##### Polymorphic maps

The functions below present the manipulation of polymorphic maps, as were provided by the Extlib PMap module.

They are similar in functionality to the functorized `Make` module, but the compiler cannot ensure that maps using different key ordering have different types: the responsibility of not mixing non-sensical comparison functions together is to the programmer. If in doubt, you should rather use the `Make` functor for additional safety.

`type ('a, +'b) t`
`val empty : ('a, 'b) t`

The empty map, using `compare` as key comparison function.

`val is_empty : ('a, 'b) t -> bool`

Returns `true` if the map is empty.

`val create : ('a -> 'a -> int) -> ('a, 'b) t`

Creates a new empty map, using the provided function for key comparison.

`val singleton : ?cmp:('a -> 'a -> int) -> 'a -> 'b -> ('a, 'b) t`

Creates a new map with a single binding.

`val cardinal : ('a, 'b) t -> int`

Return the number of bindings of a map.

`val add : 'a -> 'b -> ('a, 'b) t -> ('a, 'b) 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.

If `x` was already bound to some `z` that is physically equal to `y`, then the returned map is physically equal to `m`.

- before 3.3.0

  or OCaml 4.03 physical equality was not ensured.

`val update : 'a -> 'a -> 'b -> ('a, 'b) t -> ('a, 'b) t`

`update k1 k2 v2 m` replace the previous binding of `k1` in `m` by `k2` associated to `v2`. This is equivalent to `add k2 v2 (remove k1) m`, but more efficient in the case where `k1` and `k2` have the same key ordering. If `k1` and `k2` have the same key ordering and `v2` is physically equal to the value `k1` is bound to in `m` then the returned map will be physically equal to `m`

- raises `Not_found`

  if `k1` is not bound in `m`.

- since 2.4.0

- before 3.3.0

  physical equality was not ensured.

`val update_stdlib : 'a -> ('b option -> 'b option) -> ('a, 'b) t -> ('a, 'b) t`

`update_stdlib k f m` returns a map containing the same bindings as `m`, except `k` has a new binding as determined by `f`: First, calculate `y` as `f (find_opt k m)`. If `y = Some v` then `k` will be bound to `v` in the resulting map. Else `k` will not be bound in the resulting map. If `v` is physically equal to the value of the previous binding of `k` in `m`, then the returned map will be physically equal to `m`.

This function does the same thing as `update` in the stdlib, but has a different name for backwards compatibility reasons.

- since 3.3.0

`val find : 'a -> ('a, 'b) t -> 'b`

`find x m` returns the current binding of `x` in `m`, or raises `Not_found` if no such binding exists.

`val find_default : 'b -> 'a -> ('a, 'b) t -> 'b`

`find_default d x m` returns the current binding of `x` in `m`, or the default value `d` if no such binding exists.

`val find_first : ('a -> bool) -> ('a, 'b) t -> 'a * 'b`

`find_first f m` returns the first binding `(k, v)` for which `f k` is true or raises `Not_found` if there is no such binding. `f` must be monotonically increasing, i.e. if `k1 < k2 && f k1` is true then `f k2` must also be true.

- since 3.3.0

`val find_first_opt : ('a -> bool) -> ('a, 'b) t -> ('a * 'b) option`

`find_first_opt f m` returns `Some (k, v)` for the first binding `(k, v)` for which `f k` is true or returns `None` if there is no such binding. `f` must be monotonically increasing, i.e. if `k1 < k2 && f k1` is true then `f k2` must also be true.

- since 3.3.0

`val find_last : ('a -> bool) -> ('a, 'b) t -> 'a * 'b`

`find_last f m` returns the last binding `(k, v)` for which `f k` is true or raises `Not_found` if there is no such binding. `f` must be monotonically decreasing, i.e. if `k1 < k2 && f k2` is true then `f k1` must also be true.

- since 3.3.0

`val find_last_opt : ('a -> bool) -> ('a, 'b) t -> ('a * 'b) option`

`find_last_opt f m` returns `Some (k, v)` for the last binding `(k, v)` for which `f k` is true or returns `None` if there is no such binding. `f` must be monotonically decreasing, i.e. if `k1 < k2 && f k2` is true then `f k1` must also be true.

