(************************************************************************) (* * The Coq Proof Assistant / The Coq Development Team *) (* v * INRIA, CNRS and contributors - Copyright 1999-2018 *) (* 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 { 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 { 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 { 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 { 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 { optdepr = false; optname = "debug output for typeclasses proof search"; optkey = ["Typeclasses";"Debug"]; optread = get_typeclasses_debug; optwrite = set_typeclasses_debug; } let _ = declare_bool_option { optdepr = false; optname = "debug output for typeclasses proof search"; optkey = ["Debug";"Typeclasses"]; optread = get_typeclasses_debug; optwrite = set_typeclasses_debug; } let _ = declare_int_option { 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 { optdepr = false; optname = "depth for typeclasses proof search"; optkey = ["Typeclasses";"Depth"]; optread = get_typeclasses_depth; optwrite = set_typeclasses_depth; } type search_strategy = Dfs | Bfs let set_typeclasses_strategy = function | Dfs -> set_typeclasses_iterative_deepening false | Bfs -> set_typeclasses_iterative_deepening true let pr_ev evs ev = Printer.pr_econstr_env (Goal.V82.env evs ev) 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 = false; } 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) = let open Tacmach.New in Proofview.Goal.enter begin fun gl -> let sigma = project gl in let (c, _, _) = c in let c, sigma = if poly then let clenv', subst = Clenv.refresh_undefined_univs clenv in let evd = evars_reset_evd ~with_conv_pbs:true sigma clenv'.evd in let c = Vars.subst_univs_level_constr subst c in c, evd else c, sigma in let (sigma, t1) = Typing.type_of (pf_env gl) sigma c in Proofview.Unsafe.tclEVARS sigma <*> Clenvtac.unify ~flags t1 <*> exact_no_check c end let clenv_unique_resolver_tac with_evars ~flags clenv' = Proofview.Goal.enter begin fun gls -> let resolve = try Proofview.tclUNIT (clenv_unique_resolver ~flags clenv' gls) with e -> Proofview.tclZERO e in resolve >>= fun clenv' -> Clenvtac.clenv_refine ~with_evars ~with_classes:false clenv' end let unify_e_resolve poly flags = begin fun gls (c,_,clenv) -> let clenv', c = connect_hint_clenv poly c clenv gls in clenv_unique_resolver_tac true ~flags clenv' end let unify_resolve poly flags = begin fun gls (c,_,clenv) -> let clenv', _ = connect_hint_clenv poly c clenv gls in clenv_unique_resolver_tac false ~flags clenv' end (** Application of a lemma using [refine] instead of the old [w_unify] *) let unify_resolve_refine poly flags gls ((c, t, ctx),n,clenv) = let open Clenv in let env = Proofview.Goal.env gls in let concl = Proofview.Goal.concl gls in Refine.refine ~typecheck:false begin fun sigma -> let sigma, term, ty = if poly then let (subst, ctx) = UnivGen.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 = applist (term, List.map (fun x -> x.hole_evar) cl.cl_holes) in let sigma' = Evarconv.the_conv_x_leq env ~ts:flags.core_unify_flags.modulo_delta cl.cl_concl concl sigma' in (sigma', term) end let unify_resolve_refine poly flags gl clenv = Proofview.tclORELSE (unify_resolve_refine poly flags gl clenv) (fun ie -> match fst ie with | Evarconv.UnableToUnify _ -> Tacticals.New.tclZEROMSG (str "Unable to unify") | e when CErrors.noncritical e -> Tacticals.New.tclZEROMSG (str "Unexpected error") | _ -> iraise ie) (** 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 sigma = Tacmach.New.project gl in let ty = Retyping.get_type_of (Proofview.Goal.env gl) sigma c in let diff = nb_prod sigma ty - nprods in if Pervasives.