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(*                                                                        *)
(*                                 OCaml                                  *)
(*                                                                        *)
(*             Xavier Leroy, projet Cristal, INRIA Rocquencourt           *)
(*                                                                        *)
(*   Copyright 1996 Institut National de Recherche en Informatique et     *)
(*     en Automatique.                                                    *)
(*                                                                        *)
(*   All rights reserved.  This file is distributed under the terms of    *)
(*   the GNU Lesser General Public License version 2.1, with the          *)
(*   special exception on linking described in the file LICENSE.          *)
(*                                                                        *)
(**************************************************************************)

(** Association tables over ordered types.

    This module implements applicative association tables, also known as
    finite maps or dictionaries, given a total ordering function
    over the keys.
    All operations over maps are purely applicative (no side-effects).
    The implementation uses balanced binary trees, and therefore searching
    and insertion take time logarithmic in the size of the map.

    For instance:
    {[
      module IntPairs =
      struct
        type t = int * int
        let compare (x0,y0) (x1,y1) =
          match Pervasives.compare x0 x1 with
            0 -> Pervasives.compare y0 y1
          | c -> c
      end

      module PairsMap = Map.Make(IntPairs)

      let m = PairsMap.(empty |> add (0,1) "hello" |> add (1,0) "world")
    ]}

    This creates a new module [PairsMap], with a new type ['a PairsMap.t]
    of maps from [int * int] to ['a]. In this example, [m] contains [string]
    values so its type is [string PairsMap.t].
*)

module type OrderedType =
sig
  type t
  (** The type of the map keys. *)

  val compare : t -> t -> int
  (** A total ordering function over the keys.
      This is a two-argument function [f] such that
      [f e1 e2] is zero if the keys [e1] and [e2] are equal,
      [f e1 e2] is strictly negative if [e1] is smaller than [e2],
      and [f e1 e2] is strictly positive if [e1] is greater than [e2].
      Example: a suitable ordering function is the generic structural
      comparison function {!Pervasives.compare}. *)
end
(** Input signature of the functor {!Map.Make}. *)

module type S =
sig
  type key
  (** The type of the map keys. *)

  type (+'a) t
  (** The type of maps from type [key] to type ['a]. *)

  val empty: 'a t
  (** The empty map. *)

  val is_empty: 'a t -> bool
  (** Test whether a map is empty or not. *)

  val mem: key -> 'a t -> bool
  (** [mem x m] returns [true] if [m] contains a binding for [x],
      and [false] otherwise. *)

  val add: key -> 'a -> 'a t -> 'a t
  (** [add x y m] returns a map containing the same bindings as
      [m], plus a binding of [x] to [y]. If [x] was already bound
      in [m] to a value that is physically equal to [y],
      [m] is returned unchanged (the result of the function is
      then physically equal to [m]). Otherwise, the previous binding
      of [x] in [m] disappears.
      @before 4.03 Physical equality was not ensured. *)

  val singleton: key -> 'a -> 'a t
  (** [singleton x y] returns the one-element map that contains a binding [y]
      for [x].
      @since 3.12.0
  *)

  val remove: key -> 'a t -> 'a t
  (** [remove x m] returns a map containing the same bindings as
      [m], except for [x] which is unbound in the returned map.
      If [x] was not in [m], [m] is returned unchanged
      (the result of the function is then physically equal to [m]).
      @before 4.03 Physical equality was not ensured. *)

  val merge:
    (key -> 'a option -> 'b option -> 'c option) -> 'a t -> 'b t -> 'c t
  (** [merge f m1 m2] computes a map whose keys is a subset of keys of [m1]
      and of [m2]. The presence of each such binding, and the corresponding
      value, is determined with the function [f].
      @since 3.12.0
  *)

  val union: (key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t
  (** [union f m1 m2] computes a map whose keys is the union of keys
      of [m1] and of [m2].  When the same binding is defined in both
      arguments, the function [f] is used to combine them.
      @since 4.03.0
  *)

