grew_rule.ml 41.7 KB
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(**********************************************************************************)
(*    Libcaml-grew - a Graph Rewriting library dedicated to NLP applications      *)
(*                                                                                *)
(*    Copyright 2011-2013 Inria, Université de Lorraine                           *)
(*                                                                                *)
(*    Webpage: http://grew.loria.fr                                               *)
(*    License: CeCILL (see LICENSE folder or "http://www.cecill.info")            *)
(*    Authors: see AUTHORS file                                                   *)
(**********************************************************************************)

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open Log
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open Printf
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open Grew_base
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open Grew_types

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open Grew_ast
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open Grew_edge
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open Grew_fs
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open Grew_node
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open Grew_command
open Grew_graph
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(* ================================================================================ *)
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module Instance = struct
  type t = {
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    graph: G_graph.t;
    history: Command.h list;
    rules: string list;
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    big_step: Libgrew_types.big_step option;
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    free_index: int;
    activated_node: Gid.t list;
  }

  let empty = {graph = G_graph.empty; rules=[]; history=[]; big_step=None; free_index=0; activated_node=[];}

  let from_graph graph =
    {empty with
      graph = graph;
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      free_index = (G_graph.max_binding graph) + 1;
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    }

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  let rev_steps t =
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    { t with big_step = match t.big_step with
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      | None -> None
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      | Some bs -> Some {bs with Libgrew_types.small_step = List.rev bs.Libgrew_types.small_step }
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    }

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  let flatten t =
    (* [mapping] is list of couple (node_id, node_id) used to flatten the graph *)
    let (mapping, new_free) = List.fold_left
      (fun (acc_map, next_free) node_id ->
        (
          (node_id, Gid.Old next_free) :: acc_map,
          next_free + 1
        )
      ) ([], t.free_index) t.activated_node in
    { empty with graph = G_graph.rename mapping t.graph; free_index = new_free }
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  (* comparison is done on the list of commands *)
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  (* only graph rewritten from the same init graph can be "compared" *)
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  let compare t1 t2 = Pervasives.compare t1.history t2.history
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  let to_gr t = G_graph.to_gr t.graph

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  let to_conll t = G_graph.to_conll t.graph

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  let save_dot_png ?filter ?main_feat base t =
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    ignore (Dot.to_png_file (G_graph.to_dot ?main_feat t.graph) (base^".png"))
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  IFDEF DEP2PICT THEN
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  let save_dep_png ?filter ?main_feat base t =
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    let (_,_,highlight_position) =
      Dep2pict.Dep2pict.fromDepStringToPng_with_pos
        (G_graph.to_dep ?filter ?main_feat t.graph) (base^".png") in
    highlight_position

  let save_dep_svg ?filter ?main_feat base t =
    let (_,_,highlight_position) =
      Dep2pict.Dep2pict.fromDepStringToSvgFile_with_pos
        (G_graph.to_dep ?filter ?main_feat t.graph) (base^".svg") in
    highlight_position

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  ELSE
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  let save_dep_png ?filter ?main_feat base t = None
  let save_dep_svg ?filter ?main_feat base t = None
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  ENDIF
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end (* module Instance *)
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(* ================================================================================ *)
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module Instance_set = Set.Make (Instance)
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(* ================================================================================ *)
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module Rule = struct
  (* the rewriting depth is bounded to stop rewriting when the system is not terminating *)
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  let max_depth = ref 500
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  type const =
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    | Cst_out of Pid.t * Label_cst.t
    | Cst_in of Pid.t * Label_cst.t
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    | Feature_eq of Pid.t * string * Pid.t * string
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    | Feature_diseq of Pid.t * string * Pid.t * string
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    | Feature_ineq of Ast.ineq * Pid.t * string * Pid.t * string
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    | Feature_ineq_cst of Ast.ineq * Pid.t * string * float

