19.17 
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 sideeffects).
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 twoargument 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has been
replaced by the result of the application of f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.