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Module Map: association tables over ordered types
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<H2>17.15 Module <TT>Map</TT>: association tables over ordered types</H2><A NAME="s:Map"></A>
<A NAME="@manual384"></A><BLOCKQUOTE>
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.
</BLOCKQUOTE>
<PRE>
module type OrderedType =
sig
type t
val compare: t -> t -> int
end
</PRE>
<A NAME="@manual385"></A><BLOCKQUOTE>
The input signature of the functor <CODE>Map.Make</CODE>.
<CODE>t</CODE> is the type of the map keys.
<CODE>compare</CODE> is a total ordering function over the keys.
This is a two-argument function <CODE>f</CODE> such that
<CODE>f e1 e2</CODE> is zero if the keys <CODE>e1</CODE> and <CODE>e2</CODE> are equal,
<CODE>f e1 e2</CODE> is strictly negative if <CODE>e1</CODE> is smaller than <CODE>e2</CODE>,
and <CODE>f e1 e2</CODE> is strictly positive if <CODE>e1</CODE> is greater than <CODE>e2</CODE>.
Example: a suitable ordering function is
the generic structural comparison function <CODE>compare</CODE>.
</BLOCKQUOTE>
<PRE>
module type S =
sig
type key
</PRE>
<BLOCKQUOTE>
The type of the map keys.
</BLOCKQUOTE>
<PRE>
type 'a t
</PRE>
<BLOCKQUOTE>
The type of maps from type <CODE>key</CODE> to type <CODE>'a</CODE>.
</BLOCKQUOTE>
<PRE>
val empty: 'a t
</PRE>
<BLOCKQUOTE>
The empty map.
</BLOCKQUOTE>
<PRE>
val add: key -> 'a -> 'a t -> 'a t
</PRE>
<BLOCKQUOTE>
<CODE>add x y m</CODE> returns a map containing the same bindings as
<CODE>m</CODE>, plus a binding of <CODE>x</CODE> to <CODE>y</CODE>. If <CODE>x</CODE> was already bound
in <CODE>m</CODE>, its previous binding disappears.
</BLOCKQUOTE>
<PRE>
val find: key -> 'a t -> 'a
</PRE>
<BLOCKQUOTE>
<CODE>find x m</CODE> returns the current binding of <CODE>x</CODE> in <CODE>m</CODE>,
or raises <CODE>Not_found</CODE> if no such binding exists.
</BLOCKQUOTE>
<PRE>
val remove: key -> 'a t -> 'a t
</PRE>
<BLOCKQUOTE>
<CODE>remove x m</CODE> returns a map containing the same bindings as
<CODE>m</CODE>, except for <CODE>x</CODE> which is unbound in the returned map.
</BLOCKQUOTE>
<PRE>
val mem: key -> 'a t -> bool
</PRE>
<BLOCKQUOTE>
<CODE>mem x m</CODE> returns <CODE>true</CODE> if <CODE>m</CODE> contains a binding for <CODE>m</CODE>,
and <CODE>false</CODE> otherwise.
</BLOCKQUOTE>
<PRE>
val iter: (key -> 'a -> unit) -> 'a t -> unit
</PRE>
<BLOCKQUOTE>
<CODE>iter f m</CODE> applies <CODE>f</CODE> to all bindings in map <CODE>m</CODE>.
<CODE>f</CODE> receives the key as first argument, and the associated value
as second argument. The order in which the bindings are passed to
<CODE>f</CODE> is unspecified. Only current bindings are presented to <CODE>f</CODE>:
bindings hidden by more recent bindings are not passed to <CODE>f</CODE>.
</BLOCKQUOTE>
<PRE>
val map: ('a -> 'b) -> 'a t -> 'b t
</PRE>
<BLOCKQUOTE>
<CODE>map f m</CODE> returns a map with same domain as <CODE>m</CODE>, where the
associated value <CODE>a</CODE> of all bindings of <CODE>m</CODE> has been
replaced by the result of the application of <CODE>f</CODE> to <CODE>a</CODE>.
The order in which the associated values are passed to <CODE>f</CODE>
is unspecified.
</BLOCKQUOTE>
<PRE>
val fold: (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
</PRE>
<BLOCKQUOTE>
<CODE>fold f m a</CODE> computes <CODE>(f kN dN ... (f k1 d1 a)...)</CODE>,
where <CODE>k1 ... kN</CODE> are the keys of all bindings in <CODE>m</CODE>,
and <CODE>d1 ... dN</CODE> are the associated data.
The order in which the bindings are presented to <CODE>f</CODE> is
unspecified.
</BLOCKQUOTE>
<PRE>
end
module Make(Ord: OrderedType): (S with type key = Ord.t)
</PRE>
<A NAME="@manual386"></A><BLOCKQUOTE>
Functor building an implementation of the map structure
given a totally ordered type.
</BLOCKQUOTE>
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