1 type rel = Equal | SubsetEqual | SupersetEqual
18 (* compound operator *)
19 type compound_operator = op list
21 let string_of_cop op =
22 if op = [] then "id" else String.concat "" (List.map string_of_op op)
24 let dot_of_cop op = "\"" ^ string_of_cop op ^ "\""
26 let rec matita_of_cop v =
29 | I::tl -> "i (" ^ matita_of_cop v tl ^ ")"
30 | C::tl -> "c (" ^ matita_of_cop v tl ^ ")"
31 | M::tl -> "m (" ^ matita_of_cop v tl ^ ")"
33 (* representative, other elements in the equivalence class,
34 leq classes, geq classes *)
35 type equivalence_class =
36 compound_operator * compound_operator list *
37 equivalence_class list ref * equivalence_class list ref
39 let string_of_equivalence_class (repr,others,leq,_) =
40 String.concat " = " (List.map string_of_cop (repr::others)) ^
45 (function (repr',_,_,_) ->
46 string_of_cop repr ^ " ⊆ " ^ string_of_cop repr') !leq)
50 let dot_of_equivalence_class (repr,others,leq,_) =
52 let eq = String.concat " = " (List.map string_of_cop (repr::others)) in
53 dot_of_cop repr ^ "[label=\"" ^ eq ^ "\"];" ^
54 if !leq = [] then "" else "\n"
55 else if !leq = [] then
61 (function (repr',_,_,_) ->
62 dot_of_cop repr' ^ " -> " ^ dot_of_cop repr ^ ";") !leq)
64 (* set of equivalence classes, infima, suprema *)
66 equivalence_class list * equivalence_class list * equivalence_class list
68 let string_of_set (s,_,_) =
69 String.concat "\n" (List.map string_of_equivalence_class s)
71 let ps_of_set (to_be_considered,under_consideration,news) ?processing (s,inf,sup) =
72 let ch = open_out "xxx.dot" in
73 output_string ch "digraph G {\n";
74 (match under_consideration with
77 output_string ch (dot_of_cop repr ^ " [color=yellow];"));
79 (function (repr,_,_,_) ->
80 if List.exists (function (repr',_,_,_) -> repr=repr') sup then
81 output_string ch (dot_of_cop repr ^ " [shape=Mdiamond];")
83 output_string ch (dot_of_cop repr ^ " [shape=diamond];")
86 (function (repr,_,_,_) ->
87 if not (List.exists (function (repr',_,_,_) -> repr=repr') inf) then
88 output_string ch (dot_of_cop repr ^ " [shape=polygon];")
91 (function repr -> output_string ch (dot_of_cop repr ^ " [color=green];")
94 (function repr -> output_string ch (dot_of_cop repr ^ " [color=navy];")
96 output_string ch (String.concat "\n" (List.map dot_of_equivalence_class s));
97 output_string ch "\n";
98 (match processing with
100 | Some (repr,rel,repr') ->
101 output_string ch (dot_of_cop repr ^ " [color=red];");
104 SupersetEqual -> repr',repr
106 | SubsetEqual -> repr,repr'
109 (dot_of_cop repr' ^ " -> " ^ dot_of_cop repr ^
111 (match rel with Equal -> "arrowhead=none " | _ -> "") ^
112 "style=dashed];\n"));
113 output_string ch "}\n";
115 (*ignore (Unix.system "tred xxx.dot > yyy.dot && dot -Tps yyy.dot > xxx.ps")*)
116 ignore (Unix.system "dot -Tps xxx.dot > xxx.ps");
117 ignore (read_line ())
119 let test to_be_considered_and_now ((s,_,_) as set) rel candidate repr =
120 ps_of_set to_be_considered_and_now ~processing:(candidate,rel,repr) set;
122 (string_of_cop candidate ^ " " ^ string_of_rel rel ^ " " ^ string_of_cop repr ^ "? ");
124 assert (Unix.system "cp formal_topology.ma xxx.ma" = Unix.WEXITED 0);
125 let ch = open_out_gen [Open_append] 0 "xxx.ma" in
128 (function (repr,others,leq,_) ->
133 ("axiom ax" ^ string_of_int !i ^
135 matita_of_cop "A" repr ^ " = " ^ matita_of_cop "A" repr' ^ ".\n");
138 (function (repr',_,_,_) ->
141 ("axiom ax" ^ string_of_int !i ^
143 matita_of_cop "A" repr ^ " ⊆ " ^ matita_of_cop "A" repr' ^ ".\n");
146 let candidate',rel',repr' =
148 SupersetEqual -> repr,SubsetEqual,candidate
150 | SubsetEqual -> candidate,rel,repr
153 ("theorem foo: \\forall A." ^ matita_of_cop "A" candidate' ^
154 " " ^ string_of_rel rel' ^ " " ^
155 matita_of_cop "A" repr' ^ ". intros; auto size=6 depth=4. qed.\n");
158 (*Unix.system "../../../matitac.opt xxx.ma >> log 2>&1" = Unix.WEXITED 0*)
159 Unix.system "../../../matitac.opt xxx.ma > /dev/null 2>&1" = Unix.WEXITED 0
161 print_endline (if res then "y" else "n");
164 let remove node = List.filter (fun node' -> node != node');;
166 let add_leq_arc ((_,_,leq,_) as node) ((_,_,_,geq') as node') =
167 leq := node' :: !leq;
168 geq' := node :: !geq'
171 let add_geq_arc ((_,_,_,geq) as node) ((_,_,leq',_) as node') =
172 geq := node' :: !geq;
173 leq' := node :: !leq'
176 let remove_leq_arc ((_,_,leq,_) as node) ((_,_,_,geq') as node') =
