19.17 | Module `Map`: association tables over ordered types

> This module implements applicative association tables, also known as finite maps or dictionaries, given a total ordering function over the keys. All operations over maps are purely applicative (no side-effects). The implementation uses balanced binary trees, and therefore searching and insertion take time logarithmic in the size of the map.

    module type OrderedType =
      sig
        type t
        val compare: t -> t -> int
      end

> The input signature of the functor `Map.Make`. `t` is the type of the map keys. `compare` is a total ordering function over the keys. This is a two-argument function `f` such that `f e1 e2` is zero if the keys `e1` and `e2` are equal, `f e1 e2` is strictly negative if `e1` is smaller than `e2`, and `f e1 e2` is strictly positive if `e1` is greater than `e2`. Example: a suitable ordering function is the generic structural comparison function `compare`.

    module type S =
      sig
        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 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 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 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 mem: key -> 'a t -> bool

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

        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 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: ('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 `map f m` returns a map with same domain as `m`, where the associated value `a` of all bindings of `m` has been replaced by the result of the application of `f` to `a`.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 order in which the associated values are passed to `f` is unspecified.

        val mapi: (key -> 'a -> 'b) -> 'a t -> 'b 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: (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`, and `d1 ... dN` are the associated data. The order in which the bindings are presented to `f` is unspecified.

      end
    module Make(Ord: OrderedType): (S with type key = Ord.t)

> Functor building an implementation of the map structure given a totally ordered type.