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    | Filter of Pid.t * P_fs.t (* used when a without impose a fs on a node defined by the match basic *)
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  let build_pos_constraint ?locals pos_table const =
    let pid_of_name loc node_name = Pid.Pos (Id.build ~loc node_name pos_table) in
    match const with
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      | (Ast.Cst_out (id,label_cst), loc) ->
        Cst_out (pid_of_name loc id, Label_cst.build ~loc ?locals label_cst)
      | (Ast.Cst_in (id,label_cst), loc) ->
        Cst_in (pid_of_name loc id, Label_cst.build ~loc ?locals label_cst)
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      | (Ast.Feature_eq ((node_name1, feat_name1), (node_name2, feat_name2)), loc) ->
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        Domain.check_feature_name ~loc feat_name1;
        Domain.check_feature_name ~loc feat_name2;        
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        Feature_eq (pid_of_name loc node_name1, feat_name1, pid_of_name loc node_name2, feat_name2)
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      | (Ast.Feature_diseq ((node_name1, feat_name1), (node_name2, feat_name2)), loc) ->
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        Domain.check_feature_name ~loc feat_name1;
        Domain.check_feature_name ~loc feat_name2;        
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        Feature_diseq (pid_of_name loc node_name1, feat_name1, pid_of_name loc node_name2, feat_name2)
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      | (Ast.Feature_ineq (ineq, (node_name1, feat_name1), (node_name2, feat_name2)), loc) ->
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        Domain.check_feature_name ~loc feat_name1;
        Domain.check_feature_name ~loc feat_name2;        
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        Feature_ineq (ineq, pid_of_name loc node_name1, feat_name1, pid_of_name loc node_name2, feat_name2)
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      | (Ast.Feature_ineq_cst (ineq, (node_name1, feat_name1), constant), loc) ->
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        Domain.check_feature_name ~loc feat_name1;
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        Feature_ineq_cst (ineq, pid_of_name loc node_name1, feat_name1, constant)

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  type basic = {
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    graph: P_graph.t;
    constraints: const list;
  }
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  let build_pos_basic ?pat_vars ?(locals=[||]) basic_ast =
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    let (graph, pos_table) =
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      P_graph.build ?pat_vars ~locals basic_ast.Ast.pat_nodes basic_ast.Ast.pat_edges in
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    (
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      {
        graph = graph;
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        constraints = List.map (build_pos_constraint ~locals pos_table) basic_ast.Ast.pat_const
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      },
      pos_table
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    )

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  (* the neg part *)
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  let build_neg_constraint ?locals pos_table neg_table const =
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    let pid_of_name loc node_name =
      match Id.build_opt node_name pos_table with
        | Some i -> Pid.Pos i
        | None -> Pid.Neg (Id.build ~loc node_name neg_table) in
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    match const with
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      | (Ast.Cst_out (id,label_cst), loc) ->
        Cst_out (pid_of_name loc id, Label_cst.build ~loc ?locals label_cst)
      | (Ast.Cst_in (id,label_cst), loc) ->
        Cst_in (pid_of_name loc id, Label_cst.build ~loc ?locals label_cst)
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      | (Ast.Feature_eq (feat_id1, feat_id2), loc) ->
        let (node_name1, feat_name1) = feat_id1
        and (node_name2, feat_name2) = feat_id2 in
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        Domain.check_feature_name ~loc feat_name1;
        Domain.check_feature_name ~loc feat_name2;        
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        Feature_eq (pid_of_name loc node_name1, feat_name1, pid_of_name loc node_name2, feat_name2)
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      | (Ast.Feature_diseq (feat_id1, feat_id2), loc) ->
        let (node_name1, feat_name1) = feat_id1
        and (node_name2, feat_name2) = feat_id2 in
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        Domain.check_feature_name ~loc feat_name1;
        Domain.check_feature_name ~loc feat_name2;        
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        Feature_diseq (pid_of_name loc node_name1, feat_name1, pid_of_name loc node_name2, feat_name2)
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      | (Ast.Feature_ineq (ineq, feat_id1, feat_id2), loc) ->
        let (node_name1, feat_name1) = feat_id1
        and (node_name2, feat_name2) = feat_id2 in
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        Domain.check_feature_name ~loc feat_name1;
        Domain.check_feature_name ~loc feat_name2;        
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        Feature_ineq (ineq, pid_of_name loc node_name1, feat_name1, pid_of_name loc node_name2, feat_name2)
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      | (Ast.Feature_ineq_cst (ineq, feat_id1, constant), loc) ->
        let (node_name1, feat_name1) = feat_id1 in
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        Domain.check_feature_name ~loc feat_name1;
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        Feature_ineq_cst (ineq, pid_of_name loc node_name1, feat_name1, constant)
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  (* It may raise [P_fs.Fail_unif] in case of contradiction on constraints *)
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  let build_neg_basic ?pat_vars ?(locals=[||]) pos_table basic_ast =
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    let (extension, neg_table) =
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      P_graph.build_extension ?pat_vars ~locals pos_table basic_ast.Ast.pat_nodes basic_ast.Ast.pat_edges in
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    let filters = Pid_map.fold (fun id node acc -> Filter (id, P_node.get_fs node) :: acc) extension.P_graph.old_map [] in
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    {
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      graph = extension.P_graph.ext_map;
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      constraints = filters @ List.map (build_neg_constraint ~locals pos_table neg_table) basic_ast.Ast.pat_const ;
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    }
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  let get_edge_ids basic =
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    Pid_map.fold
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      (fun _ node acc ->
        Massoc_pid.fold
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          (fun acc2 _ edge -> match P_edge.get_id edge with None -> acc2 | Some id -> id::acc2)
          acc (P_node.get_next node)
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      ) basic.graph []
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  (* a [pattern] is described by the positive basic and a list of negative basics. *)
  type pattern = basic * basic list

