diff options
| author | Pierre-Marie Pédrot | 2015-10-12 18:54:31 +0200 |
|---|---|---|
| committer | Pierre-Marie Pédrot | 2015-10-12 18:54:31 +0200 |
| commit | 10e5883fed21f9631e1aa65adb7a7e62a529987f (patch) | |
| tree | f04cfc472e6345585eb5f606e2957fcf0f2740ea /pretyping | |
| parent | 75c5e421e91d49eec9cd55c222595d2ef45325d6 (diff) | |
| parent | 26974a4a2301cc7b1188a3f2f29f3d3368eccc0b (diff) | |
Merge branch 'v8.5'
Diffstat (limited to 'pretyping')
| -rw-r--r-- | pretyping/constr_matching.ml | 134 | ||||
| -rw-r--r-- | pretyping/constr_matching.mli | 9 | ||||
| -rw-r--r-- | pretyping/evarsolve.ml | 6 | ||||
| -rw-r--r-- | pretyping/glob_ops.ml | 111 | ||||
| -rw-r--r-- | pretyping/glob_ops.mli | 1 | ||||
| -rw-r--r-- | pretyping/pretyping.ml | 4 |
6 files changed, 162 insertions, 103 deletions
diff --git a/pretyping/constr_matching.ml b/pretyping/constr_matching.ml index a0493777a5..19c85c9e27 100644 --- a/pretyping/constr_matching.ml +++ b/pretyping/constr_matching.ml @@ -56,10 +56,6 @@ let warn_bound_meta name = let warn_bound_bound name = msg_warning (str "Collision between bound variables of name " ++ pr_id name) -let warn_bound_again name = - msg_warning (str "Collision between bound variable " ++ pr_id name ++ - str " and another bound variable of same name.") - let constrain n (ids, m as x) (names, terms as subst) = try let (ids', m') = Id.Map.find n terms in @@ -69,32 +65,33 @@ let constrain n (ids, m as x) (names, terms as subst) = let () = if Id.Map.mem n names then warn_bound_meta n in (names, Id.Map.add n x terms) -let add_binders na1 na2 (names, terms as subst) = match na1, na2 with -| Name id1, Name id2 -> - if Id.Map.mem id1 names then - let () = warn_bound_bound id1 in - (names, terms) - else - let names = Id.Map.add id1 id2 names in - let () = if Id.Map.mem id1 terms then warn_bound_again id1 in - (names, terms) -| _ -> subst - -let rec build_lambda vars stk m = match vars with +let add_binders na1 na2 binding_vars (names, terms as subst) = + match na1, na2 with + | Name id1, Name id2 when Id.Set.mem id1 binding_vars -> + if Id.Map.mem id1 names then + let () = warn_bound_bound id1 in + (names, terms) + else + let names = Id.Map.add id1 id2 names in + let () = if Id.Map.mem id1 terms then warn_bound_meta id1 in + (names, terms) + | _ -> subst + +let rec build_lambda vars ctx m = match vars with | [] -> - let len = List.length stk in + let len = List.length ctx in lift (-1 * len) m | n :: vars -> (* change [ x1 ... xn y z1 ... zm |- t ] into [ x1 ... xn z1 ... zm |- lam y. t ] *) - let len = List.length stk in + let len = List.length ctx in let init i = if i < pred n then mkRel (i + 2) else if Int.equal i (pred n) then mkRel 1 else mkRel (i + 1) in let m = substl (List.init len init) m in - let pre, suf = List.chop (pred n) stk in + let pre, suf = List.chop (pred n) ctx in match suf with | [] -> assert false | (_, na, t) :: suf -> @@ -108,21 +105,21 @@ let rec build_lambda vars stk m = match vars with let m = mkLambda (na, t, m) in build_lambda vars (pre @ suf) m -let rec extract_bound_aux k accu frels stk = match stk with +let rec extract_bound_aux k accu frels ctx = match ctx with | [] -> accu -| (na1, na2, _) :: stk -> +| (na1, na2, _) :: ctx -> if Int.Set.mem k frels then begin match na1 with | Name id -> let () = assert (match na2 with Anonymous -> false | Name _ -> true) in let () = if Id.Set.mem id accu then raise PatternMatchingFailure in - extract_bound_aux (k + 1) (Id.Set.add id accu) frels stk + extract_bound_aux (k + 1) (Id.Set.add id accu) frels ctx | Anonymous -> raise PatternMatchingFailure end - else extract_bound_aux (k + 1) accu frels stk + else extract_bound_aux (k + 1) accu frels ctx -let extract_bound_vars frels stk = - extract_bound_aux 1 Id.Set.empty frels stk +let extract_bound_vars frels ctx = + extract_bound_aux 1 Id.Set.empty frels ctx let dummy_constr = mkProp @@ -134,20 +131,20 @@ let make_renaming ids = function end | _ -> dummy_constr -let merge_binding allow_bound_rels stk n cT subst = - let c = match stk with +let merge_binding allow_bound_rels ctx n cT subst = + let c = match ctx with | [] -> (* Optimization *) ([], cT) | _ -> let frels = free_rels cT in if allow_bound_rels then - let vars = extract_bound_vars frels stk in + let vars = extract_bound_vars frels ctx in let ordered_vars = Id.Set.elements vars in let rename binding = make_renaming ordered_vars binding in - let renaming = List.map rename stk in + let renaming = List.map rename ctx in (ordered_vars, substl renaming cT) else - let depth = List.length stk in + let depth = List.length ctx in let min_elt = try Int.Set.min_elt frels with Not_found -> succ depth in if depth < min_elt then ([], lift (- depth) cT) @@ -155,7 +152,8 @@ let merge_binding allow_bound_rels stk n cT subst = in constrain n c subst -let matches_core env sigma convert allow_partial_app allow_bound_rels pat c = +let matches_core env sigma convert allow_partial_app allow_bound_rels + (binding_vars,pat) c = let convref ref c = match ref, kind_of_term c with | VarRef id, Var id' -> Names.id_eq id id' @@ -168,7 +166,7 @@ let matches_core env sigma convert allow_partial_app allow_bound_rels pat c = is_conv env sigma c' c else false) in - let rec sorec stk env subst p t = + let rec sorec ctx env subst p t = let cT = strip_outer_cast t in match p,kind_of_term cT with | PSoApp (n,args),m -> @@ -181,11 +179,11 @@ let matches_core env sigma convert allow_partial_app allow_bound_rels pat c = let relargs, relset = List.fold_left fold ([], Int.Set.empty) args in let frels = free_rels cT in if Int.Set.subset frels relset then - constrain n ([], build_lambda relargs stk cT) subst + constrain n ([], build_lambda relargs ctx cT) subst else raise PatternMatchingFailure - | PMeta (Some n), m -> merge_binding allow_bound_rels stk n cT subst + | PMeta (Some n), m -> merge_binding allow_bound_rels ctx n cT subst | PMeta None, m -> subst @@ -203,10 +201,10 @@ let matches_core env sigma convert allow_partial_app allow_bound_rels pat c = | PSort (GType _), Sort (Type _) -> subst - | PApp (p, [||]), _ -> sorec stk env subst p t + | PApp (p, [||]), _ -> sorec ctx env subst p t | PApp (PApp (h, a1), a2), _ -> - sorec stk env subst (PApp(h,Array.append a1 a2)) t + sorec ctx env subst (PApp(h,Array.append a1 a2)) t | PApp (PMeta meta,args1), App (c2,args2) when allow_partial_app -> (let diff = Array.length args2 - Array.length args1 in @@ -216,13 +214,13 @@ let matches_core env sigma convert allow_partial_app allow_bound_rels pat c = let subst = match meta with | None -> subst - | Some n -> merge_binding allow_bound_rels stk n c subst in - Array.fold_left2 (sorec stk env) subst args1 args22 + | Some n -> merge_binding allow_bound_rels ctx n c subst in + Array.fold_left2 (sorec ctx env) subst args1 args22 else (* Might be a projection on the right *) match kind_of_term c2 with | Proj (pr, c) when not (Projection.unfolded pr) -> (try let term = Retyping.expand_projection env sigma pr c (Array.to_list