- since 3.3.0

`val remove : 'a -> ('a, 'b) t -> ('a, 'b) t`

`remove x m` returns a map containing the same bindings as `m`, except for `x` which is unbound in the returned map. The returned map is physically equal to the passed one if `x` was already unbound.

- before 3.3.0

  or OCaml 4.03 physical equality was not ensured.

`val remove_exn : 'a -> ('a, 'b) t -> ('a, 'b) t`

`remove_exn x m` behaves like `remove x m` except that it raises an exception if `x` is unbound in `m`.

- raises `Not_found`

  if `x` is unbound in `m`

- since 3.2.0

`val mem : 'a -> ('a, 'b) t -> bool`

`mem x m` returns `true` if `m` contains a binding for `x`, and `false` otherwise.

`val iter : ('a -> 'b -> unit) -> ('a, 'b) 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 order in which the bindings are passed to `f` is unspecified. Only current bindings are presented to `f`: bindings hidden by more recent bindings are not passed to `f`.

`val map : ('b -> 'c) -> ('a, 'b) t -> ('a, 'c) 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 order in which the associated values are passed to `f` is unspecified.

`val mapi : ('a -> 'b -> 'c) -> ('a, 'b) t -> ('a, 'c) t`

Same as `map`, but the function receives as arguments both the key and the associated value for each binding of the map.

`val fold : ('b -> 'c -> 'c) -> ('a, 'b) t -> 'c -> 'c`

`fold f m a` computes `(f kN dN ... (f k1 d1 (f k0 d0 a))...)`, where `k0,k1..kN` are the keys of all bindings in `m`, and `d0,d1..dN` are the associated data. The order in which the bindings are presented to `f` is unspecified.

`val foldi : ('a -> 'b -> 'c -> 'c) -> ('a, 'b) t -> 'c -> 'c`

Same as `fold`, but the function receives as arguments both the key and the associated value for each binding of the map.

`val at_rank_exn : int -> ('a, 'b) t -> 'a * 'b`

`at_rank_exn i m` returns the `(key,value)` pair whose key is at rank `i` in `m`, that is the `i`-th element in increasing order of the keys (the `0`-th element being the smallest key in `m` with its associated value).

- raises `Not_found`

  if `m = empty`.

- raises `Invalid_argument`

  error_message if `i < 0 || i >= cardinal m`

- since 2.4

`val filterv : ('a -> bool) -> ('key, 'a) t -> ('key, 'a) t`

`filterv f m` returns a map where only the values `a` of `m` such that `f a = true` remain. The bindings are passed to `f` in increasing order with respect to the ordering over the type of the keys.

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

`filter f m` returns a map where only the `(key, value)` pairs of `m` such that `f key value = true` remain. The bindings are passed to `f` in increasing order with respect to the ordering over the type of the keys. If `f` returns `true` for all bindings of `m` the returned map is physically equal to `m`.

- before 3.3.0

  or OCaml 4.03 physical equality was not ensured.

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

`filter_map f m` combines the features of `filter` and `map`. It calls calls `f key0 a0`, `f key1 a1`, `f keyn an` where `a0..an` are the elements of `m` and `key0..keyn` the respective corresponding keys. It returns the map of (`keyi`, `bi`) pairs such as `f keyi ai = Some bi` (when `f` returns `None`, the corresponding element of `m` is discarded).

`val choose : ('key, 'a) t -> 'key * 'a`

Return one binding of the given map. Which binding is chosen is unspecified, but equal bindings will be chosen for equal maps.

- raises `Not_found`

  if the map is empty.

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

Return `Some (k, v)` for one binding `(k, v)` of the given map, if the map is not empty. Else, return None. Which binding is chosen is unspecified, but equal bindings will be chosen for equal maps.

- since 3.3.0

`val any : ('key, 'a) t -> 'key * 'a`

Return one binding of the given map. The difference with choose is that there is no guarantee that equals elements will be picked for equal sets. This merely returns the quickest binding to get (O(1)).

