diff options
Diffstat (limited to 'kernel/indtypes.ml')
| -rw-r--r-- | kernel/indtypes.ml | 237 |
1 files changed, 135 insertions, 102 deletions
diff --git a/kernel/indtypes.ml b/kernel/indtypes.ml index 92e121402a..33abfe5b76 100644 --- a/kernel/indtypes.ml +++ b/kernel/indtypes.ml @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) @@ -12,7 +12,6 @@ open Names open Univ open Term open Vars -open Context open Declarations open Declareops open Inductive @@ -21,6 +20,7 @@ open Reduction open Typeops open Entries open Pp +open Context.Rel.Declaration (* Tell if indices (aka real arguments) contribute to size of inductive type *) (* If yes, this is compatible with the univalent model *) @@ -117,18 +117,18 @@ let is_unit constrsinfos = | [] -> (* type without constructors *) true | _ -> false -let infos_and_sort env ctx t = - let rec aux env ctx t max = +let infos_and_sort env t = + let rec aux env t max = let t = whd_betadeltaiota env t in match kind_of_term t with | Prod (name,c1,c2) -> let varj = infer_type env c1 in - let env1 = Environ.push_rel (name,None,varj.utj_val) env in + let env1 = Environ.push_rel (LocalAssum (name,varj.utj_val)) env in let max = Universe.sup max (univ_of_sort varj.utj_type) in - aux env1 ctx c2 max + aux env1 c2 max | _ when is_constructor_head t -> max | _ -> (* don't fail if not positive, it is tested later *) max - in aux env ctx t Universe.type0m + in aux env t Universe.type0m (* Computing the levels of polymorphic inductive types @@ -153,14 +153,14 @@ let infos_and_sort env ctx t = (* This (re)computes informations relevant to extraction and the sort of an arity or type constructor; we do not to recompute universes constraints *) -let infer_constructor_packet env_ar_par ctx params lc = +let infer_constructor_packet env_ar_par params lc = (* type-check the constructors *) let jlc = List.map (infer_type env_ar_par) lc in let jlc = Array.of_list jlc in (* generalize the constructor over the parameters *) let lc'' = Array.map (fun j -> it_mkProd_or_LetIn j.utj_val params) jlc in (* compute the max of the sorts of the products of the constructors types *) - let levels = List.map (infos_and_sort env_ar_par ctx) lc in + let levels = List.map (infos_and_sort env_ar_par) lc in let isunit = is_unit levels in let min = if Array.length jlc > 1 then Universe.type0 else Universe.type0m in let level = List.fold_left (fun max l -> Universe.sup max l) min levels in @@ -169,47 +169,32 @@ let infer_constructor_packet env_ar_par ctx params lc = (* If indices matter *) let cumulate_arity_large_levels env sign = fst (List.fold_right - (fun (_,b,t as d) (lev,env) -> - if Option.is_empty b then + (fun d (lev,env) -> + match d with + | LocalAssum (_,t) -> let tj = infer_type env t in let u = univ_of_sort tj.utj_type in (Universe.sup u lev, push_rel d env) - else lev, push_rel d env) + | LocalDef _ -> + lev, push_rel d env) sign (Universe.type0m,env)) let is_impredicative env u = - is_type0m_univ u || (is_type0_univ u && engagement env = Some ImpredicativeSet) + is_type0m_univ u || (is_type0_univ u && is_impredicative_set env) +(* Returns the list [x_1, ..., x_n] of levels contributing to template + polymorphism. The elements x_k is None if the k-th parameter (starting + from the most recent and ignoring let-definitions) is not contributing + or is Some u_k if its level is u_k and is contributing. *) let param_ccls params = - let has_some_univ u = function - | Some v when Univ.Level.equal u v -> true - | _ -> false + let fold acc = function (LocalAssum (_, p)) -> + (let c = strip_prod_assum p in + match