2 let ok_time = ref 0.0;;
3 let ko_time = ref 0.0;;
6 let before = Unix.gettimeofday () in
8 let after = Unix.gettimeofday () in
9 let delta = after -. before in
10 if res = Unix.WEXITED 0 then
11 ok_time := !ok_time +. delta
13 ko_time := !ko_time +. delta;
22 ("\nTIME SPENT IN CHECKING GOOD CONJECTURES: " ^ string_of_float !ok_time);
24 ("TIME SPENT IN CHECKING BAD CONJECTURES: " ^ string_of_float !ko_time);)
27 (**** END PROFILING ****)
29 type rel = Equal | SubsetEqual | SupersetEqual
35 | SupersetEqual -> "⊇"
40 let string_of_op = function I -> "i" | C -> "c" | M -> "-"
41 let matita_of_op = function I -> "i" | C -> "c" | M -> "m"
43 (* compound operator *)
44 type compound_operator = op list
46 let string_of_cop op =
47 if op = [] then "id" else String.concat "" (List.map string_of_op op)
49 let dot_of_cop op = "\"" ^ string_of_cop op ^ "\""
55 | [op] -> matita_of_op op ^ " " ^ v
56 | op::tl -> matita_of_op op ^ " (" ^ aux tl ^ ")"
60 let name_of_theorem cop rel cop' =
63 Equal -> cop,"eq",cop'
64 | SubsetEqual -> cop,"leq",cop'
65 | SupersetEqual -> cop',"leq",cop
68 String.concat "" (List.map matita_of_op cop) ^ "_" ^
69 String.concat "" (List.map matita_of_op cop')
72 (* representative, other elements in the equivalence class,
73 leq classes, geq classes *)
74 type equivalence_class =
75 compound_operator * compound_operator list *
76 equivalence_class list ref * equivalence_class list ref
78 let (===) (repr,_,_,_) (repr',_,_,_) = repr = repr';;
79 let (<=>) (repr,_,_,_) (repr',_,_,_) = repr <> repr';;
81 let string_of_equivalence_class (repr,others,leq,_) =
82 String.concat " = " (List.map string_of_cop (repr::others)) ^
87 (function (repr',_,_,_) ->
88 string_of_cop repr ^ " ⊆ " ^ string_of_cop repr') !leq)
92 let dot_of_equivalence_class (repr,others,leq,_) =
94 let eq = String.concat " = " (List.map string_of_cop (repr::others)) in
95 dot_of_cop repr ^ "[label=\"" ^ eq ^ "\"];" ^
96 if !leq = [] then "" else "\n"
97 else if !leq = [] then
103 (function (repr',_,_,_) ->
104 dot_of_cop repr' ^ " -> " ^ dot_of_cop repr ^ ";") !leq)
106 (* set of equivalence classes, infima, suprema *)
108 equivalence_class list * equivalence_class list * equivalence_class list
110 let string_of_set (s,_,_) =
111 String.concat "\n" (List.map string_of_equivalence_class s)
113 let ps_of_set (to_be_considered,under_consideration,news) ?processing (s,inf,sup) =
114 let ch = open_out "xxx.dot" in
115 output_string ch "digraph G {\n";
116 (match under_consideration with
119 output_string ch (dot_of_cop repr ^ " [color=yellow];"));
121 (function (repr,_,_,_) ->
122 if List.exists (function (repr',_,_,_) -> repr=repr') sup then
123 output_string ch (dot_of_cop repr ^ " [shape=Mdiamond];")
125 output_string ch (dot_of_cop repr ^ " [shape=diamond];")
128 (function (repr,_,_,_) ->
129 if not (List.exists (function (repr',_,_,_) -> repr=repr') inf) then
130 output_string ch (dot_of_cop repr ^ " [shape=polygon];")
133 (function repr -> output_string ch (dot_of_cop repr ^ " [color=green];")
136 (function repr -> output_string ch (dot_of_cop repr ^ " [color=navy];")
138 output_string ch (String.concat "\n" (List.map dot_of_equivalence_class s));
139 output_string ch "\n";
140 (match processing with
142 | Some (repr,rel,repr') ->
143 output_string ch (dot_of_cop repr ^ " [color=red];");
146 SupersetEqual -> repr',repr
148 | SubsetEqual -> repr,repr'
151 (dot_of_cop repr' ^ " -> " ^ dot_of_cop repr ^
153 (match rel with Equal -> "arrowhead=none " | _ -> "") ^
154 "style=dashed];\n"));
155 output_string ch "}\n";
157 (*ignore (Unix.system "tred xxx.dot > yyy.dot && dot -Tps yyy.dot > xxx.ps")*)
158 ignore (Unix.system "cp xxx.ps xxx_old.ps && dot -Tps xxx.dot > xxx.ps");
159 (*ignore (read_line ())*)
162 let test to_be_considered_and_now ((s,_,_) as set) rel candidate repr =
163 ps_of_set to_be_considered_and_now ~processing:(candidate,rel,repr) set;
