From: Andrea Asperti Date: Fri, 13 Nov 2009 07:23:48 +0000 (+0000) Subject: Added the new auto version (not attached yet). X-Git-Tag: make_still_working~3209 X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=e97c74e4d17e6fc0ce7c39b092f3214244ae21d1;p=helm.git Added the new auto version (not attached yet). --- diff --git a/helm/software/components/ng_tactics/nnAuto.ml b/helm/software/components/ng_tactics/nnAuto.ml new file mode 100644 index 000000000..4d6d7f886 --- /dev/null +++ b/helm/software/components/ng_tactics/nnAuto.ml @@ -0,0 +1,1417 @@ +(* + ||M|| This file is part of HELM, an Hypertextual, Electronic + ||A|| Library of Mathematics, developed at the Computer Science + ||T|| Department, University of Bologna, Italy. + ||I|| + ||T|| HELM is free software; you can redistribute it and/or + ||A|| modify it under the terms of the GNU General Public License + \ / version 2 or (at your option) any later version. + \ / This software is distributed as is, NO WARRANTY. + V_______________________________________________________________ *) + +open Printf + +let debug = ref false +let debug_print ?(depth=0) s = + if !debug then prerr_endline (String.make depth '\t'^Lazy.force s) else () +let print ?(depth=0) s = + prerr_endline (String.make depth '\t'^Lazy.force s) +let debug_do f = if !debug then f () else () + +open Continuationals.Stack +open NTacStatus +module Ast = CicNotationPt +let app_counter = ref 0 + +(* =================================== paramod =========================== *) +let auto_paramod ~params:(l,_) status goal = + let gty = get_goalty status goal 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 +;; + +(* =================================== 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")) +;; +*) + +(****************** types **************) +type th_cache = (NCic.context * InvRelDiscriminationTree.t) list + +let keys_of_term status t = + let status, orig_ty = typeof status (ctx_of t) t in + let _, ty, _ = saturate ~delta:max_int status orig_ty in + let keys = [ty] in + 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))::_) + when h > 0 -> + let _,ty,_= saturate status ~delta:(h-1) orig_ty in + ty::keys + | _ -> keys + in + status, keys +;; + +let mk_th_cache status gl = + List.fold_left + (fun (status, acc) g -> + let gty = get_goalty status g in + let ctx = ctx_of gty in + debug_print(lazy("th cache for: "^ppterm status gty)); + debug_print(lazy("th cache in: "^ppcontext status ctx)); + if List.mem_assq ctx acc then status, acc else + let idx = InvRelDiscriminationTree.empty in + let status,_,idx = + 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 + let idx = + List.fold_left (fun idx k -> + InvRelDiscriminationTree.index idx k t) idx keys + in + status, i+1, idx) + (status, 1, idx) ctx + in + status, (ctx, idx) :: acc) + (status,[]) gl +;; + +let add_to_th t c ty = + let key_c = ctx_of t in + if not (List.mem_assq key_c c) then + (key_c ,InvRelDiscriminationTree.index + InvRelDiscriminationTree.empty ty t ) :: c + else + let rec replace = function + | [] -> [] + | (x, idx) :: tl when x == key_c -> + (x, InvRelDiscriminationTree.index idx ty t) :: tl + | x :: tl -> x :: replace tl + in + replace c +;; + +let pp_idx status idx = + InvRelDiscriminationTree.iter idx + (fun k set -> + debug_print(lazy("K: " ^ NCicInverseRelIndexable.string_of_path k)); + Ncic_termSet.iter + (fun t -> debug_print(lazy("\t"^ppterm status t))) + set) +;; + +let pp_th status = + List.iter + (fun ctx, idx -> + debug_print(lazy( "-----------------------------------------------")); + debug_print(lazy( (NCicPp.ppcontext ~metasenv:[] ~subst:[] ctx))); + debug_print(lazy( "||====> ")); + pp_idx status idx) +;; + + +let search_in_th gty th = + let c = ctx_of gty in + let rec aux acc = function + | [] -> Ncic_termSet.elements acc + | (_::tl) as k -> + try + let idx = List.assq k th in + let acc = Ncic_termSet.union acc + (InvRelDiscriminationTree.retrieve_unifiables idx gty) + in + aux acc tl + with Not_found -> aux acc tl + in + aux Ncic_termSet.empty c +;; + +type flags = { + do_types : bool; (* solve goals in Type *) + maxwidth : int; + maxsize : int; + maxdepth : int; + timeout : float; +} + +type sort = T | P +type goal = int * sort (* goal, depth, sort *) +type fail = goal * cic_term +type candidate = int * Ast.term (* unique candidate number, candidate *) + +module IntSet = Set.Make(struct type t = int let compare = compare end) +(* exceptions *) + +exception Gaveup of IntSet.t (* a sublist of unprovable conjunctive + atoms of the input goals *) +exception Proved of #NTacStatus.tac_status + +let close_failures _ c = c;; +let prunable _ _ _ = false;; +let cache_examine cache gty = `Notfound;; +let put_in_subst s _ _ _ = s;; +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 equational_case _ _ _ _ _ _ = [];; +let only _ _ _ = true;; + +let candidate_no = ref 0;; + +let sort_new_elems l = + List.sort (fun (_,_,_,_,l1) (_,_,_,_,l2) -> List.length l1 - List.length l2) l +;; + +let try_candidate flags depth status t g = + try + debug_print ~depth (lazy ("try " ^ CicNotationPp.pp_term t)); + (* let status = NTactics.focus_tac [g] status in *) + let status = NTactics.apply_tac ("",0,t) status in + let open_goals = head_goals status#stack in + debug_print ~depth + (lazy ("success: "^String.concat " "(List.map string_of_int open_goals))); + if List.length open_goals > flags.maxwidth || + (depth = flags.maxdepth && open_goals <> []) then + (debug_print ~depth (lazy "pruned immediately"); None) + else + (incr candidate_no; + Some ((!candidate_no,t),status,open_goals)) + with Error (msg,exn) -> debug_print ~depth (lazy "failed"); None +;; + +let get_candidates status cache_th signature gty = + let universe = status#auto_cache in + let context = ctx_of gty 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) + in + List.map (fun t -> + let _status, t = term_of_cic_term status t context in Ast.NCic t) + (search_in_th gty cache_th) + @ + List.map (function NCic.Const r -> Ast.NRef r | _ -> assert false) cands +;; + +let applicative_case depth signature status flags g gty cache = + app_counter:= !app_counter+1; + let candidates = get_candidates status cache signature gty in + debug_print ~depth + (lazy ("candidates: " ^ string_of_int (List.length candidates))); + let elems = + List.fold_left + (fun elems cand -> + match try_candidate flags depth status cand g with + | None -> elems + | Some x -> x::elems) + [] candidates + in + elems +;; + +let equational_and_applicative_case + signature flags status g depth gty cache += + let elems = + if false (*is_equational_case gty flags*) then + let elems = + equational_case + signature status flags g gty cache + in + let more_elems = + applicative_case depth + signature status flags g gty cache + in + elems@more_elems + else + let elems = + (*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 depth + signature status flags g gty cache + in + elems + in + let elems = + List.map (fun c,s,gl -> + c,1,1,s,List.map (fun i -> + let sort = + let gty = get_goalty s i in + let _, sort = typeof s (ctx_of gty) gty in + match term_of_cic_term s sort (ctx_of sort) with + | _, NCic.Sort NCic.Prop -> P + | _ -> T + in + i,sort) gl) elems + in + let elems = sort_new_elems elems in + elems, cache +;; + +let rec guess_name name ctx = + if name = "_" then guess_name "auto" ctx else + if not (List.mem_assoc name ctx) then name else + guess_name (name^"'") ctx +;; + +let intro_case status gno gty depth cache name = + (* let status = NTactics.focus_tac [gno] status in *) + let status = NTactics.intro_tac (guess_name name (ctx_of gty)) status in + 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 t = mk_cic_term ctx (NCic.Rel 1) in + let status, keys = keys_of_term status t in + let cache = List.fold_left (add_to_th t) cache keys in + debug_print ~depth (lazy ("intro: "^ string_of_int open_goal)); + incr candidate_no; + (* XXX compute the sort *) + [(!candidate_no,Ast.Implicit `JustOne),0,0,status,[open_goal,P]], + cache +;; + +let pp_goal = function + | (_,Continuationals.Stack.Open i) + | (_,Continuationals.Stack.Closed i) -> string_of_int i +;; + +let pp_goals status l = + String.concat ", " + (List.map + (fun i -> + let gty = get_goalty status i in + NTacStatus.ppterm status gty) + l) +;; + +let do_something signature flags s gno depth gty cache = + let _s, raw_gty = term_of_cic_term s gty (ctx_of gty) in + match raw_gty with + | NCic.Prod (name,_,_) -> intro_case s gno gty depth cache name + | _ -> + equational_and_applicative_case signature flags s gno depth gty cache +;; + +let deps status g = + let gty = get_goalty status g in + metas_of_term status gty +;; + +module M = + struct + type t = int + let compare = Pervasives.compare + end +;; +module MS = HTopoSort.Make(M) +;; + +let sort_tac status = + let gstatus = + match status#stack with + | [] -> 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 + 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 ) + | (_,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 + status#set_stack gstatus +;; + +let clean_up_tac status = + let