From: Claudio Sacerdoti Coen Date: Mon, 2 Mar 2009 23:33:21 +0000 (+0000) Subject: Old algorithm moved to old to leave place to the new one. X-Git-Tag: make_still_working~4183 X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=8df31f2c696c408e888fb8b94478799b04771f15;p=helm.git Old algorithm moved to old to leave place to the new one. --- diff --git a/helm/software/matita/contribs/formal_topology/bin/Makefile b/helm/software/matita/contribs/formal_topology/bin/Makefile deleted file mode 100644 index 3bfd0c9ee..000000000 --- a/helm/software/matita/contribs/formal_topology/bin/Makefile +++ /dev/null @@ -1,2 +0,0 @@ -theory_explorer: theory_explorer.ml - ocamlopt -rectypes -o theory_explorer unix.cmxa theory_explorer.ml diff --git a/helm/software/matita/contribs/formal_topology/bin/formal_topology.ma b/helm/software/matita/contribs/formal_topology/bin/formal_topology.ma deleted file mode 100644 index e84c0242e..000000000 --- a/helm/software/matita/contribs/formal_topology/bin/formal_topology.ma +++ /dev/null @@ -1,60 +0,0 @@ -(**************************************************************************) -(* ___ *) -(* ||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 *********************) - diff --git a/helm/software/matita/contribs/formal_topology/bin/old/Makefile b/helm/software/matita/contribs/formal_topology/bin/old/Makefile new file mode 100644 index 000000000..3bfd0c9ee --- /dev/null +++ b/helm/software/matita/contribs/formal_topology/bin/old/Makefile @@ -0,0 +1,2 @@ +theory_explorer: theory_explorer.ml + ocamlopt -rectypes -o theory_explorer unix.cmxa theory_explorer.ml diff --git a/helm/software/matita/contribs/formal_topology/bin/old/formal_topology.ma b/helm/software/matita/contribs/formal_topology/bin/old/formal_topology.ma new file mode 100644 index 000000000..e84c0242e --- /dev/null +++ b/helm/software/matita/contribs/formal_topology/bin/old/formal_topology.ma @@ -0,0 +1,60 @@ +(**************************************************************************) +(* ___ *) +(* ||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 *********************) + diff --git a/helm/software/matita/contribs/formal_topology/bin/old/theory_explorer.ml b/helm/software/matita/contribs/formal_topology/bin/old/theory_explorer.ml new file mode 100644 index 000000000..39a021c9d --- /dev/null +++ b/helm/software/matita/contribs/formal_topology/bin/old/theory_explorer.ml @@ -0,0 +1,568 @@ +(**** PROFILING ****) +let ok_time = ref 0.0;; +let ko_time = ref 0.0;; + +let profile f x = + let before = Unix.gettimeofday () in + let res = f x in + let after = Unix.gettimeofday () in + let delta = after -. before in + if res then + ok_time := !ok_time +. delta + else + ko_time := !ko_time +. delta; + res +;; + +let _ = + Sys.catch_break true; + at_exit + (function () -> + prerr_endline + ("\nTIME SPENT IN CHECKING GOOD CONJECTURES: " ^ string_of_float !ok_time); + prerr_endline + ("TIME SPENT IN CHECKING BAD CONJECTURES: " ^ string_of_float !ko_time);) +;; + +(**** END PROFILING ****) + +type rel = Equal | SubsetEqual | SupersetEqual + +let string_of_rel = + function + Equal -> "=" + | SubsetEqual -> "⊆" + | SupersetEqual -> "⊇" + +(* operator *) +type op = I | C | M + +let string_of_op = function I -> "i" | C -> "c" | M -> "-" +let matita_of_op = function I -> "i" | C -> "c" | M -> "m" + +(* compound operator *) +type compound_operator = op list + +let string_of_cop op = + if op = [] then "id" else String.concat "" (List.map string_of_op op) + +let dot_of_cop op = "\"" ^ string_of_cop op ^ "\"" + +let matita_of_cop v = + let rec aux = + function + | [] -> v + | [op] -> matita_of_op op ^ " " ^ v + | op::tl -> matita_of_op op ^ " (" ^ aux tl ^ ")" + in + aux + +let name_of_theorem cop rel cop' = + let cop,rel,cop' = + match rel with + Equal -> cop,"eq",cop' + | SubsetEqual -> cop,"leq",cop' + | SupersetEqual -> cop',"leq",cop + in + rel ^ "_" ^ + String.concat "" (List.map matita_of_op cop) ^ "_" ^ + String.concat "" (List.map matita_of_op cop') +;; + +(* representative, other elements in the equivalence class, + leq classes, geq classes *) +type equivalence_class = + compound_operator * compound_operator list * + equivalence_class list ref * equivalence_class list ref + +let (===) (repr,_,_,_) (repr',_,_,_) = repr = repr';; +let (<=>) (repr,_,_,_) (repr',_,_,_) = repr <> repr';; + +let string_of_equivalence_class (repr,others,leq,_) = + String.concat " = " (List.map string_of_cop (repr::others)) ^ + (if !leq <> [] then + "\n" ^ + String.concat "\n" + (List.map + (function (repr',_,_,_) -> + string_of_cop repr ^ " ⊆ " ^ string_of_cop repr') !leq) + else + "") + +let dot_of_equivalence_class (repr,others,leq,_) = + (if others <> [] then + let eq = String.concat " = " (List.map string_of_cop (repr::others)) in + dot_of_cop repr ^ "[label=\"" ^ eq ^ "\"];" ^ + if !leq = [] then "" else "\n" + else if !leq = [] then + dot_of_cop repr ^ ";" + else + "") ^ + String.concat "\n" + (List.map + (function (repr',_,_,_) -> + dot_of_cop repr' ^ " -> " ^ dot_of_cop repr ^ ";") !leq) + +(* set of equivalence