165 (string_of_cop candidate ^ " " ^ string_of_rel rel ^ " " ^ string_of_cop repr ^ "? ");
167 assert (Unix.system "cat log.ma | sed s/^theorem/axiom/g | sed 's/\\. intros.*qed\\././g' > xxx.ma" = Unix.WEXITED 0);
168 let ch = open_out_gen [Open_append] 0 "xxx.ma" in
172 (function (repr,others,leq,_) ->
177 ("axiom ax" ^ string_of_int !i ^
179 matita_of_cop "A" repr ^ " = " ^ matita_of_cop "A" repr' ^ ".\n");
182 (function (repr',_,_,_) ->
185 ("axiom ax" ^ string_of_int !i ^
187 matita_of_cop "A" repr ^ " ⊆ " ^ matita_of_cop "A" repr' ^ ".\n");
191 let candidate',rel',repr' =
193 SupersetEqual -> repr,SubsetEqual,candidate
195 | SubsetEqual -> candidate,rel,repr in
197 let name = name_of_theorem candidate' rel' repr' in
198 ("theorem " ^ name ^ ": \\forall A." ^ matita_of_cop "A" candidate' ^
199 " " ^ string_of_rel rel' ^ " " ^
200 matita_of_cop "A" repr' ^ ". intros; autobatch size=8 depth=3 width=2. qed.") in
201 output_string ch (query ^ "\n");
204 (*Unix.system "../../../matitac.opt xxx.ma >> log 2>&1" = Unix.WEXITED 0*)
205 profile Unix.system "../../../matitac.opt xxx.ma > /dev/null 2>&1" = Unix.WEXITED 0
207 ignore (Unix.system "echo '(*' >> log.ma && cat xxx.dot >> log.ma && echo '*)' >> log.ma");
208 let ch = open_out_gen [Open_append] 0o0600 "log.ma" in
210 output_string ch (query ^ "\n")
212 output_string ch ("(* " ^ query ^ "*)\n");
214 print_endline (if res then "y" else "n");
217 let remove node = List.filter (fun node' -> node <=> node');;
219 let add_leq_arc ((_,_,leq,_) as node) ((_,_,_,geq') as node') =
220 leq := node' :: !leq;
221 geq' := node :: !geq'
224 let add_geq_arc ((_,_,_,geq) as node) ((_,_,leq',_) as node') =
225 geq := node' :: !geq;
226 leq' := node :: !leq'
229 let remove_leq_arc ((_,_,leq,_) as node) ((_,_,_,geq') as node') =
230 leq := remove node' !leq;
231 geq' := remove node !geq'
234 let remove_geq_arc ((_,_,_,geq) as node) ((_,_,leq',_) as node') =
235 geq := remove node' !geq;
236 leq' := remove node !leq'
239 let leq_transitive_closure node node' =
240 add_leq_arc node node';
241 let rec remove_transitive_arcs ((_,_,_,geq) as node) (_,_,leq',_) =
242 let rec remove_arcs_to_ascendents =
245 | (_,_,leq,_) as node'::tl ->
246 remove_leq_arc node node';
247 remove_arcs_to_ascendents (!leq@tl)
249 remove_arcs_to_ascendents !leq';
250 List.iter (function son -> remove_transitive_arcs son node) !geq
252 remove_transitive_arcs node node'
255 let geq_transitive_closure node node' =
256 add_geq_arc node node';
257 let rec remove_transitive_arcs ((_,_,leq,_) as node) (_,_,_,geq') =
258 let rec remove_arcs_to_descendents =
261 | (_,_,_,geq) as node'::tl ->
262 remove_geq_arc node node';
263 remove_arcs_to_descendents (!geq@tl)
265 remove_arcs_to_descendents !geq';
266 List.iter (function father -> remove_transitive_arcs father node) !leq
268 remove_transitive_arcs node node'
271 let (@@) l1 n = if List.exists (function n' -> n===n') l1 then l1 else l1@[n]
273 let rec leq_reachable node =
276 | node'::_ when node === node' -> true
277 | (_,_,leq,_)::tl -> leq_reachable node (!leq@tl)
280 let rec geq_reachable node =
283 | node'::_ when node === node' -> true
284 | (_,_,_,geq)::tl -> geq_reachable node (!geq@tl)
287 let locate_using_leq to_be_considered_and_now ((repr,_,leq,geq) as node)
290 let rec aux ((nodes,inf,sup) as set) already_visited =
293 | (repr',_,_,geq') as node' :: tl ->
294 if List.exists (function n -> n===node') already_visited then
295 aux set already_visited tl
296 else if repr=repr' then aux set (node'::already_visited) (!geq'@tl)
297 else if leq_reachable node' !leq then
298 aux set (node'::already_visited) tl
299 else if test to_be_considered_and_now set SubsetEqual repr repr' then
301 let sup = remove node sup in
304 let inf = remove node' inf in
312 leq_transitive_closure node node';
313 aux (nodes,inf,sup) (node'::already_visited) (!geq'@tl)
316 aux set (node'::already_visited) tl