gstatus = + match status#stack with + | [] -> assert false + | (g, t, k, tag) :: s -> + let is_open = function + | (_,Continuationals.Stack.Open _) -> true + | (_,Continuationals.Stack.Closed _) -> false + in + let g' = List.filter is_open g in + (g', t, k, tag) :: s + in + status#set_stack gstatus +;; + +let focus_tac focus status = + let gstatus = + match status#stack with + | [] -> assert false + | (g, t, k, tag) :: s -> + let in_focus = function + | (_,Continuationals.Stack.Open i) + | (_,Continuationals.Stack.Closed i) -> List.mem i focus + in + let focus,others = 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 + in + status#set_stack gstatus +;; + +let rec auto_clusters + flags signature cache depth status : unit = + debug_print ~depth (lazy "entering auto clusters"); + (* 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) + else if List.length goals < 2 then + auto_main flags signature cache depth status + else + debug_print ~depth (lazy ("goals = " ^ + String.concat "," (List.map string_of_int goals))); + let classes = HExtlib.clusters (deps status) goals 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 + 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) + +and + +(* The pair solved,init_status is used for chaching purposes. + solved is the list of goals in init_status already proved. + Initially, init_status=status and k is set to [] *) +(* let rec auto_main flags signature cache status k depth = *) + +auto_main flags signature cache depth status: unit = + debug_print ~depth (lazy "entering auto main"); + (* 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) + | g::tlg -> + if depth = flags.maxdepth then raise (Gaveup IntSet.empty) + else + let status = + if tlg=[] then status + else NTactics.branch_tac status in + let gty = get_goalty status g in + let status, gty = apply_subst status (ctx_of gty) gty in + debug_print ~depth (lazy("Depth = " ^ (string_of_int depth))); + print ~depth (lazy("Attacking goal " ^ (string_of_int g) ^" : "^ppterm status gty)); + (* let closed = metas_of_term status gty = [] in *) + let alternatives, cache = + do_something signature flags status g depth gty cache in + let unsat = + List.fold_left + (* the underscore information does not need to be returned + by do_something *) + (fun unsat ((_,t),_,_,status,_) -> + let depth' = + if t=(Ast.Implicit `JustOne) then depth else depth+1 in + print (~depth:depth') + (lazy ("Case: " ^ CicNotationPp.pp_term t)); + try auto_clusters flags signature cache + depth' status; unsat + with + | Proved status -> + debug_print (~depth:depth') (lazy "proved"); + if tlg=[] then raise (Proved status) + else + let status = NTactics.merge_tac status + in + (try auto_clusters flags signature cache + depth status; unsat + with Gaveup f -> + let debug_print = print in + debug_print ~depth + (lazy ("Unsat1 at depth " ^ (string_of_int depth) + ^ ": " ^ + (pp_goals status (IntSet.elements f)))); + (* TODO: cache failures *) + IntSet.union f unsat) + | Gaveup f -> + let debug_print = print in + 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) +;; + +let int name l def = + try int_of_string (List.assoc name l) + with Failure _ | Not_found -> def +;; + +let auto_tac ~params:(_univ,flags) status = + let goals = head_goals status#stack in + let status, cache = mk_th_cache status goals in +(* pp_th status cache; *) +(* + NDiscriminationTree.DiscriminationTree.iter status#auto_cache (fun p t -> + debug_print (lazy( + NDiscriminationTree.NCicIndexable.string_of_path p ^ " |--> " ^ + String.concat "\n " (List.map ( + NCicPp.ppterm ~metasenv:[] ~context:[] ~subst:[]) + (NDiscriminationTree.TermSet.elements t)) + ))); +*) + let depth = int "depth" flags 3 in + let size = int "size" flags 10 in + let width = int "width" flags (3+List.length goals) in + (* XXX fix sort *) + let goals = List.map (fun i -> (i,P)) goals in + let signature = () in + let flags = { + maxwidth = width; + maxsize = size; + maxdepth = depth; + timeout = Unix.gettimeofday() +. 3000.; + do_types = false; + } in + let initial_time = Unix.gettimeofday() in + app_counter:= 0; + let rec up_to x y = + if x > y then 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;status + with + | Gaveup _ -> up_to (x+1) y + | Proved s -> + HLog.debug ("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 + in + s#set_stack stack + in + let s = up_to depth depth in + debug_print(lazy + ("TIME ELAPSED:"^string_of_float(Unix.gettimeofday()-.initial_time))); + debug_print(lazy + ("Applicative nodes:"^string_of_int !app_counter)); + s +;; +