X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fcomponents%2Ftactics%2Fauto.ml;h=a89bbd4a164b9e1c673b9ea9a7a0e2620788904d;hb=f9abd21eb0d26cf9b632af4df819225be4d091e3;hp=e377b63683049ae55d0fd30ea6a355d90fe0a01c;hpb=beb4e1e9549d5b43e24907dc86c7ef899e487a3c;p=helm.git diff --git a/helm/software/components/tactics/auto.ml b/helm/software/components/tactics/auto.ml index e377b6368..a89bbd4a1 100644 --- a/helm/software/components/tactics/auto.ml +++ b/helm/software/components/tactics/auto.ml @@ -24,38 +24,65 @@ *) open AutoTypes;; +open AutoCache;; + +let debug = false;; +let debug_print s = + if debug then prerr_endline (Lazy.force s);; -let debug_print s = ();;(*prerr_endline s;;*) let mk_irl ctx = CicMkImplicit.identity_relocation_list_for_metavariable ctx;; -let ugraph = CicUniv.empty_ugraph;; +let ugraph = CicUniv.oblivion_ugraph;; let typeof = CicTypeChecker.type_of_aux';; let ppterm ctx t = let names = List.map (function None -> None | Some (x,_) -> Some x) ctx in CicPp.pp t names ;; + +let is_propositional context sort = + match CicReduction.whd context sort with + | Cic.Sort Cic.Prop + | Cic.Sort (Cic.CProp _) -> true + | _-> false +;; + let is_in_prop context subst metasenv ty = - let sort,u = typeof ~subst metasenv context ty CicUniv.empty_ugraph in - fst (CicReduction.are_convertible context (Cic.Sort Cic.Prop) sort u) + let sort,u = typeof ~subst metasenv context ty CicUniv.oblivion_ugraph in + is_propositional context sort ;; -let assert_proof_is_valid proof metasenv context goalty = - let ty,u = typeof metasenv context proof CicUniv.empty_ugraph in - let b,_ = CicReduction.are_convertible context ty goalty u in - if not b then + +exception NotConvertible;; + +let check_proof_is_valid proof metasenv context goalty = + if debug then begin - prerr_endline (CicPp.ppterm proof); - prerr_endline (CicPp.ppterm ty); - prerr_endline (CicPp.ppterm goalty); - end; - assert b + try + let ty,u = typeof metasenv context proof CicUniv.oblivion_ugraph in + let b,_ = CicReduction.are_convertible context ty goalty u in + if not b then raise NotConvertible else b + with _ -> + let names = + List.map (function None -> None | Some (x,_) -> Some x) context + in + debug_print (lazy ("PROOF:" ^ CicPp.pp proof names)); + (* debug_print (lazy ("PROOFTY:" ^ CicPp.pp ty names)); *) + debug_print (lazy ("GOAL:" ^ CicPp.pp goalty names)); + debug_print (lazy ("MENV:" ^ CicMetaSubst.ppmetasenv [] metasenv)); + false + end + else true ;; -let assert_subst_are_disjoint subst subst' = - assert(List.for_all - (fun (i,_) -> List.for_all (fun (j,_) -> i<>j) subst') - subst) + +let assert_proof_is_valid proof metasenv context goalty = + assert (check_proof_is_valid proof metasenv context goalty) ;; -let sort_new_elems = - List.sort (fun (_,_,l1) (_,_,l2) -> List.length l1 - List.length l2) + +let assert_subst_are_disjoint subst subst' = + if debug then + assert(List.for_all + (fun (i,_) -> List.for_all (fun (j,_) -> i<>j) subst') + subst) + else () ;; let split_goals_in_prop metasenv subst gl = @@ -64,12 +91,13 @@ let split_goals_in_prop metasenv subst gl = let _,context,ty = CicUtil.lookup_meta g metasenv in try let sort,u = typeof ~subst metasenv context ty ugraph in - fst (CicReduction.are_convertible context (Cic.Sort Cic.Prop) sort u) + is_propositional context sort with | CicTypeChecker.AssertFailure s | CicTypeChecker.TypeCheckerFailure s -> - debug_print (ppterm context (CicMetaSubst.apply_subst subst ty)); - debug_print (Lazy.force s); + debug_print + (lazy ("NON TIPA" ^ ppterm context (CicMetaSubst.apply_subst subst ty))); + debug_print s; false) (* FIXME... they should type! *) gl @@ -86,164 +114,2073 @@ let split_goals_with_metas metasenv subst gl = let order_new_goals metasenv subst open_goals ppterm = let prop,rest = split_goals_in_prop metasenv subst open_goals in - let open_prop,closed_prop = split_goals_with_metas metasenv subst prop in + let closed_prop, open_prop = split_goals_with_metas metasenv subst prop in + let closed_type, open_type = split_goals_with_metas metasenv subst rest in let open_goals = - (List.map (fun x -> x,P) (closed_prop @ open_prop)) + (List.map (fun x -> x,P) (open_prop @ closed_prop)) @ - (List.map (fun x -> x,T) rest) + (List.map (fun x -> x,T) (open_type @ closed_type)) in let tys = List.map - (fun (i,_) -> - let _,_,ty = CicUtil.lookup_meta i metasenv in i,ty) open_goals + (fun (i,sort) -> + let _,_,ty = CicUtil.lookup_meta i metasenv in i,ty,sort) open_goals in - debug_print (" OPEN: "^ - String.concat " " - (List.map (fun (i,t) -> string_of_int i ^":"^ppterm t) tys)); + debug_print (lazy (" OPEN: "^ + String.concat "\n" + (List.map + (function + | (i,t,P) -> string_of_int i ^ ":"^ppterm t^ "Prop" + | (i,t,T) -> string_of_int i ^ ":"^ppterm t^ "Type") + tys))); open_goals ;; -let try_candidate subst fake_proof goalno depth context cand = - let ppterm = ppterm context in - try - debug_print (" PROVO: " ^ ppterm cand); - let subst', ((_,metasenv,_,_), open_goals) = - PrimitiveTactics.apply_with_subst ~term:cand ~subst (fake_proof,goalno) +let is_an_equational_goal = function + | Cic.Appl [Cic.MutInd(u,_,_);_;_;_] when LibraryObjects.is_eq_URI u -> true + | _ -> false +;; + +type auto_params = Cic.term list option * (string * string) list + +let elems = ref [] ;; + +(* closing a term w.r.t. its metavariables + very naif version: it does not take dependencies properly into account *) + +let naif_closure ?