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  type t = {
      name: string;
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      pattern: pattern;
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      commands: Command.t list;
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      param: Lex_par.t option;
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      param_names: (string list * string list);
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      loc: Loc.t;
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    }

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  let get_name t = t.name

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  let get_loc t = t.loc
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  let is_filter t = t.commands = []

  (* ====================================================================== *)
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  let to_dep t =
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    let pos_basic = fst t.pattern in
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    let buff = Buffer.create 32 in
    bprintf buff "[GRAPH] { scale = 200; }\n";

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    let nodes =
      Pid_map.fold
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        (fun id node acc ->
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          (node, sprintf "  N_%s { word=\"%s\"; subword=\"%s\"}"
            (Pid.to_id id) (P_node.get_name node) (P_fs.to_dep t.param_names (P_node.get_fs node))
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          )
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          :: acc
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        ) pos_basic.graph [] in
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    (* nodes are sorted to appear in the same order in dep picture and in input file *)
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    let sorted_nodes = List.sort (fun (n1,_) (n2,_) -> P_node.compare_pos n1 n2) nodes in
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    bprintf buff "[WORDS] {\n";
    List.iter
      (fun (_, dep_line) -> bprintf buff "%s\n" dep_line
      ) sorted_nodes;

    List_.iteri
      (fun i cst ->
        match cst with
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          | Cst_out _ | Cst_in _ -> bprintf buff "  C_%d { word=\"*\"}\n" i
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          | _ -> ()
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      ) pos_basic.constraints;
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    bprintf buff "}\n";
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    bprintf buff "[EDGES] {\n";
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    Pid_map.iter
      (fun id_src node ->
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        Massoc_pid.iter
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          (fun id_tar edge ->
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            bprintf buff "  N_%s -> N_%s { label=\"%s\"}\n"
              (Pid.to_id id_src)
              (Pid.to_id id_tar)
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              (P_edge.to_string edge)
          )
          (P_node.get_next node)
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      ) pos_basic.graph;
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    List_.iteri
      (fun i cst ->
        match cst with
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          | Cst_out (pid, label_cst) ->
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            bprintf buff "  N_%s -> C_%d {label = \"%s\"; style=dot; bottom; color=green;}\n"
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              (Pid.to_id pid) i (Label_cst.to_string label_cst)
          | Cst_in (pid, label_cst) ->
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            bprintf buff "  C_%d -> N_%s {label = \"%s\"; style=dot; bottom; color=green;}\n"
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              i (Pid.to_id pid) (Label_cst.to_string label_cst)
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          | _ -> ()
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      ) pos_basic.constraints;
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    bprintf buff "}\n";
    Buffer.contents buff
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  (* ====================================================================== *)
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  let build_commands ?param ?(locals=[||]) suffixes pos pos_table ast_commands =
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    let known_act_ids = List.map (fun x -> (Ast.No_sharp x)) (Array.to_list pos_table) in
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    let known_edge_ids = get_edge_ids pos in
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    let rec loop (kai,kei) = function
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      | [] -> []
      | ast_command :: tail ->
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          let (command, (new_kai, new_kei)) =
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            Command.build
              ?param
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              (kai,kei)
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              pos_table
              locals
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              suffixes
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              ast_command in
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          command :: (loop (new_kai,new_kei) tail) in
    loop (known_act_ids, known_edge_ids) ast_commands
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  (* ====================================================================== *)
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  let parse_vars loc vars =
    let rec parse_cmd_vars = function
      | [] -> []
      | x::t when x.[0] = '@' -> x :: parse_cmd_vars t
      | x::t -> Error.bug ~loc "Illegal feature definition '%s' in the lexical rule" x in
    let rec parse_pat_vars = function
      | [] -> ([],[])
      | x::t when x.[0] = '@' -> ([],parse_cmd_vars (x::t))
      | x::t when x.[0] = '$' -> let (pv,cv) = parse_pat_vars t in (x::pv, cv)
      | x::t -> Error.bug ~loc "Illegal feature definition '%s' in the lexical rule" x in
    parse_pat_vars vars

