X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fcontribs%2Fformal_topology%2Fbin%2Ftheory_explorer.ml;fp=matita%2Fcontribs%2Fformal_topology%2Fbin%2Ftheory_explorer.ml;h=39a021c9dc19abfbe805220c1fb85824248e38a4;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/contribs/formal_topology/bin/theory_explorer.ml b/matita/contribs/formal_topology/bin/theory_explorer.ml new file mode 100644 index 000000000..39a021c9d --- /dev/null +++ b/matita/contribs/formal_topology/bin/theory_explorer.ml @@ -0,0 +1,568 @@ +(**** PROFILING ****) +let ok_time = ref 0.0;; +let ko_time = ref 0.0;; + +let profile f x = + let before = Unix.gettimeofday () in + let res = f x in + let after = Unix.gettimeofday () in + let delta = after -. before in + if res then + ok_time := !ok_time +. delta + else + ko_time := !ko_time +. delta; + res +;; + +let _ = + Sys.catch_break true; + at_exit + (function () -> + prerr_endline + ("\nTIME SPENT IN CHECKING GOOD CONJECTURES: " ^ string_of_float !ok_time); + prerr_endline + ("TIME SPENT IN CHECKING BAD CONJECTURES: " ^ string_of_float !ko_time);) +;; + +(**** END PROFILING ****) + +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 -> "-" +let matita_of_op = function I -> "i" | C -> "c" | M -> "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 matita_of_cop v = + let rec aux = + function + | [] -> v + | [op] -> matita_of_op op ^ " " ^ v + | op::tl -> matita_of_op op ^ " (" ^ aux tl ^ ")" + in + aux + +let name_of_theorem cop rel cop' = + let cop,rel,cop' = + match rel with + Equal -> cop,"eq",cop' + | SubsetEqual -> cop,"leq",cop' + | SupersetEqual -> cop',"leq",cop + in + rel ^ "_" ^ + String.concat "" (List.map matita_of_op cop) ^ "_" ^ + String.concat "" (List.map matita_of_op cop') +;; + +(* 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 (===) (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 + "\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, infima, suprema *) +type set = + equivalence_class list * equivalence_class list * 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,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 (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")*) + ignore (Unix.system "cp xxx.ps xxx_old.ps && dot -Tps xxx.dot > xxx.ps"); + (*ignore (read_line ())*) +;; + +(******** communication with matitawiki ************) +let min_ch,mout_ch = Unix.open_process "../../../matitawiki.opt 2> /dev/null";; + +let exec_cmd ?(undo=false) s = + let un = if undo then "un" else "" in +(*prerr_endline ("<" ^ un ^ "doitem>" ^ s ^ "\n");*) + output_string mout_ch ("<" ^ un ^ "doitem>" ^ s ^ "\n"); + flush mout_ch; + let rec aux v = + let l = input_line min_ch in + let last = String.length l - 1 in + assert (last > 0); + if l.[last] = Char.chr 249 then + int_of_string (String.sub l 0 last) + else + aux l + in + aux "x" +;; + +let exec_cmds = + let rec aux undopos = + function + [] -> true + | he::tl -> + let pos = exec_cmd he in + if pos = -1 then + begin + match undopos with + None -> assert false + | Some undopos -> + assert (exec_cmd ~undo:true (string_of_int (undopos - 1)) <> -1); + false + end + else + match undopos with + None -> aux (Some pos) tl + | _ -> aux undopos tl + in + aux None + +let _ = + assert (exec_cmd "set \"baseuri\" \"cic:/matita/theory_former\"." <> -1); + assert (exec_cmd "include \"formal_topology.ma\"." <> -1); +;; + +(********* testing a conjecture *******************) + +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 ^ "? "); + flush stdout; +(* + assert (Unix.system "cat log.ma | sed s/^theorem/axiom/g | sed 's/\\. intros.*qed\\././g' > 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; + ) s; +*) + let candidate',rel',repr' = + match rel with + SupersetEqual -> repr,SubsetEqual,candidate + | Equal + | SubsetEqual -> candidate,rel,repr in + let query1 = + let name = name_of_theorem candidate' rel' repr' in + ("theorem " ^ name ^ ": \\forall A." ^ matita_of_cop "A" candidate' ^ + " " ^ string_of_rel rel' ^ " " ^ + matita_of_cop "A" repr' ^ ".") in + let query2 = "intros;" in + let query3 = "autobatch size=8 depth=3 width=2." in + let query4 = "qed." in + let query = query1 ^ query2 ^ query3 ^ query4 in +(* + output_string ch (query ^ "\n"); + close_out ch; +*) + let res = profile exec_cmds [query1; query2; query3; query4] in +(* + let res = + (*Unix.system "../../../matitac.opt xxx.ma >> log 2>&1" = Unix.WEXITED 0*) + profile Unix.system "../../../matitac.opt xxx.ma > /dev/null 2>&1" = Unix.WEXITED 0 + in +*) + ignore (Unix.system "echo '(*' >> log.ma && cat xxx.dot >> log.ma && echo '*)' >> log.ma"); + let ch = open_out_gen [Open_append] 0o0600 "log.ma" in + if res then + output_string ch (query ^ "\n") + else + output_string ch ("(* " ^ query ^ "*)\n"); + close_out ch; + print_endline (if res then "y" else "n"); + res + +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) +;; + +exception SameEquivalenceClass of set * equivalence_class * equivalence_class;; + +let locate_using_leq to_be_considered_and_now ((repr,_,leq,geq) as node) + set start += + let rec aux ((nodes,inf,sup) as set) already_visited = + function + [] -> set + | (repr',_,_,geq') as node' :: tl -> + if List.exists (function n -> n===node') already_visited then + aux set already_visited tl + else if repr=repr' then aux set (node'::already_visited) (!geq'@tl) + else if leq_reachable node' !leq then + aux set (node'::already_visited) (!geq'@tl) + else if (List.exists (function n -> not (geq_reachable n [node'])) !geq) + then + aux set (node'::already_visited) tl + else if test to_be_considered_and_now set SubsetEqual repr repr' then + begin + if List.exists (function n -> n===node') !geq then + (* We have found two equal nodes! *) + raise (SameEquivalenceClass (set,node,node')) + else + begin + let sup = remove node sup in + let inf = + if !geq' = [] then + let inf = remove node' inf in + if !geq = [] then + inf@@node + else + inf + else + inf + in + leq_transitive_closure node node'; + aux (nodes,inf,sup) (node'::already_visited) (!geq'@tl) + end + end + else + aux set (node'::already_visited) tl + in + aux set [] start +;; + +let locate_using_geq to_be_considered_and_now ((repr,_,leq,geq) as node) + set start += + let rec aux ((nodes,inf,sup) as set) already_visited = + function + [] -> set + | (repr',_,leq',_) as node' :: tl -> + if List.exists (function n -> n===node') already_visited then + aux set already_visited tl + else if repr=repr' then aux set (node'::already_visited) (!leq'@tl) + else if geq_reachable node' !geq then + aux set (node'::already_visited) (!leq'@tl) + else if (List.exists (function n -> not (leq_reachable n [node'])) !leq) + then + aux set (node'::already_visited) tl + else if test to_be_considered_and_now set SupersetEqual repr repr' then + begin + if List.exists (function n -> n===node') !leq then + (* We have found two equal nodes! *) + raise (SameEquivalenceClass (set,node,node')) + else + begin + let inf = remove node inf in + let sup = + if !leq' = [] then + let sup = remove node' sup in + if !leq = [] then + sup@@node + else + sup + else + sup + in + geq_transitive_closure node node'; + aux (nodes,inf,sup) (node'::already_visited) (!leq'@tl) + end + end + else + aux set (node'::already_visited) tl + in + aux set [] start +;; + +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) > 1 then + news,set + else + try + 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 set,start_inf,start_sup = + let repr_node = + match List.filter (fun (repr',_,_,_) -> repr=repr') nodes with + [node] -> node + | _ -> assert false + in + match hecandidate,repr with + I, I::_ -> raise (SameEquivalenceClass (set,node,repr_node)) + | I, _ -> + add_leq_arc node repr_node; + (nodes,remove repr_node inf@[node],sup),inf,sup + | C, C::_ -> raise (SameEquivalenceClass (set,node,repr_node)) + | C, _ -> + add_geq_arc node repr_node; + (nodes,inf,remove repr_node sup@[node]),inf,sup + | M, M::M::_ -> raise (SameEquivalenceClass (set,node,repr_node)) + | M, _ -> set,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 + SameEquivalenceClass ((nodes,inf,sup) as set,((r,_,leq_d,geq_d) as node_to_be_deleted),node')-> +( +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 rec clean inf sup res = + function + [] -> inf,sup,res + | node::tl when node===node_to_be_deleted -> + clean inf sup res tl + | (repr',others,leq,geq) as node::tl -> + leq := + (let rec aux res = + function + [] -> res + | (_,_,leq,_) as node::tl -> + if node_to_be_deleted <=> node then + aux (res@[node]) tl + else + (List.filter (fun n ->not (leq_reachable n (res@tl))) !leq)@tl + in + aux [] !leq); + let sup = if !leq = [] then sup@@node else sup in + geq := + (let rec aux res = + function + [] -> res + | (_,_,_,geq) as node::tl -> + if node_to_be_deleted <=> node then + aux (res@[node]) tl + else + (List.filter (fun n ->not (geq_reachable n (res@tl))) !geq)@tl + in + aux [] !geq); + let inf = if !geq = [] then inf@@node else inf in + if node===node' then + clean inf sup ((repr',others@[candidate],leq,geq)::res) tl + else + clean inf sup (node::res) tl + in + let inf,sup,nodes = clean inf sup [] nodes in + let inf = remove node_to_be_deleted inf in + let sup = remove node_to_be_deleted sup in +let set = nodes,inf,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); +); + news,(nodes,inf,sup) +;; + +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 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 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");*) + assert (Unix.system "cp formal_topology.ma log.ma" = Unix.WEXITED 0); + ps_of_set ([id],None,[]) set; + explore 1 set [id] +;;