  val compare: ('a -> 'a -> int) -> 'a t -> 'a 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: ('a -> 'a -> bool) -> 'a t -> 'a 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 iter: (key -> 'a -> unit) -> 'a t -> unit
  (** [iter f m] applies [f] to all bindings in map [m].
      [f] receives the key as first argument, and the associated value
      as second argument.  The bindings are passed to [f] in increasing
      order with respect to the ordering over the type of the keys. *)

  val fold: (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
  (** [fold f m a] computes [(f kN dN ... (f k1 d1 a)...)],
      where [k1 ... kN] are the keys of all bindings in [m]
      (in increasing order), and [d1 ... dN] are the associated data. *)

  val for_all: (key -> 'a -> bool) -> 'a t -> bool
  (** [for_all p m] checks if all the bindings of the map
      satisfy the predicate [p].
      @since 3.12.0
  *)

  val exists: (key -> 'a -> bool) -> 'a t -> bool
  (** [exists p m] checks if at least one binding of the map
      satisfy the predicate [p].
      @since 3.12.0
  *)

  val filter: (key -> 'a -> bool) -> 'a t -> 'a t
  (** [filter p m] returns the map with all the bindings in [m]
      that satisfy predicate [p]. If [p] satisfies every binding in [m],
      [m] is returned unchanged (the result of the function is then
      physically equal to [m])
      @since 3.12.0
      @before 4.03 Physical equality was not ensured.
  *)

  val partition: (key -> 'a -> bool) -> 'a t -> 'a t * 'a t
  (** [partition p m] returns a pair of maps [(m1, m2)], where
      [m1] contains all the bindings of [s] that satisfy the
      predicate [p], and [m2] is the map with all the bindings of
      [s] that do not satisfy [p].
      @since 3.12.0
  *)

  val cardinal: 'a t -> int
  (** Return the number of bindings of a map.
      @since 3.12.0
  *)

  val bindings: 'a t -> (key * 'a) list
  (** Return the list of all bindings of the given map.
      The returned list is sorted in increasing order with respect
      to the ordering [Ord.compare], where [Ord] is the argument
      given to {!Map.Make}.
      @since 3.12.0
  *)

  val min_binding: 'a t -> (key * 'a)
  (** Return the smallest binding of the given map
      (with respect to the [Ord.compare] ordering), or raise
      [Not_found] if the map is empty.
      @since 3.12.0
  *)

  val max_binding: 'a t -> (key * 'a)
  (** Same as {!Map.S.min_binding}, but returns the largest binding
      of the given map.
      @since 3.12.0
  *)

  val choose: 'a t -> (key * 'a)
  (** Return one binding of the given map, or raise [Not_found] if
      the map is empty. Which binding is chosen is unspecified,
      but equal bindings will be chosen for equal maps.
      @since 3.12.0
  *)

  val split: key -> 'a t -> 'a t * 'a option * 'a t
  (** [split x m] returns a triple [(l, data, r)], where
        [l] is the map with all the bindings of [m] whose key
      is strictly less than [x];
        [r] is the map with all the bindings of [m] whose key
      is strictly greater than [x];
        [data] is [None] if [m] contains no binding for [x],
        or [Some v] if [m] binds [v] to [x].
      @since 3.12.0
  *)

  val find: key -> 'a t -> 'a
  (** [find x m] returns the current binding of [x] in [m],
      or raises [Not_found] if no such binding exists. *)

  val map: ('a -> 'b) -> 'a t -> 'b t
  (** [map f m] returns a map with same domain as [m], where the
      associated value [a] of all bindings of [m] has been
      replaced by the result of the application of [f] to [a].
      The bindings are passed to [f] in increasing order
      with respect to the ordering over the type of the keys. *)

  val mapi: (key -> 'a -> 'b) -> 'a t -> 'b t
  (** Same as {!Map.S.map}, but the function receives as arguments both the
      key and the associated value for each binding of the map. *)


end
(** Output signature of the functor {!Map.Make}. *)

module Make (Ord : OrderedType) : S with type key = Ord.t
(** Functor building an implementation of the map structure
    given a totally ordered type. *)