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
"")
(function (repr',_,_,_) ->
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 (to_be_considered,under_consideration,news) ?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,_,_,_) ->
+ output_string ch (dot_of_cop repr ^ " [shape=diamond];")
+ ) inf ;
+ List.iter
+ (function (repr,_,_,_) ->
+ 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 ;
close_out ch;
ignore (Unix.system "tred xxx.dot > yyy.dot && dot -Tps yyy.dot > xxx.ps")
-let test to_be_considered_and_now set rel candidate repr =
+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 ^ "? ");
": \\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
print_endline (if res then "y" else "n");
res
-let normalize to_be_considered_and_now candidate set =
- let rec aux =
+let rec leq_transitive_closure leq node ((repr,_,leq',geq') as node') =
+ if not (List.mem node' !leq) then leq := node' :: !leq;
+ if not (List.mem node !geq') then geq' := node :: !geq';
+ List.iter (leq_transitive_closure leq node) !leq'
+;;
+
+let rec geq_transitive_closure geq node ((_,_,leq',geq') as node') =
+ if not (List.mem node' !geq) then geq := node' :: !geq;
+ if not (List.mem node !leq') then leq' := node :: !leq';
+ List.iter (geq_transitive_closure geq node) !geq'
+;;
+
+let remove node l =
+ let l' = List.filter (fun node' -> node != node') l in
+ if List.length l = List.length l' then
+ assert false
+ else
+ l'
+;;
+
+let locate_using_leq to_be_considered_and_now ((repr,_,leq,_) as node)
+ ((nodes,inf,sup) as set)
+=
+ let rec aux is_sup inf =
function
- [] -> raise Not_found
- | (repr,others,leq,geq) as eqclass :: tl ->
- if test to_be_considered_and_now set Equal candidate repr then
- (repr,others@[candidate],leq,geq)::tl
+ [] -> is_sup,inf
+ | (repr',_,_,geq') as node' :: sup ->
+ if repr=repr' then aux is_sup inf (!geq'@sup)
+ else if List.mem node' !leq
+ || test to_be_considered_and_now set SubsetEqual repr repr'
+ then
+ begin
+ let inf = if !geq' = [] then remove node' inf else inf in
+ leq_transitive_closure leq node node';
+ aux false inf (!geq'@sup)
+ end
else
- eqclass::(aux tl)
+ aux is_sup inf sup
in
- aux set
+ let is_sup,inf = aux true inf sup in
+ if is_sup then
+ nodes,inf,sup@[node]
+ else
+ nodes,inf,sup
;;
-let locate to_be_considered_and_now ((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)
+ ((nodes,inf,sup) as set)
+=
+ let rec aux is_inf sup =
function
- [] -> ()
- | (repr',_,leq',geq') as node' :: tl ->
- if repr = repr' then ()
- else if test to_be_considered_and_now set SubsetEqual repr repr' then
+ [] -> sup,is_inf
+ | (repr',_,leq',_) as node' :: inf ->
+ if repr=repr' then aux is_inf sup (!leq'@inf)
+ else if List.mem node' !geq
+ || test to_be_considered_and_now set SupersetEqual repr repr'
+ then
begin
- leq := node' :: !leq;
- geq' := node :: !geq'
+ if List.mem node' !leq then
+ (* We have found two equal nodes! *)
+ raise (SameEquivalenceClass (node,node'))
+ else
+ begin
+ let sup = if !leq' = [] then remove node' sup else sup in
+ geq_transitive_closure geq node node';
+ aux false sup (!leq'@inf)
+ end
end
- else if test to_be_considered_and_now set SupersetEqual repr repr' then
- begin
- geq := node' :: !geq;
- leq' := node :: !leq'
- end ;
- aux tl
+ else
+ aux is_inf sup inf
in
- aux set
+ let sup,is_inf = aux true sup inf in
+ if is_inf then
+ nodes,inf@[node],sup
+ else
+ nodes,inf,sup
;;
-let analyze_one to_be_considered repr hecandidate (news,set) =
+let analyze_one to_be_considered repr hecandidate (news,((nodes,inf,sup) as set)) =
let candidate = hecandidate::repr in
