(************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) (* 0 then true else false let set_typeclasses_verbose = function None -> typeclasses_debug := 0 | Some n -> (:=) typeclasses_debug n let get_typeclasses_verbose () = if !typeclasses_debug = 0 then None else Some !typeclasses_debug let set_typeclasses_depth d = (:=) typeclasses_depth d let get_typeclasses_depth () = !typeclasses_depth open Goptions let _ = declare_bool_option { optsync = true; optdepr = false; optname = "do typeclass search modulo eta conversion"; optkey = ["Typeclasses";"Modulo";"Eta"]; optread = get_typeclasses_modulo_eta; optwrite = set_typeclasses_modulo_eta; } let _ = declare_bool_option { optsync = true; optdepr = false; optname = "do typeclass search avoiding eta-expansions " ^ " in proof terms (expensive)"; optkey = ["Typeclasses";"Limit";"Intros"]; optread = get_typeclasses_limit_intros; optwrite = set_typeclasses_limit_intros; } let _ = declare_bool_option { optsync = true; optdepr = false; optname = "during typeclass resolution, solve instances according to their dependency order"; optkey = ["Typeclasses";"Dependency";"Order"]; optread = get_typeclasses_dependency_order; optwrite = set_typeclasses_dependency_order; } let _ = declare_bool_option { optsync = true; optdepr = false; optname = "use iterative deepening strategy"; optkey = ["Typeclasses";"Iterative";"Deepening"]; optread = get_typeclasses_iterative_deepening; optwrite = set_typeclasses_iterative_deepening; } let _ = declare_bool_option { optsync = true; optdepr = false; optname = "compat"; optkey = ["Typeclasses";"Legacy";"Resolution"]; optread = get_typeclasses_legacy_resolution; optwrite = set_typeclasses_legacy_resolution; } let _ = declare_bool_option { optsync = true; optdepr = false; optname = "compat"; optkey = ["Typeclasses";"Filtered";"Unification"]; optread = get_typeclasses_filtered_unification; optwrite = set_typeclasses_filtered_unification; } let set_typeclasses_debug = declare_bool_option { optsync = true; optdepr = false; optname = "debug output for typeclasses proof search"; optkey = ["Typeclasses";"Debug"]; optread = get_typeclasses_debug; optwrite = set_typeclasses_debug; } let _ = declare_bool_option { optsync = true; optdepr = false; optname = "debug output for typeclasses proof search"; optkey = ["Debug";"Typeclasses"]; optread = get_typeclasses_debug; optwrite = set_typeclasses_debug; } let _ = declare_int_option { optsync = true; optdepr = false; optname = "verbosity of debug output for typeclasses proof search"; optkey = ["Typeclasses";"Debug";"Verbosity"]; optread = get_typeclasses_verbose; optwrite = set_typeclasses_verbose; } let set_typeclasses_depth = declare_int_option { optsync = true; optdepr = false; optname = "depth for typeclasses proof search"; optkey = ["Typeclasses";"Depth"]; optread = get_typeclasses_depth; optwrite = set_typeclasses_depth; } let pr_ev evs ev = Printer.pr_constr_env (Goal.V82.env evs ev) evs (Evarutil.nf_evar evs (Goal.V82.concl evs ev)) (** Typeclasses instance search tactic / eauto *) open Auto open Unification let auto_core_unif_flags st freeze = { modulo_conv_on_closed_terms = Some st; use_metas_eagerly_in_conv_on_closed_terms = true; use_evars_eagerly_in_conv_on_closed_terms = false; modulo_delta = st; modulo_delta_types = st; check_applied_meta_types = false; use_pattern_unification = true; use_meta_bound_pattern_unification = true; frozen_evars = freeze; restrict_conv_on_strict_subterms = false; (* ? *) modulo_betaiota = true; modulo_eta = !typeclasses_modulo_eta; } let auto_unif_flags freeze st = let fl = auto_core_unif_flags st freeze in { core_unify_flags = fl; merge_unify_flags = fl; subterm_unify_flags = fl; allow_K_in_toplevel_higher_order_unification = false; resolve_evars = false } let e_give_exact flags poly (c,clenv) gl = let (c, _, _) = c in let c, gl = if poly then let clenv', subst = Clenv.refresh_undefined_univs clenv in let evd = evars_reset_evd ~with_conv_pbs:true gl.sigma clenv'.evd in let c = Vars.subst_univs_level_constr subst c in c, {gl with sigma = evd} else c, gl in let t1 = pf_unsafe_type_of gl c in Proofview.V82.of_tactic (Clenvtac.unify ~flags t1 <*> exact_no_check c) gl let unify_e_resolve poly flags = { enter = begin fun gls (c,_,clenv) -> let clenv', c = connect_hint_clenv poly c clenv gls in let clenv' = Tacmach.New.of_old (clenv_unique_resolver ~flags clenv') gls in Clenvtac.clenv_refine true ~with_classes:false clenv' end } let unify_resolve poly flags = { enter = begin fun gls (c,_,clenv) -> let clenv', _ = connect_hint_clenv poly c clenv gls in let clenv' = Tacmach.New.of_old (clenv_unique_resolver ~flags clenv') gls in Clenvtac.clenv_refine false ~with_classes:false clenv' end } (** Application of a lemma using [refine] instead of the old [w_unify] *) let unify_resolve_refine poly flags = let open Clenv in { enter = begin fun gls ((c, t, ctx),n,clenv) -> let env = Proofview.Goal.env gls in let concl = Proofview.Goal.concl gls in Refine.refine ~unsafe:true { Sigma.run = fun sigma -> let sigma = Sigma.to_evar_map sigma in let sigma, term, ty = if poly then let (subst, ctx) = Universes.fresh_universe_context_set_instance ctx in let map c = Vars.subst_univs_level_constr subst c in let sigma = Evd.merge_context_set Evd.univ_flexible sigma ctx in sigma, map c, map t else let sigma = Evd.merge_context_set Evd.univ_flexible sigma ctx in sigma, c, t in let sigma', cl = Clenv.make_evar_clause env sigma ?len:n ty in let term = applistc term (List.map (fun x -> x.hole_evar) cl.cl_holes) in let sigma' = let evdref = ref sigma' in if not (Evarconv.e_cumul env ~ts:flags.core_unify_flags.modulo_delta evdref cl.cl_concl concl) then Type_errors.error_actual_type env {Environ.uj_val = term; Environ.uj_type = cl.cl_concl} concl; !evdref in Sigma.here term (Sigma.Unsafe.of_evar_map sigma') } end } (** Dealing with goals of the form A -> B and hints of the form C -> A -> B. *) let clenv_of_prods poly nprods (c, clenv) gl = let (c, _, _) = c in if poly || Int.equal nprods 0 then Some (None, clenv) else let ty = Retyping.get_type_of (Proofview.Goal.env gl) (Sigma.to_evar_map (Proofview.Goal.sigma gl)) c in let diff = nb_prod ty - nprods in if Pervasives.