177 leq := remove node' !leq;
178 geq' := remove node !geq'
181 let remove_geq_arc ((_,_,_,geq) as node) ((_,_,leq',_) as node') =
182 geq := remove node' !geq;
183 leq' := remove node !leq'
186 let leq_transitive_closure node node' =
187 add_leq_arc node node';
188 let rec remove_transitive_arcs ((_,_,_,geq) as node) (_,_,leq',_) =
189 let rec remove_arcs_to_ascendents =
192 | (_,_,leq,_) as node'::tl ->
193 remove_leq_arc node node';
194 remove_arcs_to_ascendents (!leq@tl)
196 remove_arcs_to_ascendents !leq';
197 List.iter (function son -> remove_transitive_arcs son node) !geq
199 remove_transitive_arcs node node'
202 let geq_transitive_closure node node' =
203 add_geq_arc node node';
204 let rec remove_transitive_arcs ((_,_,leq,_) as node) (_,_,_,geq') =
205 let rec remove_arcs_to_descendents =
208 | (_,_,_,geq) as node'::tl ->
209 remove_geq_arc node node';
210 remove_arcs_to_descendents (!geq@tl)
212 remove_arcs_to_descendents !geq';
213 List.iter (function father -> remove_transitive_arcs father node) !leq
215 remove_transitive_arcs node node'
218 let (@@) l1 e = if List.memq e l1 then l1 else l1@[e]
220 let rec leq_reachable node =
223 | node'::_ when node == node' -> true
224 | (_,_,leq,_)::tl -> leq_reachable node (!leq@tl)
227 let rec geq_reachable node =
230 | node'::_ when node == node' -> true
231 | (_,_,_,geq)::tl -> geq_reachable node (!geq@tl)
234 let locate_using_leq to_be_considered_and_now ((repr,_,leq,_) as node)
237 let rec aux is_sup ((nodes,inf,sup) as set) =
244 | (repr',_,_,geq') as node' :: tl ->
245 if repr=repr' then aux is_sup set (!geq'@tl)
246 else if leq_reachable node' !leq then
248 else if test to_be_considered_and_now set SubsetEqual repr repr' then
250 let inf = if !geq' = [] then (remove node' inf)@@node else inf in
251 leq_transitive_closure node node';
252 aux false (nodes,inf,sup) (!geq'@tl)
257 prerr_endline ("SUP: " ^ String.concat "," (List.map (fun (x,_,_,_) -> string_of_cop x) sup));
261 exception SameEquivalenceClass of equivalence_class * equivalence_class;;
263 let locate_using_geq to_be_considered_and_now ((repr,_,leq,geq) as node)
266 let rec aux is_inf ((nodes,inf,sup) as set) =
273 | (repr',_,leq',_) as node' :: tl ->
274 if repr=repr' then aux is_inf set (!leq'@tl)
275 else if geq_reachable node' !geq then
277 else if test to_be_considered_and_now set SupersetEqual repr repr' then
279 if List.mem node' !leq then
280 (* We have found two equal nodes! *)
281 raise (SameEquivalenceClass (node,node'))
284 let sup = if !leq' = [] then (remove node' sup)@@node else sup in
285 geq_transitive_closure node node';
286 aux false (nodes,inf,sup) (!leq'@tl)
292 prerr_endline ("INF: " ^ String.concat "," (List.map (fun (x,_,_,_) -> string_of_cop x) inf));
296 let analyze_one to_be_considered repr hecandidate (news,((nodes,inf,sup) as set)) =
297 let candidate = hecandidate::repr in
298 if List.length (List.filter ((=) M) candidate) > 1 then
304 let node = candidate,[],leq,geq in
305 let nodes = nodes@[node] in
306 let set = nodes,inf,sup in
307 let set = locate_using_leq (to_be_considered,Some repr,news) node set in
308 let set = locate_using_geq (to_be_considered,Some repr,news) node set in
311 SameEquivalenceClass (node_to_be_deleted,node') ->
315 | (repr',others,leq,geq) as node::tl ->
316 leq := List.filter (function node -> node_to_be_deleted != node) !leq;
317 geq := List.filter (function node -> node_to_be_deleted != node) !geq;
319 (repr',others@[candidate],leq,geq)::clean tl
321 (repr',others,leq,geq)::clean tl
323 let nodes = clean nodes in
327 let rec explore i (set:set) news =
328 let rec aux news set =
333 List.fold_right (analyze_one tl repr) [I;C;M] (news,set)
337 let news,set = aux [] set news in
340 print_endline ("PUNTO FISSO RAGGIUNTO! i=" ^ string_of_int i);
341 print_endline (string_of_set set ^ "\n----------------");
342 ps_of_set ([],None,[]) set
346 print_endline ("NUOVA ITERAZIONE, i=" ^ string_of_int i);
347 print_endline (string_of_set set ^ "\n----------------");
348 explore (i+1) set news
352 let id_node = id,[],ref [], ref [] in
353 let set = [id_node],[id_node],[id_node] in
354 print_endline ("PRIMA ITERAZIONE, i=0, j=0");
355 print_endline (string_of_set set ^ "\n----------------");
356 (*ignore (Unix.system "rm -f log");*)
357 ps_of_set ([id],None,[]) set;