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  (* ====================================================================== *)
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  let build ?(locals=[||]) suffixes dir rule_ast =
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    let (param, pat_vars, cmd_vars) =
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      match rule_ast.Ast.param with
      | None -> (None,[],[])
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      | Some (files,vars) ->
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          let (pat_vars, cmd_vars) = parse_vars rule_ast.Ast.rule_loc vars in
          let nb_pv = List.length pat_vars in
          let nb_cv = List.length cmd_vars in
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          let local_param = match rule_ast.Ast.lex_par with
          | None -> None
          | Some lines -> Some (Lex_par.from_lines ~loc:rule_ast.Ast.rule_loc nb_pv nb_cv lines) in

          let full_param = List.fold_left
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            (fun acc file ->
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              match acc with
              | None -> Some (Lex_par.load ~loc:rule_ast.Ast.rule_loc dir nb_pv nb_cv file)
              | Some lp -> Some (Lex_par.append (Lex_par.load ~loc:rule_ast.Ast.rule_loc dir nb_pv nb_cv file) lp)
            ) local_param files in

          (full_param, pat_vars, cmd_vars) in
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    let (pos, pos_table) = build_pos_basic ~pat_vars ~locals rule_ast.Ast.pos_basic in
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    let (negs,_) =
      List.fold_left
      (fun (acc,pos) basic_ast ->
        try ((build_neg_basic ~pat_vars ~locals pos_table basic_ast) :: acc, pos+1)
        with P_fs.Fail_unif ->
          Log.fwarning "In rule \"%s\" [%s], the wihtout number %d cannot be satisfied, it is skipped"
            rule_ast.Ast.rule_id (Loc.to_string rule_ast.Ast.rule_loc) pos;
          (acc, pos+1)
      ) ([],1) rule_ast.Ast.neg_basics in
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    {
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      name = rule_ast.Ast.rule_id;
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      pattern = (pos, negs);
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      commands = build_commands ~param:(pat_vars,cmd_vars) ~locals suffixes pos pos_table rule_ast.Ast.commands;
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      loc = rule_ast.Ast.rule_loc;
      param = param;
      param_names = (pat_vars,cmd_vars)
    }

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  let build_pattern pattern_ast =
    let (pos, pos_table) = build_pos_basic pattern_ast.Ast.pat_pos in
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    let negs = List_.try_map P_fs.Fail_unif (fun basic_ast -> build_neg_basic pos_table basic_ast) pattern_ast.Ast.pat_negs in
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    (pos, negs)

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  (* ====================================================================== *)
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  type matching = {
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      n_match: Gid.t Pid_map.t;                     (* partial fct: pattern nodes |--> graph nodes *)
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      e_match: (string*(Gid.t*Label.t*Gid.t)) list; (* edge matching: edge ident  |--> (src,label,tar) *)
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      a_match: (Gid.t*Label.t*Gid.t) list;          (* anonymous edge matched *)
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      m_param: Lex_par.t option;
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    }
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  let empty_matching param = { n_match = Pid_map.empty; e_match = []; a_match = []; m_param = param;}
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  let e_comp (e1,_) (e2,_) = compare e1 e2

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  let e_match_add ?pos edge_id matching =
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    match List_.usort_insert ~compare:e_comp edge_id matching.e_match with
    | Some new_e_match -> { matching with e_match = new_e_match }
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    | None -> Error.bug "The edge identifier '%s' is binded twice in the same pattern" (fst edge_id)
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  let a_match_add edge matching = {matching with a_match = edge::matching.a_match }

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  let match_deco pattern matching =
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    { G_deco.nodes =
        Pid_map.fold
          (fun pid gid acc ->
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            let pnode = P_graph.find pid (fst pattern).graph in
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            (gid, (P_node.get_name pnode, P_fs.feat_list (P_node.get_fs pnode))) ::acc
          ) matching.n_match [];
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      G_deco.edges = List.fold_left (fun acc (_,edge) -> edge::acc) matching.a_match matching.e_match;
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    }

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  let find cnode ?loc (matching, (created_nodes,activated_nodes)) =
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    match cnode with
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    | Command.Pat pid ->
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        (try Pid_map.find pid matching.n_match
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        with Not_found -> Error.bug ?loc "Inconsistent matching pid '%s' not found" (Pid.to_string pid))
    | Command.New name ->
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        (try List.assoc name created_nodes
        with Not_found -> Error.run ?loc "Identifier '%s' not found" name)
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    | Command.Act (pid, new_name) ->
        (try List.assoc (pid, new_name) activated_nodes
        with Not_found -> Error.run ?loc "Activated identifier with suffix '%s' not found" new_name)

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  let down_deco (matching,created_nodes) commands =
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    let feat_to_highlight = List.fold_left
      (fun acc -> function
        | (Command.UPDATE_FEAT (tar_cn,feat_name,_),loc) ->
          (* | (Command.SHIFT_EDGE (_,tar_cn),loc) *)
          let gid = find tar_cn (matching, created_nodes) in
          let old_feat_list = try Gid_map.find gid acc with Not_found -> [] in
          Gid_map.add gid (feat_name :: old_feat_list) acc
        | _ -> acc
      ) Gid_map.empty commands in

