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open Utilopen Namesopen Univopen UVarsopen Termopen Constropen Declarationsopen Environopen Entriesopen Type_errorsopen Context.Rel.Declaration
type inductive_arity = { user_arity : Constr.types; sort : Sorts.t }
(** Check name unicity. Redundant with safe_typing's add_field checks -> to remove?. *)
(* [check_constructors_names id s cl] checks that all the constructors names appearing in [l] are not present in the set [s], and returns the new set of names. The name [id] is the name of the current inductive type, used when reporting the error. *)
let check_constructors_names env idset ids = let rec check idset = function | [] -> idset | c::cl -> if Id.Set.mem c idset then raise (InductiveError (env, SameNamesConstructors c)) else check (Id.Set.add c idset) cl in check idset ids
(* [mind_check_names mie] checks the names of an inductive types declaration, and raises the corresponding exceptions when two types or two constructors have the same name. *)
let mind_check_names env mie = let rec check indset cstset = function | [] -> () | ind::inds -> let id = ind.mind_entry_typename in let cl = ind.mind_entry_consnames in if Id.Set.mem id indset then raise (InductiveError (env, SameNamesTypes id)) else let cstset' = check_constructors_names env cstset cl in check (Id.Set.add id indset) cstset' inds in check Id.Set.empty Id.Set.empty mie.mind_entry_inds(* The above verification is not necessary from the kernel point of vue since inductive and constructors are not referred to by their name, but only by the name of the inductive packet and an index. *)
(************************************************************************)(************************** Type checking *******************************)(************************************************************************)
type record_arg_info = | NoRelevantArg | MaybeRelevantArg (** At least one arg with variable relevance. *) | HasRelevantArg (** HasRelevantArg means when the record is relevant at least one arg is relevant. When the record is in a polymorphic sort this can mean one arg is in the same sort. *)
type univ_info = { ind_squashed : squash_info option ; record_arg_info : record_arg_info ; ind_template : bool ; ind_univ : Sorts.t ; missing : Sorts.t list (* missing u <= ind_univ constraints *) }
let add_squash q info = match q, Sorts.quality info.ind_univ with | Sorts.Quality.QVar _, _ | _, QVar _ -> begin match info.ind_squashed with | None -> { info with ind_squashed = Some (SometimesSquashed (Sorts.Quality.Set.singleton q)) } | Some AlwaysSquashed -> info | Some (SometimesSquashed qs) -> (* XXX dedup insertion *) { info with ind_squashed = Some (SometimesSquashed (Sorts.Quality.Set.add q qs)) } end | _ -> (* no qvar involved: no instantiation can resolve this constraint *) { info with ind_squashed = Some AlwaysSquashed }
let compute_elim_squash ?(is_real_arg=false) env u info = let open Sorts.Quality in let info = if not is_real_arg then info else match info.record_arg_info with | HasRelevantArg -> info | NoRelevantArg | MaybeRelevantArg -> match Sorts.relevance_of_sort u with | Irrelevant -> info | Relevant -> { info with record_arg_info = HasRelevantArg } | RelevanceVar q -> if Environ.Internal.is_above_prop env q || equal (QVar q) (Sorts.quality info.ind_univ) then { info with record_arg_info = HasRelevantArg } else { info with record_arg_info = MaybeRelevantArg } in if Environ.ignore_elim_constraints env then info else let indu = info.ind_univ in
if not @@ UGraph.check_leq (universes env) (Sorts.univ_of_sort u) (Sorts.univ_of_sort indu) then if Environ.is_impredicative_sort env indu then add_squash (Sorts.quality u) info else { info with missing = u :: info.missing } else if Inductive.eliminates_to (Environ.qualities env) (Sorts.quality indu) (Sorts.quality u) then info else match indu, u with (* XXX add a constraint q -> Prop in push_template_context, then we don't need this above_prop test *) | VSort (q, _), (SProp | Prop) when Environ.Internal.is_above_prop env q -> info | _ -> add_squash (Sorts.quality u) info
