(**** 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 ^ "" ^ un ^ "doitem>\n");*)
output_string mout_ch ("<" ^ un ^ "doitem>" ^ s ^ "" ^ un ^ "doitem>\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]
;;