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    {
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     G_deco.nodes = List.map (fun (gid,feat_list) -> (gid, ("",feat_list))) (Gid_map.bindings feat_to_highlight);
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     G_deco.edges = List.fold_left
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       (fun acc -> function
         | (Command.ADD_EDGE (src_cn,tar_cn,edge),loc) ->
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             (find src_cn (matching, created_nodes), edge, find tar_cn (matching, created_nodes)) :: acc
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         | _ -> acc
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       ) [] commands
   }

  exception Fail
  type partial = {
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      sub: matching;
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      unmatched_nodes: Pid.t list;
      unmatched_edges: (Pid.t * P_edge.t * Pid.t) list;
      already_matched_gids: Gid.t list; (* to ensure injectivity *)
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      check: const list (* constraints to verify at the end of the matching *)
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    }

        (* PREREQUISITES:
           - all partial matching have the same domain
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           - the domain of the pattern P is the disjoint union of domain([sub]) and [unmatched_nodes]
         *)
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  (*  ---------------------------------------------------------------------- *)
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  let init param basic =
    let roots = P_graph.roots basic.graph in
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    let node_list = Pid_map.fold (fun pid _ acc -> pid::acc) basic.graph [] in
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    (* put all roots in the front of the list to speed up the algo *)
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    let sorted_node_list =
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      List.sort
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        (fun n1 n2 -> match (List.mem n1 roots, List.mem n2 roots) with
        | true, false -> -1
        | false, true -> 1
        | _ -> 0) node_list in
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    { sub = empty_matching param;
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      unmatched_nodes = sorted_node_list;
      unmatched_edges = [];
      already_matched_gids = [];
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      check = basic.constraints;
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    }