(>=) diff 0 then (* Was Some clenv... *) Some (Some diff, Tacmach.New.of_old (fun gls -> mk_clenv_from_n gls (Some diff) (c,ty)) gl) else None let with_prods nprods poly (c, clenv) f = if get_typeclasses_limit_intros () then Proofview.Goal.nf_enter { enter = begin fun gl -> match clenv_of_prods poly nprods (c, clenv) gl with | None -> Tacticals.New.tclZEROMSG (str"Not enough premisses") | Some (diff, clenv') -> f.enter gl (c, diff, clenv') end } else Proofview.Goal.nf_enter { enter = begin fun gl -> if Int.equal nprods 0 then f.enter gl (c, None, clenv) else Tacticals.New.tclZEROMSG (str"Not enough premisses") end } let matches_pattern concl pat = let matches env sigma = match pat with | None -> Proofview.tclUNIT () | Some pat -> let sigma = Sigma.to_evar_map sigma in if Constr_matching.is_matching env sigma pat concl then Proofview.tclUNIT () else Tacticals.New.tclZEROMSG (str "conclPattern") in Proofview.Goal.enter { enter = fun gl -> let env = Proofview.Goal.env gl in let sigma = Proofview.Goal.sigma gl in matches env sigma } (** Semantics of type class resolution lemma application: - Use unification to find a well-typed substitution. There might be evars in the goal and the lemma. Evars in the goal can get refined. - Independent evars are turned into goals, whatever their kind is. - Dependent evars of the lemma corresponding to arguments which appear in independent goals or the conclusion are turned into subgoals iff they are of typeclass kind. - The remaining dependent evars not of typeclass type are shelved, and resolution must fill them for it to succeed, otherwise we backtrack. *) let pr_gls sigma gls = prlist_with_sep spc (fun ev -> int (Evar.repr ev) ++ spc () ++ pr_ev sigma ev) gls (** Ensure the dependent subgoals are shelved after an apply/eapply. *) let shelve_dependencies gls = let open Proofview in tclEVARMAP >>= fun sigma -> (if !typeclasses_debug > 1 then Feedback.msg_debug (str" shelving goals: " ++ pr_gls sigma gls); shelve_goals gls) (** Hack to properly solve dependent evars that are typeclasses *) let rec e_trivial_fail_db only_classes db_list local_db secvars = let open Tacticals.New in let open Tacmach.New in let trivial_fail = Proofview.Goal.nf_enter { enter = begin fun gl -> let env = Proofview.Goal.env gl in let sigma = Tacmach.New.project gl in let d = pf_last_hyp gl in let hintl = make_resolve_hyp env sigma d in let hints = Hint_db.add_list env sigma hintl local_db in e_trivial_fail_db only_classes db_list hints secvars end } in let trivial_resolve = Proofview.Goal.nf_enter { enter = begin fun gl -> let tacs = e_trivial_resolve db_list local_db secvars only_classes (project gl) (pf_concl gl) in tclFIRST (List.map (fun (x,_,_,_,_) -> x) tacs) end} in let tacl = Eauto.registered_e_assumption :: (tclTHEN Tactics.intro trivial_fail :: [trivial_resolve]) in tclFIRST (List.map tclCOMPLETE tacl) and e_my_find_search db_list local_db secvars hdc complete only_classes sigma concl = let open Proofview.Notations in let prods, concl = decompose_prod_assum concl in let nprods = List.length prods in let freeze = try let cl = Typeclasses.class_info (fst hdc) in if cl.cl_strict then Evd.evars_of_term concl else Evar.Set.empty with e when CErrors.noncritical e -> Evar.Set.empty in let hintl = List.map_append (fun db -> let tacs = if Hint_db.use_dn db then (* Using dnet *) Hint_db.map_eauto secvars hdc concl db else Hint_db.map_existential secvars hdc concl db in let flags = auto_unif_flags freeze (Hint_db.transparent_state db) in List.map (fun x -> (flags, x)) tacs) (local_db::db_list) in let tac_of_hint = fun (flags, {pri = b; pat = p; poly = poly; code = t; secvars; name = name}) -> let tac = function | Res_pf (term,cl) -> if get_typeclasses_filtered_unification () then let tac = with_prods nprods poly (term,cl) ({ enter = fun gl clenv -> (matches_pattern concl p) <*> ((unify_resolve_refine poly flags).enter gl clenv)}) in Tacticals.New.tclTHEN tac Proofview.shelve_unifiable else let tac = with_prods nprods poly (term,cl) (unify_resolve poly flags) in if get_typeclasses_legacy_resolution () then Tacticals.New.tclTHEN tac Proofview.shelve_unifiable else Proofview.tclBIND (Proofview.with_shelf tac) (fun (gls, ()) -> shelve_dependencies gls) | ERes_pf (term,cl) -> if get_typeclasses_filtered_unification () then let tac = (with_prods nprods poly (term,cl) ({ enter = fun gl clenv -> (matches_pattern concl p) <*> ((unify_resolve_refine poly flags).enter gl clenv)})) in Tacticals.New.tclTHEN tac Proofview.shelve_unifiable else let tac = with_prods nprods poly (term,cl) (unify_e_resolve poly flags) in if get_typeclasses_legacy_resolution () then Tacticals.New.tclTHEN tac Proofview.shelve_unifiable else Proofview.tclBIND (Proofview.with_shelf tac) (fun (gls, ()) -> shelve_dependencies gls) | Give_exact c -> Proofview.V82.tactic (e_give_exact flags poly c) | Res_pf_THEN_trivial_fail (term,cl) -> let fst = with_prods nprods poly (term,cl) (unify_e_resolve poly flags) in let snd = if complete then Tacticals.New.tclIDTAC else e_trivial_fail_db only_classes db_list local_db secvars in Tacticals.New.tclTHEN fst snd | Unfold_nth c -> let tac = Proofview.V82.of_tactic (unfold_in_concl [AllOccurrences,c]) in Proofview.V82.tactic (tclWEAK_PROGRESS tac) | Extern tacast -> conclPattern concl p tacast in let tac = run_hint t tac in let tac = if complete then Tacticals.New.tclCOMPLETE tac else tac in let pp = match p with | Some pat when get_typeclasses_filtered_unification () -> str " with pattern " ++ Printer.pr_constr_pattern pat | _ -> mt () in match repr_hint t with | Extern _ -> (tac, b, true, name, lazy (pr_hint t ++ pp)) | _ -> (tac, b, false, name, lazy (pr_hint t ++ pp)) in List.map tac_of_hint hintl and e_trivial_resolve db_list local_db secvars only_classes sigma concl = try e_my_find_search db_list local_db secvars (decompose_app_bound concl) true only_classes sigma concl with Bound | Not_found -> [] let e_possible_resolve db_list local_db secvars only_classes sigma concl = try e_my_find_search db_list local_db secvars (decompose_app_bound concl) false only_classes sigma concl with Bound | Not_found -> [] let cut_of_hints h = List.fold_left (fun cut db -> PathOr (Hint_db.cut db, cut)) PathEmpty h let catchable = function | Refiner.FailError _ -> true | e -> Logic.catchable_exception e let pr_depth l = prlist_with_sep (fun () -> str ".") int (List.rev l) let is_Prop env sigma concl = let ty = Retyping.get_type_of env sigma concl in match kind_of_term ty with | Sort (Prop Null) -> true | _ -> false let is_unique env concl = try let (cl,u), args = dest_class_app env concl in cl.cl_unique with e when CErrors.noncritical e -> false (** Sort the undefined variables from the least-dependent to most dependent. *) let top_sort evm undefs = let l' = ref [] in let tosee = ref undefs in let rec visit ev evi = let evs = Evarutil.undefined_evars_of_evar_info evm evi in Evar.Set.iter (fun ev -> if Evar.Map.mem ev !tosee then visit ev (Evar.Map.find ev !tosee)) evs; tosee := Evar.Map.remove ev !tosee; l' := ev :: !l'; in while not (Evar.Map.is_empty !tosee) do let ev, evi = Evar.Map.min_binding !tosee in visit ev evi done; List.rev !l' (** We transform the evars that are concerned by this resolution (according to predicate p) into goals. Invariant: function p only manipulates and returns undefined evars *) let evars_to_goals p evm = let goals = ref Evar.Map.empty in let map ev evi = let evi, goal = p evm ev evi in let () = if goal then goals := Evar.Map.add ev evi !goals in evi in let evm = Evd.raw_map_undefined map evm in if Evar.Map.is_empty !goals then None else Some (!goals, evm) (** Making local hints *) let make_resolve_hyp env sigma st flags only_classes pri decl = let id = NamedDecl.get_id decl in let cty = Evarutil.nf_evar sigma (NamedDecl.get_type decl) in let rec iscl env ty = let ctx, ar = decompose_prod_assum ty in match kind_of_term (fst (decompose_app ar)) with | Const (c,_) -> is_class (ConstRef c) | Ind (i,_) -> is_class (IndRef i) | _ -> let env' = Environ.push_rel_context ctx env in let ty' = whd_all env' ar in if not (Term.eq_constr ty' ar) then iscl env' ty' else false in let is_class = iscl env cty in let keep = not only_classes || is_class in if keep then let c = mkVar id in let name = PathHints [VarRef id] in let hints = if is_class then let hints = build_subclasses ~check:false env sigma (VarRef id) None in (List.map_append (fun (path,pri, c) -> make_resolves env sigma ~name:(PathHints path) (true,false,Flags.is_verbose()) pri false (IsConstr (c,Univ.ContextSet.empty))) hints) else [] in (hints @ List.map_filter (fun f -> try Some (f (c, cty, Univ.ContextSet.empty)) with Failure _ | UserError _ -> None) [make_exact_entry ~name env sigma pri false; make_apply_entry ~name env sigma flags pri false]) else [] let make_hints g st only_classes sign = let hintlist = List.fold_left (fun hints hyp -> let consider = try let t = hyp |> NamedDecl.get_id |> Global.lookup_named |> NamedDecl.get_type in (* Section variable, reindex only if the type changed *) not (Term.eq_constr t (NamedDecl.get_type hyp)) with Not_found -> true in if consider then let hint = pf_apply make_resolve_hyp g st (true,false,false) only_classes None hyp in hint @ hints else hints) ([]) sign in Hint_db.add_list (pf_env g) (project g) hintlist (Hint_db.empty st true) (** <= 8.5 resolution *) module V85 = struct type autoinfo = { hints : hint_db; is_evar: existential_key option; only_classes: bool; unique : bool; auto_depth: int list; auto_last_tac: std_ppcmds Lazy.t; auto_path : global_reference option list; auto_cut : hints_path } type autogoal = goal * autoinfo type failure = NotApplicable | ReachedLimit type 'ans fk = failure -> 'ans type ('a,'ans) sk = 'a -> 'ans fk -> 'ans type 'a tac = { skft : 'ans. ('a,'ans) sk -> 'ans fk -> autogoal sigma -> 'ans } type auto_result = autogoal list sigma type atac = auto_result tac (* Some utility types to avoid the need of -rectypes *) type 'a optionk = | Nonek | Somek of 'a * 'a optionk fk type ('a,'b) optionk2 = | Nonek2 of failure | Somek2 of 'a * 'b * ('a,'b) optionk2 fk let pf_filtered_hyps gls = Goal.V82.hyps gls.Evd.sigma (sig_it gls) let make_autogoal_hints = let cache = ref (true, Environ.empty_named_context_val, Hint_db.empty full_transparent_state true) in fun only_classes ?