147 lines
5.4 KiB
OCaml
147 lines
5.4 KiB
OCaml
(***********************************************************************)
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(* *)
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(* Objective Caml *)
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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. All rights reserved. This file is distributed *)
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(* under the terms of the GNU Library General Public License, with *)
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(* the special exception on linking described in file ../LICENSE. *)
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(* *)
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(***********************************************************************)
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(* $Id$ *)
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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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*)
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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
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the generic structural comparison function {!Pervasives.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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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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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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(** Set difference. *)
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val diff: t -> t -> t
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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 order in which the elements of [s] are presented to [f]
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is unspecified. *)
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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].
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The order in which elements of [s] are presented to [f] is
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unspecified. *)
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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]. *)
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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 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 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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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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