(prefix_name="xxx_") t metasenv context = + let in_term t (i,_,_) = + List.exists (fun (j,_) -> j=i) (CicUtil.metas_of_term t) + in + let metasenv = List.filter (in_term t) metasenv in + let metasenv = ProofEngineHelpers.sort_metasenv metasenv in + let n = List.length metasenv in + let what = List.map (fun (i,cc,ty) -> Cic.Meta(i,[])) metasenv in + let _,with_what = + List.fold_left + (fun (i,acc) (_,cc,ty) -> (i-1,Cic.Rel i::acc)) + (n,[]) metasenv + in + let t = CicSubstitution.lift n t in + let body = + ProofEngineReduction.replace_lifting + ~equality:(fun c t1 t2 -> + match t1,t2 with + | Cic.Meta(i,_),Cic.Meta(j,_) -> i = j + | _ -> false) + ~context ~what ~with_what ~where:t + in + let _, t = + List.fold_left + (fun (n,t) (_,cc,ty) -> + n-1, Cic.Lambda(Cic.Name (prefix_name^string_of_int n), + CicSubstitution.lift n ty,t)) + (n-1,body) metasenv + in + t, List.length metasenv +;; + +let lambda_close ?prefix_name t menv ctx = + let t, num_lambdas = naif_closure ?prefix_name t menv ctx in + List.fold_left + (fun (t,i) -> function + | None -> CicSubstitution.subst (Cic.Implicit None) t,i (* delift *) + | Some (name, Cic.Decl ty) -> Cic.Lambda (name, ty, t),i+1 + | Some (name, Cic.Def (bo, ty)) -> Cic.LetIn (name, bo, ty, t),i+1) + (t,num_lambdas) ctx +;; + +(* functions for retrieving theorems *) + + +exception FillingFailure of AutoCache.cache * AutomationCache.tables + +let rec unfold context = function + | Cic.Prod(name,s,t) -> + let t' = unfold ((Some (name,Cic.Decl s))::context) t in + Cic.Prod(name,s,t') + | t -> ProofEngineReduction.unfold context t + +let find_library_theorems dbd proof goal = + let univ = MetadataQuery.universe_of_goal ~dbd false proof goal in + let terms = List.map CicUtil.term_of_uri univ in + List.map + (fun t -> + (t,fst(CicTypeChecker.type_of_aux' [] [] t CicUniv.oblivion_ugraph))) + terms + +let find_context_theorems context metasenv = + let l,_ = + List.fold_left + (fun (res,i) ctxentry -> + match ctxentry with + | Some (_,Cic.Decl t) -> + (Cic.Rel i, CicSubstitution.lift i t)::res,i+1 + | Some (_,Cic.Def (_,t)) -> + (Cic.Rel i, CicSubstitution.lift i t)::res,i+1 + | None -> res,i+1) + ([],1) context + in l + +let rec is_an_equality = function + | Cic.Appl [Cic.MutInd (uri, _, _); _; _; _] + when (LibraryObjects.is_eq_URI uri) -> true + | Cic.Prod (_, _, t) -> is_an_equality t + | _ -> false +;; + +let partition_equalities = + List.partition (fun (_,ty) -> is_an_equality ty) + + +let default_auto tables _ cache _ _ _ _ = [],cache,tables ;; + +(* giusto per provare che succede +let is_unit_equation context metasenv oldnewmeta term = + let head, metasenv, args, newmeta = + TermUtil.saturate_term oldnewmeta metasenv context term 0 + in + let newmetas = + List.filter (fun (i,_,_) -> i >= oldnewmeta) metasenv + in + Some (args,metasenv,newmetas,head,newmeta) *) + +let is_unit_equation context metasenv oldnewmeta term = + let head, metasenv, args, newmeta = + TermUtil.saturate_term oldnewmeta metasenv context term 0 + in + let propositional_args = + HExtlib.filter_map + (function + | Cic.Meta(i,_) -> + let _,_,mt = CicUtil.lookup_meta i metasenv in + let sort,u = + CicTypeChecker.type_of_aux' metasenv context mt + CicUniv.oblivion_ugraph + in + if is_propositional context sort then Some i else None + | _ -> assert false) + args + in + if propositional_args = [] then + let newmetas = + List.filter (fun (i,_,_) -> i >= oldnewmeta) metasenv + in + Some (args,metasenv,newmetas,head,newmeta) + else None +;; + +let get_candidates skip_trie_filtering universe cache t = + let t = if skip_trie_filtering then Cic.Meta(0,[]) else t in + let candidates= + (Universe.get_candidates universe t)@(AutoCache.get_candidates cache t) + in + let debug_msg = + (lazy ("candidates for " ^ (CicPp.ppterm t) ^ " = " ^ + (String.concat "\n" (List.map CicPp.ppterm candidates)))) in + debug_print debug_msg; + candidates +;; + +let only signature context metasenv t = + try + let ty,_ = + CicTypeChecker.type_of_aux' metasenv context t CicUniv.oblivion_ugraph in - debug_print (" OK: " ^ ppterm cand); - (*FIXME:sicuro che posso @?*) - 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 - Some (metasenv,subst,open_goals) - with ProofEngineTypes.Fail s -> (*debug_print(" KO: "^Lazy.force s);*)None + let consts = MetadataConstraints.constants_of ty in + let b = MetadataConstraints.UriManagerSet.subset consts signature in +(* if b then (prerr_endline ("keeping " ^ (CicPp.ppterm t)); b) *) + if b then b + else + let ty' = unfold context ty in + let consts' = MetadataConstraints.constants_of ty' in + let b = MetadataConstraints.UriManagerSet.subset consts' signature in +(* + if not b then prerr_endline ("filtering " ^ (CicPp.ppterm t)) + else prerr_endline ("keeping " ^ (CicPp.ppterm t)); +*) + b + with + | CicTypeChecker.TypeCheckerFailure _ -> assert false + | ProofEngineTypes.Fail _ -> false (* unfold may fail *) +;; + +let not_default_eq_term t = + try + let uri = CicUtil.uri_of_term t in + not (LibraryObjects.in_eq_URIs uri) + with Invalid_argument _ -> true + +let retrieve_equations dont_filter signature universe cache context metasenv = + match LibraryObjects.eq_URI() with + | None -> [] + | Some eq_uri -> + let eq_uri = UriManager.strip_xpointer eq_uri in + let fake= Cic.Meta(-1,[]) in + let fake_eq = Cic.Appl [Cic.MutInd (eq_uri,0, []);fake;fake;fake] in + let candidates = get_candidates false universe cache fake_eq in + if dont_filter then candidates + else let eq_uri = UriManager.uri_of_uriref eq_uri 0 None in + (* let candidates = List.filter not_default_eq_term candidates in *) + List.filter + (only (MetadataConstraints.UriManagerSet.add eq_uri signature) + context metasenv) candidates + +let build_equality bag head args proof newmetas = + match head with + | Cic.Appl [Cic.MutInd (uri, _, _); ty; t1; t2] -> + let p = + if args = [] then proof else Cic.Appl (proof::args) + in + let o = !Utils.compare_terms t1 t2 in + let stat = (ty,t1,t2,o) in + (* let w = compute_equality_weight stat in *) + let w = 0 in + let proof = Equality.Exact p in + let bag, e = Equality.mk_equality bag (w, proof, stat, newmetas) in + (* to clean the local context of metas *) + Equality.fix_metas bag e + | _ -> assert false +;; + +let partition_unit_equalities context metasenv newmeta bag equations = + List.fold_left + (fun (bag,units,other,maxmeta)(t,ty) -> + if not (CicUtil.is_meta_closed t && CicUtil.is_meta_closed ty) then + let _ = + HLog.warn + ("Skipping " ^ CicMetaSubst.ppterm_in_context ~metasenv [] t context + ^ " since it is not meta closed") + in + bag, units,(t,ty)::other,maxmeta + else + match is_unit_equation context metasenv maxmeta ty with + | Some (args,metasenv,newmetas,head,newmeta') -> + let bag, equality = + build_equality