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 =
val compare: t -> t -> int
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 =
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 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associated value a of all bindings of m has been
replaced by the result of the application of f to a.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
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
module Make(Ord: OrderedType): (S with type key = Ord.t)
Functor building an implementation of the map structure
given a totally ordered type.