args2) in - sorec stk env subst p term + sorec ctx env subst p term with Retyping.RetypeError _ -> raise PatternMatchingFailure) | _ -> raise PatternMatchingFailure) @@ -233,15 +231,15 @@ let matches_core env sigma convert allow_partial_app allow_bound_rels pat c = raise PatternMatchingFailure | PProj (pr1,c1), Proj (pr,c) -> if Projection.equal pr1 pr then - try Array.fold_left2 (sorec stk env) (sorec stk env subst c1 c) arg1 arg2 + try Array.fold_left2 (sorec ctx env) (sorec ctx env subst c1 c) arg1 arg2 with Invalid_argument _ -> raise PatternMatchingFailure else raise PatternMatchingFailure | _, Proj (pr,c) when not (Projection.unfolded pr) -> (try let term = Retyping.expand_projection env sigma pr c (Array.to_list arg2) in - sorec stk env subst p term + sorec ctx env subst p term with Retyping.RetypeError _ -> raise PatternMatchingFailure) | _, _ -> - try Array.fold_left2 (sorec stk env) (sorec stk env subst c1 c2) arg1 arg2 + try Array.fold_left2 (sorec ctx env) (sorec ctx env subst c1 c2) arg1 arg2 with Invalid_argument _ -> raise PatternMatchingFailure) | PApp (PRef (ConstRef c1), _), Proj (pr, c2) @@ -250,37 +248,37 @@ let matches_core env sigma convert allow_partial_app allow_bound_rels pat c = | PApp (c, args), Proj (pr, c2) -> (try let term = Retyping.expand_projection env sigma pr c2 [] in - sorec stk env subst p term + sorec ctx env subst p term with Retyping.RetypeError _ -> raise PatternMatchingFailure) | PProj (p1,c1), Proj (p2,c2) when Projection.equal p1 p2 -> - sorec stk env subst c1 c2 + sorec ctx env subst c1 c2 | PProd (na1,c1,d1), Prod(na2,c2,d2) -> - sorec ((na1,na2,c2)::stk) (Environ.push_rel (na2,None,c2) env) - (add_binders na1 na2 (sorec stk env subst c1 c2)) d1 d2 + sorec ((na1,na2,c2)::ctx) (Environ.push_rel (na2,None,c2) env) + (add_binders na1 na2 binding_vars (sorec ctx env subst c1 c2)) d1 d2 | PLambda (na1,c1,d1), Lambda(na2,c2,d2) -> - sorec ((na1,na2,c2)::stk) (Environ.push_rel (na2,None,c2) env) - (add_binders na1 na2 (sorec stk env subst c1 c2)) d1 d2 + sorec ((na1,na2,c2)::ctx) (Environ.push_rel (na2,None,c2) env) + (add_binders na1 na2 binding_vars (sorec ctx env subst c1 c2)) d1 d2 | PLetIn (na1,c1,d1), LetIn(na2,c2,t2,d2) -> - sorec ((na1,na2,t2)::stk) (Environ.push_rel (na2,Some c2,t2) env) - (add_binders na1 na2 (sorec stk env subst c1 c2)) d1 d2 + sorec ((na1,na2,t2)::ctx) (Environ.push_rel (na2,Some c2,t2) env) + (add_binders na1 na2 binding_vars (sorec ctx env subst c1 c2)) d1 d2 | PIf (a1,b1,b1'), Case (ci,_,a2,[|b2;b2'|]) -> - let ctx,b2 = decompose_lam_n_assum ci.ci_cstr_ndecls.(0) b2 in - let ctx',b2' = decompose_lam_n_assum ci.ci_cstr_ndecls.(1) b2' in - let n = rel_context_length ctx in - let n' = rel_context_length ctx' in + let ctx_b2,b2 = decompose_lam_n_assum ci.ci_cstr_ndecls.(0) b2 in + let ctx_b2',b2' = decompose_lam_n_assum ci.ci_cstr_ndecls.(1) b2' in + let n = rel_context_length ctx_b2 in + let n' = rel_context_length ctx_b2' in if noccur_between 1 n b2 && noccur_between 1 n' b2' then - let s = - List.fold_left (fun l (na,_,t) -> (Anonymous,na,t)::l) stk ctx in - let s' = - List.fold_left (fun l (na,_,t) -> (Anonymous,na,t)::l) stk ctx' in + let f l (na,_,t) = (Anonymous,na,t)::l in + let ctx_br = List.fold_left f ctx ctx_b2 in + let ctx_br' = List.fold_left f ctx ctx_b2' in let b1 = lift_pattern n b1 and b1' = lift_pattern n' b1' in - sorec s' (Environ.push_rel_context ctx' env) - (sorec s (Environ.push_rel_context ctx env) (sorec stk env subst a1 a2) b1 b2) b1' b2' + sorec ctx_br' (Environ.push_rel_context ctx_b2' env) + (sorec ctx_br (Environ.push_rel_context ctx_b2 env) + (sorec ctx env subst a1 a2) b1 b2) b1' b2' else raise PatternMatchingFailure @@ -301,9 +299,9 @@ let matches_core env sigma convert allow_partial_app allow_bound_rels pat c = (* (ind,j+1) is normally known to be a correct constructor and br2 a correct match over the same inductive *) assert (j < n2); - sorec stk env subst c br2.