classes, infima, suprema *) +type set = + equivalence_class list * equivalence_class list * equivalence_class list + +let string_of_set (s,_,_) = + String.concat "\n" (List.map string_of_equivalence_class s) + +let ps_of_set (to_be_considered,under_consideration,news) ?processing (s,inf,sup) = + let ch = open_out "xxx.dot" in + output_string ch "digraph G {\n"; + (match under_consideration with + None -> () + | Some repr -> + output_string ch (dot_of_cop repr ^ " [color=yellow];")); + List.iter + (function (repr,_,_,_) -> + if List.exists (function (repr',_,_,_) -> repr=repr') sup then + output_string ch (dot_of_cop repr ^ " [shape=Mdiamond];") + else + output_string ch (dot_of_cop repr ^ " [shape=diamond];") + ) inf ; + List.iter + (function (repr,_,_,_) -> + if not (List.exists (function (repr',_,_,_) -> repr=repr') inf) then + output_string ch (dot_of_cop repr ^ " [shape=polygon];") + ) sup ; + List.iter + (function repr -> output_string ch (dot_of_cop repr ^ " [color=green];") + ) to_be_considered ; + List.iter + (function repr -> output_string ch (dot_of_cop repr ^ " [color=navy];") + ) news ; + output_string ch (String.concat "\n" (List.map dot_of_equivalence_class s)); + output_string ch "\n"; + (match processing with + None -> () + | Some (repr,rel,repr') -> + output_string ch (dot_of_cop repr ^ " [color=red];"); + let repr,repr' = + match rel with + SupersetEqual -> repr',repr + | Equal + | SubsetEqual -> repr,repr' + in + output_string ch + (dot_of_cop repr' ^ " -> " ^ dot_of_cop repr ^ + " [" ^ + (match rel with Equal -> "arrowhead=none " | _ -> "") ^ + "style=dashed];\n")); + output_string ch "}\n"; + close_out ch; + (*ignore (Unix.system "tred xxx.dot > yyy.dot && dot -Tps yyy.dot > xxx.ps")*) + ignore (Unix.system "cp xxx.ps xxx_old.ps && dot -Tps xxx.dot > xxx.ps"); + (*ignore (read_line ())*) +;; + +(******** communication with matitawiki ************) +let min_ch,mout_ch = Unix.open_process "../../../matitawiki.opt 2> /dev/null";; + +let exec_cmd ?(undo=false) s = + let un = if undo then "un" else "" in +(*prerr_endline ("<" ^ un ^ "doitem>" ^ s ^ "\n");*) + output_string mout_ch ("<" ^ un ^ "doitem>" ^ s ^ "\n"); + flush mout_ch; + let rec aux v = + let l = input_line min_ch in + let last = String.length l - 1 in + assert (last > 0); + if l.[last] = Char.chr 249 then + int_of_string (String.sub l 0 last) + else + aux l + in + aux "x" +;; + +let exec_cmds = + let rec aux undopos = + function + [] -> true + | he::tl -> + let pos = exec_cmd he in + if pos = -1 then + begin + match undopos with + None -> assert false + | Some undopos -> + assert (exec_cmd ~undo:true (string_of_int (undopos - 1)) <> -1); + false + end + else + match undopos with + None -> aux (Some pos) tl + | _ -> aux undopos tl + in + aux None + +let _ = + assert (exec_cmd "set \"baseuri\" \"cic:/matita/theory_former\"." <> -1); + assert (exec_cmd "include \"formal_topology.ma\"." <> -1); +;; + +(********* testing a conjecture *******************) + +let test to_be_considered_and_now ((s,_,_) as set) rel candidate repr = + ps_of_set to_be_considered_and_now ~processing:(candidate,rel,repr) set; + print_string + (string_of_cop candidate ^ " " ^ string_of_rel rel ^ " " ^ string_of_cop repr ^ "? "); + flush stdout; +(* + assert (Unix.system "cat log.ma | sed s/^theorem/axiom/g | sed 's/\\. intros.*qed\\././g' > xxx.ma" = Unix.WEXITED 0); + let ch = open_out_gen [Open_append] 0 "xxx.ma" in +*) +(* + let i = ref 0 in + List.iter + (function (repr,others,leq,_) -> + List.iter + (function repr' -> + incr i; + output_string ch + ("axiom ax" ^ string_of_int !i ^ + ": \\forall A." ^ + matita_of_cop "A" repr ^ " = " ^ matita_of_cop "A" repr' ^ ".\n"); + ) others; + List.iter + (function (repr',_,_,_) -> + incr i; + output_string ch + ("axiom ax" ^ string_of_int !i ^ + ": \\forall A." ^ + matita_of_cop "A" repr ^ " ⊆ " ^ matita_of_cop "A" repr' ^ ".\n"); + ) !leq; + ) s; +*) + let candidate',rel',repr' = + match rel with + SupersetEqual -> repr,SubsetEqual,candidate + | Equal + | SubsetEqual -> candidate,rel,repr in + let query1 = + let name = name_of_theorem candidate' rel' repr' in + ("theorem " ^ name ^ ": \\forall A." ^ matita_of_cop "A" candidate' ^ + " " ^ string_of_rel rel' ^ " " ^ + matita_of_cop "A" repr' ^ ".") in + let query2 = "intros;" in + let query3 = "autobatch size=8 depth=3 width=2." in + let query4 = "qed." in + let query = query1 ^ query2 ^ query3 ^ query4 in +(* + output_string ch (query ^ "\n"); + close_out ch; +*) + let res = profile exec_cmds [query1; query2; query3; query4] in +(* + let res = + (*Unix.system "../../../matitac.opt xxx.ma >> log 2>&1" = Unix.WEXITED 0*) + profile Unix.system "../../../matitac.opt xxx.ma > /dev/null 2>&1" = Unix.WEXITED 0 + in +*) + ignore (Unix.system "echo '(*' >> log.ma && cat xxx.dot >> log.ma && echo '*)' >> log.ma"); + let ch = open_out_gen [Open_append] 0o0600 "log.ma" in + if res then + output_string ch (query ^ "\n") + else + output_string ch ("(* " ^ query ^ "*)\n"); + close_out ch; + print_endline (if res then "y" else "n"); + res + +let remove