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batSet.mli
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batSet.mli
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(*
* ExtSet - Extended operations on sets
* Copyright (C) 1996 Xavier Leroy
* 2009 David Rajchenbach-Teller, LIFO, Universite d'Orleans
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version,
* with the special exception on linking described in file LICENSE.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*)
(** Sets over ordered types.
This module implements the set data structure, given a total
ordering function over the set elements. All operations over sets
are purely applicative (no side-effects). The implementation uses
balanced binary trees, and is therefore reasonably efficient:
insertion and membership take time logarithmic in the size of the
set, for instance.
{b Note} OCaml, Batteries Included, provides two implementations
of sets: polymorphic sets and functorized sets. Functorized sets
(see {!S} and {!Make}) are slightly more complex to use but offer
stronger type-safety. Polymorphic sets make it easier to shoot
yourself in the foot. In case of doubt, you should use functorized
sets.
The functorized set implementation is built upon Stdlib's
{{:http://caml.inria.fr/pub/docs/manual-ocaml/libref/Set.html}Set}
module, but provides the complete interface.
@author Xavier Leroy
@author Nicolas Cannasse
@author Markus Mottl
@author David Rajchenbach-Teller
*)
(** {4 Functorized Sets} *)
module type OrderedType = BatInterfaces.OrderedType
(** Input signature of the functor {!Set.Make}. *)
module type S =
sig
type elt
(** The type of the set elements. *)
type t
(** The type of sets. *)
val empty: t
(** The empty set. *)
val is_empty: t -> bool
(** Test whether a set is empty or not. *)
val singleton: elt -> t
(** [singleton x] returns the one-element set containing only [x]. *)
val mem: elt -> t -> bool
(** [mem x s] tests whether [x] belongs to the set [s]. *)
val add: elt -> t -> t
(** [add x s] returns a set containing all elements of [s],
plus [x]. If [x] was already in [s], [s] is returned unchanged. *)
val remove: elt -> t -> t
(** [remove x s] returns a set containing all elements of [s],
except [x]. If [x] was not in [s], [s] is returned unchanged. *)
val union: t -> t -> t
(** Set union. *)
val inter: t -> t -> t
(** Set intersection. *)
val diff: t -> t -> t
(** Set difference. *)
val compare: t -> t -> int
(** Total ordering between sets. Can be used as the ordering function
for doing sets of sets. *)
val equal: t -> t -> bool
(** [equal s1 s2] tests whether the sets [s1] and [s2] are
equal, that is, contain equal elements. *)
val subset: t -> t -> bool
(** [subset s1 s2] tests whether the set [s1] is a subset of
the set [s2]. *)
val compare_subset: t -> t -> int
(** Partial ordering between sets as generated by [subset] *)
val iter: (elt -> unit) -> t -> unit
(** [iter f s] applies [f] in turn to all elements of [s].
The elements of [s] are presented to [f] in increasing order
with respect to the ordering over the type of the elements. *)
val map: (elt -> elt) -> t -> t
(** [map f x] creates a new set with elements [f a0],
[f a1]... [f aN], where [a0],[a1]..[aN] are the
values contained in [x]*)
val filter: (elt -> bool) -> t -> t
(** [filter p s] returns the set of all elements in [s]
that satisfy predicate [p]. *)
val filter_map: (elt -> elt option) -> t -> t
(** [filter_map f m] combines the features of [filter] and
[map]. It calls calls [f a0], [f a1], [f aN] where [a0],[a1]..[aN]
are the elements of [m] and returns the set of pairs [bi]
such as [f ai = Some bi] (when [f] returns [None], the
corresponding element of [m] is discarded). *)
val fold: (elt -> 'a -> 'a) -> t -> 'a -> 'a
(** [fold f s a] computes [(f xN ... (f x1 (f x0 a))...)],
where [x0],[x1]..[xN] are the elements of [s], in increasing order. *)
val for_all: (elt -> bool) -> t -> bool
(** [for_all p s] checks if all elements of the set
satisfy the predicate [p]. *)
val exists: (elt -> bool) -> t -> bool
(** [exists p s] checks if at least one element of
the set satisfies the predicate [p]. *)
val partition: (elt -> bool) -> t -> t * t
(** [partition p s] returns a pair of sets [(s1, s2)], where
[s1] is the set of all the elements of [s] that satisfy the
predicate [p], and [s2] is the set of all the elements of
[s] that do not satisfy [p]. *)
val split: elt -> t -> t * bool * t
(** [split x s] returns a triple [(l, present, r)], where
[l] is the set of elements of [s] that are
strictly less than [x];
[r] is the set of elements of [s] that are
strictly greater than [x];
[present] is [false] if [s] contains no element equal to [x],
or [true] if [s] contains an element equal to [x]. *)
val cardinal: t -> int
(** Return the number of elements of a set. *)
val elements: t -> elt list
(** Return the list of all elements of the given set.
