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307 lines
11 KiB
307 lines
11 KiB
4 years ago
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(**************************************************************************)
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(* *)
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(* OCaml *)
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(* *)
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(* Xavier Leroy, projet Cristal, INRIA Rocquencourt *)
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(* *)
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(* Copyright 1996 Institut National de Recherche en Informatique et *)
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(* en Automatique. *)
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(* *)
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(* All rights reserved. This file is distributed under the terms of *)
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(* the GNU Lesser General Public License version 2.1, with the *)
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(* special exception on linking described in the file LICENSE. *)
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(* *)
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(**************************************************************************)
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(** Sets over ordered types.
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This module implements the set data structure, given a total ordering
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function over the set elements. All operations over sets
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are purely applicative (no side-effects).
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The implementation uses balanced binary trees, and is therefore
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reasonably efficient: insertion and membership take time
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logarithmic in the size of the set, for instance.
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The {!Make} functor constructs implementations for any type, given a
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[compare] function.
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For instance:
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{[
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module IntPairs =
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struct
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type t = int * int
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let compare (x0,y0) (x1,y1) =
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match Stdlib.compare x0 x1 with
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0 -> Stdlib.compare y0 y1
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end
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module PairsSet = Set.Make(IntPairs)
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let m = PairsSet.(empty |> add (2,3) |> add (5,7) |> add (11,13))
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]}
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This creates a new module [PairsSet], with a new type [PairsSet.t]
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of sets of [int * int].
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*)
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module type OrderedType =
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sig
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type t
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(** The type of the set elements. *)
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val compare : t -> t -> int
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(** A total ordering function over the set elements.
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This is a two-argument function [f] such that
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[f e1 e2] is zero if the elements [e1] and [e2] are equal,
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[f e1 e2] is strictly negative if [e1] is smaller than [e2],
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and [f e1 e2] is strictly positive if [e1] is greater than [e2].
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Example: a suitable ordering function is the generic structural
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comparison function {!Stdlib.compare}. *)
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end
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(** Input signature of the functor {!Set.Make}. *)
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module type S =
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sig
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type elt
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(** The type of the set elements. *)
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type t
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(** The type of sets. *)
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val empty: t
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(** The empty set. *)
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val is_empty: t -> bool
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(** Test whether a set is empty or not. *)
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val mem: elt -> t -> bool
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(** [mem x s] tests whether [x] belongs to the set [s]. *)
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val add: elt -> t -> t
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(** [add x s] returns a set containing all elements of [s],
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plus [x]. If [x] was already in [s], [s] is returned unchanged
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(the result of the function is then physically equal to [s]).
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@before 4.03 Physical equality was not ensured. *)
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val singleton: elt -> t
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(** [singleton x] returns the one-element set containing only [x]. *)
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val remove: elt -> t -> t
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(** [remove x s] returns a set containing all elements of [s],
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except [x]. If [x] was not in [s], [s] is returned unchanged
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(the result of the function is then physically equal to [s]).
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@before 4.03 Physical equality was not ensured. *)
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val union: t -> t -> t
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(** Set union. *)
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val inter: t -> t -> t
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(** Set intersection. *)
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val disjoint: t -> t -> bool
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(** Test if two sets are disjoint.
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@since 4.08.0 *)
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val diff: t -> t -> t
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(** Set difference: [diff s1 s2] contains the elements of [s1]
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that are not in [s2]. *)
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val compare: t -> t -> int
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(** Total ordering between sets. Can be used as the ordering function
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for doing sets of sets. *)
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val equal: t -> t -> bool
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(** [equal s1 s2] tests whether the sets [s1] and [s2] are
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equal, that is, contain equal elements. *)
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val subset: t -> t -> bool
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(** [subset s1 s2] tests whether the set [s1] is a subset of
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the set [s2]. *)
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val iter: (elt -> unit) -> t -> unit
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(** [iter f s] applies [f] in turn to all elements of [s].
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The elements of [s] are presented to [f] in increasing order
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with respect to the ordering over the type of the elements. *)
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val map: (elt -> elt) -> t -> t
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(** [map f s] is the set whose elements are [f a0],[f a1]... [f
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aN], where [a0],[a1]...[aN] are the elements of [s].
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The elements are passed to [f] in increasing order
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with respect to the ordering over the type of the elements.
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If no element of [s] is changed by [f], [s] is returned
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unchanged. (If each output of [f] is physically equal to its
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input, the returned set is physically equal to [s].)
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@since 4.04.0 *)
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val fold: (elt -> 'a -> 'a) -> t -> 'a -> 'a
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(** [fold f s a] computes [(f xN ... (f x2 (f x1 a))...)],
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where [x1 ... xN] are the elements of [s], in increasing order. *)
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val for_all: (elt -> bool) -> t -> bool
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(** [for_all p s] checks if all elements of the set
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satisfy the predicate [p]. *)
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val exists: (elt -> bool) -> t -> bool
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(** [exists p s] checks if at least one element of
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the set satisfies the predicate [p]. *)
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val filter: (elt -> bool) -> t -> t
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(** [filter p s] returns the set of all elements in [s]
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that satisfy predicate [p]. If [p] satisfies every element in [s],
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[s] is returned unchanged (the result of the function is then
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physically equal to [s]).
