;;
(* =================================== auto =========================== *)
+(****************** AUTO ********************
+
+let calculate_timeout flags =
+ if flags.timeout = 0. then
+ (debug_print (lazy "AUTO WITH NO TIMEOUT");
+ {flags with timeout = infinity})
+ else
+ flags
+;;
+let is_equational_case goalty flags =
+ let ensure_equational t =
+ if is_an_equational_goal t then true
+ else false
+ in
+ (flags.use_paramod && is_an_equational_goal goalty) ||
+ (flags.use_only_paramod && ensure_equational goalty)
+;;
+
+type menv = Cic.metasenv
+type subst = Cic.substitution
+type goal = ProofEngineTypes.goal * int * AutoTypes.sort
+let candidate_no = ref 0;;
+type candidate = int * Cic.term Lazy.t
+type cache = AutoCache.cache
+
+type fail =
+ (* the goal (mainly for depth) and key of the goal *)
+ goal * AutoCache.cache_key
+type op =
+ (* goal has to be proved *)
+ | D of goal
+ (* goal has to be cached as a success obtained using candidate as the first
+ * step *)
+ | S of goal * AutoCache.cache_key * candidate * int
+type elem =
+ (* menv, subst, size, operations done (only S), operations to do, failures to cache if any op fails *)
+ menv * subst * int * op list * op list * fail list
+type status =
+ (* list of computations that may lead to the solution: all op list will
+ * end with the same (S(g,_)) *)
+ elem list
+type auto_result =
+ (* menv, subst, alternatives, tables, cache *)
+ | Proved of menv * subst * elem list * AutomationCache.tables * cache
+ | Gaveup of AutomationCache.tables * cache
+
+
+(* the status exported to the external observer *)
+type auto_status =
+ (* context, (goal,candidate) list, and_list, history *)
+ Cic.context * (int * Cic.term * bool * int * (int * Cic.term Lazy.t) list) list *
+ (int * Cic.term * int) list * Cic.term Lazy.t list
+
+let d_prefix l =
+ let rec aux acc = function
+ | (D g)::tl -> aux (acc@[g]) tl
+ | _ -> acc
+ in
+ aux [] l
+;;
+
+let calculate_goal_ty (goalno,_,_) s m =
+ try
+ let _,cc,goalty = CicUtil.lookup_meta goalno m in
+ (* XXX applicare la subst al contesto? *)
+ Some (cc, CicMetaSubst.apply_subst s goalty)
+ with CicUtil.Meta_not_found i when i = goalno -> None
+;;
+
+let calculate_closed_goal_ty (goalno,_,_) s =
+ try
+ let cc,_,goalty = List.assoc goalno s in
+ (* XXX applicare la subst al contesto? *)
+ Some (cc, CicMetaSubst.apply_subst s goalty)
+ with Not_found ->
+ None
+;;
+
+let pp_status ctx status =
+ if debug then
+ let names = Utils.names_of_context ctx in
+ let pp x =
+ let x =
+ ProofEngineReduction.replace
+ ~equality:(fun a b -> match b with Cic.Meta _ -> true | _ -> false)
+ ~what:[Cic.Rel 1] ~with_what:[Cic.Implicit None] ~where:x
+ in
+ CicPp.pp x names
+ in
+ let string_of_do m s (gi,_,_ as g) d =
+ match calculate_goal_ty g s m with
+ | Some (_,gty) -> Printf.sprintf "D(%d, %s, %d)" gi (pp gty) d
+ | None -> Printf.sprintf "D(%d, _, %d)" gi d
+ in
+ let string_of_s m su k (ci,ct) gi =
+ Printf.sprintf "S(%d, %s, %s, %d)" gi (pp k) (pp (Lazy.force ct)) ci
+ in
+ let string_of_ol m su l =
+ String.concat " | "
+ (List.map
+ (function
+ | D (g,d,s) -> string_of_do m su (g,d,s) d
+ | S ((gi,_,_),k,c,_) -> string_of_s m su k c gi)
+ l)
+ in
+ let string_of_fl m s fl =
+ String.concat " | "
+ (List.map (fun ((i,_,_),ty) ->
+ Printf.sprintf "(%d, %s)" i (pp ty)) fl)
+ in
+ let rec aux = function
+ | [] -> ()
+ | (m,s,_,_,ol,fl)::tl ->
+ Printf.eprintf "< [%s] ;;; [%s]>\n"
+ (string_of_ol m s ol) (string_of_fl m s fl);
+ aux tl
+ in
+ Printf.eprintf "-------------------------- status -------------------\n";
+ aux status;
+ Printf.eprintf "-----------------------------------------------------\n";
+;;
+
+let auto_status = ref [] ;;
+let auto_context = ref [];;
+let in_pause = ref false;;
+let pause b = in_pause := b;;
+let cond = Condition.create ();;
+let mutex = Mutex.create ();;
+let hint = ref None;;
+let prune_hint = ref [];;
+
+let step _ = Condition.signal cond;;
+let give_hint n = hint := Some n;;
+let give_prune_hint hint =
+ prune_hint := hint :: !prune_hint