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  (*  ---------------------------------------------------------------------- *)
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  let apply_cst graph matching cst =
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    let get_node pid = G_graph.find (Pid_map.find pid matching.n_match) graph in
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    let get_string_feat pid = function
      | "position" -> Some (sprintf "%g" (G_node.get_position (get_node pid)))
      | feat_name -> G_fs.get_string_atom feat_name (G_node.get_fs (get_node pid)) in
    let get_float_feat pid = function
      | "position" -> Some (G_node.get_position (get_node pid))
      | feat_name -> G_fs.get_float_feat feat_name (G_node.get_fs (get_node pid)) in
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    match cst with
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      | Cst_out (pid,label_cst) ->
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        let gid = Pid_map.find pid matching.n_match in
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        if G_graph.edge_out graph gid label_cst
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        then matching
        else raise Fail
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      | Cst_in (pid,label_cst) ->
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        let gid = Pid_map.find pid matching.n_match in
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        if G_graph.node_exists
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          (fun node ->
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            List.exists (fun e -> Label_cst.match_ e label_cst) (Massoc_gid.assoc gid (G_node.get_next node))
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          ) graph
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        then matching
        else raise Fail
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      | Filter (pid, fs) ->
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        begin
          try
            let gid = Pid_map.find pid matching.n_match in
            let gnode = G_graph.find gid graph in
            let new_param = P_fs.match_ ?param:matching.m_param fs (G_node.get_fs gnode) in
            {matching with m_param = new_param }
          with P_fs.Fail -> raise Fail
        end
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      | Feature_eq (pid1, feat_name1, pid2, feat_name2) ->
        begin
          match (get_string_feat pid1 feat_name1, get_string_feat pid2 feat_name2) with
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            | Some fv1, Some fv2 when fv1 = fv2 -> matching
            | _ -> raise Fail
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        end
      | Feature_diseq (pid1, feat_name1, pid2, feat_name2) ->
        begin
          match (get_string_feat pid1 feat_name1, get_string_feat pid2 feat_name2) with
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            | Some fv1, Some fv2 when fv1 <> fv2 -> matching
            | _ -> raise Fail
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        end
      | Feature_ineq (ineq, pid1, feat_name1, pid2, feat_name2) ->
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        begin
          match (ineq, get_float_feat pid1 feat_name1, get_float_feat pid2 feat_name2) with
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            | (Ast.Lt, Some fv1, Some fv2) when fv1 < fv2 -> matching
            | (Ast.Gt, Some fv1, Some fv2) when fv1 > fv2 -> matching
            | (Ast.Le, Some fv1, Some fv2) when fv1 <= fv2 -> matching
            | (Ast.Ge, Some fv1, Some fv2) when fv1 >= fv2 -> matching
            | _ -> raise Fail
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          end
      | Feature_ineq_cst (ineq, pid1, feat_name1, constant) ->
        begin
          match (ineq, get_float_feat pid1 feat_name1) with
            | (Ast.Lt, Some fv1) when fv1 < constant -> matching
            | (Ast.Gt, Some fv1) when fv1 > constant -> matching
            | (Ast.Le, Some fv1) when fv1 <= constant -> matching
            | (Ast.Ge, Some fv1) when fv1 >= constant -> matching
            | _ -> raise Fail
          end
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  (*  ---------------------------------------------------------------------- *)
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  (* returns all extension of the partial input matching *)
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  let rec extend_matching (positive,neg) (graph:G_graph.t) (partial:partial) =
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    match (partial.unmatched_edges, partial.unmatched_nodes) with
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    | [], [] ->
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      begin
        try
          let new_matching =
            List.fold_left
              (fun acc const ->
                apply_cst graph acc const
              ) partial.sub partial.check in
          [new_matching, partial.already_matched_gids]
        with Fail -> []
      end
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    | (src_pid, p_edge, tar_pid)::tail_ue, _ ->
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        begin
          try (* is the tar already found in the matching ? *)
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            let new_partials =
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              let src_gid = Pid_map.find src_pid partial.sub.n_match in
              let tar_gid = Pid_map.find tar_pid partial.sub.n_match in
              let src_gnode = G_graph.find src_gid graph in
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              let g_edges = Massoc_gid.assoc tar_gid (G_node.get_next src_gnode) in
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              match P_edge.match_list p_edge g_edges with
              | P_edge.Fail -> (* no good edge in graph for this pattern edge -> stop here *)
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                  []
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              | P_edge.Ok label -> (* at least an edge in the graph fits the p_edge "constraint" -> go on *)
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                  [ {partial with unmatched_edges = tail_ue; sub = a_match_add (src_gid,label,tar_gid) partial.sub} ]
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              | P_edge.Binds (id,labels) -> (* n edges in the graph match the identified p_edge -> make copies of the [k] matchings (and returns n*k matchings) *)
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                  List.map
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                    (fun label ->
                      {partial with sub = e_match_add (id,(src_gid,label,tar_gid)) partial.sub; unmatched_edges = tail_ue }
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                    ) labels
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            in List_.flat_map (extend_matching (positive,neg) graph) new_partials
          with Not_found -> (* p_edge goes to an unmatched node *)
            let candidates = (* candidates (of type (gid, matching)) for m(tar_pid) = gid) with new partial matching m *)
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              let (src_gid : Gid.t) = Pid_map.find src_pid partial.sub.n_match in
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              let src_gnode = G_graph.find src_gid graph in
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              Massoc_gid.fold
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                (fun acc gid_next g_edge ->
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                  match P_edge.match_ p_edge g_edge with
                  | P_edge.Fail -> (* g_edge does not fit, no new candidate *)
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                      acc
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                  | P_edge.Ok label -> (* g_edge fits with the same matching *)
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                      (gid_next, a_match_add (src_gid, label, gid_next) partial.sub) :: acc
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                  | P_edge.Binds (id,[label]) -> (* g_edge fits with an extended matching *)
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                      (gid_next, e_match_add (id, (src_gid, label, gid_next)) partial.sub) :: acc
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                  | _ -> Error.bug "P_edge.match_ must return exactly one label"
                ) [] (G_node.get_next src_gnode) in
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            List_.flat_map
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              (fun (gid_next, matching) ->
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                extend_matching_from (positive,neg) graph tar_pid gid_next
                  {partial with sub=matching; unmatched_edges = tail_ue}
              ) candidates
        end
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    | [], pid :: _ ->
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        G_graph.fold_gid
          (fun gid acc ->
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            (extend_matching_from (positive,neg) graph pid gid partial) @ acc
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          ) graph []
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  (*  ---------------------------------------------------------------------- *)
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  and extend_matching_from (positive,neg) (graph:G_graph.t) pid (gid : Gid.t) partial =
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    if List.mem gid partial.already_matched_gids
    then [] (* the required association pid -> gid is not injective *)
    else
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      let p_node =
        try P_graph.find pid positive
        with Not_found ->
          try P_graph.find pid neg
          with Not_found -> Error.bug "[Grew_rule.extend_matching_from] cannot find node" in