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@before 4.03 Physical equality was not ensured.*)
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val filter_map: (elt -> elt option) -> t -> t
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(** [filter_map f s] returns the set of all [v] such that
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[f x = Some v] for some element [x] of [s].
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For example,
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{[filter_map (fun n -> if n mod 2 = 0 then Some (n / 2) else None) s]}
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is the set of halves of the even elements of [s].
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If no element of [s] is changed or dropped by [f] (if
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[f x = Some x] for each element [x]), then
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[s] is returned unchanged: the result of the function
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is then physically equal to [s].
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@since 4.11.0
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*)
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val partition: (elt -> bool) -> t -> t * t
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(** [partition p s] returns a pair of sets [(s1, s2)], where
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[s1] is the set of all the elements of [s] that satisfy the
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predicate [p], and [s2] is the set of all the elements of
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[s] that do not satisfy [p]. *)
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val cardinal: t -> int
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(** Return the number of elements of a set. *)
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val elements: t -> elt list
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(** Return the list of all elements of the given set.
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The returned list is sorted in increasing order with respect
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to the ordering [Ord.compare], where [Ord] is the argument
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given to {!Set.Make}. *)
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val min_elt: t -> elt
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(** Return the smallest element of the given set
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(with respect to the [Ord.compare] ordering), or raise
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[Not_found] if the set is empty. *)
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val min_elt_opt: t -> elt option
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(** Return the smallest element of the given set
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(with respect to the [Ord.compare] ordering), or [None]
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if the set is empty.
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@since 4.05
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*)
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val max_elt: t -> elt
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(** Same as {!Set.S.min_elt}, but returns the largest element of the
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given set. *)
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val max_elt_opt: t -> elt option
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(** Same as {!Set.S.min_elt_opt}, but returns the largest element of the
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given set.
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@since 4.05
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*)
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val choose: t -> elt
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(** Return one element of the given set, or raise [Not_found] if
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the set is empty. Which element is chosen is unspecified,
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but equal elements will be chosen for equal sets. *)
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val choose_opt: t -> elt option
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(** Return one element of the given set, or [None] if
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the set is empty. Which element is chosen is unspecified,
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but equal elements will be chosen for equal sets.
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@since 4.05
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*)
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val split: elt -> t -> t * bool * t
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(** [split x s] returns a triple [(l, present, r)], where
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[l] is the set of elements of [s] that are
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strictly less than [x];
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[r] is the set of elements of [s] that are
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strictly greater than [x];
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[present] is [false] if [s] contains no element equal to [x],
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or [true] if [s] contains an element equal to [x]. *)
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val find: elt -> t -> elt
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(** [find x s] returns the element of [s] equal to [x] (according
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to [Ord.compare]), or raise [Not_found] if no such element
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exists.
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@since 4.01.0 *)
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val find_opt: elt -> t -> elt option
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(** [find_opt x s] returns the element of [s] equal to [x] (according
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to [Ord.compare]), or [None] if no such element
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exists.
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@since 4.05 *)
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val find_first: (elt -> bool) -> t -> elt
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(** [find_first f s], where [f] is a monotonically increasing function,
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returns the lowest element [e] of [s] such that [f e],
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or raises [Not_found] if no such element exists.
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For example, [find_first (fun e -> Ord.compare e x >= 0) s] will return
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the first element [e] of [s] where [Ord.compare e x >= 0] (intuitively:
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[e >= x]), or raise [Not_found] if [x] is greater than any element of
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[s].
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@since 4.05
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*)
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val find_first_opt: (elt -> bool) -> t -> elt option
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(** [find_first_opt f s], where [f] is a monotonically increasing function,
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returns an option containing the lowest element [e] of [s] such that
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[f e], or [None] if no such element exists.
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@since 4.05
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*)
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val find_last: (elt -> bool) -> t -> elt
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(** [find_last f s], where [f] is a monotonically decreasing function,
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returns the highest element [e] of [s] such that [f e],
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or raises [Not_found] if no such element exists.
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@since 4.05
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*)
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val find_last_opt: (elt -> bool) -> t -> elt option
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(** [find_last_opt f s], where [f] is a monotonically decreasing function,
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returns an option containing the highest element [e] of [s] such that
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[f e], or [None] if no such element exists.
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@since 4.05
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*)
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val of_list: elt list -> t
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(** [of_list l] creates a set from a list of elements.
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This is usually more efficient than folding [add] over the list,
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except perhaps for lists with many duplicated elements.
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@since 4.02.0 *)
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(** {1 Iterators} *)
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val to_seq_from : elt -> t -> elt Seq.t
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(** [to_seq_from x s] iterates on a subset of the elements of [s]
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in ascending order, from [x] or above.
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@since 4.07 *)
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val to_seq : t -> elt Seq.t
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(** Iterate on the whole set, in ascending order
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@since 4.07 *)
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val add_seq : elt Seq.t -> t -> t
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(** Add the given elements to the set, in order.
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@since 4.07 *)
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val of_seq : elt Seq.t -> t
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(** Build a set from the given bindings
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@since 4.07 *)
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end
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(** Output signature of the functor {!Set.Make}. *)
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module Make (Ord : OrderedType) : S with type elt = Ord.t
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(** Functor building an implementation of the set structure
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given a totally ordered type. *)
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