X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fformal_topology%2Fbin%2Ftheory_explorer.ml;h=82850e40d2581be9943818389e972d5aa561cf03;hb=7329247b6325d8890f13898c25e68255e843e498;hp=be1e107fb21081f8d62ea0bcc0bec192692f656f;hpb=99ca90bf28a25fcd1cd84596c37be43c97f74e6e;p=helm.git

diff --git a/helm/software/matita/contribs/formal_topology/bin/theory_explorer.ml b/helm/software/matita/contribs/formal_topology/bin/theory_explorer.ml
index be1e107fb..82850e40d 100644
--- a/helm/software/matita/contribs/formal_topology/bin/theory_explorer.ml
+++ b/helm/software/matita/contribs/formal_topology/bin/theory_explorer.ml
@@ -1,3 +1,11 @@
+type rel = Equal | SubsetEqual | SupersetEqual
+
+let string_of_rel =
+ function
+    Equal -> "="
+  | SubsetEqual -> "⊆"
+  | SupersetEqual -> "⊇"
+
 (* operator *)
 type op = I | C | M
 
@@ -13,6 +21,8 @@ type compound_operator = op list
 let string_of_cop op =
  if op = [] then "id" else String.concat "" (List.map string_of_op op)
 
+let dot_of_cop op = "\"" ^ string_of_cop op ^ "\""
+
 let rec matita_of_cop v =
  function
   | [] -> v
@@ -26,6 +36,9 @@ type equivalence_class =
  compound_operator * compound_operator list *
   equivalence_class list ref * equivalence_class list ref
 
+let (===) (repr,_,_,_) (repr',_,_,_) = repr = repr';;
+let (<=>) (repr,_,_,_) (repr',_,_,_) = repr <> repr';;
+
 let string_of_equivalence_class (repr,others,leq,_) =
  String.concat " = " (List.map string_of_cop (repr::others)) ^
   (if !leq <> [] then
@@ -33,46 +46,84 @@ let string_of_equivalence_class (repr,others,leq,_) =
      String.concat "\n" 
       (List.map
         (function (repr',_,_,_) ->
-           string_of_cop repr ^ " <= " ^ string_of_cop repr') !leq)
+           string_of_cop repr ^ " ⊆ " ^ string_of_cop repr') !leq)
    else
     "")
 
 let dot_of_equivalence_class (repr,others,leq,_) =
  (if others <> [] then
    let eq = String.concat " = " (List.map string_of_cop (repr::others)) in
-    string_of_cop repr ^ "[label=\"" ^ eq ^ "\"];\n"
-  else "") ^
+    dot_of_cop repr ^ "[label=\"" ^ eq ^ "\"];" ^
+     if !leq = [] then "" else "\n"
+  else if !leq = [] then
+   dot_of_cop repr ^ ";"
+  else
+   "") ^
    String.concat "\n" 
     (List.map
       (function (repr',_,_,_) ->
-         string_of_cop repr' ^ " -> " ^ string_of_cop repr ^ ";") !leq)
+         dot_of_cop repr' ^ " -> " ^ dot_of_cop repr ^ ";") !leq)
 
-(* set of equivalence classes *)
-type set = equivalence_class list
+(* set of equivalence classes, infima, suprema *)
+type set =
+ equivalence_class list * equivalence_class list * equivalence_class list
 
-let string_of_set s =
+let string_of_set (s,_,_) =
  String.concat "\n" (List.map string_of_equivalence_class s)
 
