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Module Map

module Map: sig .. end
This module defines the Map module for Core.Std. We use "core_map" as the file name rather than "map" to avoid conflicts with OCaml's standard map module. In this documentation, we use Map to mean this module, not the OCaml standard one.

Map is a functional datastructure (balanced binary tree) implementing finite maps over a totally-ordered domain, called a "key". 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, ...

One 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, one should strive to use the corresponding Key.Map function, which will use the comparison function specifically for Key. As a last resort, if one does not have easy access to a comparison function for the keys in one's map, use Map.Poly to create the map. This will use OCaml's built-in polymorphic comparison to compare keys, which has all the usual performance and robustness problems that entails.

Parallel to the three kinds of map modules, 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, unlike a map. The main disadvantages of using trees are needing to be more explicit about the comparator, and the possibility of accidental use of polymorphic equality on a tree (for which maps dynamically detect failure due to the presence of a closure in the data structure).

For a detailed explanation of the interface design, read on.

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   ) 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 are defined in the module type AccessorsN (resp. CreatorsN) in Core_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 Tree: sig .. end
type ('key, +'value, 'cmp) t 
val invariants : ('a, 'b, 'c) t -> bool
Test if invariants of internal AVL search tree hold.
val comparator : ('a, 'b, 'cmp) t -> ('a, 'cmp) Comparator.t
val empty : comparator:('a, 'cmp) Comparator.t -> ('a, 'b, 'cmp) t
the empty map
val singleton : comparator:('a, 'cmp) Comparator.t -> 'a -> 'b -> ('a, 'b, 'cmp) t
map with one key, data pair
val of_alist : comparator:('a, 'cmp) Comparator.t ->
       ('a * 'b) list -> [ `Duplicate_key of 'a | `Ok of ('a, 'b, 'cmp) t ]
creates map from association list with unique keys
val of_alist_exn : comparator:('a, 'cmp) Comparator.t ->
       ('a * 'b) list -> ('a, 'b, 'cmp) t
creates map from association list with unique keys. Raises an exception if duplicate 'a keys are found.
val of_alist_multi : comparator:('a, 'cmp) Comparator.t ->
       ('a * 'b) list -> ('a, 'b list, 'cmp) t
creates map from association list with possibly repeated keys.
val of_alist_fold : comparator:('a, 'cmp) Comparator.t ->
       ('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 to_tree : ('k, 'v, 'cmp) t -> ('k, 'v, 'cmp) Tree.t
val of_tree : comparator:('k, 'cmp) Comparator.t ->
       ('k, 'v, 'cmp) Tree.t -> ('k, 'v, 'cmp) t
val of_sorted_array : comparator:('a, 'cmp) Comparator.t ->
       ('a * 'b) array -> ('a, 'b, 'cmp) t Or_error.t
creates map from 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 do not hold, an error is returned.
val of_sorted_array_unchecked : comparator:('a, 'cmp) Comparator.t ->
       ('a * 'b) array -> ('a, 'b, 'cmp) t
Like of_sorted_array except behavior is undefined when an Error would have been returned.
val is_empty : ('a, 'b, 'c) t -> bool
Test whether a map is empty or not.
val length : ('a, 'b, 'c) t -> int
length map
Returns number of elements in map.
val add : ('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_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 on the head of the existing list.
val change : ('k, 'v, 'cmp) t ->
       'k -> ('v option -> 'v option) -> ('k, 'v, 'cmp) t
change map key f updates the given map by changing the value stored under key according to f. Thus, for example, one might write: 

change m k (function None -> Some 0 | Some x -> Some (x + 1))

to produce a new map where the integer stored under key k is incremented by one (treating an unknown key as zero).

