X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fcomponents%2Fng_tactics%2FnnAuto.ml;h=f64bb20acef98da8b2a81d5cd07c0a4485050021;hb=12f96bd48b460d06f9858a334ee7c52d6831712f;hp=515622d4e02b054ae743c28ba81e27960fc7cf2e;hpb=1e5771907d96b66df32beb557bf775add3fb8dd7;p=helm.git diff --git a/helm/software/components/ng_tactics/nnAuto.ml b/helm/software/components/ng_tactics/nnAuto.ml index 515622d4e..f64bb20ac 100644 --- a/helm/software/components/ng_tactics/nnAuto.ml +++ b/helm/software/components/ng_tactics/nnAuto.ml @@ -11,12 +11,11 @@ open Printf -let debug = ref true -let debug_print ?(depth=0) s = - if !debug then prerr_endline (String.make depth '\t'^Lazy.force s) else () -(* let print= debug_print *) - let print ?(depth=0) s = +let debug = ref false +let print ?(depth=0) s = prerr_endline (String.make depth '\t'^Lazy.force s) +let debug_print ?(depth=0) s = + if !debug then print ~depth s else () let debug_do f = if !debug then f () else () @@ -53,27 +52,40 @@ let menv_closure status gl = in closure IntSet.empty gl ;; -(* we call a "fact" an object whose hypothesis occurs in the goal +(* we call a "fact" an object whose hypothesis occur in the goal or in types of goal-variables *) -let is_a_fact status ty = - let status, ty, _ = saturate ~delta:max_int status ty in +let is_a_fact status ty = + let status, ty, metas = saturate ~delta:0 status ty in + debug_print (lazy ("saturated ty :" ^ (ppterm status ty))); let g_metas = metas_of_term status ty in let clos = menv_closure status g_metas in - let _,_,metasenv,_,_ = status#obj in + (* let _,_,metasenv,_,_ = status#obj in *) let menv = List.fold_left - (fun acc (i,_) -> IntSet.add i acc) - IntSet.empty metasenv - in IntSet.equal clos menv;; + (fun acc m -> + let _, m = term_of_cic_term status m (ctx_of m) in + match m with + | NCic.Meta(i,_) -> IntSet.add i acc + | _ -> assert false) + IntSet.empty metas + in IntSet.subset menv clos;; let is_a_fact_obj s uri = let obj = NCicEnvironment.get_checked_obj uri in match obj with | (_,_,[],[],NCic.Constant(_,_,Some(t),ty,_)) -> - is_a_fact s (mk_cic_term [] ty) + is_a_fact s (mk_cic_term [] ty) (* aggiungere i costruttori *) | _ -> false +let is_a_fact_ast status subst metasenv ctx cand = + debug_print ~depth:0 + (lazy ("------- checking " ^ CicNotationPp.pp_term cand)); + let status, t = disambiguate status ctx ("",0,cand) None in + let status,t = term_of_cic_term status t ctx in + let ty = NCicTypeChecker.typeof subst metasenv ctx t in + is_a_fact status (mk_cic_term ctx ty) + let current_goal status = let open_goals = head_goals status#stack in assert (List.length open_goals = 1); @@ -83,69 +95,114 @@ let current_goal status = open_goal, ctx, gty - (* =============================== paramod =========================== *) -let auto_paramod ~params:(l,_) status goal = - let gty = get_goalty status goal in +let solve fast status eq_cache goal = + let f = + if fast then NCicParamod.fast_eq_check + else NCicParamod.paramod in let n,h,metasenv,subst,o = status#obj in - let status,t = term_of_cic_term status gty (ctx_of gty) in - let status, l = - List.fold_left - (fun (status, l) t -> - let status, t = disambiguate status (ctx_of gty) t None in - let status, ty = typeof status (ctx_of t) t in - let status, t = term_of_cic_term status t (ctx_of gty) in - let status, ty = term_of_cic_term status ty (ctx_of ty) in - (status, (t,ty) :: l)) - (status,[]) l - in - match - NCicParamod.nparamod status metasenv subst (ctx_of gty) (NCic.Rel ~-1,t) l - with - | [] -> raise (Error (lazy "no proof found",None)) - | (pt, metasenv, subst)::_ -> - let status = status#set_obj (n,h,metasenv,subst,o) in - instantiate status goal (mk_cic_term (ctx_of gty) pt) -;; - -let auto_paramod_tac ~params status = - NTactics.distribute_tac (auto_paramod ~params) status -;; - -let fast_eq_check_all status eq_cache goal = - let gty = get_goalty status goal in - let ctx = ctx_of gty in - let n,h,metasenv,subst,o = status#obj in - let status,t = term_of_cic_term status gty ctx in - let build_status (pt, metasenv, subst) = - let status = status#set_obj (n,h,metasenv,subst,o) in - let gty = get_goalty status goal in - instantiate status goal (mk_cic_term ctx pt) - in - List.map build_status - (NCicParamod.fast_eq_check status metasenv subst ctx - eq_cache (NCic.Rel ~-1,t)) + let gname, ctx, gty = List.assoc goal metasenv in + let gty = NCicUntrusted.apply_subst subst ctx gty in + let build_status (pt, _, metasenv, subst) = + try + debug_print (lazy ("refining: "^(NCicPp.ppterm ctx subst metasenv pt))); + let stamp = Unix.gettimeofday () in + let metasenv, subst, pt, pty = + NCicRefiner.typeof status + (* (status#set_coerc_db NCicCoercion.empty_db) *) + metasenv subst ctx pt None in + debug_print (lazy ("refined: "^(NCicPp.ppterm ctx subst metasenv pt))); + debug_print (lazy ("synt: "^(NCicPp.ppterm ctx subst metasenv pty))); + let metasenv, subst = + NCicUnification.unify status metasenv subst ctx gty pty + (* the previous code is much less expensive than directly refining + pt with expected type pty + in + prerr_endline ("exp: "^(NCicPp.ppterm ctx subst metasenv gty)); + NCicRefiner.typeof + (status#set_coerc_db NCicCoercion.empty_db) + metasenv subst ctx pt (Some gty) *) + in + debug_print (lazy (Printf.sprintf "Refined in %fs" + (Unix.gettimeofday() -. stamp))); + let status = status#set_obj (n,h,metasenv,subst,o) in + let metasenv = List.filter (fun