(st=full_transparent_state) g -> let sign = pf_filtered_hyps g in let (onlyc, sign', cached_hints) = !cache in if onlyc == only_classes && (sign == sign' || Environ.eq_named_context_val sign sign') && Hint_db.transparent_state cached_hints == st then cached_hints else let hints = make_hints g st only_classes (Environ.named_context_of_val sign) in cache := (only_classes, sign, hints); hints let lift_tactic tac (f : goal list sigma -> autoinfo -> autogoal list sigma) : 'a tac = { skft = fun sk fk {it = gl,hints; sigma=s;} -> let res = try Some (tac {it=gl; sigma=s;}) with e when catchable e -> None in match res with | Some gls -> sk (f gls hints) fk | None -> fk NotApplicable } let intro_tac : atac = let tac {it = gls; sigma = s} info = let gls' = List.map (fun g' -> let env = Goal.V82.env s g' in let context = Environ.named_context_of_val (Goal.V82.hyps s g') in let hint = make_resolve_hyp env s (Hint_db.transparent_state info.hints) (true,false,false) info.only_classes None (List.hd context) in let ldb = Hint_db.add_list env s hint info.hints in (g', { info with is_evar = None; hints = ldb; auto_last_tac = lazy (str"intro") })) gls in {it = gls'; sigma = s;} in lift_tactic (Proofview.V82.of_tactic Tactics.intro) tac let normevars_tac : atac = { skft = fun sk fk {it = (gl, info); sigma = s;} -> let gl', sigma' = Goal.V82.nf_evar s gl in let info' = { info with auto_last_tac = lazy (str"normevars") } in sk {it = [gl', info']; sigma = sigma';} fk } let merge_failures x y = match x, y with | _, ReachedLimit | ReachedLimit, _ -> ReachedLimit | NotApplicable, NotApplicable -> NotApplicable let or_tac (x : 'a tac) (y : 'a tac) : 'a tac = { skft = fun sk fk gls -> x.skft sk (fun f -> y.skft sk (fun f' -> fk (merge_failures f f')) gls) gls } let or_else_tac (x : 'a tac) (y : failure -> 'a tac) : 'a tac = { skft = fun sk fk gls -> x.skft sk (fun f -> (y f).skft sk fk gls) gls } let needs_backtrack env evd oev concl = if Option.is_empty oev || is_Prop env evd concl then occur_existential concl else true let hints_tac hints sk fk {it = gl,info; sigma = s} = let env = Goal.V82.env s gl in let concl = Goal.V82.concl s gl in let tacgl = {it = gl; sigma = s;} in let secvars = secvars_of_hyps (Environ.named_context_of_val (Goal.V82.hyps s gl)) in let poss = e_possible_resolve hints info.hints secvars info.only_classes s concl in let unique = is_unique env concl in let rec aux i foundone = function | (tac, _, extern, name, pp) :: tl -> let derivs = path_derivate info.auto_cut name in let res = try if path_matches derivs [] then None else Some (Proofview.V82.of_tactic tac tacgl) with e when catchable e -> None in (match res with | None -> aux i foundone tl | Some {it = gls; sigma = s';} -> if !typeclasses_debug > 0 then Feedback.msg_debug (pr_depth (i :: info.auto_depth) ++ str": " ++ Lazy.force pp ++ str" on" ++ spc () ++ pr_ev s gl); let sgls = evars_to_goals (fun evm ev evi -> if Typeclasses.is_resolvable evi && not (Evd.is_undefined s ev) && (not info.only_classes || Typeclasses.is_class_evar evm evi) then Typeclasses.mark_unresolvable evi, true else evi, false) s' in let newgls, s' = let gls' = List.map (fun g -> (None, g)) gls in match sgls with | None -> gls', s' | Some (evgls, s') -> if not !typeclasses_dependency_order then (gls' @ List.map (fun (ev,_) -> (Some ev, ev)) (Evar.Map.bindings evgls), s') else (* Reorder with dependent subgoals. *) let evm = List.fold_left (fun acc g -> Evar.Map.add g (Evd.find_undefined s' g) acc) evgls gls in let gls = top_sort s' evm in (List.map (fun ev -> Some ev, ev) gls, s') in let reindex g = let open Goal.V82 in extern && not (Environ.eq_named_context_val (hyps s' g) (hyps s' gl)) in let gl' j (evar, g) = let hints' = if reindex g then make_autogoal_hints info.only_classes ~st:(Hint_db.transparent_state info.hints) {it = g; sigma = s';} else info.hints in { info with auto_depth = j :: i :: info.auto_depth; auto_last_tac = pp; is_evar = evar; hints = hints'; auto_cut = derivs } in let gls' = List.map_i (fun i g -> snd g, gl' i g) 1 newgls in let glsv = {it = gls'; sigma = s';} in let fk' = (fun e -> let do_backtrack = if unique then occur_existential concl else if info.unique then true else if List.is_empty gls' then needs_backtrack env s' info.is_evar concl else true in let e' = match foundone with None -> e | Some e' -> merge_failures e e' in if !typeclasses_debug > 0 then Feedback.msg_debug ((if do_backtrack then str"Backtracking after " else str "Not backtracking after ") ++ Lazy.force pp); if do_backtrack then aux (succ i) (Some e') tl else fk e') in sk glsv fk') | [] -> if foundone == None && !typeclasses_debug > 0 then Feedback.msg_debug (pr_depth info.auto_depth ++ str": no match for " ++ Printer.pr_constr_env (Goal.V82.env s gl) s concl ++ spc () ++ str ", " ++ int (List.length poss) ++ str" possibilities"); match foundone with | Some e -> fk e | None -> fk NotApplicable in aux 1 None poss let hints_tac hints = { skft = fun sk fk gls -> hints_tac hints sk fk gls } let then_list (second : atac) (sk : (auto_result, 'a) sk) : (auto_result, 'a) sk = let rec aux s (acc : autogoal list list) fk = function | (gl,info) :: gls -> Control.check_for_interrupt (); (match info.is_evar with | Some ev when Evd.is_defined s ev -> aux s acc fk gls | _ -> second.skft (fun {it=gls';sigma=s'} fk' -> let fk'' = if not info.unique && List.is_empty gls' && not (needs_backtrack (Goal.V82.env s gl) s info.is_evar (Goal.V82.concl s gl)) then fk else fk' in aux s' (gls'::acc) fk'' gls) fk {it = (gl,info); sigma = s; }) | [] -> Somek2 (List.rev acc, s, fk) in fun {it = gls; sigma = s; } fk -> let rec aux' = function | Nonek2 e -> fk e | Somek2 (res, s', fk') -> let goals' = List.concat res in sk {it = goals'; sigma = s'; } (fun e -> aux' (fk' e)) in aux' (aux s [] (fun e -> Nonek2 e) gls) let then_tac (first : atac) (second : atac) : atac = { skft = fun sk fk -> first.skft (then_list second sk) fk } let run_tac (t : 'a tac) (gl : autogoal sigma) : auto_result option = t.skft (fun x _ -> Some x) (fun _ -> None) gl type run_list_res = auto_result optionk let run_list_tac (t : 'a tac) p goals (gl : autogoal list sigma) : run_list_res = (then_list t (fun x fk -> Somek (x, fk))) gl (fun _ -> Nonek) let fail_tac reason : atac = { skft = fun sk fk _ -> fk reason } let rec fix (t : 'a tac) : 'a tac = then_tac t { skft = fun sk fk -> (fix t).skft sk fk } let rec fix_limit limit (t : 'a tac) : 'a tac = if Int.equal limit 0 then fail_tac ReachedLimit else then_tac t { skft = fun sk fk -> (fix_limit (pred limit) t).skft sk fk } let fix_iterative t = let rec aux depth = or_else_tac (fix_limit depth t) (function | NotApplicable as e -> fail_tac e | ReachedLimit -> aux (succ depth)) in aux 1 let fix_iterative_limit limit (t : 'a tac) : 'a tac = let rec aux depth = if Int.equal limit depth then fail_tac ReachedLimit else or_tac (fix_limit depth t) { skft = fun sk fk -> (aux (succ depth)).skft sk fk } in aux 1 let make_autogoal ?