+;;
+
+let check_pause _ =
+ if !in_pause then
+ begin
+ Mutex.lock mutex;
+ Condition.wait cond mutex;
+ Mutex.unlock mutex
+ end
+;;
+
+let get_auto_status _ =
+ let status = !auto_status in
+ let and_list,elems,last =
+ match status with
+ | [] -> [],[],[]
+ | (m,s,_,don,gl,fail)::tl ->
+ let and_list =
+ HExtlib.filter_map
+ (fun (id,d,_ as g) ->
+ match calculate_goal_ty g s m with
+ | Some (_,x) -> Some (id,x,d) | None -> None)
+ (d_goals gl)
+ in
+ let rows =
+ (* these are the S goalsin the or list *)
+ let orlist =
+ List.map
+ (fun (m,s,_,don,gl,fail) ->
+ HExtlib.filter_map
+ (function S (g,k,c,_) -> Some (g,k,c) | _ -> None)
+ (List.rev don @ gl))
+ status
+ in
+ (* this function eats id from a list l::[id,x] returning x, l *)
+ let eat_tail_if_eq id l =
+ let rec aux (s, l) = function
+ | [] -> s, l
+ | ((id1,_,_),k1,c)::tl when id = id1 ->
+ (match s with
+ | None -> aux (Some c,l) tl
+ | Some _ -> assert false)
+ | ((id1,_,_),k1,c as e)::tl -> aux (s, e::l) tl
+ in
+ let c, l = aux (None, []) l in
+ c, List.rev l
+ in
+ let eat_in_parallel id l =
+ let rec aux (b,eaten, new_l as acc) l =
+ match l with
+ | [] -> acc
+ | l::tl ->
+ match eat_tail_if_eq id l with
+ | None, l -> aux (b@[false], eaten, new_l@[l]) tl
+ | Some t,l -> aux (b@[true],eaten@[t], new_l@[l]) tl
+ in
+ aux ([],[],[]) l
+ in
+ let rec eat_all rows l =
+ match l with
+ | [] -> rows
+ | elem::or_list ->
+ match List.rev elem with
+ | ((to_eat,depth,_),k,_)::next_lunch ->
+ let b, eaten, l = eat_in_parallel to_eat l in
+ let eaten = HExtlib.list_uniq eaten in
+ let eaten = List.rev eaten in
+ let b = true (* List.hd (List.rev b) *) in
+ let rows = rows @ [to_eat,k,b,depth,eaten] in
+ eat_all rows l
+ | [] -> eat_all rows or_list
+ in
+ eat_all [] (List.rev orlist)
+ in
+ let history =
+ HExtlib.filter_map
+ (function (S (_,_,(_,c),_)) -> Some c | _ -> None)
+ gl
+ in
+(* let rows = List.filter (fun (_,l) -> l <> []) rows in *)
+ and_list, rows, history
+ in
+ !auto_context, elems, and_list, last
+;;
+
+(* Works if there is no dependency over proofs *)
+let is_a_green_cut goalty =
+ CicUtil.is_meta_closed goalty
+;;
+let rec first_s = function
+ | (D _)::tl -> first_s tl
+ | (S (g,k,c,s))::tl -> Some ((g,k,c,s),tl)
+ | [] -> None
+;;
+let list_union l1 l2 =
+ (* TODO ottimizzare compare *)
+ HExtlib.list_uniq (List.sort compare (l1 @ l1))
+;;
+let rec eq_todo l1 l2 =
+ match l1,l2 with
+ | (D g1) :: tl1,(D g2) :: tl2 when g1=g2 -> eq_todo tl1 tl2
+ | (S (g1,k1,(c1,lt1),i1)) :: tl1, (S (g2,k2,(c2,lt2),i2)) :: tl2
+ when i1 = i2 && g1 = g2 && k1 = k2 && c1 = c2 ->
+ if Lazy.force lt1 = Lazy.force lt2 then eq_todo tl1 tl2 else false
+ | [],[] -> true
+ | _ -> false
+;;
+let eat_head todo id fl orlist =
+ let rec aux acc = function
+ | [] -> [], acc
+ | (m, s, _, _, todo1, fl1)::tl as orlist ->
+ let rec aux1 todo1 =
+ match first_s todo1 with
+ | None -> orlist, acc
+ | Some (((gno,_,_),_,_,_), todo11) ->
+ (* TODO confronto tra todo da ottimizzare *)
+ if gno = id && eq_todo todo11 todo then
+ aux (list_union fl1 acc) tl
+ else
+ aux1 todo11
+ in
+ aux1 todo1
+ in
+ aux fl orlist
+;;
+let close_proof p ty menv context =
+ let metas =
+ List.map fst (CicUtil.metas_of_term p @ CicUtil.metas_of_term ty)
+ in
+ let menv = List.filter (fun (i,_,_) -> List.exists ((=)i) metas) menv in
+ naif_closure p menv context
+;;
+(* XXX capire bene quando aggiungere alla cache *)
+let add_to_cache_and_del_from_orlist_if_green_cut
+ g s m cache key todo orlist fl ctx size minsize
+=
+ let cache = cache_remove_underinspection cache key in
+ (* prima per fare la irl usavamo il contesto vero e proprio e non quello
+ * canonico! XXX *)
+ match calculate_closed_goal_ty g s with
+ | None -> assert false
+ | Some (canonical_ctx , gty) ->
+ let goalno,depth,sort = g in
+ let irl = mk_irl canonical_ctx in
+ let goal = Cic.Meta(goalno, irl) in
+ let proof = CicMetaSubst.apply_subst s goal in
+ let green_proof, closed_proof =
+ let b = is_a_green_cut proof in
+ if not b then
