+++ /dev/null
-theory_explorer: theory_explorer.ml
- ocamlopt -rectypes -o theory_explorer unix.cmxa theory_explorer.ml
+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-set "baseuri" "cic:/matita/formal_topology/".
-include "logic/equality.ma".
-
-axiom S: Type.
-
-axiom leq: S → S → Prop.
-
-notation "hvbox(A break ⊆ B)" with precedence 59
-for @{ 'subseteq $A $B}.
-
-interpretation "Subseteq" 'subseteq A B = (leq A B).
-
-axiom leq_refl: ∀A. A ⊆ A.
-axiom leq_antisym: ∀A,B. A ⊆ B → B ⊆ A → A=B.
-axiom leq_tran: ∀A,B,C. A ⊆ B → B ⊆ C → A ⊆ C.
-
-axiom i: S → S.
-
-axiom i_contrattivita: ∀A. i A ⊆ A.
-axiom i_idempotenza: ∀A. i (i A) = i A.
-axiom i_monotonia: ∀A,B. A ⊆ B → i A ⊆ i B.
-
-axiom c: S → S.
-
-axiom c_espansivita: ∀A. A ⊆ c A.
-axiom c_idempotenza: ∀A. c (c A) = c A.
-axiom c_monotonia: ∀A,B. A ⊆ B → c A ⊆ c B.
-
-axiom m: S → S.
-
-axiom m_antimonotonia: ∀A,B. A ⊆ B → m B ⊆ m A.
-axiom m_saturazione: ∀A. A ⊆ m (m A).
-axiom m_puntofisso: ∀A. m A = m (m (m A)).
-
-lemma l1: ∀A,B. i A ⊆ B → i A ⊆ i B.
- intros; rewrite < i_idempotenza; apply (i_monotonia (i A) B H).
-qed.
-lemma l2: ∀A,B. A ⊆ c B → c A ⊆ c B.
- intros; rewrite < c_idempotenza in ⊢ (? ? %); apply (c_monotonia A (c B) H).
-qed.
-
-axiom th1: ∀A. c (m A) ⊆ m (i A).
-axiom th2: ∀A. i (m A) ⊆ m (c A).
-
-(************** start of generated part *********************)
-
--- /dev/null
+theory_explorer: theory_explorer.ml
+ ocamlopt -rectypes -o theory_explorer unix.cmxa theory_explorer.ml
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/formal_topology/".
+include "logic/equality.ma".
+
+axiom S: Type.
+
+axiom leq: S → S → Prop.
+
+notation "hvbox(A break ⊆ B)" with precedence 59
+for @{ 'subseteq $A $B}.
+
+interpretation "Subseteq" 'subseteq A B = (leq A B).
+
+axiom leq_refl: ∀A. A ⊆ A.
+axiom leq_antisym: ∀A,B. A ⊆ B → B ⊆ A → A=B.
+axiom leq_tran: ∀A,B,C. A ⊆ B → B ⊆ C → A ⊆ C.
+
+axiom i: S → S.
+
+axiom i_contrattivita: ∀A. i A ⊆ A.
+axiom i_idempotenza: ∀A. i (i A) = i A.
+axiom i_monotonia: ∀A,B. A ⊆ B → i A ⊆ i B.
+
+axiom c: S → S.
+
+axiom c_espansivita: ∀A. A ⊆ c A.
+axiom c_idempotenza: ∀A. c (c A) = c A.
+axiom c_monotonia: ∀A,B. A ⊆ B → c A ⊆ c B.
+
+axiom m: S → S.
+
+axiom m_antimonotonia: ∀A,B. A ⊆ B → m B ⊆ m A.
+axiom m_saturazione: ∀A. A ⊆ m (m A).
+axiom m_puntofisso: ∀A. m A = m (m (m A)).
+
+lemma l1: ∀A,B. i A ⊆ B → i A ⊆ i B.
+ intros; rewrite < i_idempotenza; apply (i_monotonia (i A) B H).
+qed.
+lemma l2: ∀A,B. A ⊆ c B → c A ⊆ c B.
+ intros; rewrite < c_idempotenza in ⊢ (? ? %); apply (c_monotonia A (c B) H).
+qed.
+
+axiom th1: ∀A. c (m A) ⊆ m (i A).
+axiom th2: ∀A. i (m A) ⊆ m (c A).
+
+(************** start of generated part *********************)
+
--- /dev/null
+(**** 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 ("<pgip><" ^ un ^ "doitem>" ^ s ^ "</" ^ un ^ "doitem></pgip>\n");*)
+ output_string mout_ch ("<pgip><" ^ un ^ "doitem>" ^ s ^ "</" ^ un ^ "doitem></pgip>\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]
+;;
--- /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]
+;;
+++ /dev/null
-(**** 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 ("<pgip><" ^ un ^ "doitem>" ^ s ^ "</" ^ un ^ "doitem></pgip>\n");*)
- output_string mout_ch ("<pgip><" ^ un ^ "doitem>" ^ s ^ "</" ^ un ^ "doitem></pgip>\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]
-;;
+++ /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