j,_ -> j <> goal) metasenv in + let subst = (goal,(gname,ctx,pt,pty)) :: subst in + Some (status#set_obj (n,h,metasenv,subst,o)) + with + NCicRefiner.RefineFailure msg + | NCicRefiner.Uncertain msg -> + debug_print (lazy ("WARNING: refining in fast_eq_check failed" ^ + snd (Lazy.force msg))); None + | NCicRefiner.AssertFailure msg -> + debug_print (lazy ("WARNING: refining in fast_eq_check failed" ^ + Lazy.force msg)); None + | _ -> None + in + HExtlib.filter_map build_status + (f status metasenv subst ctx eq_cache (NCic.Rel ~-1,gty)) ;; let fast_eq_check eq_cache status goal = - match fast_eq_check_all status eq_cache goal with + match solve true status eq_cache goal with | [] -> raise (Error (lazy "no proof found",None)) | s::_ -> s ;; -let fast_eq_check_tac ~params s = - NTactics.distribute_tac (fast_eq_check s#eq_cache) s +let dist_fast_eq_check eq_cache s = + NTactics.distribute_tac (fast_eq_check eq_cache) s ;; let auto_eq_check eq_cache status = try - let s = - NTactics.distribute_tac (fast_eq_check eq_cache) status in + let s = dist_fast_eq_check eq_cache status in [s] with | Error _ -> [] ;; +(* warning: ctx is supposed to be already instantiated w.r.t subst *) +let index_local_equations eq_cache status = + debug_print (lazy "indexing equations"); + let open_goals = head_goals status#stack in + let open_goal = List.hd open_goals in + let ngty = get_goalty status open_goal in + let ctx = ctx_of ngty in + let c = ref 0 in + List.fold_left + (fun eq_cache _ -> + c:= !c+1; + let t = NCic.Rel !c in + try + let ty = NCicTypeChecker.typeof [] [] ctx t in + if is_a_fact status (mk_cic_term ctx ty) then + (debug_print(lazy("eq indexing " ^ (NCicPp.ppterm ctx [] [] ty))); + NCicParamod.forward_infer_step eq_cache t ty) + else + (debug_print (lazy ("not a fact: " ^ (NCicPp.ppterm ctx [] [] ty))); + eq_cache) + with + | NCicTypeChecker.TypeCheckerFailure _ + | NCicTypeChecker.AssertFailure _ -> eq_cache) + eq_cache ctx +;; + +let fast_eq_check_tac ~params s = + let unit_eq = index_local_equations s#eq_cache s in + dist_fast_eq_check unit_eq s +;; + +let paramod eq_cache status goal = + match solve false status eq_cache goal with + | [] -> raise (Error (lazy "no proof found",None)) + | s::_ -> s +;; + +let paramod_tac ~params s = + let unit_eq = index_local_equations s#eq_cache s in + NTactics.distribute_tac (paramod unit_eq) s +;; + (* let fast_eq_check_tac_all ~params eq_cache status = let g,_,_ = current_goal status in @@ -158,12 +215,23 @@ let fast_eq_check_tac_all ~params eq_cache status = ;; *) +(* +let demod status eq_cache goal = + let n,h,metasenv,subst,o = status#obj in + let gname, ctx, gty = List.assoc goal metasenv in + let gty = NCicUntrusted.apply_subst subst ctx gty in + +let demod_tac ~params s = + let unit_eq = index_local_equations s#eq_cache s in + dist_fast_eq_check unit_eq s +*) + (*************** subsumption ****************) let close_wrt_context = List.fold_left (fun ty ctx_entry -> - match ctx_entry with + match ctx_entry with | name, NCic.Decl t -> NCic.Prod(name,t,ty) | name, NCic.Def(bo, _) -> NCicSubstitution.subst bo ty) ;; @@ -172,9 +240,9 @@ let args_for_context ?(k=1) ctx = let _,args = List.fold_left (fun (n,l) ctx_entry -> - match ctx_entry with - | name, NCic.Decl t -> n+1,NCic.Rel(n)::l - | name, NCic.Def(bo, _) -> n+1,l) + match ctx_entry with + | name, NCic.Decl t -> n+1,NCic.Rel(n)::l + | name, NCic.Def(bo, _) -> n+1,l) (k,[]) ctx in args @@ -194,11 +262,11 @@ let refresh metasenv = (fun (metasenv,subst) (i,(iattr,ctx,ty)) -> let ikind = NCicUntrusted.kind_of_meta iattr in let metasenv,j,instance,ty = - NCicMetaSubst.mk_meta ~attrs:iattr - metasenv ctx ~with_type:ty ikind in + NCicMetaSubst.mk_meta ~attrs:iattr + metasenv ctx ~with_type:ty ikind in let s_entry = i,(iattr, ctx, instance, ty) in let metasenv = List.filter (fun x,_ -> i <> x) metasenv in - metasenv,s_entry::subst) + metasenv,s_entry::subst) (metasenv,[]) metasenv (* close metasenv returns a ground instance of all the metas in the @@ -210,24 +278,24 @@ let close_metasenv metasenv subst = let metasenv = NCicUntrusted.sort_metasenv subst metasenv in List.fold_left (fun (subst,objs) (i,(iattr,ctx,ty)) -> - let ty = NCicUntrusted.apply_subst subst ctx ty in + let ty = NCicUntrusted.apply_subst subst ctx ty in let ctx = - NCicUntrusted.apply_subst_context ~fix_projections:true - subst ctx in - let (uri,_,_,_,obj) as okind = - constant_for_meta ctx ty i in - try - NCicEnvironment.check_and_add_obj okind; - let iref = NReference.reference_of_spec uri NReference.Decl in - let iterm = - let args = args_for_context ctx in - if args = [] then NCic.Const iref - else NCic.Appl(NCic.Const iref::args) - in + NCicUntrusted.apply_subst_context ~fix_projections:true + subst ctx in + let (uri,_,_,_,obj) as okind = + constant_for_meta ctx ty i in + try + NCicEnvironment.check_and_add_obj okind; + let iref = NReference.reference_of_spec uri NReference.Decl in + let iterm = + let args = args_for_context ctx in + if args = [] then NCic.Const iref + else NCic.Appl(NCic.Const iref::args) + in (* prerr_endline (NCicPp.ppterm ctx [] [] iterm); *) - let s_entry = i, ([], ctx, iterm, ty) - in s_entry::subst,okind::objs - with _ -> assert false) + let s_entry = i, ([], ctx, iterm, ty) + in s_entry::subst,okind::objs + with _ -> assert false) (subst,[]) metasenv ;; @@ -242,13 +310,13 @@ let ground_instances status gl = try List.iter (fun i -> - let (_, ctx, t, _) = List.assoc i subst in - debug_print (lazy (NCicPp.ppterm ctx [] [] t)); - List.iter - (fun (uri,_,_,_,_) as obj -> - NCicEnvironment.invalidate_item (`Obj (uri, obj))) - objs; - ()) + let (_, ctx, t, _) = List.assoc i subst in + debug_print (lazy (NCicPp.ppterm ctx [] [] t)); + List.iter + (fun (uri,_,_,_,_) as obj -> + NCicEnvironment.invalidate_item (`Obj (uri, obj))) + objs; + ()) gl with Not_found -> assert false @@ -259,11 +327,11 @@ let replace_meta i args target = let rec aux k = function (* TODO: local context *) | NCic.Meta (j,lc) when i = j -> - (match args with - | [] -> NCic.Rel 1 - | _ -> let args = - List.map (NCicSubstitution.subst_meta lc) args in - NCic.Appl(NCic.Rel k::args)) + (match args with + | [] -> NCic.Rel 1 + | _ -> let args = + List.map (NCicSubstitution.subst_meta lc) args in + NCic.Appl(NCic.Rel k::args)) | NCic.Meta (j,lc) as m -> (match lc with _,NCic.Irl _ -> m @@ -282,8 +350,8 @@ let close_wrt_metasenv subst = (fun ty (i,(iattr,ctx,mty)) -> let mty = NCicUntrusted.apply_subst subst ctx mty in let ctx = - NCicUntrusted.apply_subst_context ~fix_projections:true - subst ctx in + NCicUntrusted.apply_subst_context ~fix_projections:true + subst ctx in let cty = close_wrt_context mty ctx in let name = "foo"^(string_of_int i) in let ty = NCicSubstitution.lift 1 ty in @@ -912,10 +980,10 @@ let smart_applicative_case dbd with | None, tables -> (* if normal application fails we try to be smart *) - (match try_smart_candidate dbd goalty + (match try_smart_candidate dbd goalty tables subst fake_proof goalno depth context cand - with - | None, tables -> tables, elems + with + | None, tables -> tables, elems | Some x, tables -> tables, x::elems) | Some x, tables -> tables, x::elems) (tables,[]) candidates @@ -976,14 +1044,14 @@ let prunable_for_size flags s m todo = | (S _)::tl -> aux b tl | (D (_,_,T))::tl -> aux b tl | (D g)::tl -> - (match calculate_goal_ty g s m with + (match calculate_goal_ty g s m with | None -> aux b tl - | Some (canonical_ctx, gty) -> + | 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) + ~consider_metas:false ~count_metas_occurrences:true gty in + let newb = b || gsize > flags.maxgoalsizefactor in + aux newb tl) | [] -> b in aux false todo @@ -1003,22 +1071,22 @@ let prunable ty 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*)) + (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 + (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 + (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); @@ -1029,8 +1097,8 @@ let prunable menv subst ty todo = prerr_endline (CicMetaSubst.ppsubst ~metasenv:menv variant); prerr_endline "---------- menv"; prerr_endline (CicMetaSubst.ppmetasenv [] menv); - no_progress variant tl) *) - else false)) + no_progress variant tl) *) + else false)) | _::tl -> no_progress variant tl in aux todo @@ -1059,8 +1127,8 @@ let let signature = List.fold_left (fun set g -> - MetadataConstraints.UriManagerSet.union set - (MetadataQuery.signature_of metasenv g) + MetadataConstraints.UriManagerSet.union set + (MetadataQuery.signature_of metasenv g) ) MetadataConstraints.UriManagerSet.empty gl in @@ -1104,8 +1172,8 @@ let auto dbd flags metasenv tables universe cache context metasenv gl = let signature = List.fold_left (fun set g -> - MetadataConstraints.UriManagerSet.union set - (MetadataQuery.signature_of metasenv g) + MetadataConstraints.UriManagerSet.union set + (MetadataQuery.signature_of metasenv g) ) MetadataConstraints.UriManagerSet.empty gl in @@ -1138,11 +1206,11 @@ let auto_tac ~(dbd:HSql.dbd) ~params:(univ,params) ~automation_cache (proof, goa 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) + CicTypeChecker.type_of_aux' metasenv context t + CicUniv.oblivion_ugraph + in + MetadataConstraints.UriManagerSet.union set + (MetadataConstraints.constants_of ty) ) signature univ in @@ -1179,6 +1247,47 @@ let auto_tac ~(dbd:HSql.dbd) ~params:(univ,params) ~automation_cache (proof, goa ;; *) +(****************** smart application ********************) + + +let smart_apply t unit_eq status g = + let n,h,metasenv,subst,o = status#obj in + let gname, ctx, gty = List.assoc g metasenv in + (* let ggty = mk_cic_term context gty in *) + let status, t = disambiguate status ctx t None in + let status,t = term_of_cic_term status t ctx in + let ty = NCicTypeChecker.typeof subst metasenv ctx t in + let ty,metasenv,args = NCicMetaSubst.saturate metasenv subst ctx ty 0 in + let metasenv,j,inst,_ = NCicMetaSubst.mk_meta metasenv ctx `IsTerm in + let status = status#set_obj (n,h,metasenv,subst,o) in + let pterm = if args=[] then t else NCic.Appl(t::args) in + let eq_coerc = + let uri = + NUri.uri_of_string "cic:/matita/ng/Plogic/equality/eq_coerc.con" in + let ref = NReference.reference_of_spec uri (NReference.Def(2)) in + NCic.Const ref + in + let smart = + NCic.Appl[eq_coerc;ty;NCic.Implicit `Type;pterm;inst] in + let smart = mk_cic_term ctx smart in + try + let status = instantiate status g smart in + let _,_,metasenv,subst,_ = status#obj in + let _,ctx,jty = List.assoc j metasenv in + let jty = NCicUntrusted.apply_subst subst ctx jty in + debug_print(lazy("goal " ^ (NCicPp.ppterm ctx [] [] jty))); + fast_eq_check unit_eq status j + with + | Error _ as e -> debug_print (lazy "error"); raise e + +let smart_apply_tac t s = + let unit_eq = index_local_equations s#eq_cache s in + NTactics.distribute_tac (smart_apply t