The returned list is sorted in increasing order with respect
to the ordering [Ord.compare], where [Ord] is the argument
given to {!Set.Make}. *)
val min_elt: t -> elt
(** Return the smallest element of the given set
(with respect to the [Ord.compare] ordering).
@raise Not_found if the set is empty. *)
val max_elt: t -> elt
(** Same as {!Set.S.min_elt}, but returns the largest element of the
given set. *)
val choose: t -> elt
(** Return one element of the given set, or raise [Not_found] if
the set is empty. Which element is chosen is unspecified,
but equal elements will be chosen for equal sets. *)
val pop : t -> elt * t
(** returns one element of the set and the set without that element.
Raises [Not_found] if given an empty set *)
val enum: t -> elt BatEnum.t
(** Return an enumeration of all elements of the given set.
The returned enumeration is sorted in increasing order with respect
to the ordering [Ord.compare], where [Ord] is the argument
given to {!Set.Make}. *)
val backwards: t -> elt BatEnum.t
(** Return an enumeration of all elements of the given set.
The returned enumeration is sorted in decreasing order with respect
to the ordering [Ord.compare], where [Ord] is the argument
given to {!Set.Make}. *)
val of_enum: elt BatEnum.t -> t
(** {6 Boilerplate code}*)
(** {7 Printing}*)
val print : ?first:string -> ?last:string -> ?sep:string ->
('a BatInnerIO.output -> elt -> unit) ->
'a BatInnerIO.output -> t -> unit
(** {6 Override modules}*)
(**
The following modules replace functions defined in {!Set} with functions
behaving slightly differently but having the same name. This is by design:
the functions meant to override the corresponding functions of {!Set}.
*)
(** Operations on {!Set} without exceptions.*)
module Exceptionless : sig
val min_elt: t -> elt option
val max_elt: t -> elt option
val choose: t -> elt option
end
(** Operations on {!Set} with labels.
This module overrides a number of functions of {!Set} by
functions in which some arguments require labels. These labels are
there to improve readability and safety and to let you change the
order of arguments to functions. In every case, the behavior of the
function is identical to that of the corresponding function of {!Set}.
*)
module Labels : sig
val iter : f:(elt -> unit) -> t -> unit
val fold : f:(elt -> 'a -> 'a) -> t -> init:'a -> 'a
val for_all : f:(elt -> bool) -> t -> bool
val exists : f:(elt -> bool) -> t -> bool
val map: f:(elt -> elt) -> t -> t
val filter : f:(elt -> bool) -> t -> t
val filter_map: f:(elt -> elt option) -> t -> t
val partition : f:(elt -> bool) -> t -> t * t
end
end
(** Output signature of the functor {!Set.Make}. *)
(*
module StringSet : S with type elt = String.t
(** A set of strings. Comparison of strings takes case into account (i.e. "foo" <> "Foo")*)
module IStringSet : S with type elt = String.t
(** A set of strings. Comparison of strings ignores case (i.e. "foo" = "Foo")*)
module NumStringSet : S with type elt = String.t
(** A set of strings. Comparison of strings takes into account embedded numbers (i.e. "a23" < "a123", "a01" = "a1") *)
module RopeSet : S with type elt = BatRope.t
(** A set of ropes. Comparison of ropes takes case into account (i.e. r"foo" <> r"Foo")*)
module IRopeSet : S with type elt = BatRope.t
(** A set of ropes. Comparison of ropes ignores case (i.e. r"foo" = r"Foo")*)
module IntSet : S with type elt = BatInt.t
(** A set of integers.*)
module CharSet : S with type elt = Char.t
(** A set of characters. May be better to use a bitarray or ISet,
depending on your situation *)
*)
module Make (Ord : OrderedType) : S with type elt = Ord.t
(** Functor building an implementation of the set structure
given a totally ordered type.
@documents Set.Make
*)
(** {6 Polymorphic sets}
The definitions below describe the polymorphic set interface.
They are similar in functionality to the functorized {!Make}
module, but the compiler cannot ensure that sets using different
element ordering have different types: the responsibility of not
mixing non-sensical comparison functions together is to the
programmer. If in doubt, you should rather use the {!Make}
functor for additional safety.
