10 (* compound operator *)
11 type compound_operator = op list
13 let string_of_cop op =
14 if op = [] then "id" else String.concat "" (List.map string_of_op op)
16 let dot_of_cop op = "\"" ^ string_of_cop op ^ "\""
18 let rec matita_of_cop v =
21 | I::tl -> "i (" ^ matita_of_cop v tl ^ ")"
22 | C::tl -> "c (" ^ matita_of_cop v tl ^ ")"
23 | M::tl -> "m (" ^ matita_of_cop v tl ^ ")"
25 (* representative, other elements in the equivalence class,
26 leq classes, geq classes *)
27 type equivalence_class =
28 compound_operator * compound_operator list *
29 equivalence_class list ref * equivalence_class list ref
31 let string_of_equivalence_class (repr,others,leq,_) =
32 String.concat " = " (List.map string_of_cop (repr::others)) ^
37 (function (repr',_,_,_) ->
38 string_of_cop repr ^ " <= " ^ string_of_cop repr') !leq)
42 let dot_of_equivalence_class (repr,others,leq,_) =
44 let eq = String.concat " = " (List.map string_of_cop (repr::others)) in
45 dot_of_cop repr ^ "[label=\"" ^ eq ^ "\"];" ^
46 if !leq = [] then "" else "\n"
50 (function (repr',_,_,_) ->
51 dot_of_cop repr' ^ " -> " ^ dot_of_cop repr ^ ";") !leq)
53 (* set of equivalence classes *)
54 type set = equivalence_class list
57 String.concat "\n" (List.map string_of_equivalence_class s)
59 let ps_of_set ?processing s =
60 let ch = open_out "xxx.dot" in
61 output_string ch "digraph G {\n";
62 output_string ch (String.concat "\n" (List.map dot_of_equivalence_class s));
63 output_string ch "\n";
64 (match processing with
66 | Some (repr,rel,repr') ->
68 (dot_of_cop repr' ^ " -> " ^ dot_of_cop repr ^
70 (if rel="=" then "arrowhead=none " else "") ^
72 output_string ch "}\n";
74 ignore (Unix.system "dot -Tps xxx.dot > xxx.ps")
76 let test set rel candidate repr =
77 ps_of_set ~processing:(candidate,rel,repr) set;
79 (string_of_cop candidate ^ " " ^ rel ^ " " ^ string_of_cop repr ^ "? ");
81 assert (Unix.system "cp formal_topology.ma xxx.ma" = Unix.WEXITED 0);
82 let ch = open_out_gen [Open_append] 0 "xxx.ma" in
85 (function (repr,others,leq,_) ->
90 ("axiom ax" ^ string_of_int !i ^
92 matita_of_cop "A" repr ^ " = " ^ matita_of_cop "A" repr' ^ ".\n");
95 (function (repr',_,_,_) ->
98 ("axiom ax" ^ string_of_int !i ^
100 matita_of_cop "A" repr ^ " ⊆ " ^ matita_of_cop "A" repr' ^ ".\n");
104 ("theorem foo: \\forall A." ^ matita_of_cop "A" candidate ^ " " ^ rel ^ " " ^
105 matita_of_cop "A" repr ^ ". intros; auto size=6 depth=4. qed.\n");
108 Unix.system "../../../matitac.opt xxx.ma >> log 2>&1" = Unix.WEXITED 0
110 print_endline (if res then "y" else "n");
113 let normalize candidate set =
116 [] -> raise Not_found
117 | (repr,others,leq,geq) as eqclass :: tl ->
118 if test set "=" candidate repr then
119 (repr,others@[candidate],leq,geq)::tl
126 let locate ((repr,_,leq,geq) as node) set =
130 | (repr',_,leq',geq') as node' :: tl ->
131 if repr = repr' then ()
132 else if test set "⊆" repr repr' then
134 leq := node' :: !leq;
135 geq' := node :: !geq'
137 else if test set "⊆" repr' repr then
139 geq := node' :: !geq;
140 leq' := node :: !leq'
147 let analyze_one i repr hecandidate (news,set) =
148 let candidate = hecandidate::repr in
149 if List.length (List.filter ((=) M) candidate) > i then
153 let set = normalize candidate set in
159 let node = candidate,[],leq,geq in
160 let set = node::set in
165 let rec explore i j set news =
166 let rec aux news set =
171 List.fold_right (analyze_one i repr) [I;C;M] (news,set)
175 let news,set = aux [] set news in
178 print_endline ("PUNTO FISSO RAGGIUNTO! i=" ^ string_of_int i ^ " j=" ^ string_of_int j);
179 print_endline (string_of_set set ^ "\n----------------");
181 explore (i+1) 1 set (List.map (function (repr,_,_,_) -> repr) set)
187 print_endline ("NUOVA ITERAZIONE, i=" ^ string_of_int i ^ " j=" ^ string_of_int j);
188 print_endline (string_of_set set ^ "\n----------------");
189 explore i (j+1) set news
193 let set = [id,[],ref [], ref []] in
194 print_endline ("PRIMA ITERAZIONE, i=0, j=0");
195 print_endline (string_of_set set ^ "\n----------------");
196 ignore (Unix.system "rm -f log");