+ b, (* close_proof proof gty m ctx *) proof
+ else
+ b, proof
+ in
+ debug_print (lazy ("TENTATIVE CACHE: " ^ CicPp.ppterm key));
+ if is_a_green_cut key then
+ (* if the initia goal was closed, we cut alternatives *)
+ let _ = debug_print (lazy ("MANGIO: " ^ string_of_int goalno)) in
+ let orlist, fl = eat_head todo goalno fl orlist in
+ let cache =
+ if size < minsize then
+ (debug_print (lazy ("NO CACHE: 2 (size <= minsize)"));cache)
+ else
+ (* if the proof is closed we cache it *)
+ if green_proof then cache_add_success cache key proof
+ else (* cache_add_success cache key closed_proof *)
+ (debug_print (lazy ("NO CACHE: (no gree proof)"));cache)
+ in
+ cache, orlist, fl, true
+ else
+ let cache =
+ debug_print (lazy ("TENTATIVE CACHE: " ^ CicPp.ppterm gty));
+ if size < minsize then
+ (debug_print (lazy ("NO CACHE: (size <= minsize)")); cache) else
+ (* if the substituted goal and the proof are closed we cache it *)
+ if is_a_green_cut gty then
+ if green_proof then cache_add_success cache gty proof
+ else (* cache_add_success cache gty closed_proof *)
+ (debug_print (lazy ("NO CACHE: (no green proof (gty))"));cache)
+ else (*
+ try
+ let ty, _ =
+ CicTypeChecker.type_of_aux' ~subst:s
+ m ctx closed_proof CicUniv.oblivion_ugraph
+ in
+ if is_a_green_cut ty then
+ cache_add_success cache ty closed_proof
+ else cache
+ with
+ | CicTypeChecker.TypeCheckerFailure _ ->*)
+ (debug_print (lazy ("NO CACHE: (no green gty )"));cache)
+ in
+ cache, orlist, fl, false
+;;
+let close_failures (fl : fail list) (cache : cache) =
+ List.fold_left
+ (fun cache ((gno,depth,_),gty) ->
+ if CicUtil.is_meta_closed gty then
+ ( debug_print (lazy ("FAIL: INDUCED: " ^ string_of_int gno));
+ cache_add_failure cache gty depth)
+ else
+ cache)
+ cache fl
+;;
+let put_in_subst subst metasenv (goalno,_,_) canonical_ctx t ty =
+ let entry = goalno, (canonical_ctx, t,ty) in
+ assert_subst_are_disjoint subst [entry];
+ let subst = entry :: subst in
+
+ let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
+
+ subst, metasenv
+;;
+
+let mk_fake_proof metasenv subst (goalno,_,_) goalty context =
+ None,metasenv,subst ,(lazy (Cic.Meta(goalno,mk_irl context))),goalty, []
+;;
+
+let equational_case
+ tables cache depth fake_proof goalno goalty subst context
+ flags
+=
+ let active,passive,bag = tables in
+ let ppterm = ppterm context in
+ let status = (fake_proof,goalno) in
+ if flags.use_only_paramod then
+ begin
+ debug_print (lazy ("PARAMODULATION SU: " ^
+ string_of_int goalno ^ " " ^ ppterm goalty ));
+ let goal_steps, saturation_steps, timeout =
+ max_int,max_int,flags.timeout
+ in
+ match
+ Saturation.given_clause bag status active passive
+ goal_steps saturation_steps timeout
+ with
+ | None, active, passive, bag ->
+ [], (active,passive,bag), cache, flags
+ | Some(subst',(_,metasenv,_subst,proof,_, _),open_goals),active,
+ passive,bag ->
+ assert_subst_are_disjoint subst subst';
+ let subst = subst@subst' in
+ let open_goals =
+ order_new_goals metasenv subst open_goals ppterm
+ in
+ let open_goals =
+ List.map (fun (x,sort) -> x,depth-1,sort) open_goals
+ in
+ incr candidate_no;
+ [(!candidate_no,proof),metasenv,subst,open_goals],
+ (active,passive,bag), cache, flags
+ end
+ else
+ begin
+ debug_print (lazy ("NARROWING DEL GOAL: " ^
+ string_of_int goalno ^ " " ^ ppterm goalty ));
+ let goal_steps, saturation_steps, timeout =
+ 1,0,flags.timeout
+ in
+ match
+ Saturation.solve_narrowing bag status active passive goal_steps
+ with
+ | None, active, passive, bag ->
+ [], (active,passive,bag), cache, flags
+ | Some(subst',(_,metasenv,_subst,proof,_, _),open_goals),active,
+ passive,bag ->
+ assert_subst_are_disjoint subst subst';
+ let subst = subst@subst' in
+ let open_goals =
+ order_new_goals metasenv subst open_goals ppterm
+ in
+ let open_goals =
+ List.map (fun (x,sort) -> x,depth-1,sort) open_goals
+ in
+ incr candidate_no;
+ [(!candidate_no,proof),metasenv,subst,open_goals],
+ (active,passive,bag), cache, flags
+ end
+(*
+ begin
+ let params = ([],["use_context","false"]) in