@author Nicolas Cannasse
@author Markus Mottl
@author David Rajchenbach-Teller
*)
type 'a t
(** The type of sets. *)
include BatEnum.Enumerable with type 'a enumerable = 'a t
include BatInterfaces.Mappable with type 'a mappable = 'a t
val empty: 'a t
(** The empty set, using [compare] as comparison function *)
val create : ('a -> 'a -> int) -> 'a t
(** Creates a new empty set, using the provided function for key comparison.*)
val is_empty: 'a t -> bool
(** Test whether a set is empty or not. *)
val singleton : ?cmp:('a -> 'a -> int) -> 'a -> 'a t
(** Creates a new set with the single given element in it. *)
val mem: 'a -> 'a t -> bool
(** [mem x s] tests whether [x] belongs to the set [s]. *)
val add: 'a -> 'a t -> 'a t
(** [add x s] returns a set containing all elements of [s],
plus [x]. If [x] was already in [s], [s] is returned unchanged. *)
val remove: 'a -> 'a t -> 'a t
(** [remove x s] returns a set containing all elements of [s],
except [x]. If [x] was not in [s], [s] is returned unchanged. *)
val union: 'a t -> 'a t -> 'a t
(** [union s t] returns the union of [s] and [t] - the set containing
all elements in either [s] and [t]. The returned set uses [t]'s
comparison function. The current implementation works better for
small [s]. *)
(* Set.Make uses intersect *)
val intersect: 'a t -> 'a t -> 'a t
(** [intersect s t] returns a new set of those elements that are in
both [s] and [t]. The returned set uses [s]'s comparison function. *)
val diff: 'a t -> 'a t -> 'a t
(** [diff s t] returns the set of all elements in [s] but not in
[t]. The returned set uses [s]'s comparison function.*)
(* No compare nor equal; they don't make sense if the comparison
functions of the two sets may be different, but apparently this
wasn't a problem for 'subset'? *)
val subset: 'a t -> 'a t -> bool
(** [subset a b] returns true if [a] is a subset of [b]. O(|a|). *)
val iter: ('a -> unit) -> 'a t -> unit
(** [iter f s] applies [f] in turn to all elements of [s].
The elements of [s] are presented to [f] in increasing order
with respect to the ordering over the type of the elements. *)
(* under-specified; either give a 'b comparison,
or keep ('a -> 'a) (preferred choice) *)
val map: ('a -> 'b) -> 'a t -> 'b t
(** [map f x] creates a new set with elements [f a0],
[f a1]... [f aN], where [a0], [a1], ..., [aN] are the
values contained in [x]*)
val filter: ('a -> bool) -> 'a t -> 'a t
(** [filter p s] returns the set of all elements in [s]
that satisfy predicate [p]. *)
(* as under-specified as 'map' *)
val filter_map: ('a -> 'b option) -> 'a t -> 'b t
(** [filter_map f m] combines the features of [filter] and
[map]. It calls calls [f a0], [f a1], [f aN] where [a0,a1..an]
are the elements of [m] and returns the set of pairs [bi]
such as [f ai = Some bi] (when [f] returns [None], the
corresponding element of [m] is discarded). *)
val fold: ('a -> 'b -> 'b) -> 'a t -> 'b -> 'b
(** [fold f s a] computes [(f xN ... (f x1 (f x0 a))...)],
where [x0,x1..xN] are the elements of [s], in increasing order. *)
val exists: ('a -> bool) -> 'a t -> bool
(** [exists p s] checks if at least one element of
the set satisfies the predicate [p]. *)
val for_all : ('a -> bool) -> 'a t -> bool
(** Returns whether the given predicate applies to all elements in the set *)
val partition : ('a -> bool) -> 'a t -> 'a t * 'a t
(** returns two disjoint subsets, those that satisfy the given
predicate and those that don't *)
val split : 'a -> 'a t -> 'a t * bool * 'a t
(** [split x s] returns a triple [(l, present, r)], where
[l] is the set of elements of [s] that are
strictly less than [x];
[r] is the set of elements of [s] that are
strictly greater than [x];
[present] is [false] if [s] contains no element equal to [x],
or [true] if [s] contains an element equal to [x]. *)
val cardinal: 'a t -> int
(** Return the number of elements of a set. *)
(* 'elements' missing *)
val min_elt : 'a t -> 'a
(** returns the smallest element of the set. Raises
[Invalid_argument] if given an empty set. *)
val max_elt : 'a t -> 'a
(** returns the largest element of the set. Raises
[Invalid_argument] if given an empty set.*)
val choose : 'a t -> 'a
(** returns an arbitrary (but deterministic) element of the given set.
Raises [Invalid_argument] if given an empty set. *)
val pop : 'a t -> 'a * 'a t
(** returns one element of the set and the set without that element.
Raises [Not_found] if given an empty set *)
val enum: 'a t -> 'a BatEnum.t
(** Return an enumeration of all elements of the given set.
The returned enumeration is sorted in increasing order with respect
to the ordering of this set.*)
val of_enum: 'a BatEnum.t -> 'a t
val of_enum_cmp: cmp:('a -> 'a -> int) -> 'a BatEnum.t -> 'a t
(* of_list has no Set.Make counterpart *)
val of_list: 'a list -> 'a t
(** builds a set from the given list, using the default comparison
function *)
(** {6 Boilerplate code}*)
(** {7 Printing}*)
val print : ?first:string -> ?last:string -> ?sep:string ->
('a BatInnerIO.output -> 'c -> unit) ->
'a BatInnerIO.output -> 'c t -> unit