let check_context_univs ~ctor env info ctx = let check_one d (info,env) = let info = match d with | LocalAssum (_,t) -> (* could be retyping if it becomes available in the kernel *) let tj = Typeops.infer_type env t in compute_elim_squash ~is_real_arg:ctor env tj.utj_type info | LocalDef _ -> info in info, push_rel d env in fst (Context.Rel.fold_outside ~init:(info,env) check_one ctx)
let eq_squashed a b = match a, b with | SometimesSquashed a, SometimesSquashed b -> Sorts.Quality.Set.equal a b | AlwaysSquashed, AlwaysSquashed -> true | (SometimesSquashed _ | AlwaysSquashed), _ -> false
let check_indices_matter env_params info indices = let with_indices = check_context_univs ~ctor:false env_params info indices in let relies_on_indices_not_mattering = not (Option.equal eq_squashed info.ind_squashed with_indices.ind_squashed) || not (List.equal Sorts.equal info.missing with_indices.missing) in if indices_matter env_params then (* indices constraints are enforced, so this inductive does not rely on indices not mattering *) (with_indices, false) else (info, relies_on_indices_not_mattering)
(* env_ar contains the inductives before the current ones in the block, and no parameters *)let check_arity ~template env_params env_ar (na, arity) = let {utj_val=arity;utj_type=_} = Typeops.infer_type env_params arity in let indices, ind_sort = Reduction.dest_arity env_params arity in let univ_info = { ind_squashed=None; record_arg_info=NoRelevantArg; ind_template = template; ind_univ=ind_sort; missing=[]; } in (* We do not need to generate the universe of the arity with params; if later, after the validation of the inductive definition, full_arity is used as argument or subject to cast, an upper universe will be generated *) let arity = it_mkProd_or_LetIn arity (Environ.rel_context env_params) in let x = Context.make_annot (Name na) (Sorts.relevance_of_sort ind_sort) in push_rel (LocalAssum (x, arity)) env_ar, (arity, indices, univ_info)
let check_constructor_univs env_ar_par info (args,_) = (* We ignore the output, positivity will check that it's the expected inductive type *) check_context_univs ~ctor:true env_ar_par info args
let check_constructors ~env_params ~env_ar_par isrecord params lc (arity,indices,univ_info) = let lc = Array.map_of_list (fun c -> (Typeops.infer_type env_ar_par c).utj_val) lc in let splayed_lc = Array.map (Reduction.whd_decompose_prod_decls env_ar_par) lc in let univ_info = (* SProp and sort poly primitive records are OK, if we squash and become fakerecord also OK *) if isrecord then univ_info else match Array.length lc with (* Empty type: sort poly must squash *) | 0 -> compute_elim_squash env_ar_par Sorts.sprop univ_info
| 1 -> (* 1 constructor with no arguments also OK in SProp (to make things easier on ourselves when reducing we forbid letins) unless ind_univ is sort polymorphic (for ease of implementation) *) if (Environ.typing_flags env_ar_par).allow_uip && fst (splayed_lc.(0)) = [] && List.for_all Context.Rel.Declaration.is_local_assum params && List.for_all Context.Rel.Declaration.is_local_assum indices && Sorts.is_sprop univ_info.ind_univ then univ_info (* 1 constructor with arguments must squash if SProp / sort poly (we could allow arguments in SProp but the reduction rule is a pain) *) else compute_elim_squash env_ar_par Sorts.prop univ_info
(* More than 1 constructor: must squash if Prop/SProp *) | _ -> compute_elim_squash env_ar_par Sorts.set univ_info in let univ_info = Array.fold_left (check_constructor_univs env_ar_par) univ_info splayed_lc in let () = if univ_info.ind_template then match univ_info.ind_squashed with | None | Some AlwaysSquashed -> () | Some (SometimesSquashed _) -> CErrors.user_err Pp.(str "Cannot handle sometimes squashed template polymorphic type.") in (* generalize the constructors over the parameters *) let lc = Array.map (fun c -> Term.it_mkProd_or_LetIn c params) lc in let univ_info, relies_on_indices_not_mattering = check_indices_matter env_params univ_info indices in (arity, lc), (indices, splayed_lc), univ_info, relies_on_indices_not_mattering
module NotPrimRecordReason = struct
type t = | MustNotBeSquashed | MustHaveRelevantProj | MustHaveProj | MustNotHaveAnonProj
