+type rel = Equal | SubsetEqual | SupersetEqual
+
+let string_of_rel =
+ function
+ Equal -> "="
+ | SubsetEqual -> "⊆"
+ | SupersetEqual -> "⊇"
+
(* operator *)
type op = I | C | M
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 rec matita_of_cop v =
function
| [] -> v
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
String.concat "\n"
(List.map
(function (repr',_,_,_) ->
- string_of_cop repr ^ " <= " ^ string_of_cop repr') !leq)
+ 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
- string_of_cop repr ^ "[label=\"" ^ eq ^ "\"];\n"
- else "") ^
+ 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',_,_,_) ->
- string_of_cop repr' ^ " -> " ^ string_of_cop repr ^ ";") !leq)
+ dot_of_cop repr' ^ " -> " ^ dot_of_cop repr ^ ";") !leq)
-(* set of equivalence classes *)
-type set = equivalence_class list
+(* set of equivalence classes, infima, suprema *)
+type set =
+ equivalence_class list * equivalence_class list * equivalence_class list
-let string_of_set s =
+let string_of_set (s,_,_) =
String.concat "\n" (List.map string_of_equivalence_class s)
-let ps_of_set ?processing 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
- (string_of_cop repr' ^ " -> " ^ string_of_cop repr ^
- " [" ^
- (if rel="=" then "arrowhead=none " else "") ^
- "style=dashed];\n"));
+ 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 "dot -Tps xxx.dot > xxx.ps")
+ (*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 ())*)
+;;
-let test set rel candidate repr =
- ps_of_set ~processing:(candidate,rel,repr) set;
+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 ^ " " ^ rel ^ " " ^ string_of_cop repr ^ "? ");
+ (string_of_cop candidate ^ " " ^ string_of_rel rel ^ " " ^ string_of_cop repr ^ "? ");
flush stdout;
assert (Unix.system "cp formal_topology.ma xxx.ma" = Unix.WEXITED 0);
let ch = open_out_gen [Open_append] 0 "xxx.ma" in
": \\forall A." ^
matita_of_cop "A" repr ^ " ⊆ " ^ matita_of_cop "A" repr' ^ ".\n");
) !leq;
- ) set;
+ ) s;
+ let candidate',rel',repr' =
+ match rel with
+ SupersetEqual -> repr,SubsetEqual,candidate
+ | Equal
+ | SubsetEqual -> candidate,rel,repr
+ in
output_string ch
- ("theorem foo: \\forall A." ^ matita_of_cop "A" candidate ^ " " ^ rel ^ " " ^
- matita_of_cop "A" repr ^ ". intros; auto size=6 depth=4. qed.\n");
+ ("theorem foo: \\forall A." ^ matita_of_cop "A" candidate' ^
+ " " ^ string_of_rel rel' ^ " " ^
+ matita_of_cop "A" repr' ^ ". intros; auto size=6 depth=4. qed.\n");
close_out ch;
let res =
- Unix.system "../../../matitac.opt xxx.ma >> log 2>&1" = Unix.WEXITED 0
+ (*Unix.system "../../../matitac.opt xxx.ma >> log 2>&1" = Unix.WEXITED 0*)
+ Unix.system "../../../matitac.opt xxx.ma > /dev/null 2>&1" = Unix.WEXITED 0
in
print_endline (if res then "y" else "n");
res
-let normalize candidate set =
- let rec aux =
+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)
+;;
+
+let locate_using_leq to_be_considered_and_now ((repr,_,leq,_) as node)
+ set start
+=
+ let rec aux ((nodes,inf,sup) as set) =
function
- [] -> raise Not_found
- | (repr,others,leq,geq) as eqclass :: tl ->
- if test set "=" candidate repr then
- (repr,others@[candidate],leq,geq)::tl
+ [] -> set
+ | (repr',_,_,geq') as node' :: tl ->
+ if repr=repr' then aux set (!geq'@tl)
+ else if leq_reachable node' !leq then
+ aux set tl
+ else if test to_be_considered_and_now set SubsetEqual repr repr' then
+ begin
+ let sup = remove node sup in
+ let inf = if !geq' = [] then (remove node' inf)@@node else inf in
+ leq_transitive_closure node node';
+ aux (nodes,inf,sup) (!geq'@tl)
+ end
