module type S = sig .. end
Output signature of the functor Map.Make.
type
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 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.
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.
Since 3.12.0
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.
The predicate p is tested on bindings according to the key order.
val exists : (key -> 'a -> bool) -> 'a t -> bool
exists p m checks if at least one binding of the map
satisfy the predicate p.
The predicate p is tested on bindings according to the key order.
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.
The predicate p is tested on bindings according to the key order.
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 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 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 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 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.
Additional functions
val of_list : (key * 'a) list -> 'a t
of_list l converts an association list to a map.
val map2 : (key -> 'a -> 'b -> 'c) ->
'a t -> 'b t -> 'c t
map2 f m1 m2 is similar to map but applies f to pairs
of bindings a1 from m1 and a2 from m2 corresponding to
the same key to construct a new map with the same key set.
m1 and m2 must have the same key sets.
The binging are passed to f in increasing order of key.
val iter2 : (key -> 'a -> 'b -> unit) -> 'a t -> 'b t -> unit
iter2 f m1 m2 is similar to map but applies f to pairs
of bindings a1 from m1 and a2 from m2 corresponding to
the same key.
m1 and m2 must have the same key sets.
The binging are passed to f in increasing order of key.
val fold2 : (key -> 'a -> 'b -> 'c -> 'c) ->
'a t -> 'b t -> 'c -> 'c
fold2 f m1 m2 x is similar to fold but applies f to pairs
of bindings a1 from m1 and a2 from m2 corresponding to
the same key.
m1 and m2 must have the same key sets.
The bindings are passed to f in increasing order of keys.
val for_all2 : (key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
for_all2 f m1 m2 is similar to for_all but applies f to pairs
of bindings a1 from m1 and a2 from m2 corresponding to
the same key.
m1 and m2 must have the same key sets.
The bindings are passed to f in increasing order of keys.
val exists2 : (key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
exists2 f m1 m2 is similar to exists but applies f to pairs
of bindings a1 from m1 and a2 from m2 corresponding to
the same key.
m1 and m2 must have the same key sets.
The bindings are passed to f in increasing order of keys.
val map2z : (key -> 'a -> 'a -> 'a) ->
'a t -> 'a t -> 'a t
map2z f m1 m2 is similar to map2 f m1 m2, but physically
equal subtrees are put unchanged into the result instead of
being traversed.
This is more efficient than map2, and equivalent if f is
side-effect free and idem-potent (f k a a = a).
m1 and m2 must have the same key sets.
The bindings are passed to f in increasing order of keys.
val iter2z : (key -> 'a -> 'a -> unit) -> 'a t -> 'a t -> unit
iter2z f m1 m2 is similar to iter2 f m1 m2, but physically
equal subtrees are ignored.
This is more efficient than iter2, and equivalent if
f k a a has no effect.
m1 and m2 must have the same key sets.
The bindings are passed to f in increasing order of keys.
val fold2z : (key -> 'a -> 'a -> 'b -> 'b) ->
'a t -> 'a t -> 'b -> 'b
fold2z f m1 m2 a is similar to fold2 f m1 m2 a, but physically
equal subtrees are ignored.
This is more efficient than fold2, and equivalent if
f k a a x = x and has no effect.
m1 and m2 must have the same key sets.
The bindings are passed to f in increasing order of keys.
val for_all2z : (key -> 'a -> 'a -> bool) -> 'a t -> 'a t -> bool
for_all2z f m1 m2 is similar to for_all2 f m1 m2, but returns
true for physically equal subtrees without traversing them.
This is more efficient than for_all2z, and equivalent if
f k a a = true and has no effect.
m1 and m2 must have the same key sets.
The bindings are passed to f in increasing order of keys.
val exists2z : (key -> 'a -> 'a -> bool) -> 'a t -> 'a t -> bool
exists2z f m1 m2 is similar to exists2 f m1 m2, but returns
false for physically equal subtrees without traversing them.
This is more efficient than exists2z, and equivalent if
f k a a = false and has no effect.
m1 and m2 must have the same key sets.