(only_classes=true) ?(unique=false) ?(st=full_transparent_state) cut ev g = let hints = make_autogoal_hints only_classes ~st g in (g.it, { hints = hints ; is_evar = ev; unique = unique; only_classes = only_classes; auto_depth = []; auto_last_tac = lazy (str"none"); auto_path = []; auto_cut = cut }) let make_autogoals ?(only_classes=true) ?(unique=false) ?(st=full_transparent_state) hints gs evm' = let cut = cut_of_hints hints in let gl i g = let (gl, auto) = make_autogoal ~only_classes ~unique ~st cut (Some g) {it = g; sigma = evm'; } in (gl, { auto with auto_depth = [i]}) in { it = List.map_i gl 1 gs; sigma = evm' } let get_result r = match r with | Nonek -> None | Somek (gls, fk) -> Some (gls.sigma,fk) let run_on_evars ?(only_classes=true) ?(unique=false) ?(st=full_transparent_state) p evm hints tac = match evars_to_goals p evm with | None -> None (* This happens only because there's no evar having p *) | Some (goals, evm') -> let goals = if !typeclasses_dependency_order then top_sort evm' goals else List.map (fun (ev, _) -> ev) (Evar.Map.bindings goals) in let res = run_list_tac tac p goals (make_autogoals ~only_classes ~unique ~st hints goals evm') in match get_result res with | None -> raise Not_found | Some (evm', fk) -> Some (evars_reset_evd ~with_conv_pbs:true ~with_univs:false evm' evm, fk) let eauto_tac hints = then_tac normevars_tac (or_tac (hints_tac hints) intro_tac) let eauto_tac depth hints = if get_typeclasses_iterative_deepening () then match depth with | None -> fix_iterative (eauto_tac hints) | Some depth -> fix_iterative_limit depth (eauto_tac hints) else match depth with | None -> fix (eauto_tac hints) | Some depth -> fix_limit depth (eauto_tac hints) let real_eauto ?depth unique st hints p evd = let res = run_on_evars ~st ~unique p evd hints (eauto_tac depth hints) in match res with | None -> evd | Some (evd', fk) -> if unique then (match get_result (fk NotApplicable) with | Some (evd'', fk') -> error "Typeclass resolution gives multiple solutions" | None -> evd') else evd' let resolve_all_evars_once debug depth unique p evd = let db = searchtable_map typeclasses_db in real_eauto ?depth unique (Hint_db.transparent_state db) [db] p evd let eauto85 ?(only_classes=true) ?st depth hints g = let gl = { it = make_autogoal ~only_classes ?st (cut_of_hints hints) None g; sigma = project g; } in match run_tac (eauto_tac depth hints) gl with | None -> raise Not_found | Some {it = goals; sigma = s; } -> {it = List.map fst goals; sigma = s;} end (** 8.6 resolution *) module Search = struct type autoinfo = { search_depth : int list; last_tac : Pp.std_ppcmds Lazy.t; search_dep : bool; search_only_classes : bool; search_cut : hints_path; search_hints : hint_db; } (** Local hints *) let autogoal_cache = ref (DirPath.empty, true, Context.Named.empty, Hint_db.empty full_transparent_state true) let make_autogoal_hints only_classes ?(st=full_transparent_state) g = let open Proofview in let open Tacmach.New in let sign = Goal.hyps g in let (dir, onlyc, sign', cached_hints) = !autogoal_cache in let cwd = Lib.cwd () in if DirPath.equal cwd dir && (onlyc == only_classes) && Context.Named.equal sign sign' && Hint_db.transparent_state cached_hints == st then cached_hints else let hints = make_hints {it = Goal.goal g; sigma = project g} st only_classes sign in autogoal_cache := (cwd, only_classes, sign, hints); hints let make_autogoal ?(st=full_transparent_state) only_classes dep cut i g = let hints = make_autogoal_hints only_classes ~st g in { search_hints = hints; search_depth = [i]; last_tac = lazy (str"none"); search_dep = dep; search_only_classes = only_classes; search_cut = cut } (** In the proof engine failures are represented as exceptions *) exception ReachedLimitEx exception NotApplicableEx (** ReachedLimitEx has priority over NotApplicableEx to handle iterative deepening: it should fail when no hints are applicable, but go to a deeper depth otherwise. *) let merge_exceptions e e' = match fst e, fst e' with | ReachedLimitEx, _ -> e | _, ReachedLimitEx -> e' | _, _ -> e (** Determine if backtracking is needed for this goal. If the type class is unique or in Prop and there are no evars in the goal then we do NOT backtrack. *) let needs_backtrack env evd unique concl = if unique || is_Prop env evd concl then occur_existential concl else true let mark_unresolvables sigma goals = List.fold_left (fun sigma gl -> let evi = Evd.find_undefined sigma gl in let evi' = Typeclasses.mark_unresolvable evi in Evd.add sigma gl evi') sigma goals (** The general hint application tactic. tac1 + tac2 .... The choice of OR or ORELSE is determined depending on the dependencies of the goal and the unique/Prop status *) let hints_tac_gl hints info kont gl : unit Proofview.tactic = let open Proofview in let open Proofview.Notations in let env = Goal.env gl in let concl = Goal.concl gl in let sigma = Goal.sigma gl in let s = Sigma.to_evar_map sigma in let unique = not