end
(* Checks whether the record can have primitive projections, and if so, whether it has eta *)let check_record ~ignore_elim data = let open NotPrimRecordReason in List.fold_left (fun res (_, (_, splayed_lc), info, _) -> if Result.is_error res then res else if Option.has_some info.ind_squashed (* records must have all projections definable -> equivalent to not being squashed *) then Result.Error MustNotBeSquashed else let res = match splayed_lc with (* records must have 1 constructor with at least 1 argument, and no anonymous fields *) (* XXX MustHaveProj is redundant with MustHaveRelevantProj except for SProp records, but the condition does not seem useful for SProp records. Should we allow 0-projection SProp records? *) (* XXX if we stop needing compatibility constants we could allow anonymous projections *) | [|ctx,_|] -> let module D = Context.Rel.Declaration in if not @@ List.exists D.is_local_assum ctx then Some MustHaveProj else if List.exists (fun d -> D.is_local_assum d && Name.is_anonymous (D.get_name d)) ctx then Some MustNotHaveAnonProj else None | _ -> CErrors.anomaly ~label:"Indtyping.check_record" Pp.(str "not 1 constructor") in match res with | Some reason -> Result.Error reason | None -> (* Otherwise, we allow primitive projections but check if it has eta *) if ignore_elim then Result.Ok AlwaysEta else match info.record_arg_info with | HasRelevantArg -> Result.Ok AlwaysEta | MaybeRelevantArg -> begin match info.ind_univ with | SProp -> Result.Ok AlwaysEta | _ -> Result.Ok MaybeEta end | NoRelevantArg -> (* If there is no relevant projection, then we consider the sort of the record to decide if it has eta *) match info.ind_univ with | SProp -> Result.Ok AlwaysEta | GSort _ | Set | Type _ | Prop -> Result.Ok NoEta (* relevant sorts don't have eta *) | VSort _ -> Result.Ok MaybeEta (* For sort variables it depends on the instantiation *) ) (Result.Ok NoEta) data
(* Template univs must be unbounded from below for subject reduction (with partially applied template poly, cf RFC 90).
We also forbid strict bounds from above because they lead to problems when instantiated with algebraic universes (template_u < v can become w+1 < v which we cannot yet handle). *)let check_unbounded_from_below (univs, csts) = Univ.UnivConstraints.iter (fun (l,d,r) -> let bad = match d with | UnivConstraint.Eq | UnivConstraint.Lt -> if Level.Set.mem l univs then Some l else if Level.Set.mem r univs then Some r else None | UnivConstraint.Le -> if Level.Set.mem r univs then Some r else None in bad |> Option.iter (fun bad -> CErrors.user_err Pp.(str "Universe level " ++ Level.raw_pr bad ++ str " cannot be template because it appears in constraint " ++ Level.raw_pr l ++ UnivConstraint.pr_kind d ++ Level.raw_pr r))) csts
let check_not_appearing_univs ~template_univs univs = let univs = Level.Set.inter template_univs univs in if Level.Set.is_empty univs then () else CErrors.user_err Pp.(str "Template " ++ str (CString.plural (Level.Set.cardinal univs) "universe") ++ spc() ++ Level.Set.pr Level.raw_pr univs ++ spc() ++ str "appear in illegal positions.")
let get_template_binding_arity ~template_univs c = let decls, c = Term.decompose_prod_decls c in let check_level u = match Universe.level u with | None -> let () = check_not_appearing_univs ~template_univs (Universe.levels u) in None | Some l -> if Level.Set.mem l template_univs then Some l else None in match kind c with | Sort (Type u as s) -> Some (decls, None, check_level u, s) | Sort (VSort (q, u) as s) -> (* XXX check if q is a template qvar in anticipation of global qvars existing *) Some (decls, Some q, check_level u, s) | _ -> None
let check_no_increment ~template_univs u = (* forbid template poly with an increment on a template univ in the conclusion otherwise repeatedly applying it can generate universes with +2 which we cannot yet handle. *) let has_increment = Universe.exists (fun (u,n) -> if Level.Set.mem u template_univs then not (Int.equal n 0) else false) u in if has_increment then CErrors.user_err Pp.(str "Template polymorphism with conclusion strictly larger than a bound universe not supported.")
