(***********************************************************************)
(* *)
(* Objective Caml *)
(* *)
(* 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 Library General Public License, with *)
(* the special exception on linking described in file ../LICENSE. *)
(* *)
(***********************************************************************)
(* $Id: map.mli 10483 2010-05-31 12:48:13Z doligez $ *)
module Map : sig
(** 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.
*)
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], its previous binding disappears. *)
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. *)
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 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].
@since 3.12.0 *)
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.max_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. *)
(** {3} Added into why stdlib version *)
val is_num_elt : int -> 'a t -> bool
(** check if the map has the given number of elements *)
val change : ('a option -> 'a option) -> key -> 'a t -> 'a t
(** [change f x m] returns a map containing the same bindings as
[m], except the binding of [x] in [m] is changed from [y] to
[f (Some y)] if [m] contains a binding of [x], otherwise the
binding of [x] becomes [f None].
[change f x m] corresponds to a more efficient way to do
[match (try f (Some (find x m)) with Not_found -> f None) with
| None -> m
| Some v -> add x v] *)
val union : (key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t
(** [union f m1 m2] computes a map whose keys is a subset of keys
of [m1] and of [m2]. If a binding is present in [m1] (resp. [m2])
and not in [m2] (resp. [m1]) the same binding is present in
the result. The function [f] is called only in ambiguous cases. *)
val inter : (key -> 'a -> 'b -> 'c option) -> 'a t -> 'b t -> 'c t
(** [inter f m1 m2] computes a map whose keys is a subset of
the intersection of keys of [m1] and of [m2]. *)
val diff : (key -> 'a -> 'b -> 'a option) -> 'a t -> 'b t -> 'a t
(** [diff f m1 m2] computes a map whose keys is a subset of keys
of [m1]. [f] is applied on key which belongs to [m1] and [m2]
if [f] returns [None] the binding is removed from [m1],
otherwise [Some d1] is returned, the key binds to [d1] in [m1] *)
val submap : (key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
(** [submap pr m1 m2] verifies that all the keys in m1 are in m2
and that for each such binding pr is verified. *)
val disjoint : (key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
(** [disjoint pr m1 m2] verifies that for every common key in m1
and m2, pr is verified. *)
val set_union : 'a t -> 'a t -> 'a t
(** [set_union = union (fun _ x _ -> Some x)] *)
val set_inter : 'a t -> 'b t -> 'a t
(** [set_inter = inter (fun _ x _ -> Some x)] *)
val set_diff : 'a t -> 'b t -> 'a t
(** [set_diff = diff (fun _ _ _ -> None)] *)
val set_submap : 'a t -> 'b t -> bool
(** [set_submap = submap (fun _ _ _ -> true)] *)
val set_disjoint : 'a t -> 'b t -> bool
(** [set_disjoint = disjoint (fun _ _ _ -> false)] *)
val find_def : 'a -> key -> 'a t -> 'a
(** [find_def x d m] returns the current binding of [x] in [m],
or return [d] if no such binding exists. *)
val find_opt : key -> 'a t -> 'a option
(** [find_opt x m] returns the [Some] of the current binding
of [x] in [m], or return [None] if no such binding exists. *)
val find_exn : exn -> key -> 'a t -> 'a
(** [find_exn exn x d m] returns the current binding
of [x] in [m], or raise [exn] if no such binding exists. *)
val map_filter: ('a -> 'b option) -> 'a t -> 'b t
(** Same as {!Map.S.map}, but may remove bindings. *)
val mapi_filter: (key -> 'a -> 'b option) -> 'a t -> 'b t
(** Same as {!Map.S.mapi}, but may remove bindings. *)
val mapi_fold:
(key -> 'a -> 'acc -> 'acc * 'b) -> 'a t -> 'acc -> 'acc * 'b t
(** fold and map at the same time *)
val fold2_inter: (key -> 'a -> 'b -> 'c -> 'c) -> 'a t -> 'b t -> 'c -> 'c
(** fold the common keys of two map at the same time *)
val fold2_union:
(key -> 'a option -> 'b option -> 'c -> 'c) -> 'a t -> 'b t -> 'c -> 'c
(** fold the keys which appear in one of the two maps *)
val translate : (key -> key) -> 'a t -> 'a t
(** [translate f m] translates the keys in the map [m] by the
function [f]. [f] must be strictly monotone on the key of [m].
Otherwise it raises invalid_arg *)
val mapi_filter_fold:
(key -> 'a -> 'acc -> 'acc * 'b option) -> 'a t -> 'acc -> 'acc * 'b t
(** Same as {!Map.S.mapi_fold}, but may remove bindings. *)
val add_new : exn -> key -> 'a -> 'a t -> 'a t
(** [add_new e x v m] binds [x] to [v] in [m] if [x] is not bound,
and raises [e] otherwise. *)
val keys: 'a t -> key list
(** Return the list of all keys 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}. *)
val values: 'a t -> 'a list
(** Return the list of all values of the given map.