+ let automation_cache = {
+ AutomationCache.tables = tables ;
+ AutomationCache.univ = Universe.empty; }
+ in
+ try
+ let ((_,metasenv,subst,_,_,_),open_goals) =
+
+ solve_rewrite ~params ~automation_cache
+ (fake_proof, goalno)
+ in
+ let proof = lazy (Cic.Meta (-1,[])) in
+ [(!candidate_no,proof),metasenv,subst,[]],tables, cache, flags
+ with ProofEngineTypes.Fail _ -> [], tables, cache, flags
+(*
+ let res = Saturation.all_subsumed bag status active passive in
+ let res' =
+ List.map
+ (fun (subst',(_,metasenv,_subst,proof,_, _),open_goals) ->
+ assert_subst_are_disjoint subst subst';
+ let subst = subst@subst' in
+ let open_goals =
+ order_new_goals metasenv subst open_goals ppterm
+ in
+ let open_goals =
+ List.map (fun (x,sort) -> x,depth-1,sort) open_goals
+ in
+ incr candidate_no;
+ (!candidate_no,proof),metasenv,subst,open_goals)
+ res
+ in
+ res', (active,passive,bag), cache, flags
+*)
+ end
+*)
+;;
+
+let sort_new_elems =
+ List.sort (fun (_,_,_,l1) (_,_,_,l2) ->
+ let p1 = List.length (prop_only l1) in
+ let p2 = List.length (prop_only l2) in
+ if p1 = p2 then List.length l1 - List.length l2 else p1-p2)
+;;
+
+
+let try_candidate dbd
+ goalty tables subst fake_proof goalno depth context cand
+=
+ let ppterm = ppterm context in
+ try
+ let actives, passives, bag = tables in
+ let (_,metasenv,subst,_,_,_), open_goals =
+ ProofEngineTypes.apply_tactic
+ (PrimitiveTactics.apply_tac ~term:cand)
+ (fake_proof,goalno)
+ in
+ let tables = actives, passives,
+ Equality.push_maxmeta bag
+ (max (Equality.maxmeta bag) (CicMkImplicit.new_meta metasenv subst))
+ in
+ debug_print (lazy (" OK: " ^ ppterm cand));
+ let metasenv = CicRefine.pack_coercion_metasenv metasenv in
+ let open_goals = order_new_goals metasenv subst open_goals ppterm in
+ let open_goals = List.map (fun (x,sort) -> x,depth-1,sort) open_goals in
+ incr candidate_no;
+ Some ((!candidate_no,lazy cand),metasenv,subst,open_goals), tables
+ with
+ | ProofEngineTypes.Fail s -> None,tables
+ | CicUnification.Uncertain s -> None,tables
+;;
+
+let applicative_case dbd
+ tables depth subst fake_proof goalno goalty metasenv context
+ signature universe cache flags
+=
+ (* let goalty_aux =
+ match goalty with
+ | Cic.Appl (hd::tl) ->
+ Cic.Appl (hd :: HExtlib.mk_list (Cic.Meta (0,[])) (List.length tl))
+ | _ -> goalty
+ in *)
+ let goalty_aux = goalty in
+ let candidates =
+ get_candidates flags.skip_trie_filtering universe cache goalty_aux
+ in
+ (* if the goal is an equality we skip the congruence theorems
+ let candidates =
+ if is_equational_case goalty flags
+ then List.filter not_default_eq_term candidates
+ else candidates
+ in *)
+ let candidates = List.filter (only signature context metasenv) candidates
+ in
+ let tables, elems =
+ List.fold_left
+ (fun (tables,elems) cand ->
+ match
+ try_candidate dbd goalty
+ tables subst fake_proof goalno depth context cand
+ with
+ | None, tables -> tables, elems
+ | Some x, tables -> tables, x::elems)
+ (tables,[]) candidates
+ in
+ let elems = sort_new_elems elems in
+ elems, tables, cache
+;;
+
+let try_smart_candidate dbd
+ goalty tables subst fake_proof goalno depth context cand
+=
+ let ppterm = ppterm context in
+ try
+ let params = ([],[]) in
+ let automation_cache = {
+ AutomationCache.tables = tables ;
+ AutomationCache.univ = Universe.empty; }
+ in
+ debug_print (lazy ("candidato per " ^ string_of_int goalno
+ ^ ": " ^ CicPp.ppterm cand));
+(*
+ let (_,metasenv,subst,_,_,_) = fake_proof in
+ prerr_endline ("metasenv:\n" ^ CicMetaSubst.ppmetasenv [] metasenv);
+ prerr_endline ("subst:\n" ^ CicMetaSubst.ppsubst ~metasenv subst);
+*)
+ let ((_,metasenv,subst,_,_,_),open_goals) =
+ apply_smart ~dbd ~term:cand ~params ~automation_cache
+ (fake_proof, goalno)
+ in
+ let metasenv = CicRefine.pack_coercion_metasenv metasenv in
+ let open_goals = order_new_goals metasenv subst open_goals ppterm in
+ let open_goals = List.map (fun (x,sort) -> x,depth-1,sort) open_goals in
+ incr candidate_no;
+ Some ((!candidate_no,lazy cand),metasenv,subst,open_goals), tables