(>=) diff 0 then (* Was Some clenv... *) Some (Some diff, mk_clenv_from_n gl (Some diff) (c,ty)) else None let with_prods nprods poly (c, clenv) f = if get_typeclasses_limit_intros () then Proofview.Goal.enter begin fun gl -> try match clenv_of_prods poly nprods (c, clenv) gl with | None -> Tacticals.New.tclZEROMSG (str"Not enough premisses") | Some (diff, clenv') -> f gl (c, diff, clenv') with e when CErrors.noncritical e -> Tacticals.New.tclZEROMSG (CErrors.print e) end else Proofview.Goal.enter begin fun gl -> if Int.equal nprods 0 then f 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 -> if Constr_matching.is_matching env sigma pat concl then Proofview.tclUNIT () else Tacticals.New.tclZEROMSG (str "pattern does not match") in Proofview.Goal.enter begin fun gl -> let env = Proofview.Goal.env gl in let sigma = Proofview.Goal.sigma gl in matches env sigma end (** 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 && List.length gls > 0 then Feedback.msg_debug (str" shelving dependent subgoals: " ++ pr_gls sigma gls); shelve_goals gls) let hintmap_of sigma hdc secvars concl = match hdc with | None -> fun db -> Hint_db.map_none ~secvars db | Some hdc -> fun db -> if Hint_db.use_dn db then (* Using dnet *) Hint_db.map_eauto sigma ~secvars hdc concl db else Hint_db.map_existential sigma ~secvars hdc concl db (** 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.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.enter begin fun gl -> let tacs = e_trivial_resolve db_list local_db secvars only_classes (pf_env gl) (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 env sigma concl = let open Proofview.Notations in let prods, concl = EConstr.decompose_prod_assum sigma concl in let nprods = List.length prods in let freeze = try match hdc with | Some (hd,_) when only_classes -> let cl = Typeclasses.class_info hd in if cl.cl_strict then Evarutil.undefined_evars_of_term sigma concl else Evar.Set.empty | _ -> Evar.Set.empty with e when CErrors.noncritical e -> Evar.Set.empty in let hint_of_db = hintmap_of sigma hdc secvars concl in let hintl = List.map_append (fun db -> let tacs = hint_of_db 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) (fun gl clenv -> matches_pattern concl p <*> unify_resolve_refine poly flags gl clenv) in Tacticals.New.tclTHEN tac Proofview.shelve_unifiable else let tac = with_prods nprods poly (term,cl) (unify_resolve poly flags) in 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) (fun gl clenv -> matches_pattern concl p <*> unify_resolve_refine poly flags 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 Proofview.tclBIND (Proofview.with_shelf tac) (fun (gls, ()) -> shelve_dependencies gls) | Give_exact (c,clenv) -> if get_typeclasses_filtered_unification () then let tac = matches_pattern concl p <*> Proofview.Goal.nf_enter (fun gl -> unify_resolve_refine poly flags gl (c,None,clenv)) in Tacticals.New.tclTHEN tac Proofview.shelve_unifiable else e_give_exact flags poly (c,clenv) | 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 -> Proofview.tclPROGRESS (unfold_in_concl [AllOccurrences,c]) | 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_env env sigma pat | _ -> mt () in match repr_hint t with | Extern _ -> (tac, b, true, name, lazy (pr_hint env sigma t ++ pp)) | _ -> (tac, b, false, name, lazy (pr_hint env sigma t ++ pp)) in List.map tac_of_hint hintl and e_trivial_resolve db_list local_db secvars only_classes env sigma concl = let hd = try Some (decompose_app_bound sigma concl) with Bound -> None in try e_my_find_search db_list local_db secvars hd true only_classes env sigma concl with Not_found -> [] let e_possible_resolve db_list local_db secvars only_classes env sigma concl = let hd = try Some (decompose_app_bound sigma concl) with Bound -> None in try e_my_find_search db_list local_db secvars hd false only_classes env sigma concl with 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 = let rec fmt elts = match elts with | [] -> [] | [n] -> [string_of_int n] | n1::n2::rest -> (string_of_int n1 ^ "." ^ string_of_int n2) :: fmt rest in