bag head args t newmetas in + bag, equality::units,other,maxmeta + | None -> + bag, units,(t,ty)::other,maxmeta) + (bag,[],[],newmeta) equations +;; + +let init_cache_and_tables + ?dbd ~use_library ~use_context + automation_cache restricted_univ (proof, goal) += + let _, metasenv, subst, _, _, _ = proof in + let _,context,_ = CicUtil.lookup_meta goal metasenv in + let add_list_to_tables metasenv subst automation_cache ct = + List.fold_left + (fun automation_cache (t,_) -> + AutomationCache.add_term_to_active automation_cache + metasenv subst context t None) + automation_cache ct + in + match restricted_univ with + | None -> + let ct = + if use_context then find_context_theorems context metasenv else [] + in + let lt = + match use_library, dbd with + | true, Some dbd -> find_library_theorems dbd metasenv goal + | _ -> [] + in + let cache = AutoCache.cache_empty in + let cache = cache_add_list cache context (ct@lt) in + let automation_cache = + add_list_to_tables metasenv subst automation_cache ct + in +(* AutomationCache.pp_cache automation_cache; *) + automation_cache.AutomationCache.univ, + automation_cache.AutomationCache.tables, + cache + | Some restricted_univ -> + let t_ty = + List.map + (fun t -> + let ty, _ = CicTypeChecker.type_of_aux' + metasenv ~subst:[] context t CicUniv.oblivion_ugraph + in + t, ty) + restricted_univ + in + (* let automation_cache = AutomationCache.empty () in *) + let automation_cache = + let universe = Universe.empty in + let universe = + Universe.index_list universe context t_ty + in + { automation_cache with AutomationCache.univ = universe } + in + let ct = + if use_context then find_context_theorems context metasenv else t_ty + in + let automation_cache = + add_list_to_tables metasenv subst automation_cache ct + in + (* AutomationCache.pp_cache automation_cache; *) + automation_cache.AutomationCache.univ, + automation_cache.AutomationCache.tables, + cache_empty +;; + +let fill_hypothesis context metasenv subst term tables (universe:Universe.universe) cache auto fast = + let actives, passives, bag = tables in + let bag, head, metasenv, args = + Equality.saturate_term bag metasenv subst context term + in + let tables = actives, passives, bag in + let propositional_args = + HExtlib.filter_map + (function + | Cic.Meta(i,_) -> + let _,_,mt = CicUtil.lookup_meta i metasenv in + let sort,u = + CicTypeChecker.type_of_aux' metasenv context mt + CicUniv.oblivion_ugraph + in + if is_propositional context sort then Some i else None + | _ -> assert false) + args + in + let results,cache,tables = + if propositional_args = [] then + let _,_,bag = tables in + let newmetas = Equality.filter_metasenv_gt_maxmeta bag metasenv in + [args,metasenv,newmetas,head],cache,tables + else + (* + let proof = + None,metasenv,term,term (* term non e' significativo *) + in *) + let flags = + if fast then + {AutoTypes.default_flags() with + AutoTypes.timeout = Unix.gettimeofday() +. 1.0; + maxwidth = 2;maxdepth = 2; + use_paramod=true;use_only_paramod=false} + else + {AutoTypes.default_flags() with + AutoTypes.timeout = Unix.gettimeofday() +. 1.0; + maxwidth = 2;maxdepth = 4; + use_paramod=true;use_only_paramod=false} + in + match auto tables universe cache context metasenv propositional_args flags with + | [],cache,tables -> raise (FillingFailure (cache,tables)) + | substs,cache,tables -> + let actives, passaives, bag = tables in + let bag, res = + List.fold_right + (fun subst (bag,acc) -> + let metasenv = + CicMetaSubst.apply_subst_metasenv subst metasenv + in + let head = CicMetaSubst.apply_subst subst head in + let newmetas = Equality.filter_metasenv_gt_maxmeta bag metasenv in + let args = List.map (CicMetaSubst.apply_subst subst) args in + let newm = CicMkImplicit.new_meta metasenv subst in + let bag = Equality.push_maxmeta bag newm in + bag, ((args,metasenv,newmetas,head) :: acc)) + substs (bag,[]) + in + let tables = actives, passives, bag in + res, cache, tables + in + results,cache,tables +;; + +let build_equalities auto context metasenv subst tables universe cache equations = + List.fold_left + (fun (tables,facts,cache) (t,ty) -> + (* in any case we add the equation to the cache *) + let cache = AutoCache.cache_add_list cache context [(t,ty)] in + try + let saturated, cache, tables = + fill_hypothesis context metasenv subst ty tables universe cache auto true + in + let eqs, tables = + List.fold_left + (fun (acc, tables) (args,metasenv,newmetas,head) -> + let actives, passives, bag = tables in + let bag, equality = + build_equality bag head args t newmetas + in + let tables = actives, passives, bag in + equality::acc,tables) + ([],tables) saturated + in + (tables, eqs@facts, cache) + with FillingFailure (cache,tables) -> + (* if filling hypothesis fails we add the equation to + the cache *) + (tables,facts,cache) + ) + (tables,[],cache) equations + +let close_more tables context status auto signature universe cache = + let proof, goalno = status in + let _, metasenv,subst,_,_, _ = proof in + let equations = + retrieve_equations false signature universe cache context metasenv + in + let eqs_and_types = + HExtlib.filter_map + (fun t -> + let ty,_ = + CicTypeChecker.type_of_aux' metasenv context t + CicUniv.oblivion_ugraph in + (* retrieve_equations could also return flexible terms *) + if is_an_equality ty then Some(t,ty) else None) + equations in + let tables, units, cache = + build_equalities auto context metasenv subst tables universe cache eqs_and_types + in + let active,passive,bag = tables in + let passive = Saturation.add_to_passive units passive in + let no = List.length units in + let active, passive, bag = + Saturation.pump_actives context bag active passive (no+1) infinity + in + (active,passive,bag), cache +;; + +let find_context_equalities dbd tables context proof (universe:Universe.universe) cache += + let module C = Cic in + let module S = CicSubstitution in + let module T = CicTypeChecker in + let _,metasenv,subst,_,_, _ = proof in + (* if use_auto is true, we try to close the hypothesis of equational + statements using auto; a naif, and probably