+ with
+ | ProofEngineTypes.Fail s -> None,tables
+ | CicUnification.Uncertain s -> None,tables
+;;
+
+let smart_applicative_case dbd
+ tables depth subst fake_proof goalno goalty metasenv context signature
+ universe cache flags
+=
+ let goalty_aux =
+ match goalty with
+ | Cic.Appl (hd::tl) ->
+ Cic.Appl (hd :: HExtlib.mk_list (Cic.Meta (0,[])) (List.length tl))
+ | _ -> goalty
+ in
+ let smart_candidates =
+ get_candidates flags.skip_trie_filtering universe cache goalty_aux
+ in
+ let candidates =
+ get_candidates flags.skip_trie_filtering universe cache goalty
+ in
+ let smart_candidates =
+ List.filter
+ (fun x -> not(List.mem x candidates)) smart_candidates
+ in
+ let debug_msg =
+ (lazy ("smart_candidates" ^ " = " ^
+ (String.concat "\n" (List.map CicPp.ppterm smart_candidates)))) in
+ debug_print debug_msg;
+ let candidates = List.filter (only signature context metasenv) candidates in
+ let smart_candidates =
+ List.filter (only signature context metasenv) smart_candidates
+ in
+(*
+ let penalty cand depth =
+ if only signature context metasenv cand then depth else ((prerr_endline (
+ "penalizzo " ^ CicPp.ppterm cand));depth -1)
+ in
+*)
+ let tables, elems =
+ List.fold_left
+ (fun (tables,elems) cand ->
+ match
+ try_candidate dbd goalty
+ tables subst fake_proof goalno depth context cand
+ with
+ | None, tables ->
+ (* if normal application fails we try to be smart *)
+ (match try_smart_candidate dbd goalty
+ tables subst fake_proof goalno depth context cand
+ with
+ | None, tables -> tables, elems
+ | Some x, tables -> tables, x::elems)
+ | Some x, tables -> tables, x::elems)
+ (tables,[]) candidates
+ in
+ let tables, smart_elems =
+ List.fold_left
+ (fun (tables,elems) cand ->
+ match
+ try_smart_candidate dbd goalty
+ tables subst fake_proof goalno depth context cand
+ with
+ | None, tables -> tables, elems
+ | Some x, tables -> tables, x::elems)
+ (tables,[]) smart_candidates
+ in
+ let elems = sort_new_elems (elems @ smart_elems) in
+ elems, tables, cache
+;;
+
+let equational_and_applicative_case dbd
+ signature universe flags m s g gty tables cache context
+=
+ let goalno, depth, sort = g in
+ let fake_proof = mk_fake_proof m s g gty context in
+ if is_equational_case gty flags then
+ let elems,tables,cache, flags =
+ equational_case tables cache
+ depth fake_proof goalno gty s context flags
+ in
+ let more_elems, tables, cache =
+ if flags.use_only_paramod then
+ [],tables, cache
+ else
+ applicative_case dbd
+ tables depth s fake_proof goalno
+ gty m context signature universe cache flags
+ in
+ elems@more_elems, tables, cache, flags
+ else
+ let elems, tables, cache =
+ match LibraryObjects.eq_URI () with
+ | Some _ ->
+ smart_applicative_case dbd tables depth s fake_proof goalno
+ gty m context signature universe cache flags
+ | None ->
+ applicative_case dbd tables depth s fake_proof goalno
+ gty m context signature universe cache flags
+ in
+ elems, tables, cache, flags
+;;
+let rec condition_for_hint i = function
+ | [] -> false
+ | S (_,_,(j,_),_):: tl -> j <> i (* && condition_for_hint i tl *)
+ | _::tl -> condition_for_hint i tl
+;;
+let prunable_for_size flags s m todo =
+ let rec aux b = function
+ | (S _)::tl -> aux b tl
+ | (D (_,_,T))::tl -> aux b tl
+ | (D g)::tl ->
+ (match calculate_goal_ty g s m with
+ | None -> aux b tl
+ | Some (canonical_ctx, gty) ->
+ let gsize, _ =
+ Utils.weight_of_term
+ ~consider_metas:false ~count_metas_occurrences:true gty in
+ let newb = b || gsize > flags.maxgoalsizefactor in
+ aux newb tl)
+ | [] -> b
+ in
+ aux false todo
+
+(*
+let prunable ty todo =
+ let rec aux b = function
+ | (S(_,k,_,_))::tl -> aux (b || Equality.meta_convertibility k ty) tl
+ | (D (_,_,T))::tl -> aux b tl
+ | D _::_ -> false
+ | [] -> b
+ in
+ aux false todo
+;;
+*)
+
+let prunable menv subst ty todo =
+ let rec aux = function
+ | (S(_,k,_,_))::tl ->
+ (match Equality.meta_convertibility_subst k ty menv with
+ | None -> aux tl
+ | Some variant ->
+ no_progress variant tl (* || aux tl*))
