From: Claudio Sacerdoti Coen <claudio.sacerdoticoen@unibo.it>
Date: Thu, 24 May 2007 10:56:33 +0000 (+0000)
Subject: theory_explorer_do_not_trust_auto.ml is the version that does not trust
X-Git-Tag: 0.4.95@7852~447
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=7f0536ce1295abde169046829f39dcf6f6409914;p=helm.git

theory_explorer_do_not_trust_auto.ml is the version that does not trust
 auto. The algorithm is exponential.

theory_explorer.ml trusts auto and requires only quadratic time. Not working
 properly yet.
---

diff --git a/matita/contribs/formal_topology/bin/theory_explorer.ml b/matita/contribs/formal_topology/bin/theory_explorer.ml
index 3a9dcde30..ca5c1c271 100644
--- a/matita/contribs/formal_topology/bin/theory_explorer.ml
+++ b/matita/contribs/formal_topology/bin/theory_explorer.ml
@@ -43,7 +43,7 @@ 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
     "")
 
@@ -61,19 +61,28 @@ let dot_of_equivalence_class (repr,others,leq,_) =
       (function (repr',_,_,_) ->
          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 (to_be_considered,under_consideration,news) ?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,_,_,_) ->
+     output_string ch (dot_of_cop repr ^ " [shape=diamond];")
+   ) inf ;
+  List.iter
+   (function (repr,_,_,_) ->
+     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 ;
@@ -101,7 +110,7 @@ let ps_of_set (to_be_considered,under_consideration,news) ?processing s =
   close_out ch;
   ignore (Unix.system "tred xxx.dot > yyy.dot && dot -Tps yyy.dot > xxx.ps")
 
-let test to_be_considered_and_now set rel candidate repr =
+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 ^ " " ^ string_of_rel rel ^ " " ^ string_of_cop repr ^ "? ");
@@ -127,7 +136,7 @@ let test to_be_considered_and_now 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
@@ -146,59 +155,118 @@ let test to_be_considered_and_now set rel candidate repr =
    print_endline (if res then "y" else "n");
    res
 
-let normalize to_be_considered_and_now candidate set =
- let rec aux =
+let rec leq_transitive_closure leq node ((repr,_,leq',geq') as node') =
+ if not (List.mem node' !leq) then leq := node' :: !leq;
+ if not (List.mem node !geq') then geq' := node :: !geq';
+ List.iter (leq_transitive_closure leq node) !leq'
+;;
+
+let rec geq_transitive_closure geq node ((_,_,leq',geq') as node') =
+ if not (List.mem node' !geq) then geq  := node' :: !geq;
+ if not (List.mem node !leq') then leq' := node  :: !leq';
+ List.iter (geq_transitive_closure geq node) !geq'
+;;
+
+let remove node l =
+ let l' = List.filter (fun node' -> node != node') l in
+ if List.length l = List.length l' then
+  assert false
+ else
+  l'
+;;
+
+let locate_using_leq to_be_considered_and_now ((repr,_,leq,_) as node)
+ ((nodes,inf,sup) as set)
+=
+ let rec aux is_sup inf =
   function
-     [] -> raise Not_found
-   | (repr,others,leq,geq) as eqclass :: tl ->
-       if test to_be_considered_and_now set Equal candidate repr then
-        (repr,others@[candidate],leq,geq)::tl
+     [] -> is_sup,inf
+   | (repr',_,_,geq') as node' :: sup ->
+       if repr=repr' then aux is_sup inf (!geq'@sup)
+       else if List.mem node' !leq
+            || test to_be_considered_and_now set SubsetEqual repr repr'
+       then
+        begin
+         let inf = if !geq' = [] then remove node' inf else inf in
+          leq_transitive_closure leq node node';
+          aux false inf (!geq'@sup)
+        end
        else
-        eqclass::(aux tl) 
+        aux is_sup inf sup
  in
-  aux set
+  let is_sup,inf = aux true inf sup in
+   if is_sup then
+    nodes,inf,sup@[node]
+   else
+    nodes,inf,sup
 ;;
 