- raises `Not_found`

  if the map is empty.

`val split : 'key -> ('key, 'a) t -> ('key, 'a) t * 'a option * ('key, '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 min_binding : ('key, 'a) t -> 'key * 'a`

Returns the binding with the smallest key.

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

Return `Some (key, value)` for the `key, value` pair with the smallest key, or `None` if the map is empty.

- since 3.3.0

`val pop_min_binding : ('key, 'a) t -> ('key * 'a) * ('key, 'a) t`

Return the binding with the smallest key along with the rest of the map.

`val max_binding : ('key, 'a) t -> 'key * 'a`

Returns the binding with the largest key.

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

Return `Some (key, value)` for the `key, value` pair with the largest key, or `None` if the map is empty.

- since 3.3.0

`val pop_max_binding : ('key, 'a) t -> ('key * 'a) * ('key, 'a) t`

Return the binding with the largest key along with the rest of the map.

`val enum : ('a, 'b) t -> ('a * 'b) BatEnum.t`

Creates an enumeration for this map, enumerating `(key, value)` pairs with the keys in increasing order.

`val backwards : ('a, 'b) t -> ('a * 'b) BatEnum.t`

Creates an enumeration for this map, enumerating `(key, value)` pairs with the keys in decreasing order.

`val keys : ('a, 'b) t -> 'a BatEnum.t`

Return an enumeration of all the keys of a map.

`val values : ('a, 'b) t -> 'b BatEnum.t`

Return an enumeration of all the values of a map.

`val of_enum : ?cmp:('a -> 'a -> int) -> ('a * 'b) BatEnum.t -> ('a, 'b) t`

creates a map from an enumeration, using the specified function for key comparison or `compare` by default.

`val for_all : ('a -> 'b -> bool) -> ('a, 'b) t -> bool`

Tests whether all `(key, value)` pairs satisfy a predicate function.

`val exists : ('a -> 'b -> bool) -> ('a, 'b) t -> bool`

Tests whether some `(key, value)` pair satisfies a predicate function.

`val partition : ('a -> 'b -> bool) -> ('a, 'b) t -> ('a, 'b) t * ('a, 'b) 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 add_carry : 'a -> 'b -> ('a, 'b) t -> ('a, 'b) t * 'b option`

`add_carry k v m` adds the binding `(k, v)` to `m`, returning the new map and optionally the previous value bound to `k`.

`val modify : 'a -> ('b -> 'b) -> ('a, 'b) t -> ('a, 'b) t`

`modify k f m` replaces the previous binding for `k` with `f` applied to that value. If `k` is unbound in `m` or `Not_found` is raised during the search, `Not_found` is raised.

- since 1.2.0

- raises `Not_found`

  if `k` is unbound in `m` (or `f` raises `Not_found`)

`val modify_def : 'b -> 'a -> ('b -> 'b) -> ('a, 'b) t -> ('a, 'b) t`

`modify_def v0 k f m` replaces the previous binding for `k` with `f` applied to that value. If `k` is unbound in `m` or `Not_found` is raised during the search, `f v0` is inserted (as if the value found were `v0`).

- since 1.3.0

`val modify_opt : 'a -> ('b option -> 'b option) -> ('a, 'b) t -> ('a, 'b) t`

`modify_opt k f m` allow to modify the binding for `k` in `m` or absence thereof.

- since 2.1

`val extract : 'a -> ('a, 'b) t -> 'b * ('a, 'b) t`

`extract k m` removes the current binding of `k` from `m`, returning the value `k` was bound to and the updated `m`.

`val pop : ('a, 'b) t -> ('a * 'b) * ('a, 'b) t`

`pop m` returns a binding from `m` and `m` without that binding.

`val union : ('a, 'b) t -> ('a, 'b) t -> ('a, 'b) t`

`union m1 m2` merges two maps, using the comparison function of `m1`. In case of conflicted bindings, `m2`'s bindings override `m1`'s. Equivalent to `foldi add m2 m1`. The resulting map uses the comparison function of `m1`.