+ | (D (_,_,T))::tl -> aux tl
+ | _ -> false
+ and no_progress variant = function
+ | [] -> (*prerr_endline "++++++++++++++++++++++++ no_progress";*) true
+ | D ((n,_,P) as g)::tl ->
+ (match calculate_goal_ty g subst menv with
+ | None -> no_progress variant tl
+ | Some (_, gty) ->
+ (match calculate_goal_ty g variant menv with
+ | None -> assert false
+ | Some (_, gty') ->
+ if gty = gty' then no_progress variant tl
+(*
+(prerr_endline (string_of_int n);
+ prerr_endline (CicPp.ppterm gty);
+ prerr_endline (CicPp.ppterm gty');
+ prerr_endline "---------- subst";
+ prerr_endline (CicMetaSubst.ppsubst ~metasenv:menv subst);
+ prerr_endline "---------- variant";
+ prerr_endline (CicMetaSubst.ppsubst ~metasenv:menv variant);
+ prerr_endline "---------- menv";
+ prerr_endline (CicMetaSubst.ppmetasenv [] menv);
+ no_progress variant tl) *)
+ else false))
+ | _::tl -> no_progress variant tl
+ in
+ aux todo
+
+;;
+let condition_for_prune_hint prune (m, s, size, don, todo, fl) =
+ let s =
+ HExtlib.filter_map (function S (_,_,(c,_),_) -> Some c | _ -> None) todo
+ in
+ List.for_all (fun i -> List.for_all (fun j -> i<>j) prune) s
+;;
+let filter_prune_hint c l =
+ let prune = !prune_hint in
+ prune_hint := []; (* possible race... *)
+ if prune = [] then c,l
+ else
+ cache_reset_underinspection c,
+ List.filter (condition_for_prune_hint prune) l
+;;
+
+
+
+let
+ auto_all_solutions dbd tables universe cache context metasenv gl flags
+=
+ let signature =
+ List.fold_left
+ (fun set g ->
+ MetadataConstraints.UriManagerSet.union set
+ (MetadataQuery.signature_of metasenv g)
+ )
+ MetadataConstraints.UriManagerSet.empty gl
+ in
+ let goals = order_new_goals metasenv [] gl CicPp.ppterm in
+ let goals =
+ List.map
+ (fun (x,s) -> D (x,flags.maxdepth,s)) goals
+ in
+ let elems = [metasenv,[],1,[],goals,[]] in
+ let rec aux tables solutions cache elems flags =
+ match auto_main dbd tables context flags signature universe cache elems with
+ | Gaveup (tables,cache) ->
+ solutions,cache, tables
+ | Proved (metasenv,subst,others,tables,cache) ->
+ if Unix.gettimeofday () > flags.timeout then
+ ((subst,metasenv)::solutions), cache, tables
+ else
+ aux tables ((subst,metasenv)::solutions) cache others flags
+ in
+ let rc = aux tables [] cache elems flags in
+ match rc with
+ | [],cache,tables -> [],cache,tables
+ | solutions, cache,tables ->
+ let solutions =
+ HExtlib.filter_map
+ (fun (subst,newmetasenv) ->
+ let opened =
+ ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv ~newmetasenv
+ in
+ if opened = [] then Some subst else None)
+ solutions
+ in
+ solutions,cache,tables
+;;
+
+(******************* AUTO ***************)
+
+
+let auto dbd flags metasenv tables universe cache context metasenv gl =
+ let initial_time = Unix.gettimeofday() in
+ let signature =
+ List.fold_left
+ (fun set g ->
+ MetadataConstraints.UriManagerSet.union set
+ (MetadataQuery.signature_of metasenv g)
+ )
+ MetadataConstraints.UriManagerSet.empty gl
+ in
+ let goals = order_new_goals metasenv [] gl CicPp.ppterm in
+ let goals = List.map (fun (x,s) -> D(x,flags.maxdepth,s)) goals in
+ let elems = [metasenv,[],1,[],goals,[]] in
+ match auto_main dbd tables context flags signature universe cache elems with
+ | Proved (metasenv,subst,_, tables,cache) ->
+ debug_print(lazy
+ ("TIME:"^string_of_float(Unix.gettimeofday()-.initial_time)));
+ Some (subst,metasenv), cache
+ | Gaveup (tables,cache) ->
+ debug_print(lazy
+ ("TIME:"^string_of_float(Unix.gettimeofday()-.initial_time)));
+ None,cache
+;;
+
+let auto_tac ~(dbd:HSql.dbd) ~params:(univ,params) ~automation_cache (proof, goal) =
+ let flags = flags_of_params params () in
+ let use_library = flags.use_library in
+ let universe, tables, cache =
+ init_cache_and_tables
+ ~dbd ~use_library ~use_context:(not flags.skip_context)
+ automation_cache univ (proof, goal)
+ in
+ let _,metasenv,subst,_,_, _ = proof in
+ let _,context,goalty = CicUtil.lookup_meta goal metasenv in
+ let signature = MetadataQuery.signature_of metasenv goal in