prlist_with_sep (fun () -> str "-") str (fmt (List.rev l)) let is_Prop env sigma concl = let ty = Retyping.get_type_of env sigma concl in match EConstr.kind sigma ty with | Sort s -> begin match ESorts.kind sigma s with | Prop -> true | _ -> false end | _ -> false let is_unique env sigma concl = try let (cl,u), args = dest_class_app env sigma 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 tosee := Evar.Map.remove ev !tosee; Evar.Set.iter (fun ev -> if Evar.Map.mem ev !tosee then visit ev (Evar.Map.find ev !tosee)) evs; 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 sigma ty in match EConstr.kind sigma (fst (decompose_app sigma ar)) with | Const (c,_) -> is_class (ConstRef c) | Ind (i,_) -> is_class (IndRef i) | _ -> let env' = push_rel_context ctx env in let ty' = Reductionops.whd_all env' sigma ar in if not (EConstr.eq_constr sigma 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) empty_hint_info in (List.map_append (fun (path,info,c) -> make_resolves env sigma ~name:(PathHints path) (true,false,not !Flags.quiet) info false (IsConstr (EConstr.of_constr 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 = not only_classes || try let t = hyp |> NamedDecl.get_id |> Global.lookup_named |> NamedDecl.get_type in (* Section variable, reindex only if the type changed *) not (EConstr.eq_constr (project g) (EConstr.of_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 empty_hint_info hyp in hint @ hints else hints) ([]) sign in Hint_db.add_list (pf_env g) (project g) hintlist (Hint_db.empty st true) module Search = struct type autoinfo = { search_depth : int list; last_tac : Pp.t Lazy.t; search_dep : bool; search_only_classes : bool; search_cut : hints_path; search_hints : hint_db; } (** Local hints *) let autogoal_cache = Summary.ref ~name:"autogoal_cache" (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 let eq c1 c2 = EConstr.eq_constr (project g) c1 c2 in if DirPath.equal cwd dir && (onlyc == only_classes) && Context.Named.equal eq 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 NoApplicableEx (** ReachedLimitEx has priority over NoApplicableEx 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 evd 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 unique = not info.search_dep || is_unique env sigma concl in let backtrack = needs_backtrack env sigma unique concl in if !typeclasses_debug > 0 then Feedback.msg_debug (pr_depth info.search_depth ++ str": looking for " ++ Printer.pr_econstr_env (Goal.env gl) sigma 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 env sigma 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 let pr_error ie = if !typeclasses_debug > 1 then let idx = if fst ie == NoApplicableEx then pred !idx else !idx in let header = pr_depth (idx :: info.search_depth) ++ str": " ++ Lazy.force pp ++ (if !foundone != true then str" on" ++ spc () ++ pr_ev sigma (Proofview.Goal.goal gl) else mt ()) in let msg = match fst ie with | Pretype_errors.PretypeError (env, evd, Pretype_errors.CannotUnify (x,y,_)) -> str"Cannot unify " ++ print_constr_env env evd x ++ str" and " ++ print_constr_env env evd y | ReachedLimitEx -> str "Proof-search reached its limit." | NoApplicableEx -> str "Proof-search failed." | e -> CErrors.iprint ie in Feedback.msg_debug (header ++ str " failed with: " ++ msg) else () in let tac_of gls i j = Goal.enter begin fun gl' -> let sigma' = Goal.sigma gl' 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 sigma' (Proofview.Goal.goal gl')); let eq c1 c2 = EConstr.eq_constr sigma' c1 c2 in let hints' = if b && not (Context.Named.equal eq (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 sigma' (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' end in let rec result (shelf, ()) i k = foundone := true; Proofview.Unsafe.tclGETGOALS >>= fun gls -> let gls = CList.map Proofview.drop_state gls in 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 