-let ps_of_set ?processing s =
+let ps_of_set (to_be_considered,under_consideration,news) ?processing (s,inf,sup) =
  let ch = open_out "xxx.dot" in
   output_string ch "digraph G {\n";
+  (match under_consideration with
+      None -> ()
+    | Some repr ->
+       output_string ch (dot_of_cop repr ^ " [color=yellow];"));
+  List.iter
+   (function (repr,_,_,_) ->
+     if List.exists (function (repr',_,_,_) -> repr=repr') sup then
+      output_string ch (dot_of_cop repr ^ " [shape=Mdiamond];")
+     else
+      output_string ch (dot_of_cop repr ^ " [shape=diamond];")
+   ) inf ;
+  List.iter
+   (function (repr,_,_,_) ->
+     if not (List.exists (function (repr',_,_,_) -> repr=repr') inf) then
+      output_string ch (dot_of_cop repr ^ " [shape=polygon];")
+   ) sup ;
+  List.iter
+   (function repr -> output_string ch (dot_of_cop repr ^ " [color=green];")
+   ) to_be_considered ;
+  List.iter
+   (function repr -> output_string ch (dot_of_cop repr ^ " [color=navy];")
+   ) news ;
   output_string ch (String.concat "\n" (List.map dot_of_equivalence_class s));
+  output_string ch "\n";
   (match processing with
       None -> ()
     | Some (repr,rel,repr') ->
-       output_string ch
-        (string_of_cop repr' ^ " -> " ^ string_of_cop repr ^
-         " [" ^
-         (if rel="=" then "arrowhead=none " else "") ^
-         "style=dashed];\n"));
+       output_string ch (dot_of_cop repr ^ " [color=red];");
+       let repr,repr' =
+        match rel with
+           SupersetEqual -> repr',repr
+         | Equal
+         | SubsetEqual -> repr,repr'
+       in
+        output_string ch
+         (dot_of_cop repr' ^ " -> " ^ dot_of_cop repr ^
+          " [" ^
+          (match rel with Equal -> "arrowhead=none " | _ -> "") ^
+          "style=dashed];\n"));
   output_string ch "}\n";
   close_out ch;
-  ignore (Unix.system "dot -Tps xxx.dot > xxx.ps")
+  (*ignore (Unix.system "tred xxx.dot > yyy.dot && dot -Tps yyy.dot > xxx.ps")*)
+  ignore (Unix.system "cp xxx.ps xxx_old.ps && dot -Tps xxx.dot > xxx.ps");
+  (*ignore (read_line ())*)
+;;
 
-let test set rel candidate repr =
- ps_of_set ~processing:(candidate,rel,repr) set;
+let test to_be_considered_and_now ((s,_,_) as set) rel candidate repr =
+ ps_of_set to_be_considered_and_now ~processing:(candidate,rel,repr) set;
  print_string
-  (string_of_cop candidate ^ " " ^ rel ^ " " ^ string_of_cop repr ^ "? ");
+  (string_of_cop candidate ^ " " ^ string_of_rel rel ^ " " ^ string_of_cop repr ^ "? ");
  flush stdout;
  assert (Unix.system "cp formal_topology.ma xxx.ma" = Unix.WEXITED 0);
  let ch = open_out_gen [Open_append] 0 "xxx.ma" in
@@ -95,101 +146,252 @@ let test set rel candidate repr =
           ": \\forall A." ^
            matita_of_cop "A" repr ^ " ⊆ " ^ matita_of_cop "A" repr' ^ ".\n");
       ) !leq;
-   ) set;
+   ) s;
+  let candidate',rel',repr' =
+   match rel with
+      SupersetEqual -> repr,SubsetEqual,candidate
+    | Equal
+    | SubsetEqual -> candidate,rel,repr
+  in
   output_string ch
-   ("theorem foo: \\forall A." ^ matita_of_cop "A" candidate ^ " " ^ rel ^ " " ^
-     matita_of_cop "A" repr ^ ". intros; auto size=6 depth=4. qed.\n");
+   ("theorem foo: \\forall A." ^ matita_of_cop "A" candidate' ^
+      " " ^ string_of_rel rel' ^ " " ^
+      matita_of_cop "A" repr' ^ ". intros; auto size=6 depth=4. qed.\n");
   close_out ch;
   let res =
-   Unix.system "../../../matitac.opt xxx.ma >> log 2>&1" = Unix.WEXITED 0
+   (*Unix.system "../../../matitac.opt xxx.ma >> log 2>&1" = Unix.WEXITED 0*)
+   Unix.system "../../../matitac.opt xxx.ma > /dev/null 2>&1" = Unix.WEXITED 0
   in
    print_endline (if res then "y" else "n");
    res
 
