module Make:
Functor building an implementation of the map structure given a totally ordered type.
| Parameters: |
|
type
The type of the map keys.
type +'a t
The type of maps from type key to type 'a.
val empty : 'a tThe empty map.
val is_empty : 'a t -> boolTest whether a map is empty or not.
val mem : key -> 'a t -> boolmem x m returns true if m contains a binding for x,
and false otherwise.
val add : key -> 'a -> 'a t -> 'a tadd 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.
val update : key -> ('a option -> 'a option) -> 'a t -> 'a tupdate 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).
val singleton : key -> 'a -> 'a tsingleton x y returns the one-element map that contains a binding y
for x.
val remove : key -> 'a t -> 'a tremove 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).
val merge : (key -> 'a option -> 'b option -> 'c option) ->
'a t -> 'b t -> 'c tmerge 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.
val union : (key -> 'a -> 'a -> 'a option) ->
'a t -> 'a t -> 'a tunion 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' _key None None = Nonef' _key (Some v) None = Some vf' _key None (Some v) = Some vf' key (Some v1) (Some v2) = f key v1 v2val compare : ('a -> 'a -> int) -> 'a t -> 'a t -> intTotal 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 -> boolequal 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 -> unititer 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 -> 'bfold 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 -> boolfor_all p m checks if all the bindings of the map
satisfy the predicate p.
val exists : (key -> 'a -> bool) -> 'a t -> boolexists p m checks if at least one binding of the map
satisfies the predicate p.
val filter : (key -> 'a -> bool) -> 'a t -> 'a tfilter 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)
val partition : (key -> 'a -> bool) -> 'a t -> 'a t * 'a tpartition 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.
val cardinal : 'a t -> intReturn the number of bindings of a map.
val bindings : 'a t -> (key * 'a) listReturn the list of all bindings of the given map.
The returned list is sorted in increasing order of keys with respect
to the ordering Ord.compare, where Ord is the argument
given to Map.Make.
val min_binding : 'a t -> key * 'aReturn the binding with the smallest key in a given map
(with respect to the Ord.compare ordering), or raise
Not_found if the map is empty.
val min_binding_opt : 'a t -> (key * 'a) optionReturn the binding with the smallest key in the given map
(with respect to the Ord.compare ordering), or None
if the map is empty.
val max_binding : 'a t -> key * 'aSame as Map.S.min_binding, but returns the binding with
the largest key in the given map.
val max_binding_opt : 'a t -> (key * 'a) optionSame as Map.S.min_binding_opt, but returns the binding with
the largest key in the given map.
val choose : 'a t -> key * 'aReturn 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.
val choose_opt : 'a t -> (key * 'a) optionReturn 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.
val split : key -> 'a t -> 'a t * 'a option * 'a tsplit 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.
val find : key -> 'a t -> 'afind 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 optionfind_opt x m returns Some v if the current binding of x
in m is v, or None if no such binding exists.
val find_first : (key -> bool) -> 'a t -> key * 'afind_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.
val find_first_opt : (key -> bool) -> 'a t -> (key * 'a) optionfind_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.
val find_last : (key -> bool) -> 'a t -> key * 'afind_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.
val find_last_opt : (key -> bool) -> 'a t -> (key * 'a) optionfind_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.
val map : ('a -> 'b) -> 'a t -> 'b tmap 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 tSame as Map.S.map, but the function receives as arguments both the
key and the associated value for each binding of the map.
val to_seq : 'a t -> (key * 'a) Seq.tIterate on the whole map, in ascending order of keys
val to_seq_from : key -> 'a t -> (key * 'a) Seq.tto_seq_from k m iterates on a subset of the bindings of m,
in ascending order of keys, from key k or above.
val add_seq : (key * 'a) Seq.t -> 'a t -> 'a tAdd the given bindings to the map, in order.
val of_seq : (key * 'a) Seq.t -> 'a tBuild a map from the given bindings