kind_of_term c with + | Sort (Type u) -> Univ.Universe.level u + | _ -> None) :: acc + | LocalDef _ -> acc in - let remove_some_univ u = function - | Some v when Univ.Level.equal u v -> None - | x -> x - in - let fold l (_, b, p) = match b with - | None -> - (* Parameter contributes to polymorphism only if explicit Type *) - let c = strip_prod_assum p in - (* Add Type levels to the ordered list of parameters contributing to *) - (* polymorphism unless there is aliasing (i.e. non distinct levels) *) - begin match kind_of_term c with - | Sort (Type u) -> - (match Univ.Universe.level u with - | Some u -> - if List.exists (has_some_univ u) l then - None :: List.map (remove_some_univ u) l - else - Some u :: l - | None -> None :: l) - | _ -> - None :: l - end - | _ -> l - in - List.fold_left fold [] params + List.fold_left fold [] params (* Type-check an inductive definition. Does not check positivity conditions. *) @@ -267,7 +252,7 @@ let typecheck_inductive env mie = let full_arity = it_mkProd_or_LetIn arity params in let id = ind.mind_entry_typename in let env_ar' = - push_rel (Name id, None, full_arity) env_ar in + push_rel (LocalAssum (Name id, full_arity)) env_ar in (* (add_constraints cst2 env_ar) in *) (env_ar', (id,full_arity,sign @ params,expltype,deflev,inflev)::l)) (env',[]) @@ -283,8 +268,7 @@ let typecheck_inductive env mie = List.fold_right2 (fun ind arity_data inds -> let (lc',cstrs_univ) = - infer_constructor_packet env_ar_par ContextSet.empty - params ind.mind_entry_lc in + infer_constructor_packet env_ar_par params ind.mind_entry_lc in let consnames = ind.mind_entry_consnames in let ind' = (arity_data,consnames,lc',cstrs_univ) in ind'::inds) @@ -307,8 +291,7 @@ let typecheck_inductive env mie = let full_polymorphic () = let defu = Term.univ_of_sort def_level in let is_natural = - type_in_type env || (check_leq (universes env') infu defu && - not (is_type0m_univ defu && not is_unit)) + type_in_type env || (UGraph.check_leq (universes env') infu defu) in let _ = (** Impredicative sort, always allow *) @@ -334,7 +317,7 @@ let typecheck_inductive env mie = (* conclusions of the parameters *) (* We enforce [u >= lev] in case [lev] has a strict upper *) (* constraints over [u] *) - let b = type_in_type env || check_leq (universes env') infu u in + let b = type_in_type env || UGraph.check_leq (universes env') infu u in if not b then anomaly ~label:"check_inductive" (Pp.str"Incorrect universe " ++ @@ -360,8 +343,8 @@ let typecheck_inductive env mie = type ill_formed_ind = | LocalNonPos of int | LocalNotEnoughArgs of int - | LocalNotConstructor - | LocalNonPar of int * int + | LocalNotConstructor of Context.Rel.t * int + | LocalNonPar of int * int * int exception IllFormedInd of ill_formed_ind @@ -371,7 +354,7 @@ exception IllFormedInd of ill_formed_ind let mind_extract_params = decompose_prod_n_assum -let explain_ind_err id ntyp env nbpar c nargs err = +let explain_ind_err id ntyp env nbpar c err = let (lpar,c') = mind_extract_params nbpar c in match err with | LocalNonPos kt -> @@ -379,12 +362,13 @@ let explain_ind_err id ntyp env nbpar c nargs err = | LocalNotEnoughArgs kt -> raise (InductiveError (NotEnoughArgs (env,c',mkRel (kt+nbpar)))) - | LocalNotConstructor -> + | LocalNotConstructor (paramsctxt,nargs)-> + let nparams = Context.Rel.nhyps paramsctxt in raise (InductiveError - (NotConstructor (env,id,c',mkRel (ntyp+nbpar),nbpar,nargs))) - | LocalNonPar (n,l) -> + (NotConstructor (env,id,c',mkRel (ntyp+nbpar),nparams,nargs))) + | LocalNonPar (n,i,l) -> raise (InductiveError - (NonPar (env,c',n,mkRel (nbpar-n+1), mkRel (l+nbpar)))) + (NonPar (env,c',n,mkRel i, mkRel (l+nbpar)))) let failwith_non_pos n ntypes c = for k = n to n + ntypes - 1 do @@ -401,7 +385,7 @@ let failwith_non_pos_list n ntypes l = (* Check the inductive type is called with the expected parameters *) let check_correct_par (env,n,ntypes,_) hyps l largs = - let nparams = rel_context_nhyps hyps in + let nparams = Context.Rel.nhyps hyps in let largs = Array.of_list largs in if Array.length largs < nparams then raise (IllFormedInd (LocalNotEnoughArgs l)); @@ -409,11 +393,11 @@ let check_correct_par (env,n,ntypes,_) hyps l largs = let nhyps = List.length hyps in let rec check k index = function | [] -> () - | (_,Some _,_)::hyps -> check k (index+1) hyps + | LocalDef _ :: hyps -> check k (index+1) hyps | _::hyps -> match kind_of_term (whd_betadeltaiota env lpar.(k)) with | Rel w when Int.equal w index -> check (k-1) (index+1) hyps - | _ -> raise (IllFormedInd (LocalNonPar (k+1,l))) + | _ -> raise (IllFormedInd (LocalNonPar (k+1, index-n+nhyps+1, l))) in check (nparams-1) (n-nhyps) hyps; if not (Array.for_all (noccur_between n ntypes) largs') then failwith_non_pos_vect n ntypes largs' @@ -431,7 +415,7 @@ if Int.equal nmr 0 then 0 else function ([],_) -> nmr | (_,[]) -> assert false (* |hyps|>=nmr *) - | (lp,(_,Some _,_)::hyps) -> find k (index-1) (lp,hyps) + | (lp, LocalDef _ :: hyps) -> find k (index-1) (lp,hyps) | (p::lp,_::hyps) -> ( match kind_of_term (whd_betadeltaiota env p) with | Rel w when Int.equal w index -> find (k+1) (index-1) (lp,hyps) @@ -445,15 +429,15 @@ if Int.equal nmr 0 then 0 else [lra] is the list of recursive tree of each variable *) let ienv_push_var (env, n, ntypes, lra) (x,a,ra) = - (push_rel (x,None,a) env, n+1, ntypes, (Norec,ra)::lra) + (push_rel (LocalAssum (x,a)) env, n+1, ntypes, (Norec,ra)::lra) let ienv_push_inductive (env, n, ntypes, ra_env) ((mi,u),lpar) = let auxntyp = 1 in let specif = (lookup_mind_specif env mi, u) in let ty = type_of_inductive env specif in let env' = - push_rel (Anonymous,None, - hnf_prod_applist env ty lpar) env in + let decl = LocalAssum (Anonymous, hnf_prod_applist env ty lpar) in + push_rel decl env in let ra_env' = (Imbr mi,(Rtree.mk_rec_calls 1).(0)) :: List.map (fun (r,t) -> (r,Rtree.lift 1 t)) ra_env in @@ -481,9 +465,9 @@ let array_min nmr a = if Int.equal nmr 0 then 0 else considered sub-terms) as well as the number of of non-uniform arguments (used to generate induction schemes, so a priori less relevant to the kernel). *) -let check_positivity_one (env,_,ntypes,_ as ienv) hyps (_,i as ind) nargs lcnames indlc = - let lparams = rel_context_length hyps in - let nmr = rel_context_nhyps hyps in +let check_positivity_one recursive (env,_,ntypes,_ as ienv) hyps (_,i as ind) nargs lcnames indlc = + let lparams = Context.Rel.length hyps in + let nmr = Context.Rel.nhyps hyps in (** Positivity of one argument [c] of a constructor (i.e. the constructor [cn] has a type of the shape [… -> c … -> P], where, more generally, the arrows may be dependent). *) @@ -596,6 +580,8 @@ let check_positivity_one (env,_,ntypes,_ as ienv) hyps (_,i as ind) nargs lcname | Prod (na,b,d) -> let () = assert (List.is_empty largs) in + if not recursive && not (noccur_between n ntypes b) then + raise (InductiveError BadEntry); let nmr',recarg = check_pos ienv nmr b in let ienv' = ienv_push_var ienv (na,b,mk_norec) in check_constr_rec ienv' nmr' (recarg::lrec) d @@ -605,7 +591,7 @@ let check_positivity_one (env,_,ntypes,_ as ienv) hyps (_,i as ind) nargs lcname begin match hd with | Rel j when Int.equal j (n + ntypes - i - 1) -> check_correct_par ienv hyps (ntypes - i) largs - | _ -> raise (IllFormedInd LocalNotConstructor) + | _ -> raise (IllFormedInd (LocalNotConstructor(hyps,nargs))) end else if not (List.for_all (noccur_between n ntypes) largs) @@ -621,7 +607,7 @@ let check_positivity_one (env,_,ntypes,_ as ienv) hyps (_,i as ind) nargs lcname try check_constructors ienv true nmr rawc with IllFormedInd err -> - explain_ind_err id (ntypes-i) env lparams c nargs err) + explain_ind_err id (ntypes-i) env lparams c err) (Array.of_list lcnames) indlc in let irecargs = Array.map snd irecargs_nmr @@ -630,18 +616,20 @@ let check_positivity_one (env,_,ntypes,_ as ienv) hyps (_,i as ind) nargs lcname (** [check_positivity kn env_ar params] checks that the mutually inductive block [inds] is strictly positive. *) -let check_positivity kn env_ar params inds = +let check_positivity kn env_ar params finite inds = let ntypes = Array.length inds in - let rc = Array.mapi (fun j t -> (Mrec (kn,j),t)) (Rtree.mk_rec_calls ntypes) in + let recursive = finite != Decl_kinds.BiFinite in + let rc = Array.mapi (fun j t -> (Mrec (kn,j),t)) + (Rtree.mk_rec_calls ntypes) in let lra_ind = Array.rev_to_list rc in - let lparams = rel_context_length params in - let nmr = rel_context_nhyps params in + let lparams = Context.Rel.length params in + let nmr = Context.Rel.nhyps params in let check_one i (_,lcnames,lc,(sign,_)) = let ra_env = List.init lparams (fun _ -> (Norec,mk_norec)) @ lra_ind in let ienv = (env_ar, 1+lparams, ntypes, ra_env) in - let nargs = rel_context_nhyps sign - nmr in - check_positivity_one ienv params (kn,i) nargs lcnames lc + let nargs = Context.Rel.nhyps sign - nmr in + check_positivity_one recursive ienv params (kn,i) nargs lcnames lc in let irecargs_nmr = Array.mapi check_one inds in let irecargs = Array.map snd irecargs_nmr @@ -698,6 +686,7 @@ let used_section_variables env inds = keep_hyps env ids let rel_vect n m = Array.init m (fun i -> mkRel(n+m-i)) +let rel_list n m = Array.to_list (rel_vect n m) exception UndefinableExpansion @@ -705,13 +694,28 @@ exception UndefinableExpansion build an expansion function. The term built is expecting to be substituted first by a substitution of the form [params, x : ind params] *) -let compute_projections ((kn, _ as ind), u as indsp) n x nparamargs params - mind_consnrealdecls mind_consnrealargs ctx = +let compute_projections ((kn, _ as ind), u as indu) n x nparamargs params + mind_consnrealdecls mind_consnrealargs paramslet ctx = let mp, dp, l = repr_mind kn in - let rp = mkApp (mkIndU indsp, rel_vect 0 nparamargs) in + (** We build a substitution smashing the lets in the record parameters so + that typechecking projections requires just a substitution and not + matching with a parameter context. *) + let indty, paramsletsubst = + (* [ty] = [Ind inst] is typed in context [params] *) + let inst = Context.Rel.to_extended_vect 0 paramslet in + let ty = mkApp (mkIndU indu, inst) in + (* [Ind inst] is typed in context [params-wo-let] *) + let inst' = rel_list 0 nparamargs in + (* {params-wo-let |- subst:params] *) + let subst = subst_of_rel_context_instance paramslet inst' in + (* {params-wo-let, x:Ind inst' |- subst':(params,x:Ind inst)] *) + let subst = (* For the record parameter: *) + mkRel 1 :: List.map (lift 1) subst in + ty, subst + in let ci = let print_info = - { ind_tags = []; cstr_tags = [|rel_context_tags ctx|]; style = LetStyle } in + { ind_tags = []; cstr_tags = [|Context.Rel.to_tags ctx|]; style = LetStyle } in { ci_ind = ind; ci_npar = nparamargs; ci_cstr_ndecls = mind_consnrealdecls; @@ -721,34 +725,62 @@ let compute_projections ((kn, _ as ind), u as indsp) n x nparamargs params let len = List.length ctx in let x = Name x in let compat_body ccl i = - (* [ccl] is defined in context [params;x:rp] *) - (* [ccl'] is defined in context [params;x:rp;x:rp] *) + (* [ccl] is defined in context [params;x:indty] *) + (* [ccl'] is defined in context [params;x:indty;x:indty] *) let ccl' = liftn 1 2 ccl in - let p = mkLambda (x, lift 1 rp, ccl') in + let p = mkLambda (x, lift 1 indty, ccl') in let branch = it_mkLambda_or_LetIn (mkRel (len - i)) ctx in let body = mkCase (ci, p, mkRel 1, [|lift 1 branch|]) in - it_mkLambda_or_LetIn (mkLambda (x,rp,body)) params + it_mkLambda_or_LetIn (mkLambda (x,indty,body)) params in - let projections (na, b, t) (i, j, kns, pbs, subst) = - match b with - | Some c -> (i, j+1, kns, pbs, substl subst c :: subst) - | None -> + let projections decl (i, j, kns, pbs, subst, letsubst) = + match decl with + | LocalDef (na,c,t) -> + (* From [params, field1,..,fieldj |- c(params,field1,..,fieldj)] + to [params, x:I, field1,..,fieldj |- c(params,field1,..,fieldj)] *) + let c = liftn 1 j c in + (* From [params, x:I, field1,..,fieldj |- c(params,field1,..,fieldj)] + to [params, x:I |- c(params,proj1 x,..,projj x)] *) + let c1 = substl subst c in + (* From [params, x:I |- subst:field1,..,fieldj] + to [params, x:I |- subst:field1,..,fieldj+1] where [subst] + is represented with instance of field1 last *) + let subst = c1 :: subst in + (* From [params, x:I, field1,..,fieldj |- c(params,field1,..,fieldj)] + to [params-wo-let, x:I |- c(params,proj1 x,..,projj x)] *) + let c2 = substl letsubst c in + (* From [params-wo-let, x:I |- subst:(params, x:I, field1,..,fieldj)] + to [params-wo-let, x:I |- subst:(params, x:I, field1,..,fieldj+1)] *) + let letsubst = c2 :: letsubst in + (i, j+1, kns, pbs, subst, letsubst) + | LocalAssum (na,t) -> match na with | Name id -> let kn = Constant.make1 (KerName.make mp dp (Label.of_id id)) in - let ty = substl subst (liftn 1 j t) in + (* from [params, field1,..,fieldj |- t(params,field1,..,fieldj)] + to [params, x:I, field1,..,fieldj |- t(params,field1,..,fieldj] *) + let t = liftn 1 j t in + (* from [params, x:I, field1,..,fieldj |- t(params,field1,..,fieldj)] + to [params-wo-let, x:I |- t(params,proj1 x,..,projj x)] *) + let projty = substl letsubst t in + (* from [params, x:I, field1,..,fieldj |- t(field1,..,fieldj)] + to [params, x:I |- t(proj1 x,..,projj x)] *) + let ty = substl subst t in let term = mkProj (Projection.make kn true, mkRel 1) in let fterm = mkProj (Projection.make kn false, mkRel 1) in let compat = compat_body ty (j - 1) in - let etab = it_mkLambda_or_LetIn (mkLambda (x, rp, term)) params in - let etat = it_mkProd_or_LetIn (mkProd (x, rp, ty)) params in + let etab = it_mkLambda_or_LetIn (mkLambda (x, indty, term)) params in + let etat = it_mkProd_or_LetIn (mkProd (x, indty, ty)) params in let body = { proj_ind = fst ind; proj_npars = nparamargs; - proj_arg = i; proj_type = ty; proj_eta = etab, etat; + proj_arg = i; proj_type = projty; proj_eta = etab, etat; proj_body = compat } in - (i + 1, j + 1, kn :: kns, body :: pbs, fterm :: subst) + (i + 1, j + 1, kn :: kns, body :: pbs, + fterm :: subst, fterm :: letsubst) | Anonymous -> raise UndefinableExpansion in - let (_, _, kns, pbs, subst) = List.fold_right projections ctx (0, 1, [], [], []) in + let (_, _, kns, pbs, subst, letsubst) = + List.fold_right projections ctx (0, 1, [], [], [], paramsletsubst) + in Array.of_list (List.rev kns), Array.of_list (List.rev pbs) @@ -756,8 +788,8 @@ let build_inductive env p prv ctx env_ar params kn isrecord isfinite inds nmr re let ntypes = Array.length inds in (* Compute the set of used section variables *) let hyps = used_section_variables env inds in - let nparamargs = rel_context_nhyps params in - let nparamdecls = rel_context_length params in + let nparamargs = Context.Rel.nhyps params in + let nparamdecls = Context.Rel.length params in let subst, ctx = Univ.abstract_universes p ctx in let params = Vars.subst_univs_level_context subst params in let env_ar = @@ -772,10 +804,10 @@ let build_inductive env p prv ctx env_ar params kn isrecord isfinite inds nmr re let splayed_lc = Array.map (dest_prod_assum env_ar) lc in let nf_lc = Array.map (fun (d,b) -> it_mkProd_or_LetIn b d) splayed_lc in let consnrealdecls = - Array.map (fun (d,_) -> rel_context_length d - rel_context_length params) + Array.map (fun (d,_) -> Context.Rel.length d - Context.Rel.length params) splayed_lc in let consnrealargs = - Array.map (fun (d,_) -> rel_context_nhyps d - rel_context_nhyps params) + Array.map (fun (d,_) -> Context.Rel.nhyps d - Context.Rel.nhyps params) splayed_lc in (* Elimination sorts *) let arkind,kelim = @@ -808,8 +840,8 @@ let build_inductive env p prv ctx env_ar params kn isrecord isfinite inds nmr re { mind_typename = id; mind_arity = arkind; mind_arity_ctxt = Vars.subst_univs_level_context subst ar_sign; - mind_nrealargs = rel_context_nhyps ar_sign - nparamargs; - mind_nrealdecls = rel_context_length ar_sign - nparamdecls; + mind_nrealargs = Context.Rel.nhyps ar_sign - nparamargs; + mind_nrealdecls = Context.Rel.length ar_sign - nparamdecls; mind_kelim = kelim; mind_consnames = Array.of_list cnames; mind_consnrealdecls = consnrealdecls; @@ -822,10 +854,11 @@ let build_inductive env p prv ctx env_ar params kn isrecord isfinite inds nmr re mind_reloc_tbl = rtbl; } in let packets = Array.map2 build_one_packet inds recargs in - let pkt = packets.(0) in + let pkt = packets.(0) in let isrecord = match isrecord with - | Some (Some rid) when pkt.mind_kelim == all_sorts && Array.length pkt.mind_consnames == 1 + | Some (Some rid) when pkt.mind_kelim == all_sorts + && Array.length pkt.mind_consnames == 1 && pkt.mind_consnrealargs.(0) > 0 -> (** The elimination criterion ensures that all projections can be defined. *) let u = @@ -834,12 +867,12 @@ let build_inductive env p prv ctx env_ar params kn isrecord isfinite inds nmr re else Univ.Instance.empty in let indsp = ((kn, 0), u) in - let rctx, _ = decompose_prod_assum (subst1 (mkIndU indsp) pkt.mind_nf_lc.(0)) in + let rctx, indty = decompose_prod_assum (subst1 (mkIndU indsp) pkt.mind_nf_lc.(0)) in (try - let fields = List.firstn pkt.mind_consnrealdecls.(0) rctx in + let fields, paramslet = List.chop pkt.mind_consnrealdecls.(0) rctx in let kns, projs = compute_projections indsp pkt.mind_typename rid nparamargs params - pkt.mind_consnrealdecls pkt.mind_consnrealargs fields + pkt.mind_consnrealdecls pkt.mind_consnrealargs paramslet fields in Some (Some (rid, kns, projs)) with UndefinableExpansion -> Some None) | Some _ -> Some None @@ -866,7 +899,7 @@ let check_inductive env kn mie = (* First type-check the inductive definition *) let (env_ar, env_ar_par, params, inds) = typecheck_inductive env mie in (* Then check positivity conditions *) - let (nmr,recargs) = check_positivity kn env_ar_par params inds in + let (nmr,recargs) = check_positivity kn env_ar_par params mie.mind_entry_finite inds in (* Build the inductive packets *) build_inductive env mie.mind_entry_polymorphic mie.mind_entry_private mie.mind_entry_universes |