node = List.filter (fun node' -> node <=> node');; + +let add_leq_arc ((_,_,leq,_) as node) ((_,_,_,geq') as node') = + leq := node' :: !leq; + geq' := node :: !geq' +;; + +let add_geq_arc ((_,_,_,geq) as node) ((_,_,leq',_) as node') = + geq := node' :: !geq; + leq' := node :: !leq' +;; + +let remove_leq_arc ((_,_,leq,_) as node) ((_,_,_,geq') as node') = + leq := remove node' !leq; + geq' := remove node !geq' +;; + +let remove_geq_arc ((_,_,_,geq) as node) ((_,_,leq',_) as node') = + geq := remove node' !geq; + leq' := remove node !leq' +;; + +let leq_transitive_closure node node' = + add_leq_arc node node'; + let rec remove_transitive_arcs ((_,_,_,geq) as node) (_,_,leq',_) = + let rec remove_arcs_to_ascendents = + function + [] -> () + | (_,_,leq,_) as node'::tl -> + remove_leq_arc node node'; + remove_arcs_to_ascendents (!leq@tl) + in + remove_arcs_to_ascendents !leq'; + List.iter (function son -> remove_transitive_arcs son node) !geq + in + remove_transitive_arcs node node' +;; + +let geq_transitive_closure node node' = + add_geq_arc node node'; + let rec remove_transitive_arcs ((_,_,leq,_) as node) (_,_,_,geq') = + let rec remove_arcs_to_descendents = + function + [] -> () + | (_,_,_,geq) as node'::tl -> + remove_geq_arc node node'; + remove_arcs_to_descendents (!geq@tl) + in + remove_arcs_to_descendents !geq'; + List.iter (function father -> remove_transitive_arcs father node) !leq + in + remove_transitive_arcs node node' +;; + +let (@@) l1 n = if List.exists (function n' -> n===n') l1 then l1 else l1@[n] + +let rec leq_reachable node = + function + [] -> false + | node'::_ when node === node' -> true + | (_,_,leq,_)::tl -> leq_reachable node (!leq@tl) +;; + +let rec geq_reachable node = + function + [] -> false + | node'::_ when node === node' -> true + | (_,_,_,geq)::tl -> geq_reachable node (!geq@tl) +;; + +exception SameEquivalenceClass of set * equivalence_class * equivalence_class;; + +let locate_using_leq to_be_considered_and_now ((repr,_,leq,geq) as node) + set start += + let rec aux ((nodes,inf,sup) as set) already_visited = + function + [] -> set + | (repr',_,_,geq') as node' :: tl -> + if List.exists (function n -> n===node') already_visited then + aux set already_visited tl + else if repr=repr' then aux set (node'::already_visited) (!geq'@tl) + else if leq_reachable node' !leq then + aux set (node'::already_visited) (!geq'@tl) + else if (List.exists (function n -> not (geq_reachable n [node'])) !geq) + then + aux set (node'::already_visited) tl + else if test to_be_considered_and_now set SubsetEqual repr repr' then + begin + if List.exists (function n -> n===node') !geq then + (* We have found two equal nodes! *) + raise (SameEquivalenceClass (set,node,node')) + else + begin + let sup = remove node sup in + let inf = + if !geq' = [] then + let inf = remove node' inf in + if !geq = [] then + inf@@node + else + inf + else + inf + in + leq_transitive_closure node node'; + aux (nodes,inf,sup) (node'::already_visited) (!geq'@tl) + end + end + else + aux set (node'::already_visited) tl + in + aux set [] start +;; + +let locate_using_geq to_be_considered_and_now ((repr,_,leq,geq) as node) + set start += + let rec aux ((nodes,inf,sup) as set) already_visited = + function + [] -> set + | (repr',_,leq',_) as node' :: tl -> + if List.exists (function n -> n===node') already_visited then + aux set already_visited tl + else if repr=repr' then aux set (node'::already_visited) (!leq'@tl) + else if geq_reachable node' !geq then + aux set (node'::already_visited) (!leq'@tl) + else if (List.exists (function n -> not (leq_reachable n [node'])) !leq) + then + aux set (node'::already_visited) tl + else if test to_be_considered_and_now set SupersetEqual repr repr' then + begin + if List.exists (function n -> n===node') !leq then + (* We have found two equal nodes! *) + raise (SameEquivalenceClass (set,node,node')) + else + begin + let inf = remove node inf in + let sup = + if !leq' = [] then + let sup = remove node' sup in + if !leq = [] then + sup@@node + else + sup + else + sup + in + geq_transitive_closure node node'; + aux (nodes,inf,sup) (node'::already_visited) (!leq'@tl) + end + end + else + aux set (node'::already_visited) tl + in + aux set [] start +;; + +let analyze_one to_be_considered repr hecandidate (news,((nodes,inf,sup) as set)) = +if not (List.for_all (fun ((_,_,_,geq) as node) -> !geq = [] && let rec check_sups = function [] -> true | (_,_,leq,_) as node::tl -> if !leq = [] then List.exists (fun n -> n===node) sup && check_sups tl else check_sups (!leq@tl) in check_sups [node]) inf) then ((*ps_of_set ([],None,[]) set;*) assert false); +if not (List.for_all (fun ((_,_,leq,_) as node) -> !leq = [] && let rec check_infs = function [] -> true | (_,_,_,geq) as node::tl -> if !geq = [] then List.exists (fun n -> n===node) inf && check_infs tl else check_infs (!geq@tl) in check_infs [node]) sup) then (ps_of_set ([],None,[]) set; assert false); + let candidate = hecandidate::repr in + if List.length (List.filter ((=) M) candidate) > 1 then + news,set + else + try + let