(* ||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_______________________________________________________________ *) (* $Id: nCic.ml 9058 2008-10-13 17:42:30Z tassi $ *) open Printf let debug = ref false let debug_print s = if !debug then prerr_endline (Lazy.force s) else () open Continuationals.Stack open NTacStatus module Ast = CicNotationPt (* =================================== 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 t None (ctx_of gty) 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")) ;; *) type th_cache = (NCic.context * InvRelDiscriminationTree.t) list 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 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 let status, orig_ty = typeof status ctx t in let _, ty, _ = saturate ~delta:max_int status orig_ty in let idx = InvRelDiscriminationTree.index idx ty t in let idx = 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 InvRelDiscriminationTree.index idx ty t | _ -> idx in status, i+1, idx) (status, 1, idx) ctx in status, (ctx, idx) :: acc) (status,[]) gl ;; let add_to_th t ty c = 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 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 ;; let pp_th status = List.iter (fun ctx, idx -> prerr_endline "-----------------------------------------------"; prerr_endline (NCicPp.ppcontext ~metasenv:[] ~subst:[] ctx); prerr_endline "||====> "; InvRelDiscriminationTree.iter idx (fun k set -> prerr_endline ("K: " ^ NCicInverseRelIndexable.string_of_path k); Ncic_termSet.iter (fun t -> prerr_endline ("\t"^ppterm status t)) set)) ;; type cache_examination_result = [ `Failed_in of int | `UnderInspection | `Succeded of NCic.term | `NotFound ] type sort = T | P type goal = int * int * sort (* goal, depth, sort *) type fail = goal * cic_term type candidate = int * Ast.term (* unique candidate number, candidate *) 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 * cic_term * candidate (* int was minsize *) type 'a elem = (* menv, subst, size, operations done (only S), operations to do, * failures to cache if any op fails *) (#tac_status as 'a) * int * op list * op list * fail list type 'a auto_status = (* list of computations that may lead to the solution: all op list will * end with the same (S(g,_)) *) 'a elem list * th_cache type 'a auto_result = | Gaveup | Proved of (#tac_status as 'a) * 'a auto_status (* alt. proofs *) type flags = { do_types : bool; (* solve goals in Type *) maxwidth : int; maxsize : int; timeout : float; } 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 status t g = try debug_print (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 (lazy (" success: "^String.concat " "(List.map string_of_int open_goals))); incr candidate_no; Some ((!candidate_no,t),status,open_goals) with Error (msg,exn) -> debug_print (lazy " failed"); None ;; let rec mk_irl n = function | [] -> [] | _ :: tl -> NCic.Rel n :: mk_irl (n+1) tl ;; 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 signature status flags g gty cache = let candidates = get_candidates status cache signature gty in debug_print (lazy ("candidates: " ^ string_of_int (List.length candidates))); let elems = List.fold_left (fun elems cand -> match try_candidate 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 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 signature status flags g gty cache in elems in let elems = (* XXX calculate the sort *) List.map (fun c,s,gl -> c,s,List.map (fun i -> i,depth-1,P) gl) elems in let elems = sort_new_elems elems in elems, cache ;; let calculate_goal_ty (goalno,_,_) status = try Some (get_goalty status goalno) with Error _ -> None ;; 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 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 status, cache = 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, ty = typeof status ctx t in let _status, ty, _args = saturate status ty in status, add_to_th t ty cache in debug_print (lazy (" intro: "^ string_of_int open_goal)); (* pp_th status cache; *) incr candidate_no; (* XXX calculate the sort *) [(!candidate_no,Ast.Implicit `JustOne),status,[open_goal,depth,P]], cache ;; 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 auto_main flags signature elems cache = let rec aux (elems, cache : 'a 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) *) | [] -> debug_print (lazy "gave up"); Gaveup | (s, _, _, [],_)::orlist -> debug_print (lazy "success"); Proved (s, (orlist, cache)) | (s, size, don, (D (_,_,T))::todo, fl)::orlist when not flags.do_types -> debug_print (lazy "skip goal in Type"); aux ((s, size, don, todo, fl)::orlist, cache) | (s, size, don, (S(g, key, c) as op)::todo, fl)::orlist -> let cache, orlist, fl, sibling_pruned = add_to_cache_and_del_from_orlist_if_green_cut g s cache key todo orlist fl size in let fl = remove_s_from_fl g fl in let don = if sibling_pruned then don else op::don in let s = NTactics.unfocus_tac s in aux ((s, size, don, todo, fl)::orlist, cache) | (s, size, don, todo, fl)::orlist when List.length(prop_only (d_goals todo)) > flags.maxwidth -> debug_print (lazy ("FAIL: WIDTH")); aux (orlist, cache) | (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 | (s, size, don, (D (gno,depth,_ as g))::todo, fl)::orlist -> debug_print (lazy "attack goal"); match calculate_goal_ty g s with | None -> debug_print (lazy ("SUCCESS: SIDE EFFECT: " ^ string_of_int gno)); aux ((s,size,don,todo, fl)::orlist, cache) | Some gty -> let s, gty = apply_subst s (ctx_of gty) gty in debug_print (lazy ("EXAMINE: "^ ppterm s 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 = put_in_subst s g t gty in aux ((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 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 ^ "): "^ ppterm s gty)); (* elems are possible computations for proving gty *) let elems, cache = do_something signature flags s gno depth gty cache 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,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 *) (s, size + size_gl gl, don, todo, (g,gty)::fl) :: orlist | (cand,s,gl)::tl -> let todo = inj_gl gl @ (S(g,gty,cand))::todo in (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) : 'a auto_result) ;; 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 let depth = int "depth" flags 3 in (* XXX fix sort *) let goals = List.map (fun i -> D(i,depth,P)) goals in let elems = [status,0,[],goals,[]] in let signature = () in let flags = { maxwidth = 3 + List.length goals; maxsize = 10; timeout = Unix.gettimeofday() +. 3000.; do_types = false; } in match auto_main flags signature elems cache with | Gaveup -> raise (Error (lazy "auto gave up", None)) | Proved (s, (_orlist, _cache)) -> 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 ;; (* ========================= dispatching of auto/auto_paramod ============ *) let auto_tac ~params:(_,flags as params) = if List.mem_assoc "paramodulation" flags then auto_paramod_tac ~params else auto_tac ~params ;; (* EOF *)