+ let signature =
+ List.fold_left
+ (fun set t ->
+ let ty, _ =
+ CicTypeChecker.type_of_aux' metasenv context t
+ CicUniv.oblivion_ugraph
+ in
+ MetadataConstraints.UriManagerSet.union set
+ (MetadataConstraints.constants_of ty)
+ )
+ signature univ
+ in
+ let tables,cache =
+ if flags.close_more then
+ close_more
+ tables context (proof, goal)
+ (auto_all_solutions dbd) signature universe cache
+ else tables,cache in
+ let initial_time = Unix.gettimeofday() in
+ let (_,oldmetasenv,_,_,_, _) = proof in
+ hint := None;
+ let elem =
+ metasenv,subst,1,[],[D (goal,flags.maxdepth,P)],[]
+ in
+ match auto_main dbd tables context flags signature universe cache [elem] with
+ | Proved (metasenv,subst,_, tables,cache) ->
+ debug_print (lazy
+ ("TIME:"^string_of_float(Unix.gettimeofday()-.initial_time)));
+ let proof,metasenv =
+ ProofEngineHelpers.subst_meta_and_metasenv_in_proof
+ proof goal subst metasenv
+ in
+ let opened =
+ ProofEngineHelpers.compare_metasenvs ~oldmetasenv
+ ~newmetasenv:metasenv
+ in
+ proof,opened
+ | Gaveup (tables,cache) ->
+ debug_print
+ (lazy ("TIME:"^
+ string_of_float(Unix.gettimeofday()-.initial_time)));
+ raise (ProofEngineTypes.Fail (lazy "Auto gave up"))
+;;
+*)
+
+module CacheElem : Set.OrderedType =
+ struct
+ type t =
+ | Failed_in of int * NCic.term (* depth, goal type *)
+ | Succeded of Cic.term * Cic.term (* proof, proof type *)
+ | UnderInspection of Cic.term (* avoid looping *)
+
+ let compare = Pervasives.compare
+ end
+
+module CacheSet = Set.Make(CacheElem)
+module Cache =
+ Discrimination_tree.Make(NDiscriminationTree.NCicIndexable)(CacheSet)
+
+type cache_examination_result =
+ [ `Failed_in of int
+ | `UnderInspection
+ | `Succeded of NCic.term
+ | `NotFound
+ ]
+
+type sort = T | P
+type goal = int * int * sort
+type fail = goal * NCic.term
+type candidate = NCic.term
+type menv = NCic.metasenv
+type subst = NCic.substitution
+
+type op =
+ (* goal has to be proved *)
+ | D of goal
+ (* goal has to be cached as a success obtained using candidate as the first
+ * step *)
+ | S of goal * Cache.input * candidate (* int was minsize *)
+type elem =
+ (* menv, subst, size, operations done (only S), operations to do,
+ * failures to cache if any op fails *)
+ menv * subst * int * op list * op list * fail list
+
+type auto_status =
+ (* list of computations that may lead to the solution: all op list will
+ * end with the same (S(g,_)) *)
+ elem list * Cache.t
+
+type auto_result =
+ | Gaveup
+ | Proved of menv * subst * auto_status (* the alternative proofs *)
+
+type flags = {
+ do_types : bool; (* solve goals in Type *)
+ maxwidth : int;
+ maxsize : int;
+ timeout : float;
+}
+
+let close_failures = assert false;;
+let equational_and_applicative_case = assert false;;
+let prunable = assert false;;
+let cache_examine = assert false;;
+let put_in_subst = assert false;;
+let calculate_goal_ty = assert false;;
+let add_to_cache_and_del_from_orlist_if_green_cut = assert false;;
+let cache_add_underinspection = assert false;;
+
+let d_goals l =
+ let rec aux acc = function
+ | (D g)::tl -> aux (acc@[g]) tl
+ | (S _)::tl -> aux acc tl
+ | [] -> acc
+ in
+ aux [] l
+;;
+let prop_only l =
+ List.filter (function (_,_,P) -> true | _ -> false) l
+;;
+let remove_s_from_fl (id,_,_) (fl : fail list) =
+ let rec aux = function
+ | [] -> []
+ | ((id1,_,_),_)::tl when id = id1 -> tl
+ | hd::tl -> hd :: aux tl
+ in
+ aux fl
+;;
+
+let auto_main status context flags signature elems cache =
+ let rec aux (elems, cache : auto_status) =
+(* processa le hint dell'utente *)
+(* let cache, elems = filter_prune_hint cache elems in *)
+ match elems with
+(* USER HINT
+ | (m, s, size, don, todo, fl)::orlist when !hint <> None ->
+ debug_print (lazy "skip");
+ (match !hint with
+ | Some i when condition_for_hint i todo ->
+ aux tables flags cache orlist
+ | _ ->
+ hint := None;
+ aux tables flags cache elems)
+*)
+ | [] ->
+ (* complete failure *)
+ debug_print (lazy "gave up");
+ Gaveup
+ | (m, s, _, _, [],_)::orlist ->