leq = ref [] in + let geq = ref [] in + let node = candidate,[],leq,geq in + let nodes = nodes@[node] in + let set = nodes,inf@[node],sup@[node] in + let set,start_inf,start_sup = + let repr_node = + match List.filter (fun (repr',_,_,_) -> repr=repr') nodes with + [node] -> node + | _ -> assert false + in + match hecandidate,repr with + I, I::_ -> raise (SameEquivalenceClass (set,node,repr_node)) + | I, _ -> + add_leq_arc node repr_node; + (nodes,remove repr_node inf@[node],sup),inf,sup + | C, C::_ -> raise (SameEquivalenceClass (set,node,repr_node)) + | C, _ -> + add_geq_arc node repr_node; + (nodes,inf,remove repr_node sup@[node]),inf,sup + | M, M::M::_ -> raise (SameEquivalenceClass (set,node,repr_node)) + | M, _ -> set,inf,sup + in + let set = + locate_using_leq (to_be_considered,Some repr,news) node set start_sup in +( +let _,inf,sup = set in +if not (List.for_all (fun ((_,_,_,geq) as node) -> !geq = [] && let rec check_sups = function [] -> true | (_,_,leq,_) as node::tl -> if !leq = [] then List.exists (fun n -> n===node) sup && check_sups tl else check_sups (!leq@tl) in check_sups [node]) inf) then (ps_of_set ([],None,[]) set; assert false); +if not (List.for_all (fun ((_,_,leq,_) as node) -> !leq = [] && let rec check_infs = function [] -> true | (_,_,_,geq) as node::tl -> if !geq = [] then List.exists (fun n -> n===node) inf && check_infs tl else check_infs (!geq@tl) in check_infs [node]) sup) then (ps_of_set ([],None,[]) set; assert false); +); + let set = + locate_using_geq (to_be_considered,Some repr,news) node set start_inf + in +( +let _,inf,sup = set in +if not (List.for_all (fun ((_,_,_,geq) as node) -> !geq = [] && let rec check_sups = function [] -> true | (_,_,leq,_) as node::tl -> if !leq = [] then List.exists (fun n -> n===node) sup && check_sups tl else check_sups (!leq@tl) in check_sups [node]) inf) then (ps_of_set ([],None,[]) set; assert false); +if not (List.for_all (fun ((_,_,leq,_) as node) -> !leq = [] && let rec check_infs = function [] -> true | (_,_,_,geq) as node::tl -> if !geq = [] then List.exists (fun n -> n===node) inf && check_infs tl else check_infs (!geq@tl) in check_infs [node]) sup) then ((*ps_of_set ([],None,[]) set;*) assert false); +); + news@[candidate],set + with + SameEquivalenceClass ((nodes,inf,sup) as set,((r,_,leq_d,geq_d) as node_to_be_deleted),node')-> +( +let _,inf,sup = set in +if not (List.for_all (fun ((_,_,_,geq) as node) -> !geq = [] && let rec check_sups = function [] -> true | (_,_,leq,_) as node::tl -> if !leq = [] then List.exists (fun n -> n===node) sup && check_sups tl else check_sups (!leq@tl) in check_sups [node]) inf) then (ps_of_set ([],None,[]) set; assert false); +if not (List.for_all (fun ((_,_,leq,_) as node) -> !leq = [] && let rec check_infs = function [] -> true | (_,_,_,geq) as node::tl -> if !geq = [] then List.exists (fun n -> n===node) inf && check_infs tl else check_infs (!geq@tl) in check_infs [node]) sup) then ((*ps_of_set ([],None,[]) set;*) assert false); +); + let rec clean inf sup res = + function + [] -> inf,sup,res + | node::tl when node===node_to_be_deleted -> + clean inf sup res tl + | (repr',others,leq,geq) as node::tl -> + leq := + (let rec aux res = + function + [] -> res + | (_,_,leq,_) as node::tl -> + if node_to_be_deleted <=> node then + aux (res@[node]) tl + else + (List.filter (fun n ->not (leq_reachable n (res@tl))) !leq)@tl + in + aux [] !leq); + let sup = if !leq = [] then sup@@node else sup in + geq := + (let rec aux res = + function + [] -> res + | (_,_,_,geq) as node::tl -> + if node_to_be_deleted <=> node then + aux (res@[node]) tl + else + (List.filter (fun n ->not (geq_reachable n (res@tl))) !geq)@tl + in + aux [] !geq); + let inf = if !geq = [] then inf@@node else inf in + if node===node' then + clean inf sup ((repr',others@[candidate],leq,geq)::res) tl + else + clean inf sup (node::res) tl + in + let inf,sup,nodes = clean inf sup [] nodes in + let inf = remove node_to_be_deleted inf in + let sup = remove node_to_be_deleted sup in +let set = nodes,inf,sup in +( +let _,inf,sup = set in +if not (List.for_all (fun ((_,_,_,geq) as node) -> !geq = [] && let rec check_sups = function [] -> true | (_,_,leq,_) as node::tl -> if !leq = [] then List.exists (fun n -> n===node) sup && check_sups tl else check_sups (!leq@tl) in check_sups [node]) inf) then (ps_of_set ([],None,[]) set; assert false); +if not (List.for_all (fun ((_,_,leq,_) as node) -> !leq = [] && let rec check_infs = function [] -> true | (_,_,_,geq) as node::tl -> if !geq = [] then List.exists (fun n -> n===node) inf && check_infs tl else check_infs (!geq@tl) in check_infs [node]) sup) then (ps_of_set ([],None,[]) set; assert false); +); + news,(nodes,inf,sup) +;; + +let rec explore i (set:set) news = + let rec aux news set = + function + [] -> news,set + | repr::tl -> + let news,set = + List.fold_right (analyze_one tl repr) [I;C;M] (news,set) + in + aux news set tl + in + let news,set = aux [] set news in + if news = [] then + begin + print_endline ("PUNTO FISSO RAGGIUNTO! i=" ^ string_of_int i); + print_endline (string_of_set set ^ "\n----------------"); + ps_of_set ([],None,[]) set + end + else + begin + print_endline ("NUOVA ITERAZIONE, i=" ^ string_of_int i); + print_endline (string_of_set set ^ "\n----------------"); + explore (i+1) set news + end +in + let id = [] in + let id_node = id,[],ref [], ref [] in + let set = [id_node],[id_node],[id_node] in + print_endline ("PRIMA ITERAZIONE, i=0, j=0"); + print_endline (string_of_set set ^ "\n----------------"); + (*ignore (Unix.system "rm -f log");*) + assert (Unix.system "cp formal_topology.ma log.ma" = Unix.WEXITED 0); + ps_of_set ([id],None,[]) set; + explore 1 set [id] +;; diff --git a/helm/software/matita/contribs/formal_topology/bin/old/theory_explorer_do_not_trust_auto.ml b/helm/software/matita/contribs/formal_topology/bin/old/theory_explorer_do_not_trust_auto.ml new file mode 100644 index 000000000..3a9dcde30 --- /dev/null +++ b/helm/software/matita/contribs/formal_topology/bin/old/theory_explorer_do_not_trust_auto.ml @@ -0,0 +1,232 @@ +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] +;; diff --git a/helm/software/matita/contribs/formal_topology/bin/theory_explorer.ml b/helm/software/matita/contribs/formal_topology/bin/theory_explorer.ml deleted file mode 100644 index 39a021c9d..000000000 --- a/helm/software/matita/contribs/formal_topology/bin/theory_explorer.ml +++ /dev/null @@ -1,568 +0,0 @@ -(**** PROFILING ****) -let ok_time = ref 0.0;; -let ko_time = ref 0.0;; - -let profile f x = - let before = Unix.gettimeofday () in - let res = f x in - let after = Unix.gettimeofday () in - let delta = after -. before in - if res then - ok_time := !ok_time +. delta - else - ko_time := !ko_time +. delta; - res -;; - -let _ = - Sys.catch_break true; - at_exit - (function () -> - prerr_endline - ("\nTIME SPENT IN CHECKING GOOD CONJECTURES: " ^ string_of_float !ok_time); - prerr_endline - ("TIME SPENT IN CHECKING BAD CONJECTURES: " ^ string_of_float !ko_time);) -;; - -(**** END PROFILING ****) - -type rel = Equal | SubsetEqual | SupersetEqual - -let string_of_rel = - function - Equal -> "=" - | SubsetEqual -> "⊆" - | SupersetEqual -> "⊇" - -(* operator *) -type op = I | C | M - -let string_of_op = function I -> "i" | C -> "c" | M -> "-" -let matita_of_op = function I -> "i" | C -> "c" | M -> "m" - -(* compound operator *) -type compound_operator = op list - -let string_of_cop op = - if op = [] then "id" else String.concat "" (List.map string_of_op op) - -let dot_of_cop op = "\"" ^ string_of_cop op ^ "\"" - -let matita_of_cop v = - let rec aux = - function - | [] -> v - | [op] -> matita_of_op op ^ " " ^ v - | op::tl -> matita_of_op op ^ " (" ^ aux tl ^ ")" - in - aux - -let name_of_theorem cop rel cop' = - let cop,rel,cop' = - match rel with - Equal -> cop,"eq",cop' - | SubsetEqual -> cop,"leq",cop' - | SupersetEqual -> cop',"leq",cop - in - rel ^ "_" ^ - String.concat "" (List.map matita_of_op cop) ^ "_" ^ - String.concat "" (List.map matita_of_op cop') -;; - -(* representative, other elements in the equivalence class, - leq classes, geq classes *) -type equivalence_class = - compound_operator * compound_operator list * - equivalence_class list ref * equivalence_class list ref - -let (===) (repr,_,_,_) (repr',_,_,_) = repr = repr';; -let (<=>) (repr,_,_,_) (repr',_,_,_) = repr <> repr';; - -let string_of_equivalence_class (repr,others,leq,_) = - String.concat " = " (List.map string_of_cop (repr::others)) ^ - (if !leq <> [] then - "\n" ^ - String.concat "\n" - (List.map - (function (repr',_,_,_) -> - string_of_cop repr ^ " ⊆ " ^ string_of_cop repr') !leq) - else - "") - -let dot_of_equivalence_class (repr,others,leq,_) = - (if others <> [] then - let eq = String.concat " = " (List.map string_of_cop (repr::others)) in - dot_of_cop repr ^ "[label=\"" ^ eq ^ "\"];" ^ - if !leq = [] then "" else "\n" - else if !leq = [] then - dot_of_cop repr ^ ";" - else - "") ^ - String.concat "\n" - (List.map - (function (repr',_,_,_) -> - dot_of_cop repr' ^ " -> " ^ dot_of_cop repr ^ ";") !leq) - -(* set of equivalence classes, infima, suprema *) -type set = - equivalence_class list * equivalence_class list * equivalence_class list - -let string_of_set (s,_,_) = - String.concat "\n" (List.map string_of_equivalence_class s) - -let ps_of_set (to_be_considered,under_consideration,news) ?processing (s,inf,sup) = - let ch = open_out "xxx.dot" in - output_string ch "digraph G {\n"; - (match under_consideration with - None -> () - | Some repr -> - output_string ch (dot_of_cop repr ^ " [color=yellow];")); - List.iter - (function (repr,_,_,_) -> - if List.exists (function (repr',_,_,_) -> repr=repr') sup then - output_string ch (dot_of_cop repr ^ " [shape=Mdiamond];") - else - output_string ch (dot_of_cop repr ^ " [shape=diamond];") - ) inf ; - List.iter - (function (repr,_,_,_) -> - if not (List.exists (function (repr',_,_,_) -> repr=repr') inf) then - output_string ch (dot_of_cop repr ^ " [shape=polygon];") - ) sup ; - List.iter - (function repr -> output_string ch (dot_of_cop repr ^ " [color=green];") - ) to_be_considered ; - List.iter - (function repr -> output_string ch (dot_of_cop repr ^ " [color=navy];") - ) news ; - output_string ch (String.concat "\n" (List.map dot_of_equivalence_class s)); - output_string ch "\n"; - (match processing with - None -> () - | Some (repr,rel,repr') -> - output_string ch (dot_of_cop repr ^ " [color=red];"); - let repr,repr' = - match rel with - SupersetEqual -> repr',repr - | Equal - | SubsetEqual -> repr,repr' - in - output_string ch - (dot_of_cop repr' ^ " -> " ^ dot_of_cop repr ^ - " [" ^ - (match rel with Equal -> "arrowhead=none " | _ -> "") ^ - "style=dashed];\n")); - output_string ch "}\n"; - close_out ch; - (*ignore (Unix.system "tred xxx.dot > yyy.dot && dot -Tps yyy.dot > xxx.ps")*) - ignore (Unix.system "cp xxx.ps xxx_old.ps && dot -Tps xxx.dot > xxx.ps"); - (*ignore (read_line ())*) -;; - -(******** communication with matitawiki ************) -let min_ch,mout_ch = Unix.open_process "../../../matitawiki.opt 2> /dev/null";; - -let exec_cmd ?(undo=false) s = - let un = if undo then "un" else "" in -(*prerr_endline ("<" ^ un ^ "doitem>" ^ s ^ "\n");*) - output_string mout_ch ("<" ^ un ^ "doitem>" ^ s ^ "\n"); - flush mout_ch; - let rec aux v = - let l = input_line min_ch in - let last = String.length l - 1 in - assert (last > 0); - if l.[last] = Char.chr 249 then - int_of_string (String.sub l 0 last) - else - aux l - in - aux "x" -;; - -let exec_cmds = - let rec aux undopos = - function - [] -> true - | he::tl -> - let pos = exec_cmd he in - if pos = -1 then - begin - match undopos with - None -> assert false - | Some undopos -> - assert (exec_cmd ~undo:true (string_of_int (undopos - 1)) <> -1); - false - end - else - match undopos with - None -> aux (Some pos) tl - | _ -> aux undopos tl - in - aux None - -let _ = - assert (exec_cmd "set \"baseuri\" \"cic:/matita/theory_former\"." <> -1); - assert (exec_cmd "include \"formal_topology.ma\"." <> -1); -;; - -(********* testing a conjecture *******************) - -let test to_be_considered_and_now ((s,_,_) as set) rel candidate repr = - ps_of_set to_be_considered_and_now ~processing:(candidate,rel,repr) set; - print_string - (string_of_cop candidate ^ " " ^ string_of_rel rel ^ " " ^ string_of_cop repr ^ "? "); - flush stdout; -(* - assert (Unix.system "cat log.ma | sed s/^theorem/axiom/g | sed 's/\\. intros.*qed\\././g' > xxx.ma" = Unix.WEXITED 0); - let ch = open_out_gen [Open_append] 0 "xxx.ma" in -*) -(* - let i = ref 0 in - List.iter - (function (repr,others,leq,_) -> - List.iter - (function repr' -> - incr i; - output_string ch - ("axiom ax" ^ string_of_int !i ^ - ": \\forall A." ^ - matita_of_cop "A" repr ^ " = " ^ matita_of_cop "A" repr' ^ ".\n"); - ) others; - List.iter - (function (repr',_,_,_) -> - incr i; - output_string ch - ("axiom ax" ^ string_of_int !i ^ - ": \\forall A." ^ - matita_of_cop "A" repr ^ " ⊆ " ^ matita_of_cop "A" repr' ^ ".\n"); - ) !leq; - ) s; -*) - let candidate',rel',repr' = - match rel with - SupersetEqual -> repr,SubsetEqual,candidate - | Equal - | SubsetEqual -> candidate,rel,repr in - let query1 = - let name = name_of_theorem candidate' rel' repr' in - ("theorem " ^ name ^ ": \\forall A." ^ matita_of_cop "A" candidate' ^ - " " ^ string_of_rel rel' ^ " " ^ - matita_of_cop "A" repr' ^ ".") in - let query2 = "intros;" in - let query3 = "autobatch size=8 depth=3 width=2." in - let query4 = "qed." in - let query = query1 ^ query2 ^ query3 ^ query4 in -(* - output_string ch (query ^ "\n"); - close_out ch; -*) - let res = profile exec_cmds [query1; query2; query3; query4] in -(* - let res = - (*Unix.system "../../../matitac.opt xxx.ma >> log 2>&1" = Unix.WEXITED 0*) - profile Unix.system "../../../matitac.opt xxx.ma > /dev/null 2>&1" = Unix.WEXITED 0 - in -*) - ignore (Unix.system "echo '(*' >> log.ma && cat xxx.dot >> log.ma && echo '*)' >> log.ma"); - let ch = open_out_gen [Open_append] 0o0600 "log.ma" in - if res then - output_string ch (query ^ "\n") - else - output_string ch ("(* " ^ query ^ "*)\n"); - close_out ch; - print_endline (if res then "y" else "n"); - res - -let remove node = List.filter (fun node' -> node <=> node');; - -let add_leq_arc ((_,_,leq,_) as node) ((_,_,_,geq') as node') = - leq := node' :: !leq; - geq' := node :: !geq' -;; - -let add_geq_arc ((_,_,_,geq) as node) ((_,_,leq',_) as node') = - geq := node' :: !geq; - leq' := node :: !leq' -;; - -let remove_leq_arc ((_,_,leq,_) as node) ((_,_,_,geq') as node') = - leq := remove node' !leq; - geq' := remove node !geq' -;; - -let remove_geq_arc ((_,_,_,geq) as node) ((_,_,leq',_) as node') = - geq := remove node' !geq; - leq' := remove node !leq' -;; - -let leq_transitive_closure node node' = - add_leq_arc node node'; - let rec remove_transitive_arcs ((_,_,_,geq) as node) (_,_,leq',_) = - let rec remove_arcs_to_ascendents = - function - [] -> () - | (_,_,leq,_) as node'::tl -> - remove_leq_arc node node'; - remove_arcs_to_ascendents (!leq@tl) - in - remove_arcs_to_ascendents !leq'; - List.iter (function son -> remove_transitive_arcs son node) !geq - in - remove_transitive_arcs node node' -;; - -let geq_transitive_closure node node' = - add_geq_arc