info.search_dep || is_unique env concl in let backtrack = needs_backtrack env s unique concl in if !typeclasses_debug > 0 then Feedback.msg_debug (pr_depth info.search_depth ++ str": looking for " ++ Printer.pr_constr_env (Goal.env gl) s concl ++ (if backtrack then str" with backtracking" else str" without backtracking")); let secvars = compute_secvars gl in let poss = e_possible_resolve hints info.search_hints secvars info.search_only_classes s concl in (* If no goal depends on the solution of this one or the instances are irrelevant/assumed to be unique, then we don't need to backtrack, as long as no evar appears in the goal This is an overapproximation. Evars could appear in this goal only and not any other *) let ortac = if backtrack then Proofview.tclOR else Proofview.tclORELSE in let idx = ref 1 in let foundone = ref false in let rec onetac e (tac, pat, b, name, pp) tl = let derivs = path_derivate info.search_cut name in (if !typeclasses_debug > 1 then Feedback.msg_debug (pr_depth (!idx :: info.search_depth) ++ str": trying " ++ Lazy.force pp ++ (if !foundone != true then str" on" ++ spc () ++ pr_ev s (Proofview.Goal.goal gl) else mt ()))); let tac_of gls i j = Goal.nf_enter { enter = fun gl' -> let sigma' = Goal.sigma gl' in let s' = Sigma.to_evar_map sigma' in let _concl = Goal.concl gl' in if !typeclasses_debug > 0 then Feedback.msg_debug (pr_depth (succ j :: i :: info.search_depth) ++ str" : " ++ pr_ev s' (Proofview.Goal.goal gl')); let hints' = if b && not (Context.Named.equal (Goal.hyps gl') (Goal.hyps gl)) then let st = Hint_db.transparent_state info.search_hints in make_autogoal_hints info.search_only_classes ~st gl' else info.search_hints in let dep' = info.search_dep || Proofview.unifiable s' (Goal.goal gl') gls in let info' = { search_depth = succ j :: i :: info.search_depth; last_tac = pp; search_dep = dep'; search_only_classes = info.search_only_classes; search_hints = hints'; search_cut = derivs } in kont info' } in let rec result (shelf, ()) i k = foundone := true; Proofview.Unsafe.tclGETGOALS >>= fun gls -> let j = List.length gls in (if !typeclasses_debug > 0 then Feedback.msg_debug (pr_depth (i :: info.search_depth) ++ str": " ++ Lazy.force pp ++ str" on" ++ spc () ++ pr_ev s (Proofview.Goal.goal gl) ++ str", " ++ int j ++ str" subgoal(s)" ++ (Option.cata (fun k -> str " in addition to the first " ++ int k) (mt()) k))); let res = if j = 0 then tclUNIT () else tclDISPATCH (List.init j (fun j' -> (tac_of gls i (Option.default 0 k + j)))) in let finish sigma = let filter ev = try let evi = Evd.find_undefined sigma ev in if info.search_only_classes then Some (ev, is_class_type sigma (Evd.evar_concl evi)) else Some (ev, true) with Not_found -> None in let remaining = CList.map_filter filter shelf in (if !typeclasses_debug > 1 then let prunsolved (ev, _) = int (Evar.repr ev) ++ spc () ++ pr_ev sigma ev in let unsolved = prlist_with_sep spc prunsolved remaining in Feedback.msg_debug (pr_depth (i :: info.search_depth) ++ str": after " ++ Lazy.force pp ++ str" finished, " ++ int (List.length remaining) ++ str " goals are shelved and unsolved ( " ++ unsolved ++ str")")); begin (* Some existentials produced by the original tactic were not solved in the subgoals, turn them into subgoals now. *) let shelved, goals = List.split_when (fun (ev, s) -> s) remaining in let shelved = List.map fst shelved and goals = List.map fst goals in if !typeclasses_debug > 1 then Feedback.msg_debug (str"Adding shelved subgoals to the search: " ++ prlist_with_sep spc (pr_ev sigma) goals ++ str" while shelving " ++ prlist_with_sep spc (pr_ev sigma) shelved); shelve_goals shelved <*> (if List.is_empty goals then tclUNIT () else let sigma' = mark_unresolvables sigma goals in with_shelf (Unsafe.tclEVARS sigma' <*> Unsafe.tclNEWGOALS goals) >>= fun s -> result s i (Some (Option.default 0 k + j))) end in res <*> tclEVARMAP >>= finish in if path_matches derivs [] then aux e tl else ortac (with_shelf tac >>= fun s -> let i = !idx in incr idx; result s i None) (fun e' -> aux (merge_exceptions e e') tl) and aux e = function | x :: xs -> onetac e x xs | [] -> if !foundone == false && !typeclasses_debug > 0 then Feedback.msg_debug (pr_depth info.search_depth ++ str": no match for " ++ Printer.pr_constr_env (Goal.env gl) s concl ++ spc () ++ str ", " ++ int (List.length poss) ++ str" possibilities"); match e with | (ReachedLimitEx,ie) -> Proofview.tclZERO ~info:ie ReachedLimitEx | (_,ie) -> Proofview.tclZERO ~info:ie NotApplicableEx in if backtrack then aux (NotApplicableEx,Exninfo.null) poss else tclONCE (aux (NotApplicableEx,Exninfo.null) poss) let hints_tac hints info kont : unit Proofview.tactic = Proofview.Goal.nf_enter { enter = fun gl -> hints_tac_gl hints info kont gl } let intro_tac info kont gl = let open Proofview in let open Proofview.Notations in let env = Goal.env gl in let sigma = Goal.sigma gl in let s = Sigma.to_evar_map sigma in let decl = Tacmach.New.pf_last_hyp gl in let hint = make_resolve_hyp env s (Hint_db.transparent_state info.search_hints) (true,false,false) info.search_only_classes None decl in let ldb = Hint_db.add_list env s hint info.search_hints in let info' = { info with search_hints = ldb; last_tac = lazy (str"intro") } in kont info' let intro info kont = Proofview.tclBIND Tactics.intro (fun _ -> Proofview.Goal.nf_enter { enter = fun gl -> intro_tac info kont gl }) let rec search_tac hints limit depth = let kont info = Proofview.numgoals >>= fun i -> if !typeclasses_debug > 1 then Feedback.msg_debug (str"calling eauto recursively at depth " ++ int (succ depth) ++ str" on " ++ int i ++ str" subgoals"); search_tac hints limit (succ depth) info in fun info -> if Int.equal depth (succ limit) then Proofview.tclZERO ReachedLimitEx else Proofview.tclOR (hints_tac hints info kont) (fun e -> Proofview.tclOR (intro info kont) (fun e' -> let (e, info) = merge_exceptions e e' in Proofview.tclZERO ~info e)) let search_tac_gl ?st only_classes dep hints depth i sigma gls gl : unit Proofview.tactic = let open Proofview in let open Proofview.Notations in let dep = dep || Proofview.unifiable sigma (Goal.goal gl) gls in let info = make_autogoal ?st only_classes dep (cut_of_hints hints) i gl in search_tac hints depth 1 info let search_tac ?