unit_eq) s + +let smart_apply_auto t eq_cache = + NTactics.distribute_tac (smart_apply t eq_cache) + + (****************** types **************) @@ -1191,8 +1300,8 @@ let keys_of_term status t = let keys = let _, ty = term_of_cic_term status ty (ctx_of ty) in match ty with - | NCic.Const (NReference.Ref (_,NReference.Def h)) - | NCic.Appl (NCic.Const(NReference.Ref(_,NReference.Def h))::_) + | NCic.Const (NReference.Ref (_,(NReference.Def h | NReference.Fix (_,_,h)))) + | NCic.Appl (NCic.Const(NReference.Ref(_,(NReference.Def h | NReference.Fix (_,_,h))))::_) when h > 0 -> let _,ty,_= saturate status ~delta:(h-1) orig_ty in ty::keys @@ -1214,8 +1323,8 @@ let mk_th_cache status gl = List.fold_left (fun (status, i, idx) _ -> let t = mk_cic_term ctx (NCic.Rel i) in - debug_print(lazy("indexing: "^ppterm status t)); let status, keys = keys_of_term status t in + debug_print(lazy("indexing: "^ppterm status t ^ ": " ^ string_of_int (List.length keys))); let idx = List.fold_left (fun idx k -> InvRelDiscriminationTree.index idx k t) idx keys @@ -1242,6 +1351,19 @@ let add_to_th t c ty = replace c ;; +let rm_from_th t c ty = + let key_c = ctx_of t in + if not (List.mem_assq key_c c) then assert false + else + let rec replace = function + | [] -> [] + | (x, idx) :: tl when x == key_c -> + (x, InvRelDiscriminationTree.remove_index idx ty t) :: tl + | x :: tl -> x :: replace tl + in + replace c +;; + let pp_idx status idx = InvRelDiscriminationTree.iter idx (fun k set -> @@ -1263,7 +1385,7 @@ let pp_th status = let search_in_th gty th = let c = ctx_of gty in let rec aux acc = function - | [] -> Ncic_termSet.elements acc + | [] -> (* Ncic_termSet.elements *) acc | (_::tl) as k -> try let idx = List.assq k th in @@ -1278,6 +1400,7 @@ let search_in_th gty th = type flags = { do_types : bool; (* solve goals in Type *) + last : bool; (* last goal: take first solution only *) maxwidth : int; maxsize : int; maxdepth : int; @@ -1286,7 +1409,7 @@ type flags = { type cache = {facts : th_cache; (* positive results *) - under_inspection : th_cache; (* to prune looping *) + under_inspection : cic_term list * th_cache; (* to prune looping *) unit_eq : NCicParamod.state } @@ -1299,6 +1422,65 @@ exception Gaveup of IntSet.t (* a sublist of unprovable conjunctive atoms of the input goals *) exception Proved of NTacStatus.tac_status +let height_of_ref (NReference.Ref (uri, x)) = + match x with + | NReference.Decl + | NReference.Ind _ + | NReference.Con _ + | NReference.CoFix _ -> + let _,height,_,_,_ = NCicEnvironment.get_checked_obj uri in + height + | NReference.Def h -> h + | NReference.Fix (_,_,h) -> h +;; + +let fast_height_of_term t = + let h = ref 0 in + let rec aux = + function + NCic.Meta (_,(_,NCic.Ctx l)) -> List.iter aux l + | NCic.Meta _ -> () + | NCic.Rel _ + | NCic.Sort _ -> () + | NCic.Implicit _ -> assert false + | NCic.Const nref as t -> +(* + prerr_endline (NCicPp.ppterm ~metasenv:[] ~subst:[] + ~context:[] t ^ ":" ^ string_of_int (height_of_ref nref)); +*) + h := max !h (height_of_ref nref) + | NCic.Prod (_,t1,t2) + | NCic.Lambda (_,t1,t2) -> aux t1; aux t2 + | NCic.LetIn (_,s,ty,t) -> aux s; aux ty; aux t + | NCic.Appl l -> List.iter aux l + | NCic.Match (_,outty,t,pl) -> aux outty; aux t; List.iter aux pl + in + aux t; !h +;; + +let height_of_goals status = + let open_goals = head_goals status#stack in + assert (List.length open_goals > 0); + let h = ref 1 in + List.iter + (fun open_goal -> + let ty = get_goalty status open_goal in + let context = ctx_of ty in + let _, ty = term_of_cic_term status ty (ctx_of ty) in + h := max !h (fast_height_of_term ty); + List.iter + (function + | _, NCic.Decl ty -> h := max !h (fast_height_of_term ty) + | _, NCic.Def (bo,ty) -> + h := max !h (fast_height_of_term ty); + h := max !h (fast_height_of_term bo); + ) + context) + open_goals; + prerr_endline ("altezza sequente: " ^ string_of_int !h); + !h +;; + (* let close_failures _ c = c;; *) (* let prunable _ _ _ = false;; *) (* let cache_examine cache gty = `Notfound;; *) @@ -1306,14 +1488,29 @@ exception Proved of NTacStatus.tac_status (* let add_to_cache_and_del_from_orlist_if_green_cut _ _ c _ _ o f _ = c, o, f, false ;; *) (* let cache_add_underinspection c _ _ = c;; *) -let init_cache ?(facts=[]) ?(under_inspection=[]) +let init_cache ?(facts=[]) ?(under_inspection=[],[]) ?(unit_eq=NCicParamod.empty_state) _ = {facts = facts; under_inspection = under_inspection; unit_eq = unit_eq } -let only _ _ _ = true;; +let only signature _context candidate = + (* TASSI: nel trie ci mettiamo solo il body, non il ty *) + let candidate_ty = + NCicTypeChecker.typeof ~subst:[] ~metasenv:[] [] candidate + in + let height = fast_height_of_term candidate_ty in + let rc = signature >= height in + if rc = false then + debug_print (lazy ("Filtro: " ^ NCicPp.ppterm ~context:[] ~subst:[] + ~metasenv:[] candidate ^ ": " ^ string_of_int height)) + else + debug_print (lazy ("Tengo: " ^ NCicPp.ppterm ~context:[] ~subst:[] + ~metasenv:[] candidate ^ ": " ^ string_of_int height)); + + rc +;; let candidate_no = ref 0;; @@ -1322,53 +1519,125 @@ let openg_no status = List.length (head_goals status#stack) let sort_new_elems l = List.sort (fun (_,s1) (_,s2) -> openg_no s1 - openg_no s2) l -let try_candidate flags depth status t = +let try_candidate ?