val find : ('k, 'v, 'cmp) t -> 'k -> 'v option
returns the value bound to the given key, raising Not_found if none such exists
val find_exn : ('k, 'v, 'cmp) t -> 'k -> 'v
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, 'a, 'cmp) t -> 'k -> bool
mem map key tests whether map contains a binding for key
val iter : ('k, 'v, 'a) t -> f:(key:'k -> data:'v -> unit) -> unit
iterator for map
val iter2 : ('k, 'v1, 'cmp) t ->
       ('k, 'v2, 'cmp) t ->
       f:(key:'k ->
          data:[ `Both of 'v1 * 'v2 | `Left of 'v1 | `Right of 'v2 ] -> unit) ->
       unit
Iterate two maps side by side. 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 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 function takes both key and data as arguments
val fold : ('k, 'v, 'b) t -> init:'a -> f:(key:'k -> data:'v -> 'a -> 'a) -> 'a
folds over keys and data in map in increasing order of key.
val fold_right : ('k, 'v, 'b) t -> init:'a -> f:(key:'k -> data:'v -> 'a -> 'a) -> 'a
folds over keys and data in map in decreasing order of key.
val filter : ('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 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 function takes both key and data as arguments
val compare_direct : ('v -> 'v -> int) ->
       ('k, 'v, 'cmp) t -> ('k, 'v, 'cmp) t -> int
Total ordering between maps. The first argument is a total ordering used to compare data associated with equal keys in the two maps.
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 equal keys and associate them with equal data. cmp is the equality predicate used to compare the data associated with the keys.
val keys : ('k, 'a, 'b) t -> 'k list
returns list of keys in map
val data : ('a, 'v, 'b) t -> 'v list
returns list of data in map
val to_alist : ('k, 'v, 'a) t -> ('k * 'v) list
creates association list from map. No guarantee about order.
val validate : name:('k -> string) ->
       'v Validate.check -> ('k, 'v, 'a) t Validate.check

Additional operations on maps

val merge : ('k, 'v1, 'cmp) t ->
       ('k, 'v2, 'cmp) t ->
       f:(key:'k ->
          [ `Both of 'v1 * 'v2 | `Left of 'v1 | `Right of 'v2 ] -> 'v3 option) ->
       ('k, 'v3, 'cmp) t
merges two maps
val symmetric_diff : ('k, 'v, 'cmp) t ->
       ('k, 'v, 'cmp) t ->
       data_equal:('v -> 'v -> bool) ->
       ('k * [ `Left of 'v | `Right of 'v | `Unequal of 'v * 'v ]) list
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.
val min_elt : ('k, 'v, 'a) t -> ('k * 'v) option
min_elt map
Returns Some (key, data) pair corresponding to the minimum key in map, None if empty.
val min_elt_exn : ('k, 'v, 'a) t -> 'k * 'v
val max_elt : ('k, 'v, 'a) t -> ('k * 'v) option
max_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, 'a) t -> 'k * 'v
val for_all : ('k, 'v, 'a) t -> f:('v -> bool) -> bool
same semantics as similar functions in List
val exists : ('k, 'v, 'a) t -> f:('v -> bool) -> bool
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 prev_key : ('k, 'v, 'cmp) t -> 'k -> ('k * 'v) option
prev_key t k returns the largest (key, value) pair in t with key less than k
val next_key : ('k, 'v, 'cmp) t -> 'k -> ('k * 'v) option
next_key t k returns the smallest (key, value) pair in t with key greater than k
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, otherwise None
module Poly: sig .. end 
  with type ('a, 'b, 'c) map = ('a, 'b, 'c) t
module type Key = Core_map_intf.Key
module type Key_binable = Core_map_intf.Key_binable
module type S = S 
  with type ('a, 'b, 'c) map  := ('a, 'b, 'c) t 
  with type ('a, 'b, 'c) tree := ('a, 'b, 'c) Tree.t
module type S_binable = S_binable 
  with type ('a, 'b, 'c) map  := ('a, 'b, 'c) t 
  with type ('a, 'b, 'c) tree := ('a, 'b, 'c) Tree.t
module Make: 
functor (Key : Key) -> S  with type Key.t = Key.t
module Make_using_comparator: 
functor (Key : Comparator.S) -> S 
    with type Key.t          = Key.t 
    with type Key.comparator = Key.comparator
module Make_binable: 
functor (Key : Key_binable) -> S_binable  with type Key.t = Key.t
module Make_binable_using_comparator: 
functor (Key : Comparator.S_binable) -> S_binable 
    with type Key.t          = Key.t 
    with type Key.comparator = Key.comparator