module type S = sig
(* Keys are assumed to have a natural total order. *)
type key
(* The type of maps whose data have type ['a]. *)
type 'a t
(* The empty map. *)
val empty: 'a t
(* [lookup k m] looks up the value associated to the key [k] in the
map [m], and raises [Not_found] if no value is bound to [k]. *)
val lookup: key -> 'a t -> 'a
val find: key -> 'a t -> 'a
(* [add k d m] returns a map whose bindings are all bindings in [m],
plus a binding of the key [k] to the datum [d]. If a binding
already exists for [k], it is overridden. *)
val add: key -> 'a -> 'a t -> 'a t
(* [strict_add k d m] returns a map whose bindings are all bindings
in [m], plus a binding of the key [k] to the datum [d]. If a
binding already exists for [k] then [Unchanged] is raised. *)
exception Unchanged
val strict_add: key -> 'a -> 'a t -> 'a t
(* [fine_add decide k d m] returns a map whose bindings are all
bindings in [m], plus a binding of the key [k] to the datum
[d]. If a binding from [k] to [d0] already exists, then the
resulting map contains a binding from [k] to [decide d0 d]. *)
type 'a decision = 'a -> 'a -> 'a
val fine_add: 'a decision -> key -> 'a -> 'a t -> 'a t
(* [mem k m] tells whether the key [k] appears in the domain of the
map [m]. *)
val mem: key -> 'a t -> bool
(* [singleton k d] returns a map whose only binding is from [k] to [d]. *)
val singleton: key -> 'a -> 'a t
(* [is_empty m] returns [true] if and only if the map [m] defines no
bindings at all. *)
val is_empty: 'a t -> bool
(* [is_singleton s] returns [Some x] if [s] is a singleton
containing [x] as its only element; otherwise, it returns
[None]. *)
val is_singleton: 'a t -> (key * 'a) option
(* [cardinal m] returns [m]'s cardinal, that is, the number of keys
it binds, or, in other words, the cardinal of its domain. *)
val cardinal: 'a t -> int
(* [choose m] returns an arbitrarily chosen binding in [m], if [m]
is nonempty, and raises [Not_found] otherwise. *)
val choose: 'a t -> key * 'a
(* [lookup_and_remove k m] looks up the value [v] associated to the
key [k] in the map [m], and raises [Not_found] if no value is
bound to [k]. The call returns the value [v], together with the
map [m] deprived from the binding from [k] to [v]. *)
val lookup_and_remove: key -> 'a t -> 'a * 'a t
val find_and_remove: key -> 'a t -> 'a * 'a t
(* [remove k m] is the map [m] deprived from any binding for [k]. *)
val remove: key -> 'a t -> 'a t
(* [union m1 m2] returns the union of the maps [m1] and
[m2]. Bindings in [m2] take precedence over those in [m1]. *)
val union: 'a t -> 'a t -> 'a t
(* [fine_union decide m1 m2] returns the union of the maps [m1] and
[m2]. If a key [k] is bound to [x1] (resp. [x2]) within [m1]
(resp. [m2]), then [decide] is called. It is passed [x1] and
[x2], and must return the value that shall be bound to [k] in the
final map. *)
val fine_union: 'a decision -> 'a t -> 'a t -> 'a t
(* [iter f m] invokes [f k x], in turn, for each binding from key
[k] to element [x] in the map [m]. Keys are presented to [f] in
increasing order. *)
val iter: (key -> 'a -> unit) -> 'a t -> unit
(* [fold f m seed] invokes [f k d accu], in turn, for each binding
from key [k] to datum [d] in the map [m]. Keys are presented to
[f] in increasing order. The initial value of [accu] is [seed];
then, at each new call, its value is the value returned by the
previous invocation of [f]. The value returned by [fold] is the
final value of [accu]. *)
val fold: (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
(* [fold_rev] performs exactly the same job as [fold], but presents
keys to [f] in the opposite order. *)
val fold_rev: (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
(* It is valid to evaluate [iter2 f m1 m2] if and only if [m1] and
[m2] have equal domains. Doing so invokes [f k x1 x2], in turn,
for each key [k] bound to [x1] in [m1] and to [x2] in
[m2]. Bindings are presented to [f] in increasing order. *)
val iter2: (key -> 'a -> 'b -> unit) -> 'a t -> 'b t -> unit
(* [map f m] returns the map obtained by composing the map [m] with
the function [f]; that is, the map $k\mapsto f(m(k))$. *)
val map: ('a -> 'b) -> 'a t -> 'b t
(* [endo_map] is similar to [map], but attempts to physically share
its result with its input. This saves memory when [f] is the
identity function. *)
val endo_map: ('a -> 'a) -> 'a t -> 'a t
(* If [dcompare] is an ordering over data, then [compare dcompare]
is an ordering over maps. *)
val compare: ('a -> 'a -> int) -> 'a t -> 'a t -> int
(* A map's domain is a set. Thus, to be able to perform operations
on domains, we need set operations, provided by the [Domain]
sub-module. The two-way connection between maps and their domains
is given by two additional functions, [domain] and
[lift]. [domain m] returns [m]'s domain. [lift f s] returns the
map $k\mapsto f(k)$, where $k$ ranges over a set of keys [s]. *)
module Domain : GSet.S with type element = key
val domain: 'a t -> Domain.t
val lift: (key -> 'a) -> Domain.t -> 'a t
(* [corestrict m d] performs a co-restriction of the map [m] to the
domain [d]. That is, it returns the map $k\mapsto m(k)$, where
$k$ ranges over all keys bound in [m] but \emph{not} present in
[d]. *)
val corestrict: 'a t -> Domain.t -> 'a t
end