sigma (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 nestedshelf sigma = let filter ev = try let evi = Evd.find_undefined sigma ev in if info.search_only_classes then Some (ev, not (is_class_evar sigma 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.partition (fun (ev, s) -> s) remaining in let shelved = List.map fst shelved @ nestedshelf and goals = List.map fst goals in if !typeclasses_debug > 1 && not (List.is_empty shelved && List.is_empty goals) 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 (CList.map Proofview.with_empty_state goals)) >>= fun s -> result s i (Some (Option.default 0 k + j))) end in with_shelf res >>= fun (sh, ()) -> tclEVARMAP >>= finish sh 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' -> if CErrors.noncritical (fst e') then (pr_error e'; aux (merge_exceptions e e') tl) else iraise e') 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_econstr_env (Goal.env gl) sigma concl ++ str ", " ++ int (List.length poss) ++ str" possibilities"); match e with | (ReachedLimitEx,ie) -> Proofview.tclZERO ~info:ie ReachedLimitEx | (_,ie) -> Proofview.tclZERO ~info:ie NoApplicableEx in if backtrack then aux (NoApplicableEx,Exninfo.null) poss else tclONCE (aux (NoApplicableEx,Exninfo.null) poss) let hints_tac hints info kont : unit Proofview.tactic = Proofview.Goal.enter (fun gl -> hints_tac_gl hints info kont gl) let intro_tac info kont gl = let open Proofview in let env = Goal.env gl in let sigma = Goal.sigma gl in let decl = Tacmach.New.pf_last_hyp gl in let hint = make_resolve_hyp env sigma (Hint_db.transparent_state info.search_hints) (true,false,false) info.search_only_classes empty_hint_info decl in let ldb = Hint_db.add_list env sigma hint info.search_hints in let info' = { info with search_hints = ldb; last_tac = lazy (str"intro"); search_depth = 1 :: 1 :: info.search_depth } in kont info' let intro info kont = Proofview.tclBIND Tactics.intro (fun _ -> Proofview.Goal.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 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.enter begin fun gl -> search_tac_gl ~st only_classes dep hints depth (succ i) sigma gls gl end in Proofview.Unsafe.tclGETGOALS >>= fun gls -> let gls = CList.map Proofview.drop_state gls in 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) ?(unique=false) ~only_classes ?strategy ~depth ~dep hints = let open Proofview in let tac = let search = search_tac ~st only_classes dep hints in let dfs = match strategy with | None -> not (get_typeclasses_iterative_deepening ()) | Some Dfs -> true | Some Bfs -> false in if dfs then let depth = match depth with None -> -1 | Some d -> d in search depth else match depth with | None -> fix_iterative search | Some l -> fix_iterative_limit l search in let error (e, ie) = match e with | ReachedLimitEx -> Tacticals.New.tclFAIL 0 (str"Proof search reached its limit") | NoApplicableEx -> Tacticals.New.tclFAIL 0 (str"Proof search failed" ++ (if Option.is_empty depth then mt() else str" without reaching its limit")) | Proofview.MoreThanOneSuccess -> Tacticals.New.tclFAIL 0 (str"Proof search failed: " ++ str"more than one success found") | e -> Proofview.tclZERO ~info:ie e in let tac = Proofview.tclOR tac error in let tac = if unique then Proofview.tclEXACTLY_ONCE Proofview.MoreThanOneSuccess tac else tac in with_shelf numgoals >>= fun (initshelf, i) -> (if !typeclasses_debug > 1 then Feedback.msg_debug (str"Starting resolution with " ++ int i ++ str" goal(s) under focus and " ++ int (List.length initshelf) ++ str " shelved goal(s)" ++ (if only_classes then str " in only_classes mode" else str " in regular mode") ++ match depth with None -> str ", unbounded" | Some i -> str ", with depth limit " ++ int i)); tac let run_on_evars env evm p 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.save_future_goals evm in let _, pv = Proofview.init evm' [] in let pv = Proofview.unshelve goals pv in try let (), pv', (unsafe, shelved, gaveup), _ = Proofview.apply env tac pv in if not (List.is_empty gaveup) then CErrors.anomaly (Pp.str "run_on_evars not assumed to apply tactics generating given up goals."); 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 fgoals = Evd.shelve_on_future_goals shelved fgoals in let evm' = Evd.restore_future_goals evm' fgoals 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 evars_eauto env evd depth only_classes unique dep st hints p = let eauto_tac = eauto_tac ~st ~unique ~only_classes ~depth ~dep:(unique || dep) hints in let res = run_on_evars env evd p eauto_tac in match res with | None -> evd | Some evd' -> evd' let typeclasses_eauto env evd ?depth unique st hints p = evars_eauto env evd depth true unique false st hints p (** 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 env evd debug depth unique p = let db = searchtable_map typeclasses_db in typeclasses_eauto env evd ?depth unique (Hint_db.transparent_state db) [db] p end (** Binding to either V85 or Search implementations. *) let typeclasses_eauto ?(only_classes=false) ?(st=full_transparent_state) ?strategy ~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 Search.eauto_tac ~st ~only_classes ?strategy ~depth ~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 pred evm p = Evd.fold_undefined (fun ev evi _ -> if Typeclasses.is_resolvable evi && pred evm ev evi then let evars = Evar.Set.add ev (Evarutil.undefined_evars_of_evar_info evm evi) in Intpart.union_set evars p else ()) evm () (** [split_evars] returns groups of undefined evars according to dependencies *) let split_evars pred evm = let p = Intpart.create () in evar_dependencies pred 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 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 evd 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 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 p 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' = Search.typeclasses_resolve env evd debug depth unique p 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.solve_unif_constraints_with_heuristics ~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.from_env env) gl unique = let nc, gl, subst, _ = Evarutil.push_rel_context_to_named_context env sigma gl in let (gl,t,sigma) = Goal.V82.mk_goal sigma nc gl Store.empty in let (ev, _) = destEvar sigma t 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' = 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' = 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 sigma t = let t = strip_outer_cast sigma (collapse_appl sigma t) in match EConstr.kind sigma t with | Prod (_,_,c2) -> head_of_constr sigma c2 | LetIn (_,_,_,c2) -> head_of_constr sigma c2 | App (f,args) -> head_of_constr sigma f | _ -> t let head_of_constr h c = Proofview.tclEVARMAP >>= fun sigma -> let c = head_of_constr sigma c in letin_tac None (Name h) c None Locusops.allHyps let not_evar c = Proofview.tclEVARMAP >>= fun sigma -> match EConstr.kind sigma c with | Evar _ -> Tacticals.New.tclFAIL 0 (str"Evar") | _ -> Proofview.tclUNIT () let is_ground c = let open Tacticals.New in Proofview.tclEVARMAP >>= fun sigma -> if Evarutil.is_ground_term sigma c then tclIDTAC else tclFAIL 0 (str"Not ground") let autoapply c i = let open Proofview.Notations in Proofview.Goal.enter begin fun gl -> let hintdb = try Hints.searchtable_map i with Not_found -> CErrors.user_err (Pp.str ("Unknown hint database " ^ i ^ ".")) in let flags = auto_unif_flags Evar.Set.empty (Hints.Hint_db.transparent_state hintdb) in let cty = Tacmach.New.pf_unsafe_type_of gl c in let ce = mk_clenv_from gl (c,cty) in unify_e_resolve false flags gl ((c,cty,Univ.ContextSet.empty),0,ce) <*> Proofview.tclEVARMAP >>= (fun sigma -> let sigma = Typeclasses.mark_unresolvables ~filter:Typeclasses.all_goals sigma in Proofview.Unsafe.tclEVARS sigma) end