(smart=0) flags depth status eq_cache t = try - debug_print ~depth (lazy ("try " ^ CicNotationPp.pp_term t)); - let status = NTactics.apply_tac ("",0,t) status in - let og_no = openg_no status in - if og_no > flags.maxwidth || - (depth = flags.maxdepth && og_no <> 0) then - (debug_print ~depth (lazy "pruned immediately"); None) + debug_print ~depth (lazy ("------------ try " ^ CicNotationPp.pp_term t)); + let status = + if smart= 0 then NTactics.apply_tac ("",0,t) status + else if smart = 1 then smart_apply_auto ("",0,t) eq_cache status + else (* smart = 2: both *) + try NTactics.apply_tac ("",0,t) status + with Error _ -> + smart_apply_auto ("",0,t) eq_cache status in + let og_no = openg_no status in + if (* og_no > flags.maxwidth || *) + ((depth + 1) = flags.maxdepth && og_no <> 0) then + (debug_print ~depth (lazy "pruned immediately"); None) else (incr candidate_no; Some ((!candidate_no,t),status)) with Error (msg,exn) -> debug_print ~depth (lazy "failed"); None ;; -let get_candidates status cache signature gty = +let get_candidates ?(smart=true) status cache signature gty = let universe = status#auto_cache in let context = ctx_of gty in + let t_ast t = + let _status, t = term_of_cic_term status t context + in Ast.NCic t in + let c_ast = function + | NCic.Const r -> Ast.NRef r | _ -> assert false in let _, raw_gty = term_of_cic_term status gty context in let cands = NDiscriminationTree.DiscriminationTree.retrieve_unifiables - universe raw_gty - in - let cands = - List.filter (only signature context) - (NDiscriminationTree.TermSet.elements cands) + universe raw_gty in + let local_cands = search_in_th gty cache in + debug_print (lazy ("candidates for" ^ NTacStatus.ppterm status gty)); + debug_print (lazy ("local cands = " ^ (string_of_int (List.length (Ncic_termSet.elements local_cands))))); + let together global local = + List.map c_ast + (List.filter (only signature context) + (NDiscriminationTree.TermSet.elements global)) @ + List.map t_ast (Ncic_termSet.elements local) in + let candidates = together cands local_cands in + let smart_candidates = + if smart then + match raw_gty with + | NCic.Appl (hd::tl) -> + let weak_gty = + NCic.Appl (hd:: HExtlib.mk_list(NCic.Meta (0,(0,NCic.Irl 0))) + (List.length tl)) in + let more_cands = + NDiscriminationTree.DiscriminationTree.retrieve_unifiables + universe weak_gty in + let smart_cands = + NDiscriminationTree.TermSet.diff more_cands cands in + let cic_weak_gty = mk_cic_term context weak_gty in + let more_local_cands = search_in_th cic_weak_gty cache in + let smart_local_cands = + Ncic_termSet.diff more_local_cands local_cands in + together smart_cands smart_local_cands + | _ -> [] + else [] in - List.map (fun t -> - let _status, t = term_of_cic_term status t context in Ast.NCic t) - (search_in_th gty cache) - @ - List.map (function NCic.Const r -> Ast.NRef r | _ -> assert false) cands + candidates, smart_candidates ;; let applicative_case depth signature status flags gty (cache:cache) = - let tcache = cache.facts in app_counter:= !app_counter+1; - let candidates = get_candidates status tcache signature gty in + let _,_,metasenv,subst,_ = status#obj in + let context = ctx_of gty in + let tcache = cache.facts in + let is_eq = + let status, t = term_of_cic_term status gty context in + NCicParamod.is_equation metasenv subst context t + in + debug_print(lazy (string_of_bool is_eq)); + let candidates, smart_candidates = + get_candidates ~smart:(not is_eq) status tcache signature gty in debug_print ~depth (lazy ("candidates: " ^ string_of_int (List.length candidates))); - let elems = + debug_print ~depth + (lazy ("smart candidates: " ^ + string_of_int (List.length smart_candidates))); +(* + let sm = 0 in + let smart_candidates = [] in *) + let sm = if is_eq then 0 else 2 in + let maxd = ((depth + 1) = flags.maxdepth) in + let only_one = flags.last && maxd in + debug_print (lazy ("only_one: " ^ (string_of_bool only_one))); + debug_print (lazy ("maxd: " ^ (string_of_bool maxd))); + let elems = List.fold_left (fun elems cand -> - match try_candidate flags depth status cand with - | None -> elems - | Some x -> x::elems) + if (only_one && (elems <> [])) then elems + else + if (maxd && not(is_a_fact_ast status subst metasenv context cand)) + then (debug_print (lazy "pruned: not a fact"); elems) + else + match try_candidate (~smart:sm) + flags depth status cache.unit_eq cand with + | None -> elems + | Some x -> x::elems) [] candidates in - elems + let more_elems = + if only_one && elems <> [] then elems + else + List.fold_left + (fun elems cand -> + if (only_one && (elems <> [])) then elems + else + if (maxd && not(is_a_fact_ast status subst metasenv context cand)) + then (debug_print (lazy "pruned: not a fact"); elems) + else + match try_candidate (~smart:1) + flags depth status cache.unit_eq cand with + | None -> elems + | Some x -> x::elems) + [] smart_candidates + in + elems@more_elems ;; exception Found @@ -1377,7 +1646,7 @@ exception Found (* gty is supposed to be meta-closed *) let is_subsumed depth status gty cache = if cache=[] then false else ( - debug_print ~depth (lazy("Subsuming " ^ (ppterm status gty))); + print ~depth (lazy("Subsuming " ^ (ppterm status gty))); let n,h,metasenv,subst,obj = status#obj in let ctx = ctx_of gty in let _ , target = term_of_cic_term status gty ctx in @@ -1387,57 +1656,35 @@ let is_subsumed depth status gty cache = try let idx = List.assq ctx cache in Ncic_termSet.elements - (InvRelDiscriminationTree.retrieve_generalizations idx