|| Functor MakeMap: 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.
signature OrderedType =
val compare: t -> t -> int
The input signature of the functor
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
e2 are equal,
f e1 e2 is strictly negative if
e1 is smaller than
f e1 e2 is strictly positive if
e1 is greater than
Example: a suitable ordering function is
the generic structural comparison function
signature MAP =
The type of the map keys.
type (+'a) t
The type of maps from type
key to type
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 was already bound
m, its previous binding disappears.
val find: key -> 'a t -> 'a
find x m returns the current binding of
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
m contains a binding for
val iter: f:(key:key -> data:'a -> unit) -> 'a t -> unit
iter f m applies
f to all bindings in map
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
bindings hidden by more recent bindings are not passed to
val map: f:('a -> 'b) -> 'a t -> 'b t
map f m returns a map with same domain as
m, where the
a of all bindings of
m has been
replaced by the result of the application of
The order in which the associated values are passed to
val mapi: f:(key -> 'a -> 'b) -> 'a t -> 'b t
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)...),
k1 ... kN are the keys of all bindings in
d1 ... dN are the associated data.
The order in which the bindings are presented to
functor MakeMap(Ord: OrderedType): (MAP with type key = Ord.t)
Functor building an implementation of the map structure
given a totally ordered type.