(*
* Trie: maps over lists.
* Copyright (C) 2000 Jean-Christophe FILLIATRE
*
* This software is free software; you can redistribute it and/or
* modify it under the terms of the GNU Library General Public
* License version 2, as published by the Free Software Foundation.
*
* This software is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
*
* See the GNU Library General Public License version 2 for more details
* (enclosed in the file LGPL).
*)
(* $Id: trie.ml,v 1.5 2004/07/21 08:39:44 filliatr Exp $ *)
(*s A trie is a tree-like structure to implement dictionaries over
keys which have list-like structures. The idea is that each node
branches on an element of the list and stores the value associated
to the path from the root, if any. Therefore, a trie can be
defined as soon as a map over the elements of the list is
given. *)
module Make (M : Map.S) = struct
(*s Then a trie is just a tree-like structure, where a possible
information is stored at the node (['a option]) and where the sons
are given by a map from type [key] to sub-tries, so of type
['a t M.t]. The empty trie is just the empty map. *)
type key = M.key list
type 'a t = Node of 'a option * 'a t M.t
let empty = Node (None, M.empty)
(*s To find a mapping in a trie is easy: when all the elements of the
key have been read, we just inspect the optional info at the
current node; otherwise, we descend in the appropriate sub-trie
using [M.find]. *)
let rec find l t = match (l,t) with
| [], Node (None,_) -> raise Not_found
| [], Node (Some v,_) -> v
| x::r, Node (_,m) -> find r (M.find x m)
let rec mem l t = match (l,t) with
| [], Node (None,_) -> false
| [], Node (Some _,_) -> true
| x::r, Node (_,m) -> try mem r (M.find x m) with Not_found -> false
(*s Insertion is more subtle. When the final node is reached, we just
put the information ([Some v]). Otherwise, we have to insert the
binding in the appropriate sub-trie [t']. But it may not exists,
and in that case [t'] is bound to an empty trie. Then we get a new
sub-trie [t''] by a recursive insertion and we modify the
branching, so that it now points to [t''], with [M.add]. *)
let add l v t =
let rec ins = function
| [], Node (_,m) -> Node (Some v,m)
| x::r, Node (v,m) ->
let t' = try M.find x m with Not_found -> empty in
let t'' = ins (r,t') in
Node (v, M.add x t'' m)
in
ins (l,t)
(*s When removing a binding, we take care of not leaving bindings to empty
sub-tries in the nodes. Therefore, we test wether the result [t'] of
the recursive call is the empty trie [empty]: if so, we just remove
the branching with [M.remove]; otherwise, we modify it with [M.add]. *)
let rec remove l t = match (l,t) with
| [], Node (_,m) -> Node (None,m)
| x::r, Node (v,m) ->
try
let t' = remove r (M.find x m) in
Node (v, if t' = empty then M.remove x m else M.add x t' m)
with Not_found ->
t
(*s The iterators [map], [mapi], [iter] and [fold] are implemented in
a straigthforward way using the corresponding iterators [M.map],
[M.mapi], [M.iter] and [M.fold]. For the last three of them,
we have to remember the path from the root, as an extra argument
[revp]. Since elements are pushed in reverse order in [revp],
we have to reverse it with [List.rev] when the actual binding
has to be passed to function [f]. *)
let rec map f = function
| Node (None,m) -> Node (None, M.map (map f) m)
| Node (Some v,m) -> Node (Some (f v), M.map (map f) m)
let mapi f t =
let rec maprec revp = function
| Node (None,m) ->
Node (None, M.mapi (fun x -> maprec (x::revp)) m)
| Node (Some v,m) ->
Node (Some (f (List.rev revp) v), M.mapi (fun x -> maprec (x::revp)) m)
in
maprec [] t
let iter f t =
let rec traverse revp = function
| Node (None,m) ->
M.iter (fun x -> traverse (x::revp)) m
| Node (Some v,m) ->
f (List.rev revp) v; M.iter (fun x t -> traverse (x::revp) t) m
in
traverse [] t
let rec fold f t acc =
let rec traverse revp t acc = match t with
| Node (None,m) ->
M.fold (fun x -> traverse (x::revp)) m acc
| Node (Some v,m) ->
f (List.rev revp) v (M.fold (fun x -> traverse (x::revp)) m acc)
in
traverse [] t acc
let compare cmp a b =
let rec comp a b = match a,b with
| Node (Some _, _), Node (None, _) -> 1
| Node (None, _), Node (Some _, _) -> -1
| Node (None, m1), Node (None, m2) ->
M.compare comp m1 m2
| Node (Some a, m1), Node (Some b, m2) ->
let c = cmp a b in
if c <> 0 then c else M.compare comp m1 m2
in
comp a b
let equal eq a b =
let rec comp a b = match a,b with
| Node (None, m1), Node (None, m2) ->
M.equal comp m1 m2
| Node (Some a, m1), Node (Some b, m2) ->
eq a b && M.equal comp m1 m2
| _ ->
false
in
comp a b
(* The base case is rather stupid, but constructable *)
let is_empty = function
| Node (None, m1) -> M.is_empty m1
| _ -> false
end