t ~f:(fun ~key:_ ~data -> f data)

val partitioni_tf : ('k, 'v, 'cmp) t -> f:(key:'k -> data:'v -> bool) -> ('k, 'v, 'cmp) t * ('k, 'v, 'cmp) t
partitioni_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 -> bool) -> ('k, 'v, 'cmp) t * ('k, 'v, 'cmp) t

partition_tf t ~f = partitioni_tf t ~f:(fun ~key:_ ~data -> f data)

val compare_direct : ('v -> 'v -> int) -> ('k, 'v, 'cmp) t -> ('k, 'v, 'cmp) t -> int

Returns a total ordering between maps. The first argument is a total ordering used to compare data associated with equal keys in the two maps.

val hash_fold_direct : 'k Base.Hash.folder -> 'v Base.Hash.folder -> ('k, 'v, 'cmp) t Base.Hash.folder

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.

val equal : ('v -> 'v -> bool) -> ('k, 'v, 'cmp) t -> ('k, 'v, 'cmp) t -> bool

equal cmp m1 m2 tests whether the maps m1 and m2 are equal, that is, contain the same keys and associate each key with the same value. cmp is the equality predicate used to compare the values associated with the keys.

val keys : ('k, _, _) t -> 'k list

Returns a list of the keys in the given map.

val data : (_, 'v, _) t -> 'v list

Returns a list of the data in the given map.

val to_alist : ?⁠key_order:[ `Increasing | `Decreasing ] -> ('k, 'v, _) t -> ('k * 'v) list

Creates an association list from the given map.

val validate : name:('k -> string) -> 'v Base.Validate.check -> ('k, 'v, _) t Base.Validate.check

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 option) -> ('k, 'v3, 'cmp) t

Merges two maps. The runtime is O(length(t1) + length(t2)). 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) t

A 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 combined into a single value 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.

module Symmetric_diff_element : sig ... end
val symmetric_diff : ('k, 'v, 'cmp) t -> ('k, 'v, 'cmp) t -> data_equal:('v -> 'v -> bool) -> ('k, 'v) Symmetric_diff_element.t Base.Sequence.t

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.

It is assumed that data_equal is at least as equating as physical equality: that phys_equal x y implies data_equal x y. Otherwise, symmetric_diff may behave in unexpected ways. For example, with ~data_equal:(fun _ _ -> false) it is NOT necessarily the case the resulting change sequence will contain an element (k, `Unequal _) for every key k shared by both maps.

Warning: Float equality violates this property! phys_equal Float.nan Float.nan is true, but Float.(=) Float.nan Float.nan is false.

val fold_symmetric_diff : ('k, 'v, 'cmp) t -> ('k, 'v, 'cmp) t -> data_equal:('v -> 'v -> bool) -> init:'a -> f:('a -> ('k, 'v) Symmetric_diff_element.t -> 'a) -> 'a

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.

val min_elt : ('k, 'v, _) t -> ('k * 'v) option

min_elt map returns Some (key, data) pair corresponding to the minimum key in map, or None if empty.

val min_elt_exn : ('k, 'v, _) t -> 'k * 'v
val max_elt : ('k, 'v, _) t -> ('k * 'v) option

max_elt map returns Some (key, data) pair corresponding to the maximum key in map, or None if map is empty.

val max_elt_exn : ('k, 'v, _) t -> 'k * 'v
val for_all : ('k, 'v, _) t -> f:('v -> bool) -> bool
val for_alli : ('k, 'v, _) t -> f:(key:'k -> data:'v -> bool) -> bool
val exists : ('k, 'v, _) t -> f:('v -> bool) -> bool
val existsi : ('k, 'v, _) t -> f:(key:'k -> data:'v -> bool) -> bool
val count : ('k, 'v, _) t -> f:('v -> bool) -> int
val counti : ('k, 'v, _) t -> f:(key:'k -> data:'v -> bool) -> int
val split : ('k, 'v, 'cmp) t -> 'k -> ('k, 'v, 'cmp) t * ('k * 'v) option * ('k, 'v, 'cmp) t

split 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 ->
    Map.to_alist whole_map
    = List.append (to_alist lower_part) (to_alist upper_part)
  | `Overlapping_key_ranges -> true);
val subrange : ('k, 'v, 'cmp) t -> lower_bound:'k Base.Maybe_bound.t -> upper_bound:'k Base.Maybe_bound.t -> ('k, 'v, 'cmp) t

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) -> 'a

fold_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) list

range_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) option

closest_key t dir k returns the (key, value) pair in t with key closest to k that 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.

val nth : ('k, 'v, _) t -> int -> ('k * 'v) option

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.

val nth_exn : ('k, 'v, _) t -> int -> 'k * 'v
val rank : ('k, 'v, 'cmp) t -> 'k -> int option

rank t k If k is in t, returns the number of keys strictly less than k in t, and None otherwise.

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) Base.Sequence.t

to_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.

binary_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) option

binary_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.

module M : functor (K : sig ... end) -> sig ... end

M is meant to be used in combination with OCaml applicative functor types:

include Base__.Map_intf.For_deriving with type ('key, 'value, 'cmp) t := ('key, 'value, 'cmp) t
type ('a, 'b, 'c) t
module type Sexp_of_m = sig ... end
module type M_of_sexp = sig ... end
module type Compare_m = sig ... end
module type Equal_m = sig ... end
val sexp_of_m__t : (module Sexp_of_m with type t = 'k) -> ('v -> Base.Sexp.t) -> ('k, 'v, 'cmp) t -> Base.Sexp.t
val m__t_of_sexp : (module M_of_sexp with type comparator_witness = 'cmp and type t = 'k) -> (Base.Sexp.t -> 'v) -> Base.Sexp.t -> ('k, 'v, 'cmp) t
val compare_m__t : (module Compare_m) -> ('v -> 'v -> int) -> ('k, 'v, 'cmp) t -> ('k, 'v, 'cmp) t -> int
val equal_m__t : (module Equal_m) -> ('v -> 'v -> bool) -> ('k, 'v, 'cmp) t -> ('k, 'v, 'cmp) t -> bool
val hash_fold_m__t : (module Hash_fold_m with type t = 'k) -> (Base.Hash.state -> 'v -> Base.Hash.state) -> Base.Hash.state -> ('k, 'v, _) t -> Base.Hash.state
module Poly : Base__.Map_intf.S_poly with type ('key, +'value) t = ('key, 'value, Base.Comparator.Poly.comparator_witness) t

A polymorphic Map.

module Using_comparator : sig ... end

Using_comparator is a similar interface as the toplevel of Map, except the functions take a ~comparator:('k, 'cmp) Comparator.t, whereas the functions at the toplevel of Map take a ('k, 'cmp) comparator.

Modules and module types for extending Map

For use in extensions of Base, like Core_kernel.

module With_comparator = Base__.Map_intf.With_comparator
module With_first_class_module = Base__.Map_intf.With_first_class_module
module Without_comparator = Base__.Map_intf.Without_comparator