(st=full_transparent_state) only_classes dep hints depth = let open Proofview in let tac sigma gls i = Goal.nf_enter { enter = fun gl -> search_tac_gl ~st only_classes dep hints depth (succ i) sigma gls gl } in Proofview.Unsafe.tclGETGOALS >>= fun gls -> Proofview.tclEVARMAP >>= fun sigma -> let j = List.length gls in (tclDISPATCH (List.init j (fun i -> tac sigma gls i))) let fix_iterative t = let rec aux depth = Proofview.tclOR (t depth) (function | (ReachedLimitEx,_) -> aux (succ depth) | (e,ie) -> Proofview.tclZERO ~info:ie e) in aux 1 let fix_iterative_limit limit t = let open Proofview in let rec aux depth = if Int.equal depth (succ limit) then tclZERO ReachedLimitEx else tclOR (t depth) (function (ReachedLimitEx, _) -> aux (succ depth) | (e,ie) -> Proofview.tclZERO ~info:ie e) in aux 1 let eauto_tac ?(st=full_transparent_state) ~only_classes ~depth ~dep hints = let tac = let search = search_tac ~st only_classes dep hints in if get_typeclasses_iterative_deepening () then match depth with | None -> fix_iterative search | Some l -> fix_iterative_limit l search else let depth = match depth with None -> -1 | Some d -> d in search depth in let error (e, ie) = match e with | ReachedLimitEx -> Tacticals.New.tclFAIL 0 (str"Proof search reached its limit") | NotApplicableEx -> Tacticals.New.tclFAIL 0 (str"Proof search failed" ++ (if Option.is_empty depth then mt() else str" without reaching its limit")) | e -> Proofview.tclZERO ~info:ie e in Proofview.tclOR tac error let run_on_evars ?(unique=false) p evm tac = match evars_to_goals p evm with | None -> None (* This happens only because there's no evar having p *) | Some (goals, evm') -> let goals = if !typeclasses_dependency_order then top_sort evm' goals else List.map (fun (ev, _) -> ev) (Evar.Map.bindings goals) in let fgoals = Evd.future_goals evm in let pgoal = Evd.principal_future_goal evm in let _, pv = Proofview.init evm' [] in let pv = Proofview.unshelve goals pv in try let (), pv', (unsafe, shelved, gaveup), _ = Proofview.apply (Global.env ()) tac pv in if Proofview.finished pv' then let evm' = Proofview.return pv' in assert(Evd.fold_undefined (fun ev _ acc -> let okev = Evd.mem evm ev || List.mem ev shelved in if not okev then Feedback.msg_debug (str "leaking evar " ++ int (Evar.repr ev) ++ spc () ++ pr_ev evm' ev); acc && okev) evm' true); let evm' = Evd.restore_future_goals evm' (shelved @ fgoals) pgoal in let evm' = evars_reset_evd ~with_conv_pbs:true ~with_univs:false evm' evm in Some evm' else raise Not_found with Logic_monad.TacticFailure _ -> raise Not_found let eauto depth only_classes unique dep st hints p evd = let eauto_tac = eauto_tac ~st ~only_classes ~depth ~dep hints in let res = run_on_evars ~unique p evd eauto_tac in match res with | None -> evd | Some evd' -> evd' (* TODO treat unique solutions *) let typeclasses_eauto ?depth unique st hints p evd = eauto depth true unique false st hints p evd (** Typeclasses eauto is an eauto which tries to resolve only goals of typeclass type, and assumes that the initially selected evars in evd are independent of the rest of the evars *) let typeclasses_resolve debug depth unique p evd = let db = searchtable_map typeclasses_db in typeclasses_eauto ?depth unique (Hint_db.transparent_state db) [db] p evd end (** Binding to either V85 or Search implementations. *) let eauto depth ~only_classes ~st ~dep dbs = Search.eauto_tac ~st ~only_classes ~depth ~dep dbs let typeclasses_eauto ?(only_classes=false) ?(st=full_transparent_state) ~depth dbs = let dbs = List.map_filter (fun db -> try Some (searchtable_map db) with e when CErrors.noncritical e -> None) dbs in let st = match dbs with x :: _ -> Hint_db.transparent_state x | _ -> st in let depth = match depth with None -> get_typeclasses_depth () | Some l -> Some l in if get_typeclasses_legacy_resolution () then Proofview.V82.tactic (fun gl -> try V85.eauto85 depth ~only_classes ~st dbs gl with Not_found -> Refiner.tclFAIL 0 (str"Proof search failed") gl) else eauto depth ~only_classes ~st ~dep:true dbs (** We compute dependencies via a union-find algorithm. Beware of the imperative effects on the partition structure, it should not be shared, but only used locally. *) module Intpart = Unionfind.Make(Evar.Set)(Evar.Map) let deps_of_constraints cstrs evm p = List.iter (fun (_, _, x, y) -> let evx = Evarutil.undefined_evars_of_term evm x in let evy = Evarutil.undefined_evars_of_term evm y in Intpart.union_set (Evar.Set.union evx evy) p) cstrs let evar_dependencies evm p = Evd.fold_undefined (fun ev evi _ -> let evars = Evar.Set.add ev (Evarutil.undefined_evars_of_evar_info evm evi) in Intpart.union_set evars p) evm () (** [split_evars] returns groups of undefined evars according to dependencies *) let split_evars evm = let p = Intpart.create () in evar_dependencies evm p; deps_of_constraints (snd (extract_all_conv_pbs evm)) evm p; Intpart.partition p let is_inference_forced p evd ev = try let evi = Evd.find_undefined evd ev in if Typeclasses.is_resolvable evi && snd (p ev evi) then let (loc, k) = evar_source ev evd in match k with | Evar_kinds.ImplicitArg (_, _, b) -> b | Evar_kinds.QuestionMark _ -> false | _ -> true else true with Not_found -> assert false let is_mandatory p comp evd = Evar.Set.exists (is_inference_forced p evd) comp (** In case of unsatisfiable constraints, build a nice error message *) let error_unresolvable env comp evd = let evd = Evarutil.nf_evar_map_undefined evd in let is_part ev = match comp with | None -> true | Some s -> Evar.Set.mem ev s in let fold ev evi (found, accu) = let ev_class = class_of_constr evi.evar_concl in if not (Option.is_empty ev_class) && is_part ev then (* focus on one instance if only one was searched for *) if not found then (true, Some ev) else (found, None) else (found, accu) in let (_, ev) = Evd.fold_undefined fold evd (true, None) in Pretype_errors.unsatisfiable_constraints (Evarutil.nf_env_evar evd env) evd ev comp (** Check if an evar is concerned by the current resolution attempt, (and in particular is in the current component), and also update its evar_info. Invariant : this should only be applied to undefined evars, and return undefined evar_info *) let select_and_update_evars p oevd in_comp evd ev evi = assert (evi.evar_body == Evar_empty); try let oevi = Evd.find_undefined oevd ev in if Typeclasses.is_resolvable oevi then Typeclasses.mark_unresolvable evi, (in_comp ev && p evd ev evi) else evi, false with Not_found -> Typeclasses.mark_unresolvable evi, p evd ev evi (** Do we still have unresolved evars that should be resolved ? *) let has_undefined p oevd evd = let check ev evi = snd (p oevd ev evi) in Evar.Map.exists check (Evd.undefined_map evd) (** Revert the resolvability status of evars after resolution, potentially unprotecting some evars that were set unresolvable just for this call to resolution. *) let revert_resolvability oevd evd = let map ev evi = try if not (Typeclasses.is_resolvable evi) then let evi' = Evd.find_undefined oevd ev in if Typeclasses.is_resolvable evi' then Typeclasses.mark_resolvable evi else evi else evi with Not_found -> evi in Evd.raw_map_undefined map evd exception Unresolved (** If [do_split] is [true], we try to separate the problem in several components and then solve them separately *) let resolve_all_evars debug depth unique env p oevd do_split fail = let split = if do_split then split_evars oevd else [Evar.Set.empty] in let in_comp comp ev = if do_split then Evar.Set.mem ev comp else true in let rec docomp evd = function | [] -> revert_resolvability oevd evd | comp :: comps -> let p = select_and_update_evars p oevd (in_comp comp) in try let evd' = if get_typeclasses_legacy_resolution () then V85.resolve_all_evars_once debug depth unique p evd else Search.typeclasses_resolve debug depth unique p evd in if has_undefined p oevd evd' then raise Unresolved; docomp evd' comps with Unresolved | Not_found -> if fail && (not do_split || is_mandatory (p evd) comp evd) then (* Unable to satisfy the constraints. *) let comp = if do_split then Some comp else None in error_unresolvable env comp evd else (* Best effort: do nothing on this component *) docomp evd comps in docomp oevd split let initial_select_evars filter = fun evd ev evi -> filter ev (snd evi.Evd.evar_source) && Typeclasses.is_class_evar evd evi let resolve_typeclass_evars debug depth unique env evd filter split fail = let evd = try Evarconv.consider_remaining_unif_problems ~ts:(Typeclasses.classes_transparent_state ()) env evd with e when CErrors.noncritical e -> evd in resolve_all_evars debug depth unique env (initial_select_evars filter) evd split fail let solve_inst env evd filter unique split fail = resolve_typeclass_evars (get_typeclasses_debug ()) (get_typeclasses_depth ()) unique env evd filter split fail let _ = Hook.set Typeclasses.solve_all_instances_hook solve_inst let resolve_one_typeclass env ?(sigma=Evd.empty) gl unique = let nc, gl, subst, _, _ = Evarutil.push_rel_context_to_named_context env gl in let (gl,t,sigma) = Goal.V82.mk_goal sigma nc gl Store.empty in let gls = { it = gl ; sigma = sigma; } in let hints = searchtable_map typeclasses_db in let st = Hint_db.transparent_state hints in let depth = get_typeclasses_depth () in let gls' = if get_typeclasses_legacy_resolution () then V85.eauto85 depth ~st [hints] gls else try Proofview.V82.of_tactic (Search.eauto_tac ~st ~only_classes:true ~depth [hints] ~dep:true) gls with Refiner.FailError _ -> raise Not_found in let evd = sig_sig gls' in let t' = let (ev, inst) = destEvar t in mkEvar (ev, Array.of_list subst) in let term = Evarutil.nf_evar evd t' in evd, term let _ = Hook.set Typeclasses.solve_one_instance_hook (fun x y z w -> resolve_one_typeclass x ~sigma:y z w) (** Take the head of the arity of a constr. Used in the partial application tactic. *) let rec head_of_constr t = let t = strip_outer_cast(collapse_appl t) in match kind_of_term t with | Prod (_,_,c2) -> head_of_constr c2 | LetIn (_,_,_,c2) -> head_of_constr c2 | App (f,args) -> head_of_constr f | _ -> t let head_of_constr h c = let c = head_of_constr c in letin_tac None (Name h) c None Locusops.allHyps let not_evar c = Proofview.tclEVARMAP >>= fun sigma -> match Evarutil.kind_of_term_upto sigma c with | Evar _ -> Tacticals.New.tclFAIL 0 (str"Evar") | _ -> Proofview.tclUNIT () let is_ground c gl = if Evarutil.is_ground_term (project gl) c then tclIDTAC gl else tclFAIL 0 (str"Not ground") gl let autoapply c i gl = let flags = auto_unif_flags Evar.Set.empty (Hints.Hint_db.transparent_state (Hints.searchtable_map i)) in let cty = pf_unsafe_type_of gl c in let ce = mk_clenv_from gl (c,cty) in let tac = { enter = fun gl -> (unify_e_resolve false flags).enter gl ((c,cty,Univ.ContextSet.empty),0,ce) } in Proofview.V82.of_tactic (Proofview.Goal.nf_enter tac) gl