wrong approach *) + let rec aux tables cache index = function + | [] -> tables, [], cache + | (Some (_, C.Decl (term)))::tl -> + debug_print + (lazy + (Printf.sprintf "Examining: %d (%s)" index (CicPp.ppterm term))); + let do_find tables context term = + match term with + | C.Prod (name, s, t) when is_an_equality t -> + (try + let term = S.lift index term in + let saturated, cache, tables = + fill_hypothesis context metasenv subst term + tables universe cache default_auto false + in + let actives, passives, bag = tables in + let bag,eqs = + List.fold_left + (fun (bag,acc) (args,metasenv,newmetas,head) -> + let bag, equality = + build_equality bag head args (Cic.Rel index) newmetas + in + bag, equality::acc) + (bag,[]) saturated + in + let tables = actives, passives, bag in + tables, eqs, cache + with FillingFailure (cache,tables) -> + tables, [], cache) + | C.Appl [C.MutInd (uri, _, _); ty; t1; t2] + when LibraryObjects.is_eq_URI uri -> + let term = S.lift index term in + let actives, passives, bag = tables in + let bag, e = + build_equality bag term [] (Cic.Rel index) [] + in + let tables = actives, passives, bag in + tables, [e], cache + | _ -> tables, [], cache + in + let tables, eqs, cache = do_find tables context term in + let tables, rest, cache = aux tables cache (index+1) tl in + tables, List.map (fun x -> index,x) eqs @ rest, cache + | _::tl -> + aux tables cache (index+1) tl + in + let tables, il, cache = aux tables cache 1 context in + let indexes, equalities = List.split il in + tables, indexes, equalities, cache +;; + +(********** PARAMETERS PASSING ***************) + +let bool params name default = + try + let s = List.assoc name params in + if s = "" || s = "1" || s = "true" || s = "yes" || s = "on" then true + else if s = "0" || s = "false" || s = "no" || s= "off" then false + else + let msg = "Unrecognized value for parameter "^name^"\n" in + let msg = msg^"Accepted values are 1,true,yes,on and 0,false,no,off" in + raise (ProofEngineTypes.Fail (lazy msg)) + with Not_found -> default +;; + +let string params name default = + try List.assoc name params with + | Not_found -> default +;; + +let int params name default = + try int_of_string (List.assoc name params) with + | Not_found -> default + | Failure _ -> + raise (ProofEngineTypes.Fail (lazy (name ^ " must be an integer"))) +;; + +let flags_of_params params ?(for_applyS=false) () = + let int = int params in + let bool = bool params in + let close_more = bool "close_more" false in + let use_paramod = bool "use_paramod" true in + let skip_trie_filtering = bool "skip_trie_filtering" false in + let skip_context = bool "skip_context" false in + let use_only_paramod = + if for_applyS then true else bool "paramodulation" false in + let use_library = bool "library" + ((AutoTypes.default_flags()).AutoTypes.use_library) in + let depth = int "depth" ((AutoTypes.default_flags()).AutoTypes.maxdepth) in + let width = int "width" ((AutoTypes.default_flags()).AutoTypes.maxwidth) in + let size = int "size" ((AutoTypes.default_flags()).AutoTypes.maxsize) in + let gsize = int "gsize" ((AutoTypes.default_flags()).AutoTypes.maxgoalsizefactor) in + let do_type = bool "type" false in + let timeout = int "timeout" 0 in + { AutoTypes.maxdepth = + if use_only_paramod then 2 else depth; + AutoTypes.maxwidth = width; + AutoTypes.maxsize = size; + AutoTypes.timeout = + if timeout = 0 then + if for_applyS then Unix.gettimeofday () +. 30.0 + else + infinity + else + Unix.gettimeofday() +. (float_of_int timeout); + AutoTypes.use_library = use_library; + AutoTypes.use_paramod = use_paramod; + AutoTypes.use_only_paramod = use_only_paramod; + AutoTypes.close_more = close_more; + AutoTypes.dont_cache_failures = false; + AutoTypes.maxgoalsizefactor = gsize; + AutoTypes.do_types = do_type; + AutoTypes.skip_trie_filtering = skip_trie_filtering; + AutoTypes.skip_context = skip_context; + } + + +let eq_of_goal = function + | Cic.Appl [Cic.MutInd(uri,0,_);_;_;_] when LibraryObjects.is_eq_URI uri -> + uri + | _ -> raise (ProofEngineTypes.Fail (lazy ("The goal is not an equality "))) +;; + +(* performs steps of rewrite with the universe, obtaining if possible + * a trivial goal *) +let solve_rewrite ~automation_cache ~params:(univ,params) (proof,goal)= + let steps = int_of_string (string params "steps" "4") in + let use_context = bool params "use_context" true in + let universe, tables, cache = + init_cache_and_tables ~use_library:false ~use_context + automation_cache univ (proof,goal) + in + let actives, passives, bag = tables in + let pa,metasenv,subst,pb,pc,pd = proof in + let _,context,ty = CicUtil.lookup_meta goal metasenv in + let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in + let context = CicMetaSubst.apply_subst_context subst context in + let ty = CicMetaSubst.apply_subst subst ty in + let eq_uri = eq_of_goal ty in + let initgoal = [], metasenv, ty in + let table = + let equalities = (Saturation.list_of_passive passives) in + List.fold_left (fun tbl eq -> Indexing.index tbl eq) (snd actives) equalities + in + let env = metasenv,context,CicUniv.oblivion_ugraph in + debug_print (lazy ("demod to solve: " ^ CicPp.ppterm ty)); + match Indexing.solve_demodulating bag env table initgoal steps with + | Some (bag, gproof, metasenv, sub_subst, proof) -> + let subst_candidates,extra_infos = + List.split + (HExtlib.filter_map + (fun (i,c,_) -> + if i <> goal && c = context then Some (i,(c,ty)) else None) + metasenv) + in + let proofterm,proto_subst = + let proof = Equality.add_subst sub_subst proof in + Equality.build_goal_proof + bag eq_uri gproof proof ty subst_candidates context metasenv + in + let proofterm = Subst.apply_subst sub_subst proofterm in + let extrasubst = + HExtlib.filter_map + (fun (i,((c,ty),t)) -> + match t with + | Cic.Meta (j,_) when i=j -> None + | _ -> Some (i,(c,t,ty))) + (List.combine subst_candidates + (List.combine extra_infos proto_subst)) + in + let subst = subst @ extrasubst in + let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in + let proofterm, _, metasenv,subst, _ = + CicRefine.type_of metasenv subst