-let locate to_be_considered_and_now ((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)
+ ((nodes,inf,sup) as set)
+=
+ let rec aux is_inf sup =
   function
-     [] -> ()
-   | (repr',_,leq',geq') as node' :: tl ->
-       if repr = repr' then ()
-       else if test to_be_considered_and_now set SubsetEqual repr repr' then
+     [] -> sup,is_inf
+   | (repr',_,leq',_) as node' :: inf ->
+       if repr=repr' then aux is_inf sup (!leq'@inf)
+       else if List.mem node' !geq
+            || test to_be_considered_and_now set SupersetEqual repr repr'
+       then
         begin
-         leq  := node' :: !leq;
-         geq' := node  :: !geq'
+         if List.mem node' !leq then
+          (* We have found two equal nodes! *)
+          raise (SameEquivalenceClass (node,node'))
+         else
+          begin
+           let sup = if !leq' = [] then remove node' sup else sup in
+            geq_transitive_closure geq node node';
+            aux false sup (!leq'@inf)
+          end
         end
-       else if test to_be_considered_and_now set SupersetEqual repr repr' then
-        begin
-         geq  := node' :: !geq;
-         leq' := node  :: !leq'
-        end ;
-       aux tl
+       else
+        aux is_inf sup inf
  in
-  aux set
+  let sup,is_inf = aux true sup inf in
+   if is_inf then
+    nodes,inf@[node],sup
+   else
+    nodes,inf,sup
 ;;
 
-let analyze_one to_be_considered repr hecandidate (news,set) =
+let analyze_one to_be_considered repr hecandidate (news,((nodes,inf,sup) as set)) =
  let candidate = hecandidate::repr in
   if List.length (List.filter ((=) M) candidate) > 1 then
    news,set
   else
    try
-    let set = normalize (to_be_considered,Some repr,news) 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,sup in
+    let set = locate_using_leq (to_be_considered,Some repr,news) node set in
+    let set = locate_using_geq (to_be_considered,Some repr,news) node set in
+     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 (to_be_considered,Some repr,news) node set;
-      candidate::news,set
+    SameEquivalenceClass (node_to_be_deleted,node') ->
+     let rec clean =
+      function
+         [] -> []
+       | (repr',others,leq,geq) as node::tl ->
+          leq := List.filter (function node -> node_to_be_deleted != node) !leq;
+          geq := List.filter (function node -> node_to_be_deleted != node) !geq;
+          if node==node' then
+           (repr',others@[candidate],leq,geq)::clean tl
+          else
+           (repr',others,leq,geq)::clean tl
+     in
+     let nodes = clean nodes in
+      news,(nodes,inf,sup)
 ;;
 