      (* let p_node =  *)
      (*   if pid >= 0  *)
      (*   then try P_graph.find pid positive with Not_found -> failwith "POS" *)
      (*   else try P_graph.find pid neg with Not_found -> failwith "NEG" in *)
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      let g_node = try G_graph.find gid graph with Not_found -> failwith "INS" in
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      try
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        let new_param = P_node.match_ ?param: partial.sub.m_param p_node g_node in
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        (* add all out-edges from pid in pattern *)
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        let new_unmatched_edges =
          Massoc_pid.fold
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            (fun acc pid_next p_edge -> (pid, p_edge, pid_next) :: acc
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            ) partial.unmatched_edges (P_node.get_next p_node) in
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        let new_partial =
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          { partial with
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            unmatched_nodes = (try List_.rm pid partial.unmatched_nodes with Not_found -> failwith "List_.rm");
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            unmatched_edges = new_unmatched_edges;
            already_matched_gids = gid :: partial.already_matched_gids;
            sub = {partial.sub with n_match = Pid_map.add pid gid partial.sub.n_match; m_param = new_param};
          } in
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        extend_matching (positive,neg) graph new_partial
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      with P_fs.Fail -> []
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  (*  ---------------------------------------------------------------------- *)
  (* the exception below is added to handle unification failure in merge!! *)
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  exception Command_execution_fail
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  (*  ---------------------------------------------------------------------- *)
  (** [apply_command instance matching created_nodes command] returns [(new_instance, new_created_nodes)] *)
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  let apply_command (command,loc) instance matching (created_nodes, (activated_nodes:((Pid.t * string) * Gid.t) list)) =
    let node_find cnode = find ~loc cnode (matching, (created_nodes, activated_nodes)) in
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    match command with
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    | Command.ADD_EDGE (src_cn,tar_cn,edge) ->
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        let src_gid = node_find src_cn in
        let tar_gid = node_find tar_cn in
        begin
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          match G_graph.add_edge instance.Instance.graph src_gid edge tar_gid with
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          | Some new_graph ->
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              (
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               {instance with
                Instance.graph = new_graph;
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                history = List_.sort_insert (Command.H_ADD_EDGE (src_gid,tar_gid,edge)) instance.Instance.history
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              },
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               (created_nodes, activated_nodes)
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              )
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          | None ->
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              Error.run "ADD_EDGE: the edge '%s' already exists %s" (G_edge.to_string edge) (Loc.to_string loc)
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        end

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    | Command.DEL_EDGE_EXPL (src_cn,tar_cn,edge) ->
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        let src_gid = node_find src_cn in
        let tar_gid = node_find tar_cn in
        (
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         {instance with
          Instance.graph = G_graph.del_edge loc instance.Instance.graph src_gid edge tar_gid;
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           history = List_.sort_insert (Command.H_DEL_EDGE_EXPL (src_gid,tar_gid,edge)) instance.Instance.history
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        },
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         (created_nodes, activated_nodes)
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        )

    | Command.DEL_EDGE_NAME edge_ident ->
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        let (src_gid,edge,tar_gid) =
          try List.assoc edge_ident matching.e_match
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          with Not_found -> Error.bug "The edge identifier '%s' is undefined %s" edge_ident (Loc.to_string loc) in
        (
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         {instance with
          Instance.graph = G_graph.del_edge ~edge_ident loc instance.Instance.graph src_gid edge tar_gid;
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          history = List_.sort_insert (Command.H_DEL_EDGE_EXPL (src_gid,tar_gid,edge)) instance.Instance.history
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        },
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         (created_nodes, activated_nodes)
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        )
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    | Command.DEL_NODE node_cn ->
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        let node_gid = node_find node_cn in
        (
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         {instance with
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          Instance.graph = G_graph.del_node instance.Instance.graph node_gid;
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          history = List_.sort_insert (Command.H_DEL_NODE node_gid) instance.Instance.history
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        },
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         (created_nodes, activated_nodes)
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        )