let get_template template_context default_univs params arity lc = let ((template_qvars, _), (template_univs, _ as template_uctx)) = UVars.UContext.to_context_set (AbstractContext.repr template_context) in let () = check_unbounded_from_below template_uctx in
(* Template univs must only appear in the conclusion of the inductive and linearly in the conclusion of parameters. This makes them Irrelevant for conversion and also makes them easy to substitute. The inductive and binding parameter types must be syntactically arities. *) let check_not_appearing c = let qs, us = Vars.sort_and_universes_of_constr c in let qappearing = Sorts.QVar.Set.filter (fun qv -> Sorts.Quality.Set.mem (QVar qv) qs) template_qvars in if not (Sorts.QVar.Set.is_empty qappearing) then CErrors.user_err Pp.(str "Template " ++ str (if Int.equal 1 (Sorts.QVar.Set.cardinal qappearing) then "quality" else "qualities") ++ spc() ++ prlist_with_sep spc Sorts.QVar.raw_pr (Sorts.QVar.Set.elements qappearing) ++ spc() ++ str "appear in illegal positions.") else check_not_appearing_univs ~template_univs us in let check_not_appearing_rel_ctx ctx = List.iter (Context.Rel.Declaration.iter_constr check_not_appearing) ctx in
(** params *) (* for each non-letin param, find whether it binds a template univ or qvar *) let template_params = CList.map (fun param -> match param with | LocalDef (_,b,t) -> check_not_appearing b; check_not_appearing t; None | LocalAssum (_,t) -> match get_template_binding_arity ~template_univs t with | None | Some (_, None, None, _) -> check_not_appearing t; Some None | Some (decls, qopt, lopt, s) -> let () = check_not_appearing_rel_ctx decls in Some (Some (qopt, lopt, s))) params in let qbound, ubound = List.fold_left (fun (qbound, ubound as bound_in_params) -> function | None | Some None -> bound_in_params | Some (Some (qopt,lopt,_)) -> let ubound = match lopt with | None -> ubound | Some l -> if Level.Set.mem l ubound then CErrors.user_err Pp.(str "Non-linear template level " ++ Level.raw_pr l) else Level.Set.add l ubound in let qbound = Option.fold_right Sorts.QVar.Set.add qopt qbound in qbound, ubound) (Sorts.QVar.Set.empty,Level.Set.empty) template_params in let q_unbound = Sorts.QVar.Set.diff template_qvars qbound in let () = if not (Sorts.QVar.Set.is_empty q_unbound) then CErrors.user_err Pp.(str "Template " ++ str (if Int.equal 1 (Sorts.QVar.Set.cardinal q_unbound) then "quality" else "qualities") ++ spc() ++ prlist_with_sep spc Sorts.QVar.raw_pr (Sorts.QVar.Set.elements q_unbound) ++ spc() ++ str "not bound by parameters.")
in let u_unbound = Level.Set.diff template_univs ubound in let () = if not (Level.Set.is_empty u_unbound) then CErrors.user_err Pp.(str "Template " ++ str (CString.plural (Level.Set.cardinal u_unbound) "universe") ++ spc() ++ Level.Set.pr Level.raw_pr u_unbound ++ spc() ++ str "not bound by parameters.")
in
(** arity *) let template_concl = (* don't use get_template_binding_arity, we allow constant template poly (eg eq) *) let (decls, s) = Term.decompose_prod_decls arity in let () = if not (isSort s) then CErrors.user_err Pp.(str "Template polymorphic inductive's type must be a syntactic arity.") in check_not_appearing_rel_ctx decls; let s = destSort s in let () = match s with | SProp | Prop | Set -> () | VSort (_, u) -> (* typechecking will fail with "unbound qvar" if the quality isn't in template_qvars *) check_no_increment ~template_univs u; () | GSort (_, u) | Type u -> check_no_increment ~template_univs u; () in s in
(** ctors *) let () = List.iter check_not_appearing lc in
let template_param_arguments = let assums = CList.filter_map (fun x -> x) template_params in List.rev_map (Option.map (fun (_, _, s) -> s)) assums in
(* don't forget to check the default_univs qualities are all QType *) let () = let () = if not UVars.(eq_sizes (AbstractContext.size template_context) (Instance.length default_univs)) then CErrors.anomaly Pp.(str "Incorrect default template universes declaration.") in let default_qs, _ = UVars.Instance.to_array default_univs in assert (Array.for_all Sorts.Quality.is_qtype default_qs) in
{ template_param_arguments; template_context; template_concl; template_defaults = default_univs; }
