# Module Ptmap

    module Ptmap: sig .. end

Maps over integers implemented as Patricia trees.

The following signature is a subset of `Map.S with type key = int`, with the same specifications (not repeated here) unless specified otherwise.

These are little-endian Patricia trees, so there is no efficient ordering of keys within the structure. Consequently,

- `min/max_binding`, `find_first/last` are rather inefficient (linear)
- `iter`, `fold` *do not* iterate in the key order
- `bindings` is *not sorted* by keys

    type key = int

    type +'a t

    val empty : 'a t

    val is_empty : 'a t -> bool

    val mem : key -> 'a t -> bool

    val add : key -> 'a -> 'a t -> 'a t

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

    val singleton : key -> 'a -> 'a t

    val remove : key -> 'a t -> 'a t

    val merge : (key -> 'a option -> 'b option -> 'c option) ->
           'a t -> 'b t -> 'c t

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

    val compare : ('a -> 'a -> int) -> 'a t -> 'a t -> int

    val equal : ('a -> 'a -> bool) -> 'a t -> 'a t -> bool

    val iter : (key -> 'a -> unit) -> 'a t -> unit

    val fold : (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b

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

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

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

    val filter_map : (key -> 'a -> 'b option) -> 'a t -> 'b t

    val partition : (key -> 'a -> bool) -> 'a t -> 'a t * 'a t

    val cardinal : 'a t -> int

    val bindings : 'a t -> (key * 'a) list

    val min_binding : 'a t -> key * 'a

    val min_binding_opt : 'a t -> (key * 'a) option

    val max_binding : 'a t -> key * 'a

    val max_binding_opt : 'a t -> (key * 'a) option

    val choose : 'a t -> key * 'a

    val choose_opt : 'a t -> (key * 'a) option

    val split : key -> 'a t -> 'a t * 'a option * 'a t

    val find : key -> 'a t -> 'a

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

    val find_first : (key -> bool) -> 'a t -> key * 'a

    val find_first_opt : (key -> bool) -> 'a t -> (key * 'a) option

    val find_last : (key -> bool) -> 'a t -> key * 'a

    val find_last_opt : (key -> bool) -> 'a t -> (key * 'a) option

    val map : ('a -> 'b) -> 'a t -> 'b t

    val mapi : (key -> 'a -> 'b) -> 'a t -> 'b t

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

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

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

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