The bindings are passed to f in increasing order of keys.
val map2o : (key -> 'a -> 'c) ->
(key -> 'b -> 'c) ->
(key -> 'a -> 'b -> 'c) ->
'a t -> 'b t -> 'c t
map2o f1 f2 f m1 m2 is similar to map2 f m1 m2, but
accepts maps defined over different sets of keys.
To get a new binding, f1 is used for keys appearing only
in m1, f2 for keys appearing only in m2, and f for
keys appearing in both maps.
The returned map has bindings for all keys appearing in either
m1 or m2.
The bindings are passed to f, f1, f2 in increasing order of keys.
val iter2o : (key -> 'a -> unit) ->
(key -> 'b -> unit) ->
(key -> 'a -> 'b -> unit) -> 'a t -> 'b t -> unit
iter2o f1 f2 f m1 m2 is similar to iter2 f m1 m2, but
accepts maps defined over different sets of keys.
f1 is called for keys appearing only in m1,
f2 for keys appearing only in m2,
and f for keys appearing in both maps.
The bindings are passed to f, f1, f2 in increasing order of keys.
val fold2o : (key -> 'a -> 'c -> 'c) ->
(key -> 'b -> 'c -> 'c) ->
(key -> 'a -> 'b -> 'c -> 'c) ->
'a t -> 'b t -> 'c -> 'c
fold2o f1 f2 f m1 m2 a is similar to fold2 f m1 m2 a, but
accepts maps defined over different sets of keys.
f1 is called for keys appearing only in m1,
f2 for keys appearing only in m2,
and f for keys appearing in both maps.
The bindings are passed to f, f1, f2 in increasing order of keys.
val for_all2o : (key -> 'a -> bool) ->
(key -> 'b -> bool) ->
(key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
for_all2o f1 f2 f m1 m2 is similar to for_all2 f m1 m2, but
accepts maps defined over different sets of keys.
f1 is called for keys appearing only in m1,
f2 for keys appearing only in m2,
and f for keys appearing in both maps.
The bindings are passed to f, f1, f2 in increasing order of keys.
val exists2o : (key -> 'a -> bool) ->
(key -> 'b -> bool) ->
(key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
fexists2o f1 f2 f m1 m2 is similar to fexists2 f m1 m2, but
accepts maps defined over different sets of keys.
f1 is called for keys appearing only in m1,
f2 for keys appearing only in m2,
and f for keys appearing in both maps.
The bindings are passed to f, f1, f2 in increasing order of keys.
val map2zo : (key -> 'a -> 'a) ->
(key -> 'a -> 'a) ->
(key -> 'a -> 'a -> 'a) ->
'a t -> 'a t -> 'a t
map2zo f1 f2 f m1 m2 is similar to map2o f1 f2 f m1 m2 but,
similary to map2z, f is not called on physically equal
subtrees.
This is more efficient than map2o, and equivalent if f is
side-effect free and idem-potent (f k a a = a).
The returned map has bindings for all keys appearing in either
m1 or m2.
The bindings are passed to f, f1, f2 in increasing order of keys.
val iter2zo : (key -> 'a -> unit) ->
(key -> 'a -> unit) ->
(key -> 'a -> 'a -> unit) -> 'a t -> 'a t -> unit
iter2zo f1 f2 f m1 m2 is similar to iter2o f1 f2 f m1 m2 but,
similary to iter2z, f is not called on physically equal
subtrees.
This is more efficient than iter2o, and equivalent if f is
side-effect free.
The bindings are passed to f, f1, f2 in increasing order of keys.
val fold2zo : (key -> 'a -> 'b -> 'b) ->
(key -> 'a -> 'b -> 'b) ->
(key -> 'a -> 'a -> 'b -> 'b) ->
'a t -> 'a t -> 'b -> 'b
fold2zo f1 f2 f m1 m2 a is similar to fold2o f1 f2 f m1 m2 a but,
similary to fold2z, f is not called on physically equal
subtrees.
This is more efficient than fold2o, and equivalent if
f k a a x = x and has no side-effect.