`val diff : ('a, 'b) t -> ('a, 'b) t -> ('a, 'b) t`

`diff m1 m2` removes all bindings of keys found in `m2` from `m1`, using the comparison function of `m1`. Equivalent to `foldi (fun k _v m -> remove k m) m2 m1`. The resulting map uses the comparison function of `m1`.

`val intersect : ('b -> 'c -> 'd) -> ('a, 'b) t -> ('a, 'c) t -> ('a, 'd) t`

`intersect merge_f m1 m2` returns a map with bindings only for keys bound in both `m1` and `m2`, and with `k` bound to `merge_f v1 v2`, where `v1` and `v2` are `k`'s bindings in `m1` and `m2`. The resulting map uses the comparison function of `m1`.

`val merge : ('key -> 'a option -> 'b option -> 'c option) -> ('key, 'a) t -> ('key, 'b) t -> ('key, '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`. The resulting map uses the comparison function of `m1`.

`val merge_unsafe : ('key -> 'a option -> 'b option -> 'c option) -> ('key, 'a) t -> ('key, 'b) t -> ('key, 'c) t`

Same as merge, but assumes the comparison function of both maps are equal. If it's not the case, the result is a map using the comparison function of its first parameter, but which `'b option` elements are passed to the function is unspecified.

`val union_stdlib : ('key -> 'a -> 'a -> 'a option) -> ('key, 'a) t -> ('key, 'a) t -> ('key, '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 function is similar to `merge`, except `f` is only called if a key is present in both `m1` and `m2`. If a key is present in either `m1` or `m2` but not in both, it (and the corresponding value) will be present in the resulting map.

This is the union method from the stdlib map, renamed for backwards compatibility.

- since 3.3.0

`val to_seq : ('key, 'a) t -> ('key * 'a) BatSeq.t`

Iterate on the whole map, in ascending order of keys.

- since 3.3.0

`val to_rev_seq : ('key, 'a) t -> ('key * 'a) BatSeq.t`

Iterate on the whole map, in descending order of keys.

- since 3.3.0

`val to_seq_from : 'key -> ('key, 'a) t -> ('key * 'a) BatSeq.t`

`to_seq_from k m` iterates on a subset of the bindings in `m`, namely those bindings greater or equal to `k`, in ascending order.

- since 3.3.0

`val add_seq : ('key * 'a) BatSeq.t -> ('key, 'a) t -> ('key, 'a) t`

add the given bindings to the map, in order.

- since 3.3.0

`val of_seq : ?cmp:('key -> 'key -> int) -> ('key * 'a) BatSeq.t -> ('key, 'a) t`

build a map from the given bindings

- since 3.3.0

`val compare : ('b -> 'b -> int) -> ('a, 'b) t -> ('a, 'b) t -> int`
`val equal : ('b -> 'b -> bool) -> ('a, 'b) t -> ('a, 'b) t -> bool`

Construct a comparison or equality function for maps based on a value comparison or equality function. Uses the key comparison function to compare keys.

`module Exceptionless : sig ... end`

Exceptionless versions of functions

`module Infix : sig ... end`

Infix operators over a `PMap`

`val (-->) : ('a, 'b) t -> 'a -> 'b`

Map find and insert from Infix

`val (<--) : ('a, 'b) t -> ('a * 'b) -> ('a, 'b) t`
`val bindings : ('key, 'a) t -> ('key * 'a) list`

Return the list of all bindings of the given map. The returned list is sorted in increasing key order.

Added for compatibility with stdlib 3.12

## Boilerplate code

### Printing

`val print : ?first:string -> ?last:string -> ?sep:string -> ?kvsep:string -> ('a BatInnerIO.output -> 'b -> unit) -> ('a BatInnerIO.output -> 'c -> unit) -> 'a BatInnerIO.output -> ('b, 'c) t -> unit`
`val get_cmp : ('a, 'b) t -> 'a -> 'a -> int`

get the comparison function used for a polymorphic map