(j) + sorec ctx env subst c br2.(j) in - let chk_head = sorec stk env (sorec stk env subst a1 a2) p1 p2 in + let chk_head = sorec ctx env (sorec ctx env subst a1 a2) p1 p2 in List.fold_left chk_branch chk_head br1 | PFix c1, Fix _ when eq_constr (mkFix c1) cT -> subst @@ -319,7 +317,8 @@ let matches_core_closed env sigma convert allow_partial_app pat c = let extended_matches env sigma = matches_core env sigma false true true -let matches env sigma pat c = snd (matches_core_closed env sigma false true pat c) +let matches env sigma pat c = + snd (matches_core_closed env sigma false true (Id.Set.empty,pat) c) let special_meta = (-1) @@ -464,10 +463,10 @@ let sub_match ?(partial_app=false) ?(closed=true) env sigma pat c = let result () = aux env c (fun x -> x) lempty in IStream.thunk result -let match_subterm env sigma pat c = sub_match env sigma pat c +let match_subterm env sigma pat c = sub_match env sigma (Id.Set.empty,pat) c let match_appsubterm env sigma pat c = - sub_match ~partial_app:true env sigma pat c + sub_match ~partial_app:true env sigma (Id.Set.empty,pat) c let match_subterm_gen env sigma app pat c = sub_match ~partial_app:app env sigma pat c @@ -481,11 +480,12 @@ let is_matching_head env sigma pat c = with PatternMatchingFailure -> false let is_matching_appsubterm ?(closed=true) env sigma pat c = + let pat = (Id.Set.empty,pat) in let results = sub_match ~partial_app:true ~closed env sigma pat c in not (IStream.is_empty results) -let matches_conv env sigma c p = - snd (matches_core_closed env sigma true false c p) +let matches_conv env sigma p c = + snd (matches_core_closed env sigma true false (Id.Set.empty,p) c) let is_matching_conv env sigma pat n = try let _ = matches_conv env sigma pat n in true diff --git a/pretyping/constr_matching.mli b/pretyping/constr_matching.mli index 67854a893d..b9dcb0af26 100644 --- a/pretyping/constr_matching.mli +++ b/pretyping/constr_matching.mli @@ -41,7 +41,8 @@ val matches_head : env -> Evd.evar_map -> constr_pattern -> constr -> patvar_map variables or metavariables have the same name, the metavariable, or else the rightmost bound variable, takes precedence *) val extended_matches : - env -> Evd.evar_map -> constr_pattern -> constr -> bound_ident_map * extended_patvar_map + env -> Evd.evar_map -> Tacexpr.binding_bound_vars * constr_pattern -> + constr -> bound_ident_map * extended_patvar_map (** [is_matching pat c] just tells if [c] matches against [pat] *) val is_matching : env -> Evd.evar_map -> constr_pattern -> constr -> bool @@ -72,8 +73,10 @@ val match_subterm : env -> Evd.evar_map -> constr_pattern -> constr -> matching_ val match_appsubterm : env -> Evd.evar_map -> constr_pattern -> constr -> matching_result IStream.t (** [match_subterm_gen] calls either [match_subterm] or [match_appsubterm] *) -val match_subterm_gen : env -> Evd.evar_map -> bool (** true = with app context *) -> - constr_pattern -> constr -> matching_result IStream.t +val match_subterm_gen : env -> Evd.evar_map -> + bool (** true = with app context *) -> + Tacexpr.binding_bound_vars * constr_pattern -> constr -> + matching_result IStream.t (** [is_matching_appsubterm pat c] tells if a subterm of [c] matches against [pat] taking partial subterms into consideration *) diff --git a/pretyping/evarsolve.ml b/pretyping/evarsolve.ml index a2189d5e4f..754ad8f588 100644 --- a/pretyping/evarsolve.ml +++ b/pretyping/evarsolve.ml @@ -130,6 +130,8 @@ let add_conv_oriented_pb ?