-let rec explore i set news =
+let rec explore i (set:set) news =
  let rec aux news set =
   function
      [] -> news,set
@@ -223,7 +291,8 @@ let rec explore i 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");*)
diff --git a/matita/contribs/formal_topology/bin/theory_explorer_do_not_trust_auto.ml b/matita/contribs/formal_topology/bin/theory_explorer_do_not_trust_auto.ml
new file mode 100644
index 000000000..3a9dcde30
--- /dev/null
+++ b/matita/contribs/formal_topology/bin/theory_explorer_do_not_trust_auto.ml
@@ -0,0 +1,232 @@
+type rel = Equal | SubsetEqual | SupersetEqual
+
+let string_of_rel =
+ function
+    Equal -> "="
+  | SubsetEqual -> "⊆"
+  | SupersetEqual -> "⊇"
+
+(* operator *)
+type op = I | C | M
+
+let string_of_op =
+ function
+    I -> "i"
+  | C -> "c"
+  | M -> "-"
+
+(* compound operator *)
+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
+  | I::tl -> "i (" ^ matita_of_cop v tl ^ ")"
+  | C::tl -> "c (" ^ matita_of_cop v tl ^ ")"
+  | M::tl -> "m (" ^ matita_of_cop v tl ^ ")"
+
+(* representative, other elements in the equivalence class,
+   leq classes, geq classes *)
+type equivalence_class =
+ compound_operator * compound_operator list *
+  equivalence_class list ref * equivalence_class list ref
+
+let string_of_equivalence_class (repr,others,leq,_) =
+ String.concat " = " (List.map string_of_cop (repr::others)) ^
+  (if !leq <> [] then
+    "\n" ^
+     String.concat "\n" 
+      (List.map
+        (function (repr',_,_,_) ->
+           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
+    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',_,_,_) ->
+         dot_of_cop repr' ^ " -> " ^ dot_of_cop repr ^ ";") !leq)
+
+(* set of equivalence classes *)
+type set = equivalence_class list
+
+let string_of_set s =
+ String.concat "\n" (List.map string_of_equivalence_class s)
+
+let ps_of_set (to_be_considered,under_consideration,news) ?processing s =
+ 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 -> 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 (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 "tred xxx.dot > yyy.dot && dot -Tps yyy.dot > xxx.ps")
+
+let test to_be_considered_and_now set rel candidate repr =
+ ps_of_set to_be_considered_and_now ~processing:(candidate,rel,repr) set;
+ print_string
+  (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
+ let i = ref 0 in
+  List.iter
+   (function (repr,others,leq,_) ->
+     List.iter
+      (function repr' ->
+        incr i;
+        output_string ch
+         ("axiom ax" ^ string_of_int !i ^
+          ": \\forall A." ^
+           matita_of_cop "A" repr ^ " = " ^ matita_of_cop "A" repr' ^ ".\n");
+      ) others;
+     List.iter
+      (function (repr',_,_,_) ->
+        incr i;
+        output_string ch
+         ("axiom ax" ^ string_of_int !i ^
+          ": \\forall A." ^
+           matita_of_cop "A" repr ^ " ⊆ " ^ matita_of_cop "A" repr' ^ ".\n");
+      ) !leq;
+   ) set;
+  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' ^
+      " " ^ 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 > /dev/null 2>&1" = Unix.WEXITED 0
+  in
+   print_endline (if res then "y" else "n");
+   res
+
+let normalize to_be_considered_and_now candidate set =
+ let rec aux =
+  function
+     [] -> raise Not_found
+   | (repr,others,leq,geq) as eqclass :: tl ->
+       if test to_be_considered_and_now set Equal candidate repr then
+        (repr,others@[candidate],leq,geq)::tl
+       else
+        eqclass::(aux tl) 
+ in
+  aux set
+;;
+
+let locate to_be_considered_and_now ((repr,_,leq,geq) as node) set =
+ let rec aux =
+  function
+     [] -> ()
+   | (repr',_,leq',geq') as node' :: tl ->
+       if repr = repr' then ()
+       else if test to_be_considered_and_now set SubsetEqual repr repr' then
+        begin
+         leq  := node' :: !leq;
+         geq' := node  :: !geq'
+        end
+       else if test to_be_considered_and_now set SupersetEqual repr repr' then
+        begin
+         geq  := node' :: !geq;
+         leq' := node  :: !leq'
+        end ;
+       aux tl
+ in
+  aux set
+;;
+
+let analyze_one to_be_considered repr hecandidate (news,set) =
+ let candidate = hecandidate::repr in
+  if List.length (List.filter ((=) M) candidate) > 1 then
+   news,set
+  else
+   try
+    let set = normalize (to_be_considered,Some repr,news) candidate set in
+     news,set
+   with
+    Not_found ->
+     let leq = ref [] in
+     let geq = ref [] in
+     let node = candidate,[],leq,geq in
+     let set = node::set in
+      locate (to_be_considered,Some repr,news) node set;
+      candidate::news,set
+;;
+
+let rec explore i set news =
+ let rec aux news set =
+  function
+     [] -> news,set
+   | repr::tl ->
+      let 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);
+     print_endline (string_of_set set ^ "\n----------------");
+     ps_of_set ([],None,[]) set
+    end
+   else
+    begin
+     print_endline ("NUOVA ITERAZIONE, i=" ^ string_of_int i);
+     print_endline (string_of_set set ^ "\n----------------");
+     explore (i+1) set news
+    end
+in
+ let id = [] in
+ let set = [id,[],ref [], ref []] 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 ([id],None,[]) set;
+  explore 1 set [id]
+;;