gty) + (InvRelDiscriminationTree.retrieve_generalizations idx gty) with Not_found -> [] in debug_print ~depth (lazy ("failure candidates: " ^ string_of_int (List.length candidates))); try List.iter - (fun t -> - let _ , source = term_of_cic_term status t ctx in - let implication = - NCic.Prod("foo",source,target) in - let metasenv,j,_,_ = - NCicMetaSubst.mk_meta - metasenv ctx ~with_type:implication `IsType in - let status = status#set_obj (n,h,metasenv,subst,obj) in - let status = status#set_stack [([1,Open j],[],[],`NoTag)] in - try - let status = NTactics.intro_tac "foo" status in - let status = - NTactics.apply_tac ("",0,Ast.NCic (NCic.Rel 1)) status - in - if (head_goals status#stack = []) then raise Found - else () + (fun t -> + let _ , source = term_of_cic_term status t ctx in + let implication = + NCic.Prod("foo",source,target) in + let metasenv,j,_,_ = + NCicMetaSubst.mk_meta + metasenv ctx ~with_type:implication `IsType in + let status = status#set_obj (n,h,metasenv,subst,obj) in + let status = status#set_stack [([1,Open j],[],[],`NoTag)] in + try + let status = NTactics.intro_tac "foo" status in + let status = + NTactics.apply_tac ("",0,Ast.NCic (NCic.Rel 1)) status + in + if (head_goals status#stack = []) then raise Found + else () with - | Error _ -> ()) - candidates;false + | Error _ -> ()) + candidates;false with Found -> debug_print ~depth (lazy "success");true) ;; -(* warning: ctx is supposed to be already instantiated w.r.t subst *) -let index_local_equations eq_cache status = - let open_goals = head_goals status#stack in -(* assert (List.length open_goals = 1); *) - let open_goal = List.hd open_goals in - let ngty = get_goalty status open_goal in - let ctx = ctx_of ngty in - let c = ref 0 in - List.fold_left - (fun eq_cache _ -> - c:= !c+1; - let t = NCic.Rel !c in - try - let ty = NCicTypeChecker.typeof [] [] ctx t in - prerr_endline ("eq indexing " ^ (NCicPp.ppterm ctx [] [] ty)); - NCicParamod.forward_infer_step eq_cache t ty - with - | NCicTypeChecker.TypeCheckerFailure _ - | NCicTypeChecker.AssertFailure _ -> eq_cache) - eq_cache ctx -;; - let rec guess_name name ctx = if name = "_" then guess_name "auto" ctx else if not (List.mem_assoc name ctx) then name else @@ -1465,24 +1712,22 @@ let intro ~depth status facts name = let rec intros_facts ~depth status facts = match is_prod status with | Some(name) -> - let status,facts = - intro ~depth status facts name - in intros_facts ~depth status facts + let status,facts = + intro ~depth status facts name + in intros_facts ~depth status facts | _ -> status, facts ;; let rec intros ~depth status (cache:cache) = match is_prod status with | Some _ -> - prerr_endline "is prod"; - let status,facts = - intros_facts ~depth status cache.facts - in - (* we reindex the equation from scratch *) - let unit_eq = - index_local_equations status#eq_cache status in - (* under_inspection must be set to empty *) - status, init_cache ~facts ~unit_eq () + let status,facts = + intros_facts ~depth status cache.facts + in + (* we reindex the equation from scratch *) + let unit_eq = + index_local_equations status#eq_cache status in + status, init_cache ~facts ~unit_eq () | _ -> status, cache ;; @@ -1499,6 +1744,9 @@ let reduce ~depth status g = (g,(attr,ctx,ty'))::(List.filter (fun (i,_) -> i<>g) metasenv) in let status = status#set_obj (n,h,metasenv,subst,o) in + (* we merge to gain a depth level; the previous goal level should + be empty *) + let status = NTactics.merge_tac status in incr candidate_no; [(!candidate_no,Ast.Ident("__whd",None)),status]) ;; @@ -1507,19 +1755,22 @@ let do_something signature flags status g depth gty cache = (* whd *) let l = reduce ~depth status g in (* backward aplications *) - let l1 = applicative_case depth signature status flags gty cache in - (* fast paramodulation *) - let l2 = [] in -(* + let l1 = List.map (fun s -> - incr candidate_no; - ((!candidate_no,Ast.Ident("__paramod",None)),s)) - (auto_eq_check cache.unit_eq status) + incr candidate_no; + ((!candidate_no,Ast.Ident("__paramod",None)),s)) + (auto_eq_check cache.unit_eq status) in -*) - (* states in l2 have have an set of subgoals: no point to sort them *) - l2 @ (sort_new_elems (l@l1)), cache + let l2 = + (* if (l1 <> []) then [] else *) + applicative_case depth signature status flags gty cache + (* fast paramodulation *) + in + (* states in l1 have have an empty set of subgoals: no point to sort them *) + debug_print ~depth + (lazy ("alternatives = " ^ (string_of_int (List.length (l1@l@l2))))); + l1 @ (sort_new_elems (l@l2)), cache ;; let pp_goal = function @@ -1531,8 +1782,8 @@ let pp_goals status l = String.concat ", " (List.map (fun i -> - let gty = get_goalty status i in - NTacStatus.ppterm status gty) + let gty = get_goalty status i in + NTacStatus.ppterm status gty) l) ;; @@ -1552,20 +1803,20 @@ let sort_tac status = | [] -> assert false | (goals, t, k, tag) :: s -> let g = head_goals status#stack in - let sortedg = - (List.rev (MS.topological_sort g (deps status))) in + let sortedg = + (List.rev (MS.topological_sort g (deps status))) in debug_print (lazy ("old g = " ^ String.concat "," (List.map string_of_int g))); debug_print (lazy ("sorted goals = " ^ - String.concat "," (List.map string_of_int sortedg))); - let is_it i = function - | (_,Continuationals.Stack.Open j ) + String.concat "," (List.map string_of_int sortedg))); + let is_it i = function + | (_,Continuationals.Stack.Open j ) | (_,Continuationals.Stack.Closed j ) -> i = j - in - let sorted_goals = - List.map (fun i -> List.find (is_it i) goals) sortedg - in - (sorted_goals, t, k, tag) :: s + in + let sorted_goals = + List.map (fun i -> List.find (is_it i) goals) sortedg + in + (sorted_goals, t, k, tag) :: s in status#set_stack gstatus ;; @@ -1576,11 +1827,11 @@ let clean_up_tac status = | [] -> assert false | (g, t, k, tag) :: s -> let is_open = function - | (_,Continuationals.Stack.Open _) -> true + | (_,Continuationals.Stack.Open _) -> true | (_,Continuationals.Stack.Closed _) -> false - in - let g' = List.filter is_open g in - (g', t, k, tag) :: s + in + let g' = List.filter is_open g in + (g', t, k, tag) :: s in status#set_stack gstatus ;; @@ -1591,125 +1842,167 @@ let focus_tac focus status = | [] -> assert false | (g, t, k, tag) :: s -> let in_focus = function - | (_,Continuationals.Stack.Open i) + | (_,Continuationals.Stack.Open i) | (_,Continuationals.Stack.Closed i) -> List.mem i focus - in + in let focus,others = List.partition in_focus g - in + in + (* we need to mark it as a BranchTag, otherwise cannot merge later *) + (focus,[],[],`BranchTag) :: (others, t, k, tag) :: s + in + status#set_stack gstatus +;; + +let deep_focus_tac level focus status = + let in_focus = function + | (_,Continuationals.Stack.Open i) + | (_,Continuationals.Stack.Closed i) -> List.mem i focus + in + let rec slice level gs = + if level = 0 then [],[],gs else + match gs with + | [] -> assert false + | (g, t, k, tag) :: s -> + let f,o,gs = slice (level-1) s in + let f1,o1 = List.partition in_focus g + in (* we need to mark it as a BranchTag, otherwise cannot merge later *) - (focus,[],[],`BranchTag) :: (others, t, k, tag) :: s + (f1,[],[],`BranchTag)::f, (o1, t, k, tag)::o, gs + in + let gstatus = + let f,o,s = slice level status#stack in f@o@s in status#set_stack gstatus ;; -let rec auto_clusters +let open_goals level status = + let rec aux level gs = + if level = 0 then [] + else match gs with + | [] -> assert false + | _ :: s -> head_goals gs @ aux (level-1) s + in + aux level status#stack +;; + +let rec auto_clusters ?(top=false) flags signature cache depth status : unit = - debug_print ~depth (lazy "entering auto clusters"); + debug_print ~depth (lazy ("entering auto clusters at depth " ^ + (string_of_int depth))); (* ignore(Unix.select [] [] [] 0.01); *) let status = clean_up_tac status in let goals = head_goals status#stack in - if goals = [] then raise (Proved status) - else if depth = flags.maxdepth then raise (Gaveup IntSet.empty) + if goals = [] then + if depth = 0 then raise (Proved status) + else + let status = NTactics.merge_tac status in + auto_clusters flags signature (cache:cache) (depth-1) status else if List.length goals < 2 then auto_main flags signature cache depth status else + let all_goals = open_goals (depth+1) status in debug_print ~depth (lazy ("goals = " ^ - String.concat "," (List.map string_of_int goals))); - let classes = HExtlib.clusters (deps status) goals in + String.concat "," (List.map string_of_int all_goals))); + let classes = HExtlib.clusters (deps status) all_goals in + let classes = if top then List.rev classes else classes in debug_print ~depth - (lazy - (String.concat "\n" - (List.map - (fun l -> - ("cluster:" ^ String.concat "," (List.map string_of_int l))) - classes))); - let status = - List.fold_left - (fun status gl -> - let status = focus_tac gl status in - try + (lazy + (String.concat "\n" + (List.map + (fun l -> + ("cluster:" ^ String.concat "," (List.map string_of_int l))) + classes))); + let status,b = + List.fold_left + (fun (status,b) gl -> + let lold = List.length status#stack in + debug_print ~depth (lazy ("stack length = " ^ + (string_of_int lold))); + let fstatus = deep_focus_tac (depth+1) gl status in + try debug_print ~depth (lazy ("focusing on" ^ - String.concat "," (List.map string_of_int gl))); - auto_main flags signature cache depth status; status - with Proved(status) -> NTactics.merge_tac status) - status classes - in raise (Proved status) + String.concat "," (List.map string_of_int gl))); + auto_main flags signature cache depth fstatus; assert false + with + | Proved(status) -> + let status = NTactics.merge_tac status in + let lnew = List.length status#stack in + assert (lold = lnew); + (status,true) + | Gaveup _ when top -> (status,b) + ) + (status,false) classes + in + let rec final_merge n s = + if n = 0 then s else final_merge (n-1) (NTactics.merge_tac s) + in let status = final_merge depth status + in if b then raise (Proved status) else raise (Gaveup IntSet.empty) and - -(* let rec auto_main flags signature cache status k depth = *) - + +(* BRAND NEW VERSION *) auto_main flags signature (cache:cache) depth status: unit = debug_print ~depth (lazy "entering auto main"); + debug_print ~depth (lazy ("stack length = " ^ + (string_of_int (List.length status#stack)))); (* ignore(Unix.select [] [] [] 0.01); *) let status = sort_tac (clean_up_tac status) in let goals = head_goals status#stack in match goals with - | [] -> raise (Proved status) - | _ -> - let branch = List.length(goals)>1 in - if depth = flags.maxdepth then raise (Gaveup IntSet.empty) + | [] when depth = 0 -> raise (Proved status) + | [] -> + let status = NTactics.merge_tac status in + let cache = + let l,tree = cache.under_inspection in + match l with + | [] -> assert false + | a::tl -> let tree = rm_from_th a tree a in + {cache with under_inspection = tl,tree} + in + auto_clusters flags signature (cache:cache) (depth-1) status + | orig::_ -> + let ng = List.length goals in + if ng > flags.maxwidth then + (print (lazy "FAIL WIDTH"); raise (Gaveup IntSet.empty)) + else if depth = flags.maxdepth then raise (Gaveup IntSet.empty) else - let status = - if branch then NTactics.branch_tac status - else status in + let status = NTactics.branch_tac ~force:true status in let status, cache = intros ~depth status cache in let g,gctx, gty = current_goal status in - let ctx,ty = close status g in - let closegty = mk_cic_term ctx ty in + let ctx,ty = close status g in + let closegty = mk_cic_term ctx ty in let status, gty = apply_subst status gctx gty in - debug_print ~depth (lazy("Attacking goal " ^ (string_of_int g) ^" : "^ppterm status gty)); - if is_subsumed depth status closegty cache.under_inspection then - (debug_print (lazy "SUBSUMED"); - raise (Gaveup IntSet.add g IntSet.empty)) - else - let alternatives, cache = - do_something signature flags status g depth gty cache in - let loop_cache = - let under_inspection = - add_to_th closegty cache.under_inspection closegty in - {cache with under_inspection = under_inspection} in - let unsat = - List.fold_left - (* the underscore information does not need to be returned - by do_something *) - (fun unsat ((_,t),status) -> - let depth',looping_cache = - if t=Ast.Ident("__whd",None) then depth,cache - else depth+1, loop_cache in - debug_print (~depth:depth') - (lazy ("Case: " ^ CicNotationPp.pp_term t)); - try auto_clusters flags signature loop_cache - depth' status; unsat - with - | Proved status -> - debug_print (~depth:depth') (lazy "proved"); - if branch then - let status = NTactics.merge_tac status - in - (* old cache, here *) - try auto_clusters flags signature cache - depth status; assert false - with Gaveup f -> - debug_print ~depth - (lazy ("Unsat1 at depth " ^ (string_of_int depth) - ^ ": " ^ - (pp_goals status (IntSet.elements f)))); - (* TODO: cache failures *) - IntSet.union f unsat - else raise (Proved status) - | Gaveup f -> - debug_print (~depth:depth') - (lazy ("Unsat2 at depth " ^ (string_of_int depth') - ^ ": " ^ - (pp_goals status (IntSet.elements f)))); - (* TODO: cache local failures *) - unsat) - IntSet.empty alternatives - in - raise (Gaveup IntSet.add g unsat) -;; - + debug_print ~depth (lazy("Attacking goal " ^ (string_of_int g) ^" : "^ppterm status gty)); + if is_subsumed depth status closegty (snd cache.under_inspection) then + (print ~depth (lazy "SUBSUMED"); + raise (Gaveup IntSet.add g IntSet.empty)) + else + let do_flags = + {flags with last = flags.last && ng=1} in + let alternatives, cache = + do_something signature do_flags status g depth gty cache in + let loop_cache = + let l,tree = cache.under_inspection in + let l,tree = closegty::l, add_to_th closegty tree closegty in + {cache with under_inspection = l,tree} in + List.iter + (fun ((_,t),status) -> + debug_print ~depth + (lazy("(re)considering goal " ^ + (string_of_int g) ^" : "^ppterm status gty)); + debug_print (~depth:depth) + (lazy ("Case: " ^ CicNotationPp.pp_term t)); + let depth,cache = + if t=Ast.Ident("__whd",None) then depth, cache + else depth+1,loop_cache in + try + auto_clusters flags signature (cache:cache) depth status + with Gaveup _ -> + debug_print ~depth (lazy "Failed");()) + alternatives; + raise (Gaveup IntSet.empty) +;; + let int name l def = try int_of_string (List.assoc name l) with Failure _ | Not_found -> def @@ -1734,11 +2027,12 @@ let auto_tac ~params:(_univ,flags) status = *) let depth = int "depth" flags 3 in let size = int "size" flags 10 in - let width = int "width" flags (3+List.length goals) in + let width = int "width" flags 4 (* (3+List.length goals)*) in (* XXX fix sort *) - let goals = List.map (fun i -> (i,P)) goals in - let signature = () in +(* let goals = List.map (fun i -> (i,P)) goals in *) + let signature = height_of_goals status in let flags = { + last = true; maxwidth = width; maxsize = size; maxdepth = depth; @@ -1751,30 +2045,33 @@ let auto_tac ~params:(_univ,flags) status = if x > y then (print(lazy ("TIME ELAPSED:"^string_of_float(Unix.gettimeofday()-.initial_time))); - print(lazy + debug_print(lazy ("Applicative nodes:"^string_of_int !app_counter)); raise (Error (lazy "auto gave up", None))) else let _ = debug_print (lazy("\n\nRound "^string_of_int x^"\n")) in let flags = { flags with maxdepth = x } in - try auto_clusters flags signature cache 0 status;assert false - with - | Gaveup _ -> up_to (x+1) y - | Proved s -> - print (lazy ("proved at depth " ^ string_of_int x)); + try auto_clusters (~top:true) flags signature cache 0 status;assert false +(* + try auto_main flags signature cache 0 status;assert false +*) + with + | Gaveup _ -> up_to (x+1) y + | Proved s -> + debug_print (lazy ("proved at depth " ^ string_of_int x)); let stack = - match s#stack with - | (g,t,k,f) :: rest -> (filter_open g,t,k,f):: rest - | _ -> assert false + match s#stack with + | (g,t,k,f) :: rest -> (filter_open g,t,k,f):: rest + | _ -> assert false in - let s = s#set_stack stack in - oldstatus#set_status s + let s = s#set_stack stack in + oldstatus#set_status s in let s = up_to depth depth in - print(lazy + debug_print(lazy ("TIME ELAPSED:"^string_of_float(Unix.gettimeofday()-.initial_time))); - print(lazy + debug_print(lazy ("Applicative nodes:"^string_of_int !app_counter)); s ;;