-let normalize candidate set =
- let rec aux =
+let remove node = List.filter (fun node' -> node <=> node');;
+
+let add_leq_arc ((_,_,leq,_) as node) ((_,_,_,geq') as node') =
+ leq := node' :: !leq;
+ geq' := node :: !geq'
+;;
+
+let add_geq_arc ((_,_,_,geq) as node) ((_,_,leq',_) as node') =
+ geq := node' :: !geq;
+ leq' := node :: !leq'
+;;
+
+let remove_leq_arc ((_,_,leq,_) as node) ((_,_,_,geq') as node') =
+ leq := remove node' !leq;
+ geq' := remove node !geq'
+;;
+
+let remove_geq_arc ((_,_,_,geq) as node) ((_,_,leq',_) as node') =
+ geq := remove node' !geq;
+ leq' := remove node !leq'
+;;
+
+let leq_transitive_closure node node' =
+ add_leq_arc node node';
+ let rec remove_transitive_arcs ((_,_,_,geq) as node) (_,_,leq',_) =
+  let rec remove_arcs_to_ascendents =
+   function
+      [] -> ()
+    | (_,_,leq,_) as node'::tl ->
+       remove_leq_arc node node';
+       remove_arcs_to_ascendents (!leq@tl)
+  in
+   remove_arcs_to_ascendents !leq';
+   List.iter (function son -> remove_transitive_arcs son node) !geq
+ in
+  remove_transitive_arcs node node'
+;;
+
+let geq_transitive_closure node node' =
+ add_geq_arc node node';
+ let rec remove_transitive_arcs ((_,_,leq,_) as node) (_,_,_,geq') =
+  let rec remove_arcs_to_descendents =
+   function
+      [] -> ()
+    | (_,_,_,geq) as node'::tl ->
+       remove_geq_arc node node';
+       remove_arcs_to_descendents (!geq@tl)
+  in
+   remove_arcs_to_descendents !geq';
+   List.iter (function father -> remove_transitive_arcs father node) !leq
+ in
+  remove_transitive_arcs node node'
+;;
+
+let (@@) l1 n = if List.exists (function n' -> n===n') l1 then l1 else l1@[n]
+
+let rec leq_reachable node =
+ function
+    [] -> false
+  | node'::_ when node === node' -> true
+  | (_,_,leq,_)::tl -> leq_reachable node (!leq@tl)
+;;
+
+let rec geq_reachable node =
+ function
+    [] -> false
+  | node'::_ when node === node' -> true
+  | (_,_,_,geq)::tl -> geq_reachable node (!geq@tl)
+;;
+
+let locate_using_leq to_be_considered_and_now ((repr,_,leq,_) as node)
+ set start
+=
+ let rec aux ((nodes,inf,sup) as set) =
   function
-     [] -> raise Not_found
-   | (repr,others,leq,geq) as eqclass :: tl ->
-       if test set "=" candidate repr then
-        (repr,others@[candidate],leq,geq)::tl
+     [] -> set
+   | (repr',_,_,geq') as node' :: tl ->
+       if repr=repr' then aux set (!geq'@tl)
+       else if leq_reachable node' !leq then
+        aux set tl
+       else if test to_be_considered_and_now set SubsetEqual repr repr' then
+        begin
+         let sup = remove node sup in
+         let inf = if !geq' = [] then (remove node' inf)@@node else inf in
+          leq_transitive_closure node node';
+          aux (nodes,inf,sup) (!geq'@tl)
+        end
        else
-        eqclass::(aux tl) 
+        aux set tl
  in
-  aux set
+  aux set start
 ;;
 