+ (* complete success *)
+ debug_print (lazy "success");
+ Proved (m, s, (orlist, cache))
+ | (m, s, size, don, (D (_,_,T))::todo, fl)::orlist
+ when not flags.do_types ->
+ (* skip since not Prop, don't even check if closed by side-effect *)
+ debug_print (lazy "skip goal in Type");
+ aux ((m, s, size, don, todo, fl)::orlist, cache)
+ | (m, s, size, don, (S(g, key, c) as op)::todo, fl)::orlist ->
+ (* partial success, cache g and go on *)
+ let cache, orlist, fl, sibling_pruned =
+ add_to_cache_and_del_from_orlist_if_green_cut
+ g s m cache key todo orlist fl context size
+ in
+ let fl = remove_s_from_fl g fl in
+ let don = if sibling_pruned then don else op::don in
+ aux ((m, s, size, don, todo, fl)::orlist, cache)
+ | (m, s, size, don, todo, fl)::orlist
+ when List.length(prop_only (d_goals todo)) > flags.maxwidth ->
+ debug_print (lazy ("FAIL: WIDTH"));
+ aux (orlist, cache)
+ | (m, s, size, don, todo, fl)::orlist when size > flags.maxsize ->
+ debug_print (lazy ("FAIL: SIZE: "^string_of_int size ^
+ " > " ^ string_of_int flags.maxsize ));
+ aux (orlist, cache)
+ | _ when Unix.gettimeofday () > flags.timeout ->
+ debug_print (lazy ("FAIL: TIMEOUT"));
+ Gaveup
+ | (m, s, size, don, (D (gno,depth,_ as g))::todo, fl)::orlist as status ->
+ debug_print (lazy "attack goal");
+ match calculate_goal_ty g s m with
+ | None ->
+ debug_print (lazy ("SUCCESS: SIDE EFFECT: " ^ string_of_int gno));
+ aux ((m,s,size,don,todo, fl)::orlist, cache)
+ | Some (canonical_ctx, gty) ->
+ debug_print (lazy ("EXAMINE: "^
+ NCicPp.ppterm ~metasenv:m ~subst:s ~context gty));
+ match cache_examine cache gty with
+ | `Failed_in d when d >= depth ->
+ debug_print (lazy ("FAIL: DEPTH (cache): "^string_of_int gno));
+ let cache = close_failures fl cache in
+ aux (orlist, cache)
+ | `UnderInspection ->
+ debug_print (lazy ("FAIL: LOOP: " ^ string_of_int gno));
+ let cache = close_failures fl cache in
+ aux (orlist,cache)
+ | `Succeded t ->
+ debug_print (lazy ("SUCCESS: CACHE HIT: " ^ string_of_int gno));
+ let s, m = put_in_subst s m g canonical_ctx t gty in
+ aux ((m, s, size, don,todo, fl)::orlist, cache)
+ | `Notfound
+ | `Failed_in _ when depth > 0 ->
+ ( (* more depth or is the first time we see the goal *)
+ if prunable m s gty todo then
+ (debug_print (lazy( "FAIL: LOOP: one father is equal"));
+ let cache = close_failures fl cache in
+ aux (orlist,cache))
+ else
+ let cache = cache_add_underinspection cache gty depth in
+ debug_print (lazy ("INSPECTING: " ^
+ string_of_int gno ^ "("^ string_of_int size ^ "): "^
+ NCicPp.ppterm ~metasenv:m ~subst:s ~context gty));
+ (* elems are possible computations for proving gty *)
+ let elems =
+ equational_and_applicative_case
+ signature status flags m s g gty cache context
+ in
+ if elems = [] then
+ (* this goal has failed *)
+ let cache = close_failures ((g,gty)::fl) cache in
+ aux (orlist, cache)
+ else
+ let size_gl l = List.length
+ (List.filter (function (_,_,P) -> true | _ -> false) l)
+ in
+ let elems =
+ let inj_gl gl = List.map (fun g -> D g) gl in
+ let rec map = function
+ | [] -> assert false
+ | (cand,m,s,gl)::[] ->
+ let todo =
+ inj_gl gl @ (S(g,gty,cand))::todo
+ in
+ (* we are the last in OR, we fail on g and
+ * also on all failures implied by g *)
+ (m,s, size + size_gl gl, don, todo, (g,gty)::fl)
+ :: orlist
+ | (cand,m,s,gl)::tl ->
+ let todo =
+ inj_gl gl @ (S(g,gty,cand))::todo
+ in
+ (m,s, size + size_gl gl, don, todo, []) :: map tl
+ in
+ map elems
+ in
+ aux (elems, cache))
+ | _ ->
+ debug_print (lazy ("FAIL: DEPTH: " ^ string_of_int gno));
+ let cache = close_failures fl cache in
+ aux (orlist, cache)
+ in
+ (aux (elems, cache) : auto_result)
+;;
+
let auto_tac ~params status =
prerr_endline "I teoremi noti sono";
NDiscriminationTree.DiscriminationTree.iter status#auto_cache
status
;;
+
(* ========================= dispatching of auto/auto_paramod ============ *)
let auto_tac ~params:(_,flags as params) =
if List.mem_assoc "paramodulation" flags then
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