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 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 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.
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
.
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 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
.
val exists : (key > 'a > bool) > 'a t > bool
exists p m
checks if at least one binding of the map
satisfy the predicate p
.
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
.
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
.
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 with respect
to the ordering Ord.compare
, where Ord
is the argument
given to Extmap.Make
.
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.
val max_binding : 'a t > key * 'a
Same as Extmap.S.min_binding
, but returns the largest
binding of 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 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 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 Extmap.S.map
, but the function receives as arguments both
the key and the associated value for each binding of the map.
@Added in Why3
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 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 set_compare : 'a t > 'b t > int
set_compare = compare (fun _ _ > 0)
val set_equal : 'a t > 'b t > bool
set_equal = equal (fun _ _ > true)
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 Extmap.S.map
, but may remove bindings.
val mapi_filter : (key > 'a > 'b option) > 'a t > 'b t
Same as Extmap.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 mapi_filter_fold : (key > 'a > 'acc > 'acc * 'b option) >
'a t > 'acc > 'acc * 'b t
Same as Extmap.S.mapi_fold
, but may remove bindings.
val fold_left : ('b > key > 'a > 'b) > 'b > 'a t > 'b
same as Extmap.S.fold
but in the order of List.fold_left
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 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 replace : exn > key > 'a > 'a t > 'a t
replace e x v m
binds x
to v
in m
if x
is already 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 Extmap.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 Extmap.Make
.
val of_list : (key * 'a) list > 'a t
construct a map from a list of bindings.
val contains : 'a t > key > bool
contains m x
is the same as mem x m
.
val domain : 'a t > unit t
domain m
returns the set of keys of bindings in m
val subdomain : (key > 'a > bool) > 'a t > unit t
subdomain pr m
returns the set of keys of bindings in m
that satisfy predicate pr
val is_num_elt : int > 'a t > bool
check if the map has the given number of elements
type 'a
enumeration
enumeration: zipper style
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