-let locate ((repr,_,leq,geq) as node) set =
- let rec aux =
+exception SameEquivalenceClass of equivalence_class * equivalence_class;;
+
+let locate_using_geq to_be_considered_and_now ((repr,_,leq,geq) as node)
+ set start
+=
+ let rec aux ((nodes,inf,sup) as set) =
   function
-     [] -> ()
-   | (repr',_,leq',geq') as node' :: tl ->
-       if repr = repr' then ()
-       else if test set "⊆" repr repr' then
+     [] -> set
+   | (repr',_,leq',_) as node' :: tl ->
+       if repr=repr' then aux set (!leq'@tl)
+       else if geq_reachable node' !geq then
+        aux set tl
+       else if test to_be_considered_and_now set SupersetEqual repr repr' then
         begin
-         leq  := node' :: !leq;
-         geq' := node  :: !geq'
+         if List.exists (function n -> n===node') !leq then
+          (* We have found two equal nodes! *)
+          raise (SameEquivalenceClass (node,node'))
+         else
+          begin
+           let inf = remove node inf in
+           let sup = if !leq' = [] then (remove node' sup)@@node else sup in
+            geq_transitive_closure node node';
+            aux (nodes,inf,sup) (!leq'@tl)
+          end
         end
-       else if test set "⊆" repr' repr then
-        begin
-         geq  := node' :: !geq;
-         leq' := node  :: !leq'
-        end ;
-       aux tl
+       else
+        aux set tl
  in
-  aux set
+  aux set start
 ;;
 
-let analyze_one i repr hecandidate (news,set) =
+let analyze_one to_be_considered repr hecandidate (news,((nodes,inf,sup) as set)) =
+if not (List.for_all (fun ((_,_,_,geq) as node) -> !geq = [] && let rec check_sups = function [] -> true | (_,_,leq,_) as node::tl -> if !leq = [] then List.exists (fun n -> n===node) sup && check_sups tl else check_sups (!leq@tl) in check_sups [node]) inf) then (ps_of_set ([],None,[]) set; assert false);
+if not (List.for_all (fun ((_,_,leq,_) as node) -> !leq = [] && let rec check_infs = function [] -> true | (_,_,_,geq) as node::tl -> if !geq = [] then List.exists (fun n -> n===node) inf && check_infs tl else check_infs (!geq@tl) in check_infs [node]) sup) then (ps_of_set ([],None,[]) set; assert false);
  let candidate = hecandidate::repr in
-  if List.length (List.filter ((=) M) candidate) > i then
+  if List.length (List.filter ((=) M) candidate) > 1 then
    news,set
   else
    try
-    let set = normalize candidate set in
-     news,set
+    let leq = ref [] in
+    let geq = ref [] in
+    let node = candidate,[],leq,geq in
+    let nodes = nodes@[node] in
+    let set = nodes,inf@[node],sup@[node] in
+    let start_inf,start_sup =
+     let repr_node =
+      match List.filter (fun (repr',_,_,_) -> repr=repr') nodes with
+         [node] -> node
+       | _ -> assert false
+     in
+inf,sup(*
+     match hecandidate with
+        I -> inf,[repr_node]
+      | C -> [repr_node],sup
+      | M -> inf,sup
+*)
+    in
+    let set =
+     locate_using_leq (to_be_considered,Some repr,news) node set start_sup in
+(
+let _,inf,sup = set in
+if not (List.for_all (fun ((_,_,_,geq) as node) -> !geq = [] && let rec check_sups = function [] -> true | (_,_,leq,_) as node::tl -> if !leq = [] then List.exists (fun n -> n===node) sup && check_sups tl else check_sups (!leq@tl) in check_sups [node]) inf) then (ps_of_set ([],None,[]) set; assert false);
+if not (List.for_all (fun ((_,_,leq,_) as node) -> !leq = [] && let rec check_infs = function [] -> true | (_,_,_,geq) as node::tl -> if !geq = [] then List.exists (fun n -> n===node) inf && check_infs tl else check_infs (!geq@tl) in check_infs [node]) sup) then (ps_of_set ([],None,[]) set; assert false);
+);
+    let set =
+     locate_using_geq (to_be_considered,Some repr,news) node set start_inf
+    in
+(
+let _,inf,sup = set in
+if not (List.for_all (fun ((_,_,_,geq) as node) -> !geq = [] && let rec check_sups = function [] -> true | (_,_,leq,_) as node::tl -> if !leq = [] then List.exists (fun n -> n===node) sup && check_sups tl else check_sups (!leq@tl) in check_sups [node]) inf) then (ps_of_set ([],None,[]) set; assert false);
+if not (List.for_all (fun ((_,_,leq,_) as node) -> !leq = [] && let rec check_infs = function [] -> true | (_,_,_,geq) as node::tl -> if !geq = [] then List.exists (fun n -> n===node) inf && check_infs tl else check_infs (!geq@tl) in check_infs [node]) sup) then (ps_of_set ([],None,[]) set; assert false);
+);
+     news@[candidate],set
    with
-    Not_found ->
-     let leq = ref [] in
-     let geq = ref [] in
-     let node = candidate,[],leq,geq in
-     let set = node::set in
-      locate node set;
-      candidate::news,set
+    SameEquivalenceClass ((_,_,leq_d,geq_d) as node_to_be_deleted,node') ->
+     let rec clean =
+      function
+         [] -> []
+       | (repr',others,leq,geq) as node::tl ->
+          leq :=
+           List.fold_right
+            (fun node l ->
+              if node_to_be_deleted <=> node then
+               node::l
+              else
+               !leq_d@l
+            ) !leq [];
+          geq :=
+           List.fold_right
+            (fun node l ->
+              if node_to_be_deleted <=> node then
+               node::l
+              else
+               !geq_d@l
+            ) !geq [];
+          if node===node' then
+           (repr',others@[candidate],leq,geq)::clean tl
+          else
+           node::clean tl
+     in
+     let nodes = clean nodes in
+      news,(nodes,inf,sup)
 ;;
 