321 exception SameEquivalenceClass of set * equivalence_class * equivalence_class;;
323 let locate_using_geq to_be_considered_and_now ((repr,_,leq,geq) as node)
326 let rec aux ((nodes,inf,sup) as set) already_visited =
329 | (repr',_,leq',_) as node' :: tl ->
330 if List.exists (function n -> n===node') already_visited then
331 aux set already_visited tl
332 else if repr=repr' then aux set (node'::already_visited) (!leq'@tl)
333 else if geq_reachable node' !geq then
334 aux set (node'::already_visited) tl
335 else if test to_be_considered_and_now set SupersetEqual repr repr' then
337 if List.exists (function n -> n===node') !leq then
338 (* We have found two equal nodes! *)
339 raise (SameEquivalenceClass (set,node,node'))
342 let inf = remove node inf in
345 let sup = remove node' sup in
353 geq_transitive_closure node node';
354 aux (nodes,inf,sup) (node'::already_visited) (!leq'@tl)
358 aux set (node'::already_visited) tl
363 let analyze_one to_be_considered repr hecandidate (news,((nodes,inf,sup) as set)) =
364 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);
365 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);
366 let candidate = hecandidate::repr in
367 if List.length (List.filter ((=) M) candidate) > 1 then
373 let node = candidate,[],leq,geq in
374 let nodes = nodes@[node] in
375 let set = nodes,inf@[node],sup@[node] in
376 let start_inf,start_sup =
378 match List.filter (fun (repr',_,_,_) -> repr=repr') nodes with
383 match hecandidate with
385 | C -> [repr_node],sup
390 locate_using_leq (to_be_considered,Some repr,news) node set start_sup in
392 let _,inf,sup = set in
393 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);
394 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);
397 locate_using_geq (to_be_considered,Some repr,news) node set start_inf
400 let _,inf,sup = set in
401 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);
402 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);
406 SameEquivalenceClass ((nodes,inf,sup) as set,((r,_,leq_d,geq_d) as node_to_be_deleted),node')->
408 let _,inf,sup = set in
409 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);
410 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);
412 let rec clean inf sup res =
415 | node::tl when node===node_to_be_deleted ->
417 | (repr',others,leq,geq) as node::tl ->
422 | (_,_,leq,_) as node::tl ->
423 if node_to_be_deleted <=> node then
426 (List.filter (fun n ->not (leq_reachable n (res@tl))) !leq)@tl
429 let sup = if !leq = [] then sup@@node else sup in
434 | (_,_,_,geq) as node::tl ->
435 if node_to_be_deleted <=> node then
438 (List.filter (fun n ->not (geq_reachable n (res@tl))) !geq)@tl
441 let inf = if !geq = [] then inf@@node else inf in
443 clean inf sup ((repr',others@[candidate],leq,geq)::res) tl
445 clean inf sup (node::res) tl
447 let inf,sup,nodes = clean inf sup [] nodes in
448 let inf = remove node_to_be_deleted inf in
449 let sup = remove node_to_be_deleted sup in
450 let set = nodes,inf,sup in
452 let _,inf,sup = set in
453 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);
454 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);
459 let rec explore i (set:set) news =
460 let rec aux news set =
465 List.fold_right (analyze_one tl repr) [I;C;M] (news,set)
469 let news,set = aux [] set news in
472 print_endline ("PUNTO FISSO RAGGIUNTO! i=" ^ string_of_int i);
473 print_endline (string_of_set set ^ "\n----------------");
474 ps_of_set ([],None,[]) set
478 print_endline ("NUOVA ITERAZIONE, i=" ^ string_of_int i);
479 print_endline (string_of_set set ^ "\n----------------");
480 explore (i+1) set news
484 let id_node = id,[],ref [], ref [] in
485 let set = [id_node],[id_node],[id_node] in
486 print_endline ("PRIMA ITERAZIONE, i=0, j=0");
487 print_endline (string_of_set set ^ "\n----------------");
488 (*ignore (Unix.system "rm -f log");*)
489 assert (Unix.system "cp formal_topology.ma log.ma" = Unix.WEXITED 0);
490 ps_of_set ([id],None,[]) set;