NAME

       Map.S - Output signature of the functor Map.Make.

Module type

       Module type   Map.S

Documentation

       Module type S
        = sig end

       Output signature of the functor Map.Make .

       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 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.

       Before4.03 Physical equality was not ensured.

       val update : key -> ('a option -> 'a option) -> 'a t -> 'a t

       update 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 ).

       Since 4.06.0

       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.  If x was not in m , m is  returned  unchanged  (the  result  of  the
       function is then physically equal to m ).

       Before4.03 Physical equality was not ensured.

       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 .  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 .

       Since 3.12.0

       val union : (key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t

       union 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 = 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

       Since 4.03.0

       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 .

       Since 3.12.0

       val exists : (key -> 'a -> bool) -> 'a t -> bool

       exists p m checks if at least one binding of the map satisfies the predicate p .

       Since 3.12.0

       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  .  If  p
       satisfies every binding in m , m is returned unchanged (the result of the function is then
       physically equal to m )

       Before4.03 Physical equality was not ensured.

       Since 3.12.0

       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  of  keys  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 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.

       Since 3.12.0

       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.

       Since 4.05

       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.

       Since 3.12.0

       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.

       Since 4.05

       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 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.

       Since 4.05

       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 find_opt : key -> 'a t -> 'a option

       find_opt  x  m  returns  Some v if the current binding of x in m is v , or None if no such
       binding exists.

       Since 4.05

       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 .

       Since 4.05

       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.

       Since 4.05

       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.

       Since 4.05

       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.

       Since 4.05

       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.

   Iterators
       val to_seq : 'a t -> (key * 'a) Seq.t

       Iterate on the whole map, in ascending order of keys

       Since 4.07

       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.

       Since 4.07

       val add_seq : (key * 'a) Seq.t -> 'a t -> 'a t

       Add the given bindings to the map, in order.

       Since 4.07

       val of_seq : (key * 'a) Seq.t -> 'a t

       Build a map from the given bindings

       Since 4.07