The returned list is sorted in increasing order with respect
to the ordering [Ord.compare] of the keys, where [Ord] is the argument
given to {!Map.Make}. *)
(** enumeration: zipper style *)
type 'a enumeration
val val_enum : 'a enumeration -> (key * 'a) option
(** get the current key value pair of the enumeration, return None
if the enumeration reach the end *)
val start_enum : 'a t -> 'a enumeration
(** start the enumeration of the given map *)
val next_enum : 'a enumeration -> 'a enumeration
(** get the next step of the enumeration *)
val start_ge_enum : key -> 'a t -> 'a enumeration
(** start the enumeration of the given map at the first key which
is greater or equal than the given one *)
val next_ge_enum : key -> 'a enumeration -> 'a enumeration
(** get the next (or same) step of the enumeration which key is
greater or equal to the given key *)
module type Set =
sig
type elt = key
type set = unit t
type t = set
(** The type of sets of type [elt]. *)
val empty: t
(** The empty set. *)
val is_empty: t -> bool
(** Test whether a set is empty or not. *)
val mem: elt -> t -> bool
(** [mem x s] returns [true] if [s] contains [x],
and [false] otherwise. *)
val add: elt -> t -> t
(** [add x s] returns a set containing the same elements as
[s], plus [x]. *)
val singleton: elt -> t
(** [singleton x] returns the one-element set that contains [x]. *)
val remove: elt -> t -> t
(** [remove x s] returns a set containing the same elements as [s],
except for [x]. *)
val merge: (elt -> bool -> bool -> bool) -> t -> t -> t
(** [merge f s1 s2] computes a set whose elts is a subset of elts
of [s1] and of [s2]. The presence of each such element is
determined with the function [f]. *)
val compare: t -> t -> int
(** Total ordering between sets. *)
val equal: t -> t -> bool
(** [equal s1 s2] tests whether the sets [s1] and [s2] are equal. *)
val subset: t -> t -> bool
(** [subset s1 s2] tests whether the set [s1] is a subset of [s2]. *)
val disjoint: t -> t -> bool
(** [disjoint s1 s2] tests whether the sets [s1] and [s2]
are disjoint. *)
val iter: (elt -> unit) -> t -> unit
(** [iter f s] applies [f] to all elements of [s].
The elements are passed to [f] in increasing order with respect
to the ordering over the type of the elts. *)
val fold: (elt -> 'a -> 'a) -> t -> 'a -> 'a
(** [fold f s a] computes [(f eN ... (f e1 a)...)],
where [e1 ... eN] are the element of [s] in increasing order. *)
val for_all: (elt -> bool) -> t -> bool
(** [for_all p s] checks if all the elements of [s] satisfy
the predicate [p]. *)
val exists: (elt -> bool) -> t -> bool
(** [exists p s] checks if at least one element of [s] satisfies
the predicate [p]. *)
val filter: (elt -> bool) -> t -> t
(** [filter p s] returns the set with all the elements of [s]
that satisfy predicate [p]. *)
val partition: (elt -> bool) -> t -> t * t
(** [partition p s] returns a pair of sets [(s1, s2)], where
[s1] contains all the elements of [s] that satisfy the
predicate [p], and [s2] is the map with all the elements
of [s] that do not satisfy [p]. *)
val cardinal: t -> int
(** Return the number of elements in 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. *)
val min_elt: t -> elt
(** Return the smallest element of the given set or raise
[Not_found] if the set is empty. *)
val max_elt: t -> elt
(** Return the largest element of the given set or raise
[Not_found] if the set is empty. *)
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 split: elt -> t -> t * bool * t
(** [split x s] returns a triple [(l, mem, r)], where
[l] is the set with all the elements of [s] that are
strictly less than [x];
[r] is the set with all the elements of [s] that are
strictly greater than [x];
[mem] is [true] if [x] belongs to [s] and [false] otherwise. *)
val change : (bool -> bool) -> elt -> t -> t
(** [change f x s] returns a set containing the same elements as
[s], except [x] which is added to [s] if [f (mem x s)] returns
[true] and removed otherwise. *)
val union : t -> t -> t
(** [union f s1 s2] computes the union of two sets *)
val inter : t -> t -> t
(** [inter f s1 s2] computes the intersection of two sets *)
val diff : t -> t -> t
(** [diss f s1 s2] computes the difference of two sets *)
val fold2: (elt -> 'a -> 'a) -> t -> t -> 'a -> 'a
(** [fold2 f s1 s2 a] computes [(f eN ... (f e1 a) ...)],
where [e1 ... eN] are the elements of [union s1 s2]
in increasing order. *)
val translate : (elt -> elt) -> t -> t
(** [translate f s] translates the elements in the set [s] by the
function [f]. [f] must be strictly monotone on the elements of [s].
Otherwise it raises invalid_arg *)
val add_new : exn -> elt -> t -> t
(** [add_new e x s] adds [x] to [s] if [s] does not contain [x],
and raises [e] otherwise. *)
val is_num_elt : int -> t -> bool
(** check if the map has the given number of elements *)
end
module Set : Set
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/set structure
given a totally ordered type. *)
end