node node'; - let rec remove_transitive_arcs ((_,_,leq,_) as node) (_,_,_,geq') = - let rec remove_arcs_to_descendents = - function - [] -> () - | (_,_,_,geq) as node'::tl -> - remove_geq_arc node node'; - remove_arcs_to_descendents (!geq@tl) - in - remove_arcs_to_descendents !geq'; - List.iter (function father -> remove_transitive_arcs father node) !leq - in - remove_transitive_arcs node node' -;; - -let (@@) l1 n = if List.exists (function n' -> n===n') l1 then l1 else l1@[n] - -let rec leq_reachable node = - function - [] -> false - | node'::_ when node === node' -> true - | (_,_,leq,_)::tl -> leq_reachable node (!leq@tl) -;; - -let rec geq_reachable node = - function - [] -> false - | node'::_ when node === node' -> true - | (_,_,_,geq)::tl -> geq_reachable node (!geq@tl) -;; - -exception SameEquivalenceClass of set * equivalence_class * equivalence_class;; - -let locate_using_leq to_be_considered_and_now ((repr,_,leq,geq) as node) - set start -= - let rec aux ((nodes,inf,sup) as set) already_visited = - function - [] -> set - | (repr',_,_,geq') as node' :: tl -> - if List.exists (function n -> n===node') already_visited then - aux set already_visited tl - else if repr=repr' then aux set (node'::already_visited) (!geq'@tl) - else if leq_reachable node' !leq then - aux set (node'::already_visited) (!geq'@tl) - else if (List.exists (function n -> not (geq_reachable n [node'])) !geq) - then - aux set (node'::already_visited) tl - else if test to_be_considered_and_now set SubsetEqual repr repr' then - begin - if List.exists (function n -> n===node') !geq then - (* We have found two equal nodes! *) - raise (SameEquivalenceClass (set,node,node')) - else - begin - let sup = remove node sup in - let inf = - if !geq' = [] then - let inf = remove node' inf in - if !geq = [] then - inf@@node - else - inf - else - inf - in - leq_transitive_closure node node'; - aux (nodes,inf,sup) (node'::already_visited) (!geq'@tl) - end - end - else - aux set (node'::already_visited) tl - in - aux set [] start -;; - -let locate_using_geq to_be_considered_and_now ((repr,_,leq,geq) as node) - set start -= - let rec aux ((nodes,inf,sup) as set) already_visited = - function - [] -> set - | (repr',_,leq',_) as node' :: tl -> - if List.exists (function n -> n===node') already_visited then - aux set already_visited tl - else if repr=repr' then aux set (node'::already_visited) (!leq'@tl) - else if geq_reachable node' !geq then - aux set (node'::already_visited) (!leq'@tl) - else if (List.exists (function n -> not (leq_reachable n [node'])) !leq) - then - aux set (node'::already_visited) tl - else if test to_be_considered_and_now set SupersetEqual repr repr' then - begin - if List.exists (function n -> n===node') !leq then - (* We have found two equal nodes! *) - raise (SameEquivalenceClass (set,node,node')) - else - begin - let inf = remove node inf in - let sup = - if !leq' = [] then - let sup = remove node' sup in - if !leq = [] then - sup@@node - else - sup - else - sup - in - geq_transitive_closure node node'; - aux (nodes,inf,sup) (node'::already_visited) (!leq'@tl) - end - end - else - aux set (node'::already_visited) tl - in - aux set [] start -;; - -let analyze_one to_be_considered repr hecandidate (news,((nodes,inf,sup) as set)) = -if not (List.for_all (fun ((_,_,_,geq) as node) -> !geq = [] && let rec check_sups = function [] -> true | (_,_,leq,_) as node::tl -> if !leq = [] then List.exists (fun n -> n===node) sup && check_sups tl else check_sups (!leq@tl) in check_sups [node]) inf) then ((*ps_of_set ([],None,[]) set;*) assert false); -if not (List.for_all (fun ((_,_,leq,_) as node) -> !leq = [] && let rec check_infs = function [] -> true | (_,_,_,geq) as node::tl -> if !geq = [] then List.exists (fun n -> n===node) inf && check_infs tl else check_infs (!geq@tl) in check_infs [node]) sup) then (ps_of_set ([],None,[]) set; assert false); - let candidate = hecandidate::repr in - if List.length (List.filter ((=) M) candidate) > 1 then - news,set - else - try - let leq = ref [] in - let geq = ref [] in - let node = candidate,[],leq,geq in - let nodes = nodes@[node] in - let set = nodes,inf@[node],sup@[node] in - let set,start_inf,start_sup = - let repr_node = - match List.filter (fun (repr',_,_,_) -> repr=repr') nodes with - [node] -> node - | _ -> assert false - in - match hecandidate,repr with - I, I::_ -> raise (SameEquivalenceClass (set,node,repr_node)) - | I, _ -> - add_leq_arc node repr_node; - (nodes,remove repr_node inf@[node],sup),inf,sup - | C, C::_ -> raise (SameEquivalenceClass (set,node,repr_node)) - | C, _ -> - add_geq_arc node repr_node; - (nodes,inf,remove repr_node sup@[node]),inf,sup - | M, M::M::_ -> raise (SameEquivalenceClass (set,node,repr_node)) - | M, _ -> set,inf,sup - in - let set = - locate_using_leq (to_be_considered,Some repr,news) node set start_sup in -( -let _,inf,sup = set in -if not (List.for_all (fun ((_,_,_,geq) as node) -> !geq = [] && let rec check_sups = function [] -> true | (_,_,leq,_) as node::tl -> if !leq = [] then List.exists (fun n -> n===node) sup && check_sups tl else check_sups (!leq@tl) in check_sups [node]) inf) then (ps_of_set ([],None,[]) set; assert false); -if not (List.for_all (fun ((_,_,leq,_) as node) -> !leq = [] && let rec check_infs = function [] -> true | (_,_,_,geq) as node::tl -> if !geq = [] then List.exists (fun n -> n===node) inf && check_infs tl else check_infs (!geq@tl) in check_infs [node]) sup) then (ps_of_set ([],None,[]) set; assert false); -); - let set = - locate_using_geq (to_be_considered,Some repr,news) node set start_inf - in -( -let _,inf,sup = set in -if not (List.for_all (fun ((_,_,_,geq) as node) -> !geq = [] && let rec check_sups = function [] -> true | (_,_,leq,_) as node::tl -> if !leq = [] then List.exists (fun n -> n===node) sup && check_sups tl else check_sups (!leq@tl) in check_sups [node]) inf) then (ps_of_set ([],None,[]) set; assert false); -if not (List.for_all (fun ((_,_,leq,_) as node) -> !leq = [] && let rec check_infs = function [] -> true | (_,_,_,geq) as node::tl -> if !geq = [] then List.exists (fun n -> n===node) inf && check_infs tl else check_infs (!geq@tl) in check_infs [node]) sup) then ((*ps_of_set ([],None,[]) set;*) assert false); -); - news@[candidate],set - with - SameEquivalenceClass ((nodes,inf,sup) as set,((r,_,leq_d,geq_d) as node_to_be_deleted),node')-> -( -let _,inf,sup = set in -if not (List.for_all (fun ((_,_,_,geq) as node) -> !geq = [] && let rec check_sups = function [] -> true | (_,_,leq,_) as node::tl -> if !leq = [] then List.exists (fun n -> n===node) sup && check_sups tl else check_sups (!leq@tl) in check_sups [node]) inf) then (ps_of_set ([],None,[]) set; assert false); -if not (List.for_all (fun ((_,_,leq,_) as node) -> !leq = [] && let rec check_infs = function [] -> true | (_,_,_,geq) as node::tl -> if !geq = [] then List.exists (fun n -> n===node) inf && check_infs tl else check_infs (!geq@tl) in check_infs [node]) sup) then ((*ps_of_set ([],None,[]) set;*) assert false); -); - let rec clean inf sup res = - function - [] -> inf,sup,res - | node::tl when node===node_to_be_deleted -> - clean inf sup res tl - | (repr',others,leq,geq) as node::tl -> - leq := - (let rec aux res = - function - [] -> res - | (_,_,leq,_) as node::tl -> - if node_to_be_deleted <=> node then - aux (res@[node]) tl - else - (List.filter (fun n ->not (leq_reachable n (res@tl))) !leq)@tl - in - aux [] !leq); - let sup = if !leq = [] then sup@@node else sup in - geq := - (let rec aux res = - function - [] -> res - | (_,_,_,geq) as node::tl -> - if node_to_be_deleted <=> node then - aux (res@[node]) tl - else - (List.filter (fun n ->not (geq_reachable n (res@tl))) !geq)@tl - in - aux [] !geq); - let inf = if !geq = [] then inf@@node else inf in - if node===node' then - clean inf sup ((repr',others@[candidate],leq,geq)::res) tl - else - clean inf sup (node::res) tl - in - let inf,sup,nodes = clean inf sup [] nodes in - let inf = remove node_to_be_deleted inf in - let sup = remove node_to_be_deleted sup in -let set = nodes,inf,sup in -( -let _,inf,sup = set in -if not (List.for_all (fun ((_,_,_,geq) as node) -> !geq = [] && let rec check_sups = function [] -> true | (_,_,leq,_) as node::tl -> if !leq = [] then List.exists (fun n -> n===node) sup && check_sups tl else check_sups (!leq@tl) in check_sups [node]) inf) then (ps_of_set ([],None,[]) set; assert false); -if not (List.for_all (fun ((_,_,leq,_) as node) -> !leq = [] && let rec check_infs = function [] -> true | (_,_,_,geq) as node::tl -> if !geq = [] then List.exists (fun n -> n===node) inf && check_infs tl else check_infs (!geq@tl) in check_infs [node]) sup) then (ps_of_set ([],None,[]) set; assert false); -); - news,(nodes,inf,sup) -;; - -let rec explore i (set:set) news = - let rec aux news set = - function - [] -> news,set - | repr::tl -> - let news,set = - List.fold_right (analyze_one tl repr) [I;C;M] (news,set) - in - aux news set tl - in - let news,set = aux [] set news in - if news = [] then - begin - print_endline ("PUNTO FISSO RAGGIUNTO! i=" ^ string_of_int i); - print_endline (string_of_set set ^ "\n----------------"); - ps_of_set ([],None,[]) set - end - else - begin - print_endline ("NUOVA ITERAZIONE, i=" ^ string_of_int i); - print_endline (string_of_set set ^ "\n----------------"); - explore (i+1) set news - end -in - let id = [] in - let id_node = id,[],ref [], ref [] in - let set = [id_node],[id_node],[id_node] in - print_endline ("PRIMA ITERAZIONE, i=0, j=0"); - print_endline (string_of_set set ^ "\n----------------"); - (*ignore (Unix.system "rm -f log");*) - assert (Unix.system "cp formal_topology.ma log.ma" = Unix.WEXITED 0); - ps_of_set ([id],None,[]) set; - explore 1 set [id] -;; diff --git a/helm/software/matita/contribs/formal_topology/bin/theory_explorer_do_not_trust_auto.ml b/helm/software/matita/contribs/formal_topology/bin/theory_explorer_do_not_trust_auto.ml deleted file mode 100644 index 3a9dcde30..000000000 --- a/helm/software/matita/contribs/formal_topology/bin/theory_explorer_do_not_trust_auto.ml +++ /dev/null @@ -1,232 +0,0 @@ -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] -;;