let typecheck_inductive env ~sec_univs (mie:mutual_inductive_entry) = let () = match mie.mind_entry_inds with | [] -> CErrors.anomaly Pp.(str "empty inductive types declaration.") | _ -> () in (* Check unicity of names (redundant with safe_typing's add_field checks) *) mind_check_names env mie; assert (List.is_empty (Environ.rel_context env));
(* Abstract universes *) let env_univs, univs, template = match mie.mind_entry_universes with | Monomorphic_ind_entry -> env, Monomorphic, None | Template_ind_entry { uctx = auctx; default_univs } -> let env = Environ.Internal.push_template_context (AbstractContext.repr auctx) env in env, Monomorphic, Some (default_univs, auctx) | Polymorphic_ind_entry auctx -> let () = check_ucontext (AbstractContext.repr auctx) env in let env = Environ.push_context (AbstractContext.repr auctx) env in env, Polymorphic auctx, None in
let params = mie.mind_entry_params in let map mip = (mip.mind_entry_typename, mip.mind_entry_arity, mip.mind_entry_lc) in let blocks = List.map map mie.mind_entry_inds in
let template = match template with | None -> None | Some (default_univs, template_context) -> let arity, lc = match blocks with | [_, arity, lc] -> arity, lc | _ -> CErrors.user_err Pp.(str "Template-polymorphism not allowed with mutual inductives.") in let template = get_template template_context default_univs params arity lc in Some template in
let has_template_poly = Option.has_some template in
(* Params *) let env_params, params = Typeops.check_context env_univs params in
(* Arities *) let check_arity env_univs (name, arity, _) = check_arity ~template:has_template_poly env_params env_univs (name, arity) in let env_ar, data = List.fold_left_map check_arity env_univs blocks in let env_ar_par = push_rel_context params env_ar in
(* Constructors *) let isrecord = match mie.mind_entry_record with | Some (Some _) -> true | Some None | None -> false in let map (_, _, ctyp) data = check_constructors ~env_params ~env_ar_par isrecord params ctyp data in let data = List.map2 map blocks data in
let record = mie.mind_entry_record in let data, record, not_prim_reason_or_has_eta = match record with | None | Some None -> data, record, None (* NotRecord or FakeRecord *) | Some (Some _) -> (* PrimRecord *) (* We check if it can actually have primitive projections & eta *) match check_record ~ignore_elim:(Environ.ignore_elim_constraints env_ar_par) data with | Result.Ok has_eta -> let has_eta = match mie.mind_entry_finite with | BiFinite -> has_eta | Finite | CoFinite -> NoEta in data, record, Some (Result.Ok has_eta) | Result.Error _ as reason -> (* if someone tried to declare a record as SProp but it can't be primitive we must squash. *) let map (a, b, univs, im) = let univs = compute_elim_squash env_ar_par Sorts.prop univs in (a, b, univs, im) in let data = List.map map data in data, Some None, Some reason (* back to FakeRecord with a reason why *) in
let variance = match mie.mind_entry_variance with | None -> None | Some variances -> match univs with | Monomorphic -> CErrors.user_err Pp.(str "Inductive cannot be both monomorphic and universe cumulative.") | Polymorphic auctx -> (* no variance for qualities *) let _qualities, univs = Instance.to_array @@ UContext.instance @@ AbstractContext.repr auctx in let univs = Array.map2 (fun a b -> a,b) univs variances in let univs = match sec_univs with | None -> univs | Some sec_univs -> (* no variance for qualities *) let _, sec_univs = UVars.Instance.to_array sec_univs in let sec_univs = Array.map (fun u -> u, None) sec_univs in Array.append sec_univs univs in let arities, ctors = List.split @@ List.map (fun (_, arity, lc) -> (arity, lc)) blocks in let variances = InferCumulativity.infer_inductive ~env_params ~env_ar_par ~arities ~ctors univs in Some variances in
let check_packet env (_, _, univ_info, _) = if not (List.is_empty univ_info.missing) then raise (InductiveError (env, MissingUnivConstraints (univ_info.missing,univ_info.ind_univ))); in let () = List.iter (fun pkt -> check_packet env pkt) data in let map ((arity, lc), b, univs, relies_on_indices_not_mattering) = let arity = { user_arity = arity; sort = univs.ind_univ } in ((arity, lc), b, univs.ind_squashed, relies_on_indices_not_mattering) in let data = List.map map data in
env_ar_par, univs, template, variance, record, not_prim_reason_or_has_eta, params, Array.of_list data