(tail=true) (pbty,env,t1,t2) evd = (* We retype applications to ensure the universe constraints are collected *) +exception IllTypedInstance of env * types * types + let recheck_applications conv_algo env evdref t = let rec aux env t = match kind_of_term t with @@ -146,7 +148,7 @@ let recheck_applications conv_algo env evdref t = aux (succ i) (subst1 args.(i) codom) | UnifFailure (evd, reason) -> Pretype_errors.error_cannot_unify env evd ~reason (argsty.(i), dom)) - | _ -> assert false + | _ -> raise (IllTypedInstance (env, ty, argsty.(i))) else () in aux 0 fty | _ -> @@ -1134,8 +1136,6 @@ let project_evar_on_evar force g env evd aliases k2 pbty (evk1,argsv1 as ev1) (e else raise (CannotProject (evd,ev1')) -exception IllTypedInstance of env * types * types - let check_evar_instance evd evk1 body conv_algo = let evi = Evd.find evd evk1 in let evenv = evar_env evi in diff --git a/pretyping/glob_ops.ml b/pretyping/glob_ops.ml index 454d64f01b..3a76e8bd74 100644 --- a/pretyping/glob_ops.ml +++ b/pretyping/glob_ops.ml @@ -8,6 +8,7 @@ open Util open Names +open Nameops open Globnames open Misctypes open Glob_term @@ -183,37 +184,32 @@ let map_glob_constr_left_to_right f = function let map_glob_constr = map_glob_constr_left_to_right -let fold_glob_constr f acc = - let rec fold acc = function +let fold_return_type f acc (na,tyopt) = Option.fold_left f acc tyopt + +let fold_glob_constr f acc = function | GVar _ -> acc - | GApp (_,c,args) -> List.fold_left fold (fold acc c) args + | GApp (_,c,args) -> List.fold_left f (f acc c) args | GLambda (_,_,_,b,c) | GProd (_,_,_,b,c) | GLetIn (_,_,b,c) -> - fold (fold acc b) c + f (f acc b) c | GCases (_,_,rtntypopt,tml,pl) -> - List.fold_left fold_pattern - (List.fold_left fold (Option.fold_left fold acc rtntypopt) (List.map fst tml)) - pl - | GLetTuple (_,_,rtntyp,b,c) -> - fold (fold (fold_return_type acc rtntyp) b) c - | GIf (_,c,rtntyp,b1,b2) -> - fold (fold (fold (fold_return_type acc rtntyp) c) b1) b2 - | GRec (_,_,_,bl,tyl,bv) -> - let acc = Array.fold_left - (List.fold_left (fun acc (na,k,bbd,bty) -> - fold (Option.fold_left fold acc bbd) bty)) acc bl in - Array.fold_left fold (Array.fold_left fold acc tyl) bv - | GCast (_,c,k) -> - let r = match k with - | CastConv t | CastVM t | CastNative t -> fold acc t | CastCoerce -> acc - in - fold r c - | (GSort _ | GHole _ | GRef _ | GEvar _ | GPatVar _) -> acc - - and fold_pattern acc (_,idl,p,c) = fold acc c - - and fold_return_type acc (na,tyopt) = Option.fold_left fold acc tyopt - - in fold acc + let fold_pattern acc (_,idl,p,c) = f acc c in + List.fold_left fold_pattern + (List.fold_left f (Option.fold_left f acc rtntypopt) (List.map fst tml)) + pl + | GLetTuple (_,_,rtntyp,b,c) -> + f (f (fold_return_type f acc rtntyp) b) c + | GIf (_,c,rtntyp,b1,b2) -> + f (f (f (fold_return_type f acc rtntyp) c) b1) b2 + | GRec (_,_,_,bl,tyl,bv) -> + let acc = Array.fold_left + (List.fold_left (fun acc (na,k,bbd,bty) -> + f (Option.fold_left f acc bbd) bty)) acc bl in + Array.fold_left f (Array.fold_left f acc tyl) bv + | GCast (_,c,k) -> + let acc = match k with + | CastConv t | CastVM t | CastNative t -> f acc t | CastCoerce -> acc in + f acc c + | (GSort _ | GHole _ | GRef _ | GEvar _ | GPatVar _) -> acc let iter_glob_constr f = fold_glob_constr (fun () -> f) () @@ -328,6 +324,65 @@ let free_glob_vars = let vs = vars Id.Set.empty Id.Set.empty rt in Id.Set.elements vs +let add_and_check_ident id set = + if Id.Set.mem id set then + Pp.