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.

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

The input signature of the functor MakeMap. 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.

signature MAP =
  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:key -> data:'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 m, and false otherwise.

    val iter: f:(key:key -> data:'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: f:('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map f m returns a map with same domain as m, where the associated value a of all bindings of m has been replaced by the result of the application of f to a. The order in which the associated values are passed to f is unspecified.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: f:(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: f:(key:key -> data:'a -> 'b -> 'b) -> 'a t -> init:'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

functor MakeMap(Ord: OrderedType): (MAP with type key = Ord.t)

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