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(***************************************************************************)
(* HLins: insert http-links into HTML documents. *)
(* See http://www.lri.fr/~treinen/hlins *)
(* *)
(* Copyright (C) 1999-2024 Ralf Treinen <treinen@irif.fr> *)
(* *)
(* This program is free software; you can redistribute it and/or modify *)
(* it under the terms of the GNU General Public License as published by *)
(* the Free Software Foundation; either version 2 of the License, or (at *)
(* your option) any later version. *)
(* *)
(* This program 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 *)
(* General Public License for more details. *)
(* *)
(* You should have received a copy of the GNU General Public License *)
(* along with this program; if not, write to the Free Software *)
(* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *)
(* USA *)
(* *)
(***************************************************************************)
(*
HLins: insert http-links into HTML documents.
See http://www.lri.fr/~treinen/hlins
Copyright (C) 1999 Ralf Treinen <treinen@lri.fr>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program 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 General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*)
(***************************************************************************)
(* Module defining the type "automaton" for multi-string search *)
(***************************************************************************)
(*
Data type "automaton" used for multi-string matching la Morris - Pratt.
See Chapter 7.1 in Crochemore & Rytter, Text Algorithms, Oxford
University Press, 1994.
*)
(* Type of the transition tables of a single state. An element of type
transitions is a partial mapping from characters to integers.
*)
type transitions;;
(* create an empty transition table *)
val empty_transitions : transitions;;
(* (get_transition t c) returns the result of the transition t under
character c. Raises Not_found if the transition is not defined.
*)
val get_transition : transitions -> char -> int;;
(* (add_transition t c p) yields the transition t plus c -> p *)
val add_transition : transitions -> char -> int -> transitions;;
(* fold function on transitions: let the transition function t be
[c1 -> q1; ... ; cn -> qn] (where this could have been in any order).
Then (transitions_fold f i t) yields
f ( ... (f (f i c1 q1) c2 q2) ... ) cn qn
*)
val transitions_fold :
('a -> char -> int -> 'a) -> 'a -> transitions -> 'a;;
type automaton = {
max_path_length: int;
number_of_states: int;
tree: transitions array;
level: int array;
board: int array;
suf: int array;
found: (int list) array;
expand: (int list) array
};;
(*
First some terminology:
- a word x is a prefix of a word y if exists z with y = x^z
- suffix if exists z with y = z^x
- factor if exists z1,z2 with y = z1^x^z2
A prefix (resp. suffix) is proper if z is not empty.
When building the automaton we are given an array W of length L of
non-empty words. Furthermore, there is some notion of an
abbreviation of a word. Let V be the set consisting of the elements
of W plus all their abbreviations. Let N be the cardinality of the
prefix-closure of V. We call "nodes" the numbers n with
0<=n<N. max_path_length is the maximal length of a word in W.
The size of the arrays f is at least N = number_of_states.
The array tree defines a graph where a directed edge labeled with
character c goes from node n to node m iff (c,m) in n. We require
that
- the graph is a tree.
- for any node n and character c there is at most one node m with
(c,m) in tree.(n).
Hence, the graph is in fact a feature tree.
For any node n, let path(n) be the word of characters on the edges
from the root to the node n. We require that
- path(0) = the empty word
- the set of all pathes in the tree = V
We require that for any node n that
- level.(n) is the length of path(n).
- board.(0) = -1
- if n >= 1: board(n) is the node m such that path(m) is the
longest proper suffix of path(n) that is a prefix of a word in V.
- suf.(n) is the node m such that path(m) is the longest (not
necessarily proper) suffix of path(n) that is a word in V.
suf.(n) = 0 if such a m does not exist.
Furthermore, we require for all nodes n that
- found.(n) = list of indices in W of path(n)
- expand.(n) = list of all indices of words w in W such that
path(n) is an abbreviation of w.
Hence, we have the following equivalence:
suf(n) = n
iff path(n) is a word in V
iff found.(n) @ expand.(n) <> nil.
*)
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