The bindings are passed to f, f1, f2 in increasing order of keys.
val for_all2zo : (key -> 'a -> bool) ->
(key -> 'a -> bool) ->
(key -> 'a -> 'a -> bool) -> 'a t -> 'a t -> bool
for_all2zo f1 f2 f m1 m2 is similar to for_all2o f1 f2 f m1 m2 but,
similary to for_all2z, f is not called on physically equal
subtrees.
This is more efficient than for_all2o, and equivalent if
f k a a = true and has no side-effect.
The bindings are passed to f, f1, f2 in increasing order of keys.
val exists2zo : (key -> 'a -> bool) ->
(key -> 'a -> bool) ->
(key -> 'a -> 'a -> bool) -> 'a t -> 'a t -> bool
exists2zo f1 f2 f m1 m2 is similar to exists2o f1 f2 f m1 m2 but,
similary to exists2z, f is not called on physically equal
subtrees.
This is more efficient than exists2o, and equivalent if
f k a a = false and has no side-effect.
The bindings are passed to f, f1, f2 in increasing order of keys.
val map_slice : (key -> 'a -> 'a) ->
'a t -> key -> key -> 'a t
map_slice f m k1 k2 is similar to map f m, but only applies
f to bindings with key greater or equal to k1 and smaller
or equal to k2 to construct the returned map. Bindings with
keys outside this range in m are put unchanged in the result.
It is as if, outside this range, f k a = a and has no effect.
The result has the same key set as m.
The bindings are passed to f in increasing order of keys,
between k1 and k2.
val iter_slice : (key -> 'a -> unit) ->
'a t -> key -> key -> unit
iter_slice f m k1 k2 is similar to iter f m, but only calls
f on bindings with key greater or equal to k1 and smaller
or equal to k2.
It is as if, outside this range, f k a has no effect.
The bindings are passed to f in increasing order of keys,
between k1 and k2.
val fold_slice : (key -> 'a -> 'b -> 'b) ->
'a t -> key -> key -> 'b -> 'b
fold_slice f m k1 k2 a is similar to fold f m, but only calls
f on bindings with key greater or equal to k1 and smaller
or equal to k2.
It is as if, outside this range, f k a x = x and has no effect.
The bindings are passed to f in increasing order of keys,
between k1 and k2.
val for_all_slice : (key -> 'a -> bool) ->
'a t -> key -> key -> bool
for_all_slice f m k1 k2 a is similar to for_all f m, but only calls
f on bindings with key greater or equal to k1 and smaller
or equal to k2.
It is as if, outside this range, f k a = true and has no effect.
The bindings are passed to f in increasing order of keys,
between k1 and k2.
val exists_slice : (key -> 'a -> bool) ->
'a t -> key -> key -> bool
exists_slice f m k1 k2 a is similar to exists f m, but only calls
f on bindings with key greater or equal to k1 and smaller
or equal to k2.
It is as if, outside this range, f k a = false and has no effect.
The bindings are passed to f in increasing order of keys,
between k1 and k2.
val key_equal : 'a t -> 'a t -> bool
key_equal m1 m2 returns true if m1 and m2 are defined
over exactly the same set of keys (but with possibly different
values).
val key_subset : 'a t -> 'a t -> bool
key_equal m1 m2 returns true if m1 is defined on a subset of
the keys of m2 (but with possibly different values).
val find_greater : key -> 'a t -> key * 'a
find_greater k m returns the binding (key and value) in m
with key strictly greater than k and as small as possible.
Raises Not_found if m has no binding for a key strictly greater
than k.
val find_less : key -> 'a t -> key * 'a
find_less k m returns the binding (key and value) in m
with key strictly less than k and as large as possible.
Raises Not_found if m has no binding for a key strictly less
than k.
val find_greater_equal : key -> 'a t -> key * 'a
find_greater_euql k m returns the binding (key and value) in m
with key greater or equal to k and as small as possible.
Raises Not_found if m has no binding for a key greater or equal
to k.
val find_less_equal : key -> 'a t -> key * 'a
find_less_equal k m returns the binding (key and value) in m
with key less or equal to k and as large as possible.
Raises Not_found if m has no binding for a key less or equal
to k.