(**************************************************************************)
(* *)
(* 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 update: key -> ('a option -> 'a option) -> 'a t -> 'a t
(** [update x f m] returns a map containing the same bindings as
[m], except for the binding of [x]. Depending on the value of
[y] where [y] is [f (find_opt x m)], the binding of [x] is
added, removed or updated. If [y] is [None], the binding is
removed if it exists; otherwise, if [y] is [Some z] then [x]
is associated to [z] in the resulting map. If [x] was already
bound in [m] to a value that is physically equal to [z], [m]
is returned unchanged (the result of the function is then
physically equal to [m]).
@since 4.06.0
*)
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].
In terms of the [find_opt] operation, we have
[find_opt x (merge f m1 m2) = f (find_opt x m1) (find_opt x m2)]
for any key [x], provided that [f None None = None].
@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.
This is a special case of [merge]: [union f m1 m2] is equivalent
to [merge f' m1 m2], where
- [f' None None = None]
- [f' (Some v) None = Some v]
- [f' None (Some v) = Some v]
- [f' (Some v1) (Some v2) = f v1 v2]
@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
satisfies 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 min_binding_opt: 'a t -> (key * 'a) option
(** Return the smallest binding of the given map
(with respect to the [Ord.compare] ordering), or [None]
if the map is empty.
@since 4.05
*)
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 max_binding_opt: 'a t -> (key * 'a) option
(** Same as {!Map.S.min_binding_opt}, but returns the largest binding
of the given map.
@since 4.05
*)
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 choose_opt: 'a t -> (key * 'a) option
(** Return one binding of the given map, or [None] if
the map is empty. Which binding is chosen is unspecified,
but equal bindings will be chosen for equal maps.
@since 4.05
*)
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 find_opt: key -> 'a t -> 'a option
(** [find_opt x m] returns [Some v] if the current binding of [x]
in [m] is [v], or [None] if no such binding exists.
@since 4.05
*)
val find_first: (key -> bool) -> 'a t -> key * 'a
(** [find_first f m], where [f] is a monotonically increasing function,
returns the binding of [m] with the lowest key [k] such that [f k],
or raises [Not_found] if no such key exists.
For example, [find_first (fun k -> Ord.compare k x >= 0) m] will return
the first binding [k, v] of [m] where [Ord.compare k x >= 0]
(intuitively: [k >= x]), or raise [Not_found] if [x] is greater than any
element of [m].
@since 4.05
*)
val find_first_opt: (key -> bool) -> 'a t -> (key * 'a) option
(** [find_first_opt f m], where [f] is a monotonically increasing function,
returns an option containing the binding of [m] with the lowest key [k]
such that [f k], or [None] if no such key exists.
@since 4.05
*)
val find_last: (key -> bool) -> 'a t -> key * 'a
(** [find_last f m], where [f] is a monotonically decreasing function,
returns the binding of [m] with the highest key [k] such that [f k],
or raises [Not_found] if no such key exists.
@since 4.05
*)
val find_last_opt: (key -> bool) -> 'a t -> (key * 'a) option
(** [find_last_opt f m], where [f] is a monotonically decreasing function,
returns an option containing the binding of [m] with the highest key [k]
such that [f k], or [None] if no such key exists.
@since 4.05
*)
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. *)
(** {6 Iterators} *)
val to_seq : 'a t -> (key * 'a) Seq.t
(** Iterate on the whole map, in ascending order
@since 4.07 *)
val to_seq_from : key -> 'a t -> (key * 'a) Seq.t
(** [to_seq_from k m] iterates on a subset of the bindings of [m],
in ascending order, from key [k] or above.
@since 4.07 *)
val add_seq : (key * 'a) Seq.t -> 'a t -> 'a t
(** Add the given bindings to the map, in order.
@since 4.07 *)
val of_seq : (key * 'a) Seq.t -> 'a t
(** Build a map from the given bindings
@since 4.07 *)
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. *)
|