    | Command.MERGE_NODE (src_cn, tar_cn) ->
        let src_gid = node_find src_cn in
        let tar_gid = node_find tar_cn in
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        (match G_graph.merge_node loc instance.Instance.graph src_gid tar_gid with
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        | Some new_graph ->
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            (
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             {instance with
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              Instance.graph = new_graph;
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              history = List_.sort_insert (Command.H_MERGE_NODE (src_gid,tar_gid)) instance.Instance.history
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            },
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             (created_nodes, activated_nodes)
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            )
        | None -> raise Command_execution_fail
        )
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    | Command.UPDATE_FEAT (tar_cn,tar_feat_name, item_list) ->
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        let tar_gid = node_find tar_cn in
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        let rule_items = List.map
            (function
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              | Command.Feat (cnode, feat_name) -> Concat_item.Feat (node_find cnode, feat_name)
              | Command.String s -> Concat_item.String s
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              | Command.Param_out index ->
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                  (match matching.m_param with
                  | None -> Error.bug "Cannot apply a UPDATE_FEAT command without parameter"
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                  | Some param -> Concat_item.String (Lex_par.get_command_value index param))
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              | Command.Param_in index ->
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                  (match matching.m_param with
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                  | None -> Error.bug "Cannot apply a UPDATE_FEAT command without parameter"
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                  | Some param -> Concat_item.String (Lex_par.get_param_value index param))
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            ) item_list in
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        let (new_graph, new_feature_value) =
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          G_graph.update_feat ~loc instance.Instance.graph tar_gid tar_feat_name rule_items in
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        (
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         {instance with
          Instance.graph = new_graph;
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          history = List_.sort_insert (Command.H_UPDATE_FEAT (tar_gid,tar_feat_name,new_feature_value)) instance.Instance.history
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        },
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         (created_nodes, activated_nodes)
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        )
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    | Command.DEL_FEAT (tar_cn,feat_name) ->
        let tar_gid = node_find tar_cn in
        (
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         {instance with
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          Instance.graph = G_graph.del_feat instance.Instance.graph tar_gid feat_name;
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          history = List_.sort_insert (Command.H_DEL_FEAT (tar_gid,feat_name)) instance.Instance.history
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        },
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         (created_nodes, activated_nodes)
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        )
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    | Command.NEW_NEIGHBOUR (created_name,edge,base_pid) ->
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        let base_gid = Pid_map.find base_pid matching.n_match in
        let (new_gid,new_graph) = G_graph.add_neighbour loc instance.Instance.graph base_gid edge in
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        (
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         {instance with
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          Instance.graph = new_graph;
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          history = List_.sort_insert (Command.H_NEW_NEIGHBOUR (created_name,edge,new_gid)) instance.Instance.history;
          activated_node = new_gid :: instance.Instance.activated_node;
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        },
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         ((created_name,new_gid) :: created_nodes, activated_nodes)
        )

    | Command.ACT_NODE (Command.Act (pid, new_name)) ->
        let node_gid = node_find (Command.Pat(pid)) in
        let (new_gid, new_graph) = G_graph.activate loc node_gid new_name instance.Instance.graph in
        (
         {instance with
          Instance.graph = new_graph;
          history = List_.sort_insert (Command.H_ACT_NODE (node_gid,new_name)) instance.Instance.history
        },
         (created_nodes, ((pid, new_name), new_gid) :: activated_nodes)
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        )
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    | Command.ACT_NODE _ -> Error.bug "Try to activate a node without suffix" (Loc.to_string loc)
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    | Command.SHIFT_IN (src_cn,tar_cn,label_cst) ->
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        let src_gid = node_find src_cn in
        let tar_gid = node_find tar_cn in
        (
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         {instance with
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          Instance.graph = G_graph.shift_in loc src_gid tar_gid label_cst instance.Instance.graph;
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          history = List_.sort_insert (Command.H_SHIFT_IN (src_gid,tar_gid)) instance.Instance.history
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        },
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         (created_nodes, activated_nodes)
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        )

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    | Command.SHIFT_OUT (src_cn,tar_cn,label_cst) ->
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        let src_gid = node_find src_cn in
        let tar_gid = node_find tar_cn in
        (
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         {instance with
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          Instance.graph = G_graph.shift_out loc src_gid tar_gid label_cst instance.Instance.graph;
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          history = List_.sort_insert (Command.H_SHIFT_OUT (src_gid,tar_gid)) instance.Instance.history
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        },
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         (created_nodes, activated_nodes)
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        )

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    | Command.SHIFT_EDGE (src_cn,tar_cn,label_cst) ->
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        let src_gid = node_find src_cn in
        let tar_gid = node_find tar_cn in
        (
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          {instance with
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            Instance.graph = G_graph.shift_edges loc src_gid tar_gid label_cst instance.Instance.graph;
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            history = List_.sort_insert (Command.H_SHIFT_EDGE (src_gid,tar_gid)) instance.Instance.history
          },
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          (created_nodes, activated_nodes)
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        )
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  (*  ---------------------------------------------------------------------- *)
  (** [apply_rule instance matching rule] returns a new instance after the application of the rule
      [Command_execution_fail] is raised if some merge unification fails *)
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  let apply_rule instance matching rule =
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    (* Timeout check *)
    (try Timeout.check () with Timeout.Stop -> Error.run "Time out");

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    (* limit the rewriting depth to avoid looping rewriting *)
    begin
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      if List.length instance.Instance.rules >= !max_depth
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      then Error.run "Bound reached (when applying rule %s)" rule.name
    end;
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    let (new_instance, created_nodes) =
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      List.fold_left
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        (fun (instance, created_nodes) command ->
          apply_command command instance matching created_nodes
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        )