module Make:
Functor building an implementation of the map structure given a totally ordered type.
Parameters: 

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 key data m
returns a map containing the same bindings as
m
, plus a binding of key
to data
. If key
was already bound
in m
to a value that is physically equal to data
,
m
is returned unchanged (the result of the function is
then physically equal to m
). Otherwise, the previous binding
of key
in m
disappears.
val update : key > ('a option > 'a option) > 'a t > 'a t
update key f m
returns a map containing the same bindings as
m
, except for the binding of key
. Depending on the value of
y
where y
is f (find_opt key m)
, the binding of key
is
added, removed or updated. If y
is None
, the binding is
removed if it exists; otherwise, if y
is Some z
then key
is associated to z
in the resulting map. If key
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 t
singleton x y
returns the oneelement map that contains a binding
y
for x
.
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
).
val merge : (key > 'a option > 'b option > 'c option) >
'a t > 'b t > 'c t
merge f m1 m2
computes a map whose keys are a subset of the 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 x (find_opt x m1) (find_opt x m2)
for any key x
, provided that f x None None = None
.
val union : (key > 'a > 'a > 'a option) >
'a t > 'a t > 'a t
union f m1 m2
computes a map whose keys are a subset of the 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 = None
f' _key (Some v) None = Some v
f' _key None (Some v) = Some v
f' key (Some v1) (Some v2) = f key v1 v2
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 init
computes (f kN dN ... (f k1 d1 init)...)
,
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 f m
checks if all the bindings of the map
satisfy the predicate f
.
val exists : (key > 'a > bool) > 'a t > bool
exists f m
checks if at least one binding of the map
satisfies the predicate f
.
val filter : (key > 'a > bool) > 'a t > 'a t
filter f m
returns the map with all the bindings in m
that satisfy predicate p
. If every binding in m
satisfies f
,
m
is returned unchanged (the result of the function is then
physically equal to m
)
val filter_map : (key > 'a > 'b option) > 'a t > 'b t
filter_map f m
applies the function f
to every binding of
m
, and builds a map from the results. For each binding
(k, v)
in the input map:
f k v
is None
then k
is not in the result,f k v
is Some v'
then the binding (k, v')
is in the output map.For example, the following function on maps whose values are lists
filter_map
(fun _k li > match li with [] > None  _::tl > Some tl)
m
drops all bindings of m
whose value is an empty list, and pops
the first element of each value that is nonempty.
val partition : (key > 'a > bool) > 'a t > 'a t * 'a t
partition f m
returns a pair of maps (m1, m2)
, where
m1
contains all the bindings of m
that satisfy the
predicate f
, and m2
is the map with all the bindings of
m
that do not satisfy f
.
val cardinal : 'a t > int
Return the number of bindings of a map.
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 of keys with respect
to the ordering Ord.compare
, where Ord
is the argument
given to Map.Make
.
val min_binding : 'a t > key * 'a
Return 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) option
Return 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 * 'a
Same 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) option
Same as Map.S.min_binding_opt
, but returns the binding with
the largest key in the given map.
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.
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.
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
.
val find : key > 'a t > 'a
find x m
returns the current value of x
in m
,
or raises Not_found
if no binding for x
exists.
val find_opt : key > 'a t > 'a option
find_opt x m
returns Some v
if the current value of x
in m
is v
, or None
if no binding for x
exists.
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
.
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.
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.
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.
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.
val to_seq : 'a t > (key * 'a) Seq.t
Iterate on the whole map, in ascending order of keys
val to_rev_seq : 'a t > (key * 'a) Seq.t
Iterate on the whole map, in descending order of keys
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 of keys, from key k
or above.
val add_seq : (key * 'a) Seq.t > 'a t > 'a t
Add the given bindings to the map, in order.
val of_seq : (key * 'a) Seq.t > 'a t
Build a map from the given bindings