else
- eqclass::(aux tl)
+ aux set tl
in
- aux set
+ aux set start
;;
-let locate ((repr,_,leq,geq) as node) set =
- let rec aux =
+exception SameEquivalenceClass of equivalence_class * equivalence_class;;
+
+let locate_using_geq to_be_considered_and_now ((repr,_,leq,geq) as node)
+ set start
+=
+ let rec aux ((nodes,inf,sup) as set) =
function
- [] -> ()
- | (repr',_,leq',geq') as node' :: tl ->
- if repr = repr' then ()
- else if test set "⊆" repr repr' then
+ [] -> set
+ | (repr',_,leq',_) as node' :: tl ->
+ if repr=repr' then aux set (!leq'@tl)
+ else if geq_reachable node' !geq then
+ aux set tl
+ else if test to_be_considered_and_now set SupersetEqual repr repr' then
begin
- leq := node' :: !leq;
- geq' := node :: !geq'
+ if List.exists (function n -> n===node') !leq then
+ (* We have found two equal nodes! *)
+ raise (SameEquivalenceClass (node,node'))
+ else
+ begin
+ let inf = remove node inf in
+ let sup = if !leq' = [] then (remove node' sup)@@node else sup in
+ geq_transitive_closure node node';
+ aux (nodes,inf,sup) (!leq'@tl)
+ end
end
- else if test set "⊆" repr' repr then
- begin
- geq := node' :: !geq;
- leq' := node :: !leq'
- end ;
- aux tl
+ else
+ aux set tl
in
- aux set
+ aux set start
;;
-let analyze_one i repr hecandidate (news,set) =
+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) > i then
+ if List.length (List.filter ((=) M) candidate) > 1 then
news,set
else
try
- let set = normalize candidate set in
- news,set
+ 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 start_inf,start_sup =
+ let repr_node =
+ match List.filter (fun (repr',_,_,_) -> repr=repr') nodes with
+ [node] -> node
+ | _ -> assert false
+ in
+inf,sup(*
+ match hecandidate with
+ I -> inf,[repr_node]
+ | C -> [repr_node],sup
+ | M -> 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
- Not_found ->
- let leq = ref [] in
- let geq = ref [] in
- let node = candidate,[],leq,geq in
- let set = node::set in
- locate node set;
- candidate::news,set
+ SameEquivalenceClass ((_,_,leq_d,geq_d) as node_to_be_deleted,node') ->
+ let rec clean =
+ function
+ [] -> []
+ | (repr',others,leq,geq) as node::tl ->
+ leq :=
+ List.fold_right
+ (fun node l ->
+ if node_to_be_deleted <=> node then
+ node::l
+ else
+ !leq_d@l
+ ) !leq [];
+ geq :=
+ List.fold_right
+ (fun node l ->
+ if node_to_be_deleted <=> node then
+ node::l
+ else
+ !geq_d@l
+ ) !geq [];
+ if node===node' then
+ (repr',others@[candidate],leq,geq)::clean tl
+ else
+ node::clean tl
+ in
+ let nodes = clean nodes in
+ news,(nodes,inf,sup)
;;
-let rec explore i j set news =
+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 i repr) [I;C;M] (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 ^ " j=" ^ string_of_int j);
+ print_endline ("PUNTO FISSO RAGGIUNTO! i=" ^ string_of_int i);
print_endline (string_of_set set ^ "\n----------------");
- if i < 2 then
- explore (i+1) 1 set (List.map (function (repr,_,_,_) -> repr) set)
- else
- ps_of_set set
+ ps_of_set ([],None,[]) set
end
else
begin
- print_endline ("NUOVA ITERAZIONE, i=" ^ string_of_int i ^ " j=" ^ string_of_int j);
+ print_endline ("NUOVA ITERAZIONE, i=" ^ string_of_int i);
print_endline (string_of_set set ^ "\n----------------");
- explore i (j+1) set news
+ explore (i+1) set news
end
in
let id = [] in
- let set = [id,[],ref [], ref []] 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");
- ps_of_set set;
- explore 0 1 set [id]
+ (*ignore (Unix.system "rm -f log");*)
+ ps_of_set ([id],None,[]) set;
+ explore 1 set [id]
;;
projects / helm.git / blobdiff