-let rec explore i j set news =
+let rec explore i (set:set) news =
  let rec aux news set =
   function
      [] -> news,set
    | repr::tl ->
       let news,set =
-       List.fold_right (analyze_one i repr) [I;C;M] (news,set)
+       List.fold_right (analyze_one tl repr) [I;C;M] (news,set)
       in
        aux news set tl
  in
   let news,set = aux [] set news in
    if news = [] then
     begin
-     print_endline ("PUNTO FISSO RAGGIUNTO! i=" ^ string_of_int i ^ " j=" ^ string_of_int j);
+     print_endline ("PUNTO FISSO RAGGIUNTO! i=" ^ string_of_int i);
      print_endline (string_of_set set ^ "\n----------------");
-     if i < 2 then
-      explore (i+1) 1 set (List.map (function (repr,_,_,_) -> repr) set)
-     else
-      ps_of_set set
+     ps_of_set ([],None,[]) set
     end
    else
     begin
-     print_endline ("NUOVA ITERAZIONE, i=" ^ string_of_int i ^ " j=" ^ string_of_int j);
+     print_endline ("NUOVA ITERAZIONE, i=" ^ string_of_int i);
      print_endline (string_of_set set ^ "\n----------------");
-     explore i (j+1) set news
+     explore (i+1) set news
     end
 in
  let id = [] in
- let set = [id,[],ref [], ref []] in
+ let id_node = id,[],ref [], ref [] in
+ let set = [id_node],[id_node],[id_node] in
   print_endline ("PRIMA ITERAZIONE, i=0, j=0");
   print_endline (string_of_set set ^ "\n----------------");
-  ignore (Unix.system "rm -f log");
-  ps_of_set set;
-  explore 0 1 set [id]
+  (*ignore (Unix.system "rm -f log");*)
+  ps_of_set ([id],None,[]) set;
+  explore 1 set [id]
 ;;