(msg_warning + (str "Collision between bound variables of name " ++ Id.print id)); + Id.Set.add id set + +let bound_glob_vars = + let rec vars bound = function + | GLambda (_,na,_,_,_) | GProd (_,na,_,_,_) | GLetIn (_,na,_,_) as c -> + let bound = name_fold add_and_check_ident na bound in + fold_glob_constr vars bound c + | GCases (loc,sty,rtntypopt,tml,pl) -> + let bound = vars_option bound rtntypopt in + let bound = + List.fold_left (fun bound (tm,_) -> vars bound tm) bound tml in + List.fold_left vars_pattern bound pl + | GLetTuple (loc,nal,rtntyp,b,c) -> + let bound = vars_return_type bound rtntyp in + let bound = vars bound b in + let bound = List.fold_right (name_fold add_and_check_ident) nal bound in + vars bound c + | GIf (loc,c,rtntyp,b1,b2) -> + let bound = vars_return_type bound rtntyp in + let bound = vars bound c in + let bound = vars bound b1 in + vars bound b2 + | GRec (loc,fk,idl,bl,tyl,bv) -> + let bound = Array.fold_right Id.Set.add idl bound in + let vars_fix i bound fid = + let bound = + List.fold_left + (fun bound (na,k,bbd,bty) -> + let bound = vars_option bound bbd in + let bound = vars bound bty in + name_fold add_and_check_ident na bound + ) + bound + bl.(i) + in + let bound = vars bound tyl.(i) in + vars bound bv.(i) + in + Array.fold_left_i vars_fix bound idl + | (GSort _ | GHole _ | GRef _ | GEvar _ | GPatVar _ | GVar _) -> bound + | GApp _ | GCast _ as c -> fold_glob_constr vars bound c + + and vars_pattern bound (loc,idl,p,c) = + let bound = List.fold_right add_and_check_ident idl bound in + vars bound c + + and vars_option bound = function None -> bound | Some p -> vars bound p + + and vars_return_type bound (na,tyopt) = + let bound = name_fold add_and_check_ident na bound in + vars_option bound tyopt + in + fun rt -> + vars Id.Set.empty rt + (** Mapping of names in binders *) (* spiwack: I used a smartmap-style kind of mapping here, because the diff --git a/pretyping/glob_ops.mli b/pretyping/glob_ops.mli index e514fd529e..25746323fb 100644 --- a/pretyping/glob_ops.mli +++ b/pretyping/glob_ops.mli @@ -38,6 +38,7 @@ val fold_glob_constr : ('a -> glob_constr -> 'a) -> 'a -> glob_constr -> 'a val iter_glob_constr : (glob_constr -> unit) -> glob_constr -> unit val occur_glob_constr : Id.t -> glob_constr -> bool val free_glob_vars : glob_constr -> Id.t list +val bound_glob_vars : glob_constr -> Id.Set.t val loc_of_glob_constr : glob_constr -> Loc.t (** [map_pattern_binders f m c] applies [f] to all the binding names diff --git a/pretyping/pretyping.ml b/pretyping/pretyping.ml index 17eafb19ef..bb21b87d37 100644 --- a/pretyping/pretyping.ml +++ b/pretyping/pretyping.ml @@ -322,8 +322,8 @@ let ltac_interp_name_env k0 lvar env = push_rel_context ctxt env let invert_ltac_bound_name lvar env id0 id = - let id = Id.Map.find id lvar.ltac_idents in - try mkRel (pi1 (lookup_rel_id id (rel_context env))) + let id' = Id.Map.find id lvar.ltac_idents in + try mkRel (pi1 (lookup_rel_id id' (rel_context env))) with Not_found -> errorlabstrm "" (str "Ltac variable " ++ pr_id id0 ++ str " depends on pattern variable name " ++ pr_id id ++ |