context proofterm + CicUniv.oblivion_ugraph + in + let status = (pa,metasenv,subst,pb,pc,pd), goal in + ProofEngineTypes.apply_tactic + (PrimitiveTactics.apply_tac ~term:proofterm) status + | None -> + raise + (ProofEngineTypes.Fail (lazy + ("Unable to solve with " ^ string_of_int steps ^ " demodulations"))) +;; + +(* Demodulate thorem *) +let open_type ty bo = + let rec open_type_aux context ty k args = + match ty with + | Cic.Prod (n,s,t) -> + let n' = + FreshNamesGenerator.mk_fresh_name [] context n ~typ:s ~subst:[] in + let entry = match n' with + | Cic.Name _ -> Some (n',(Cic.Decl s)) + | Cic.Anonymous -> None + in + open_type_aux (entry::context) t (k+1) ((Cic.Rel k)::args) + | Cic.LetIn (n,s,sty,t) -> + let entry = Some (n,(Cic.Def (s,sty))) + in + open_type_aux (entry::context) t (k+1) args + | _ -> context, ty, args + in + let context, ty, args = open_type_aux [] ty 1 [] in + match args with + | [] -> context, ty, bo + | _ -> context, ty, Cic.Appl (bo::args) +;; + +let rec close_type bo ty context = + match context with + | [] -> assert_proof_is_valid bo [] [] ty; (bo,ty) + | Some (n,(Cic.Decl s))::tl -> + close_type (Cic.Lambda (n,s,bo)) (Cic.Prod (n,s,ty)) tl + | Some (n,(Cic.Def (s,sty)))::tl -> + close_type (Cic.LetIn (n,s,sty,bo)) (Cic.LetIn (n,s,sty,ty)) tl + | _ -> assert false +;; + +let is_subsumed univ context ty = + let candidates = Universe.get_candidates univ ty in + List.fold_left + (fun res cand -> + match res with + | Some found -> Some found + | None -> + try + let mk_irl = + CicMkImplicit.identity_relocation_list_for_metavariable in + let metasenv = [(0,context,ty)] in + let fake_proof = + None,metasenv,[] , (lazy (Cic.Meta(0,mk_irl context))),ty,[] + in + let (_,metasenv,subst,_,_,_), open_goals = + ProofEngineTypes.apply_tactic + (PrimitiveTactics.apply_tac ~term:cand) + (fake_proof,0) + in + let prop_goals, other = + split_goals_in_prop metasenv subst open_goals + in + if prop_goals = [] then Some cand else None + with + | ProofEngineTypes.Fail s -> None + | CicUnification.Uncertain s -> None + ) None candidates +;; + +let demodulate_theorem ~automation_cache uri = + let eq_uri = + match LibraryObjects.eq_URI () with + | Some (uri) -> uri + | None -> raise (ProofEngineTypes.Fail (lazy "equality not declared")) in + let obj,_ = CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri + in + let context,ty,bo = + match obj with + | Cic.Constant(n, _, ty ,_, _) -> open_type ty (Cic.Const(uri,[])) + | _ -> raise (ProofEngineTypes.Fail (lazy "not a theorem")) + in + if CicUtil.is_closed ty then + raise (ProofEngineTypes.Fail (lazy ("closed term: dangerous reduction"))); + let initgoal = [], [], ty in + (* compute the signature *) + let signature = + let ty_set = MetadataConstraints.constants_of ty in + let hyp_set = MetadataQuery.signature_of_hypothesis context [] in + let set = MetadataConstraints.UriManagerSet.union ty_set hyp_set in + MetadataQuery.close_with_types set [] context + in + (* retrieve equations from the universe universe *) + (* XXX automation_cache *) + let universe = automation_cache.AutomationCache.univ in + let equations = + retrieve_equations true signature universe AutoCache.cache_empty context [] + in + debug_print + (lazy ("ho trovato equazioni n. "^(string_of_int (List.length equations)))); + let eqs_and_types = + HExtlib.filter_map + (fun t -> + let ty,_ = + CicTypeChecker.type_of_aux' [] context t CicUniv.oblivion_ugraph + in + (* retrieve_equations could also return flexible terms *) + if is_an_equality ty then Some(t,ty) + else + try + let ty' = unfold context ty in + if is_an_equality ty' then Some(t,ty') else None + with ProofEngineTypes.Fail _ -> None) + equations + in + let bag = Equality.mk_equality_bag () in + + let bag, units, _, newmeta = + partition_unit_equalities context [] (CicMkImplicit.new_meta [] []) bag eqs_and_types + in + let table = + List.fold_left + (fun tbl eq -> Indexing.index tbl eq) + Indexing.empty units + in + let changed,(newproof,newmetasenv, newty) = + Indexing.demod bag + ([],context,CicUniv.oblivion_ugraph) table initgoal in + if changed then + begin + let oldproof = Equality.Exact bo in + let proofterm,_ = + Equality.build_goal_proof (~contextualize:false) (~forward:true) bag + eq_uri newproof oldproof ty [] context newmetasenv + in + if newmetasenv <> [] then + raise (ProofEngineTypes.Fail (lazy ("metasenv not empty"))) + else + begin + assert_proof_is_valid proofterm newmetasenv context newty; + match is_subsumed universe context newty with + | Some t -> raise + (ProofEngineTypes.Fail (lazy ("subsumed by " ^ CicPp.ppterm t))) + | None -> close_type proofterm newty context + end + end + else (* if newty = ty then *) + raise (ProofEngineTypes.Fail (lazy "no progress")) + (*else ProofEngineTypes.apply_tactic + (ReductionTactics.simpl_tac + ~pattern:(ProofEngineTypes.conclusion_pattern None)) initialstatus*) +;; + + +(* NEW DEMODULATE *) +let demodulate ~dbd ~automation_cache ~params:(univ, params) (proof,goal)= + let universe, tables, cache = + init_cache_and_tables + ~dbd ~use_library:false ~use_context:true + automation_cache univ (proof,goal) + in + let eq_uri = + match LibraryObjects.eq_URI () with + | Some (uri) -> uri + | None -> raise (ProofEngineTypes.Fail (lazy "equality not declared")) in + let active, passive, bag = tables in + let curi,metasenv,subst,pbo,pty, attrs = proof in + let metano,context,ty = CicUtil.lookup_meta goal metasenv in + let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in + let initgoal = [], metasenv, ty in + let equalities = (Saturation.list_of_passive passive) in + (* we demodulate using both actives passives *) + let env = metasenv,context,CicUniv.empty_ugraph in + debug_print (lazy ("PASSIVES:" ^ string_of_int(List.length equalities))); + List.iter (fun e -> debug_print (lazy (Equality.string_of_equality ~env e))) + equalities; + let table = + List.fold_left + (fun tbl eq -> Indexing.index tbl eq) + (snd active) equalities + in + let changed,(newproof,newmetasenv, newty) = + (* Indexing.demodulation_goal bag *) + Indexing.demod bag + (metasenv,context,CicUniv.oblivion_ugraph) table initgoal + in + if changed then + begin + let maxm = CicMkImplicit.new_meta metasenv subst in + let opengoal = Equality.Exact (Cic.Meta(maxm,irl)) in + let subst_candidates = List.map (fun (i,_,_) -> i) metasenv in + let subst_candidates = List.filter (fun x-> x <> goal) subst_candidates in + let proofterm, proto_subst = + Equality.build_goal_proof (~contextualize:false) bag + eq_uri newproof opengoal ty subst_candidates context metasenv + in + (* XXX understan what to do with proto subst *) + let metasenv = (maxm,context,newty)::metasenv in + let proofterm, _, metasenv, subst, _ = + CicRefine.type_of metasenv subst context proofterm + CicUniv.oblivion_ugraph + in + let extended_status = (curi,metasenv,subst,pbo,pty, attrs),goal in + let proof,gl = + ProofEngineTypes.apply_tactic + (PrimitiveTactics.apply_tac ~term:proofterm) extended_status + in + proof,maxm::gl + end + else + raise (ProofEngineTypes.Fail (lazy "no progress")) +;; + +let demodulate_tac ~dbd ~params:(_,flags as params) ~automation_cache = + ProofEngineTypes.mk_tactic + (fun status -> + let all = bool flags "all" false in + if all then + solve_rewrite ~params ~automation_cache status + else + demodulate ~dbd ~params ~automation_cache status) +;; +(***************** applyS *******************) + +let apply_smart_aux + dbd automation_cache (params:auto_params) proof goal newmeta' metasenv' subst + context term' ty termty goal_arity += + let consthead,newmetasenv,arguments,_ = + TermUtil.saturate_term newmeta' metasenv' context termty goal_arity in + let term'' = + match arguments with + | [] -> term' + | _ -> Cic.Appl (term'::arguments) + in + let consthead = + let rec aux t = function + | [] -> + let t = CicReduction.normalize ~delta:false context t in + (match t, ty with + | Cic.Appl (hd1::_), Cic.Appl (hd2::_) when hd1 <> hd2 -> + let t = ProofEngineReduction.unfold context t in + (match t with + | Cic.Appl (hd1'::_) when hd1' = hd2 -> t + | _ -> raise (ProofEngineTypes.Fail (lazy "incompatible head"))) + | _ -> t) + | arg :: tl -> + match CicReduction.whd context t with + | Cic.Prod (_,_,tgt) -> + aux (CicSubstitution.subst arg tgt) tl + | _ -> assert false + in + aux termty arguments + in + let goal_for_paramod = + match LibraryObjects.eq_URI () with + | Some uri -> + Cic.Appl [Cic.MutInd (uri,0,[]); Cic.Implicit (Some `Type); consthead; ty] + | None -> raise (ProofEngineTypes.Fail (lazy "No equality defined")) + in + try + let goal_for_paramod, _, newmetasenv, subst, _ = + CicRefine.type_of newmetasenv subst context goal_for_paramod + CicUniv.oblivion_ugraph + in + let newmeta = CicMkImplicit.new_meta newmetasenv subst in + let metasenv_for_paramod = (newmeta,context,goal_for_paramod)::newmetasenv in + let proof'' = + let uri,_,_,p,ty, attrs = proof in + uri,metasenv_for_paramod,subst,p,ty, attrs + in + let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in +(* + prerr_endline ("------ prima di rewrite su ------ " ^ string_of_int goal); + prerr_endline ("menv:\n"^CicMetaSubst.ppmetasenv [] metasenv_for_paramod); + prerr_endline ("subst:\n"^CicMetaSubst.ppsubst + ~metasenv:(metasenv_for_paramod) + subst); +*) + + let (proof''',goals) = + ProofEngineTypes.apply_tactic + (EqualityTactics.rewrite_tac ~direction:`RightToLeft + ~pattern:(ProofEngineTypes.conclusion_pattern None) + (Cic.Meta(newmeta,irl)) []) (proof'',goal) + in + let goal = match goals with [g] -> g | _ -> assert false in + let proof'''', _ = + ProofEngineTypes.apply_tactic + (PrimitiveTactics.apply_tac term'') + (proof''',goal) + in + + + let (_,m,_,_,_,_ as p) = + let pu,metasenv,subst,proof,px,py = proof'''' in + let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in + let proof'''' = pu,metasenv,subst,proof,px,py in + let univ, params = params in + let use_context = bool params "use_context" true in + let universe, (active,passive,bag), cache = + init_cache_and_tables ~use_library:false ~use_context + automation_cache univ (proof'''',newmeta) + in + match + Saturation.solve_narrowing bag (proof'''',newmeta) active passive + 2 (*0 infinity*) + with + | None, active, passive, bag -> + raise (ProofEngineTypes.Fail (lazy ("paramod fails"))) + | Some(subst',(pu,metasenv,_,proof,px, py),open_goals),active, + passive,bag -> + assert_subst_are_disjoint subst subst'; + let subst = subst@subst' in + pu,metasenv,subst,proof,px,py + in + +(* + let (_,m,_,_,_,_ as p),_ = + solve_rewrite ~params ~automation_cache (proof'''',newmeta) + in +*) + + let open_goals = + ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv' ~newmetasenv:m + in + p, open_goals + with + CicRefine.RefineFailure msg -> + raise (ProofEngineTypes.Fail msg) +;; + +let apply_smart + ~dbd ~term ~automation_cache ~params (proof, goal) += + let module T = CicTypeChecker in + let module R = CicReduction in + let module C = Cic in + let (_,metasenv,subst,_,_, _) = proof in + let metano,context,ty = CicUtil.lookup_meta goal metasenv in + let newmeta = CicMkImplicit.new_meta metasenv subst in + let exp_named_subst_diff,newmeta',newmetasenvfragment,term' = + match term with + C.Var (uri,exp_named_subst) -> + let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff = + PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri + exp_named_subst + in + exp_named_subst_diff,newmeta',newmetasenvfragment, + C.Var (uri,exp_named_subst') + | C.Const (uri,exp_named_subst) -> + let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff = + PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri + exp_named_subst + in + exp_named_subst_diff,newmeta',newmetasenvfragment, + C.Const (uri,exp_named_subst') + | C.MutInd (uri,tyno,exp_named_subst) -> + let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff = + PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri + exp_named_subst + in + exp_named_subst_diff,newmeta',newmetasenvfragment, + C.MutInd (uri,tyno,exp_named_subst') + | C.MutConstruct (uri,tyno,consno,exp_named_subst) -> + let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff = + PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri + exp_named_subst + in + exp_named_subst_diff,newmeta',newmetasenvfragment, + C.MutConstruct (uri,tyno,consno,exp_named_subst') + | _ -> [],newmeta,[],term + in + let metasenv' = metasenv@newmetasenvfragment in + let termty,_ = + CicTypeChecker.type_of_aux' + metasenv' ~subst context term' CicUniv.oblivion_ugraph + in + let termty = CicSubstitution.subst_vars exp_named_subst_diff termty in + let goal_arity = + let rec count_prods context ty = + match CicReduction.whd ~subst context ty with + | Cic.Prod (n,s,t) -> 1 + count_prods (Some (n,Cic.Decl s)::context) t + | _ -> 0 + in + count_prods context ty + in + apply_smart_aux dbd automation_cache params proof goal + newmeta' metasenv' subst context term' ty termty goal_arity +;; + +let applyS_tac ~dbd ~term ~params ~automation_cache = + ProofEngineTypes.mk_tactic + (fun status -> + try + apply_smart ~dbd ~term ~params ~automation_cache status + with + | CicUnification.UnificationFailure msg + | CicTypeChecker.TypeCheckerFailure msg -> + raise (ProofEngineTypes.Fail msg)) +;; + + +(****************** 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 prop_only l = + List.filter (function (_,_,P) -> true | _ -> false) l +;; + +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 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 prop = function (_,_,P) -> true | _ -> false;; +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 -let auto_main context flags elems cache universe = - let timeout = - if flags.timeout = 0. then - infinity - else - Unix.gettimeofday () +. flags.timeout + 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 - let irl = mk_irl context in - let rec aux cache = function (* elems in OR *) - | [] -> Fail "no more steps can be done", cache (* COMPLETE FAILURE *) - | (metasenv,subst,[])::tl -> - Success (metasenv,subst,tl), cache (* solution::cont *) - | (metasenv,subst,goals)::tl when - List.length (List.filter prop goals) > flags.maxwidth -> - debug_print (" FAILURE(width): " ^ string_of_int (List.length goals)); - aux cache tl (* FAILURE (width) *) - | (metasenv,subst,((goalno,depth,sort) as elem)::gl)::tl -> - if Unix.gettimeofday() > timeout then Fail "timeout",cache - else - try - let _,cc,goalty = CicUtil.lookup_meta goalno metasenv in - debug_print ("INSPECTING " ^ string_of_int goalno^ ":"^ppterm goalty); - if sort = T then - (debug_print (" FAILURE(not in prop)"); - aux cache tl (* FAILURE (not in prop) *)) - else - match aux_single cache metasenv subst elem goalty cc with - | Fail _, cache -> - debug_print (" FAIL: " ^string_of_int goalno^ ":"^ppterm goalty); - let cache = cache_add_failure cache goalty depth in - aux cache tl - | Success (metasenv,subst,others), cache -> - (* others are alternatives in OR *) - try - let goal = Cic.Meta(goalno,irl) in - let proof = CicMetaSubst.apply_subst subst goal in - debug_print ("DONE: " ^ ppterm goalty^" with: "^ppterm proof); - if is_a_green_cut goalty then - (assert_proof_is_valid proof metasenv context goalty; - let cache = cache_add_success cache goalty proof in - aux cache ((metasenv,subst,gl)::tl)) - else - (let goalty = CicMetaSubst.apply_subst subst goalty in - assert_proof_is_valid proof metasenv context goalty; - let cache = - if is_a_green_cut goalty then - cache_add_success cache goalty proof - else - cache - in - let others = - List.map - (fun (metasenv,subst,goals) -> (metasenv,subst,goals@gl)) - others - in - aux cache ((metasenv,subst,gl)::others@tl)) - with CicUtil.Meta_not_found i when i = goalno -> - assert false - with CicUtil.Meta_not_found i when i = goalno -> - (* goalno was closed by sideeffect *) - aux cache ((metasenv,subst,gl)::tl) - and aux_single cache metasenv subst (goalno, depth, _) goalty cc = - let goalty = CicMetaSubst.apply_subst subst goalty in -(* else if not (is_in_prop context subst metasenv goalty) then Fail,cache *) - (* FAILURE (euristic cut) *) - match cache_examine cache goalty with - | Failed_in d when d >= depth -> Fail "depth",cache(*FAILURE(depth)*) - | Succeded t -> - assert(List.for_all (fun (i,_) -> i <> goalno) subst); - let entry = goalno, (cc, t,goalty) in - assert_subst_are_disjoint subst [entry]; - let subst = entry :: subst in - let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in - debug_print (" CACHE HIT!"); - Success (metasenv, subst, []),cache - | UnderInspection -> Fail "looping",cache - | Notfound - | Failed_in _ when depth > 0 -> (* we have more depth now *) - let cache = cache_add_underinspection cache goalty depth in - let candidates = get_candidates universe goalty in - let fake_proof = None,metasenv,Cic.Meta(goalno,irl),goalty in - let elems = - HExtlib.filter_map - (try_candidate subst fake_proof goalno depth context) - candidates + try + let params = (None,[]) 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 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 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_main dbd tables context flags signature universe cache elems = + auto_context := context; + let rec aux tables flags cache (elems : status) = + pp_status context elems; +(* DEBUGGING CODE: uncomment these two lines to stop execution at each iteration + auto_status := elems; + check_pause (); +*) + let cache, elems = filter_prune_hint cache elems in + match elems with + | (m, s, size, don, todo, fl)::orlist when !hint <> None -> + debug_print (lazy "skip"); + (match !hint with + | Some i when condition_for_hint i todo -> + aux tables flags cache orlist + | _ -> + hint := None; + aux tables flags cache elems) + | [] -> + (* complete failure *) + debug_print (lazy "give up"); + Gaveup (tables, cache) + | (m, s, _, _, [],_)::orlist -> + (* complete success *) + debug_print (lazy "success"); + Proved (m, s, orlist, tables, cache) + | (m, s, size, don, (D (_,_,T))::todo, fl)::orlist + when not flags.AutoTypes.do_types -> + (* skip since not Prop, don't even check if closed by side-effect *) + debug_print (lazy "skip existential goal"); + aux tables flags cache ((m, s, size, don, todo, fl)::orlist) + | (m, s, size, don, (S(g, key, c,minsize) as op)::todo, fl)::orlist -> + (* partial success, cache g and go on *) + let cache, orlist, fl, sibling_pruned = + add_to_cache_and_del_from_orlist_if_green_cut + g s m cache key todo orlist fl context size minsize in - let elems = sort_new_elems elems in - aux cache elems - | _ -> Fail "??",cache + debug_print (lazy (AutoCache.cache_print context cache)); + let fl = remove_s_from_fl g fl in + let don = if sibling_pruned then don else op::don in + aux tables flags cache ((m, s, size, don, todo, fl)::orlist) + | (m, s, size, don, todo, fl)::orlist + when List.length(prop_only (d_goals todo)) > flags.maxwidth -> + debug_print (lazy ("FAIL: WIDTH")); + (* too many goals in and generated by last th *) + let cache = close_failures fl cache in + aux tables flags cache orlist + | (m, s, size, don, todo, fl)::orlist when size > flags.maxsize -> + debug_print + (lazy ("FAIL: SIZE: "^string_of_int size ^ + " > " ^ string_of_int flags.maxsize )); + (* we already have a too large proof term *) + let cache = close_failures fl cache in + aux tables flags cache orlist + | _ when Unix.gettimeofday () > flags.timeout -> + (* timeout *) + debug_print (lazy ("FAIL: TIMEOUT")); + Gaveup (tables, cache) + | (m, s, size, don, (D (gno,depth,_ as g))::todo, fl)::orlist as status -> + (* attack g *) + debug_print (lazy "attack goal"); + match calculate_goal_ty g s m with + | None -> + (* closed by side effect *) + debug_print (lazy ("SUCCESS: SIDE EFFECT: " ^ string_of_int gno)); + aux tables flags cache ((m,s,size,don,todo, fl)::orlist) + | Some (canonical_ctx, gty) -> + let gsize, _ = + Utils.weight_of_term ~consider_metas:false ~count_metas_occurrences:true gty + in + if gsize > flags.maxgoalsizefactor then + (debug_print (lazy ("FAIL: SIZE: goal: "^string_of_int gsize)); + aux tables flags cache orlist) + else if prunable_for_size flags s m todo then + (debug_print (lazy ("POTO at depth: "^(string_of_int depth))); + aux tables flags cache orlist) + else + (* still to be proved *) + (debug_print (lazy ("EXAMINE: "^CicPp.ppterm gty)); + match cache_examine cache gty with + | Failed_in d when d >= depth -> + (* fail depth *) + debug_print (lazy ("FAIL: DEPTH (cache): "^string_of_int gno)); + let cache = close_failures fl cache in + aux tables flags cache orlist + | UnderInspection -> + (* fail loop *) + debug_print (lazy ("FAIL: LOOP: " ^ string_of_int gno)); + let cache = close_failures fl cache in + aux tables flags cache orlist + | Succeded t -> + debug_print (lazy ("SUCCESS: CACHE HIT: " ^ string_of_int gno)); + let s, m = put_in_subst s m g canonical_ctx t gty in + aux tables flags cache ((m, s, size, don,todo, fl)::orlist) + | Notfound + | Failed_in _ when depth > 0 -> + ( (* more depth or is the first time we see the goal *) + if prunable m s gty todo then + (debug_print (lazy( + "FAIL: LOOP: one father is equal")); + aux tables flags cache orlist) + else + let cache = cache_add_underinspection cache gty depth in + auto_status := status; + check_pause (); + debug_print + (lazy ("INSPECTING: " ^ + string_of_int gno ^ "("^ string_of_int size ^ "): "^ + CicPp.ppterm gty)); + (* elems are possible computations for proving gty *) + let elems, tables, cache, flags = + equational_and_applicative_case dbd + signature universe flags m s g gty tables cache context + in + if elems = [] then + (* this goal has failed *) + let cache = close_failures ((g,gty)::fl) cache in + aux tables flags cache orlist + else + (* elems = (cand,m,s,gl) *) + let size_gl l = List.length + (List.filter (function (_,_,P) -> true | _ -> false) l) + in + let elems = + let inj_gl gl = List.map (fun g -> D g) gl in + let rec map = function + | [] -> assert false + | (cand,m,s,gl)::[] -> + (* in the last one we add the failure *) + let todo = + inj_gl gl @ (S(g,gty,cand,size+1))::todo + in + (* we are the last in OR, we fail on g and + * also on all failures implied by g *) + (m,s, size + size_gl gl, don, todo, (g,gty)::fl) + :: orlist + | (cand,m,s,gl)::tl -> + (* we add the S step after gl and before todo *) + let todo = + inj_gl gl @ (S(g,gty,cand,size+1))::todo + in + (* since we are not the last in OR, we do not + * imply failures *) + (m,s, size + size_gl gl, don, todo, []) :: map tl + in + map elems + in + aux tables flags cache elems) + | _ -> + (* no more depth *) + debug_print (lazy ("FAIL: DEPTH: " ^ string_of_int gno)); + let cache = close_failures fl cache in + aux tables flags cache orlist) in - aux cache elems + (aux tables flags cache elems : auto_result) ;; -let auto universe cache context metasenv gl flags = + +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) -> x,flags.maxdepth,s) goals in - let elems = [metasenv,[],goals] in - match auto_main context flags elems cache universe with - | Fail s,cache -> prerr_endline s;None,cache - | Success (metasenv,subst,_), cache -> Some (subst,metasenv), cache + 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 ;; -let auto_all_solutions universe cache context metasenv gl flags = +(******************* 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) -> x,flags.maxdepth,s) goals in - let elems = [metasenv,[],goals] in - let bigbang = Unix.gettimeofday () in - let rec aux solutions cache elems flags = - match auto_main context flags elems cache universe with - | Fail s,cache ->prerr_endline s; solutions,cache - | Success (metasenv,subst,others), cache -> - let elapsed = Unix.gettimeofday () -. bigbang in - if elapsed > flags.timeout then - ((subst,metasenv)::solutions), cache - else - aux ((subst,metasenv)::solutions) cache others - {flags with timeout = flags.timeout -. elapsed} + 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 = + match univ with + | None -> signature + | Some l -> + 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 l in - aux [] cache elems flags + 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")) ;; + +let auto_tac ~dbd ~params ~automation_cache = + ProofEngineTypes.mk_tactic (auto_tac ~params ~dbd ~automation_cache);; + +let pp_proofterm = Equality.pp_proofterm;; + +let revision = "$Revision$";; +let size_and_depth context metasenv t = 100, 100