if List.length (List.filter ((=) M) candidate) > 1 then
news,set
else
try
- let set = normalize (to_be_considered,Some repr,news) 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,sup in
+ let set = locate_using_leq (to_be_considered,Some repr,news) node set in
+ let set = locate_using_geq (to_be_considered,Some repr,news) node set in
+ 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 (to_be_considered,Some repr,news) node set;
- candidate::news,set
+ SameEquivalenceClass (node_to_be_deleted,node') ->
+ let rec clean =
+ function
+ [] -> []
+ | (repr',others,leq,geq) as node::tl ->
+ leq := List.filter (function node -> node_to_be_deleted != node) !leq;
+ geq := List.filter (function node -> node_to_be_deleted != node) !geq;
+ if node==node' then
+ (repr',others@[candidate],leq,geq)::clean tl
+ else
+ (repr',others,leq,geq)::clean tl
+ in
+ let nodes = clean nodes in
+ news,(nodes,inf,sup)
;;
-let rec explore i set news =
+let rec explore i (set:set) news =
let rec aux news set =
function
[] -> news,set
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");*)
--- /dev/null
+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 -> "-"
+
+(* 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 rec matita_of_cop v =
+ function
+ | [] -> v
+ | I::tl -> "i (" ^ matita_of_cop v tl ^ ")"
+ | C::tl -> "c (" ^ matita_of_cop v tl ^ ")"
+ | M::tl -> "m (" ^ matita_of_cop v tl ^ ")"
+
+(* 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 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 *)
+type set = 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 =
+ 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 -> 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")
+
+let test to_be_considered_and_now 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 "cp formal_topology.ma 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;
+ ) set;
+ 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' ^
+ " " ^ 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 > /dev/null 2>&1" = Unix.WEXITED 0
+ in
+ print_endline (if res then "y" else "n");
+ res
+
+let normalize to_be_considered_and_now candidate set =
+ let rec aux =
+ function
+ [] -> raise Not_found
+ | (repr,others,leq,geq) as eqclass :: tl ->
+ if test to_be_considered_and_now set Equal candidate repr then
+ (repr,others@[candidate],leq,geq)::tl
+ else
+ eqclass::(aux tl)
+ in
+ aux set
+;;
+
+let locate to_be_considered_and_now ((repr,_,leq,geq) as node) set =
+ let rec aux =
+ function
+ [] -> ()
+ | (repr',_,leq',geq') as node' :: tl ->
+ if repr = repr' then ()
+ else if test to_be_considered_and_now set SubsetEqual repr repr' then
+ begin
+ leq := node' :: !leq;
+ geq' := node :: !geq'
+ end
+ else if test to_be_considered_and_now set SupersetEqual repr repr' then
+ begin
+ geq := node' :: !geq;
+ leq' := node :: !leq'
+ end ;
+ aux tl
+ in
+ aux set
+;;
+
+let analyze_one to_be_considered repr hecandidate (news,set) =
+ let candidate = hecandidate::repr in
+ if List.length (List.filter ((=) M) candidate) > 1 then
+ news,set
+ else
+ try
+ let set = normalize (to_be_considered,Some repr,news) candidate set in
+ news,set
+ with
+ Not_found ->
+ let leq = ref [] in
+ let geq = ref [] in
+ let node = candidate,[],leq,geq in
+ let set = node::set in
+ locate (to_be_considered,Some repr,news) node set;
+ candidate::news,set
+;;
+
+let rec explore i 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 set = [id,[],ref [], ref []] 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 ([id],None,[]) set;
+ explore 1 set [id]
+;;
projects / helm.git / commitdiff