Move inductive typecheck to file independent from positivity check.

This is strictly code movement.

5 files changed, 392 insertions, 349 deletions

diff --git a/kernel/indTyping.ml b/kernel/indTyping.ml
new file mode 100644
index 0000000000..8bf34398d7
--- /dev/null
+++ b/kernel/indTyping.ml
@@ -0,0 +1,365 @@
+(************************************************************************)
+(*         *   The Coq Proof Assistant / The Coq Development Team       *)
+(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
+(* <O___,, *       (see CREDITS file for the list of authors)           *)
+(*   \VV/  **************************************************************)
+(*    //   *    This file is distributed under the terms of the         *)
+(*         *     GNU Lesser General Public License Version 2.1          *)
+(*         *     (see LICENSE file for the text of the license)         *)
+(************************************************************************)
+
+open CErrors
+open Util
+open Names
+open Univ
+open Term
+open Constr
+open Vars
+open Declarations
+open Environ
+open Reduction
+open Typeops
+open Entries
+open Pp
+open Type_errors
+open Context.Rel.Declaration
+
+let is_constructor_head t =
+  isRel(fst(decompose_app t))
+
+(************************************************************************)
+(* Various well-formedness check for inductive declarations            *)
+
+(* [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 =
+  let rec check idset = function
+    | [] -> idset
+    | c::cl ->
+        if Id.Set.mem c idset then
+          raise (InductiveError (SameNamesConstructors c))
+        else
+          check (Id.Set.add c idset) cl
+  in
+  check
+
+(* [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 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 (SameNamesTypes id))
+        else
+          let cstset' = check_constructors_names 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. *)
+
+(************************************************************************)
+(************************************************************************)
+
+(* Typing the arities and constructor types *)
+
+let infos_and_sort env t =
+  let rec aux env t max =
+    let t = whd_all env t in
+      match kind t with
+      | Prod (name,c1,c2) ->
+        let varj = infer_type env c1 in
+        let env1 = Environ.push_rel (LocalAssum (name,varj.utj_val)) env in
+        let max = Universe.sup max (Sorts.univ_of_sort varj.utj_type) in
+          aux env1 c2 max
+    | _ when is_constructor_head t -> max
+    | _ -> (* don't fail if not positive, it is tested later *) max
+  in aux env t Universe.type0m
+
+(* Computing the levels of polymorphic inductive types
+
+   For each inductive type of a block that is of level u_i, we have
+   the constraints that u_i >= v_i where v_i is the type level of the
+   types of the constructors of this inductive type. Each v_i depends
+   of some of the u_i and of an extra (maybe non variable) universe,
+   say w_i that summarize all the other constraints. Typically, for
+   three inductive types, we could have
+
+   u1,u2,u3,w1 <= u1
+   u1       w2 <= u2
+      u2,u3,w3 <= u3
+
+   From this system of inequations, we shall deduce
+
+   w1,w2,w3 <= u1
+   w1,w2 <= u2
+   w1,w2,w3 <= u3
+*)
+
+(* 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 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 -> Term.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) lc 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
+  (lc'', level)
+
+(* If indices matter *)
+let cumulate_arity_large_levels env sign =
+  fst (List.fold_right
+    (fun d (lev,env) ->
+     match d with
+     | LocalAssum (_,t) ->
+        let tj = infer_type env t in
+        let u = Sorts.univ_of_sort tj.utj_type in
+          (Universe.sup u 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 && 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 paramsctxt =
+  let fold acc = function
+    | (LocalAssum (_, p)) ->
+      (let c = Term.strip_prod_assum p in
+      match kind c with
+        | Sort (Type u) -> Univ.Universe.level u
+        | _ -> None) :: acc
+    | LocalDef _ -> acc
+  in
+  List.fold_left fold [] paramsctxt
+
+(* Check arities and constructors *)
+let check_subtyping_arity_constructor env (subst : constr -> constr) (arcn : types) numparams is_arity =
+  let numchecked = ref 0 in
+  let basic_check ev tp =
+    if !numchecked < numparams then () else conv_leq ev tp (subst tp);
+    numchecked := !numchecked + 1
+  in
+  let check_typ typ typ_env =
+    match typ with
+    | LocalAssum (_, typ') ->
+      begin
+       try
+          basic_check typ_env typ'; Environ.push_rel typ typ_env
+        with NotConvertible ->
+          anomaly ~label:"bad inductive subtyping relation" (Pp.str "Invalid subtyping relation")
+      end
+    | _ -> anomaly (Pp.str "")
+  in
+  let typs, codom = dest_prod env arcn in
+  let last_env = Context.Rel.fold_outside check_typ typs ~init:env in
+  if not is_arity then basic_check last_env codom else ()
+
+(* Check that the subtyping information inferred for inductive types in the block is correct. *)
+(* This check produces a value of the unit type if successful or raises an anomaly if check fails. *)
+let check_subtyping cumi paramsctxt env_ar inds =
+    let numparams = Context.Rel.nhyps paramsctxt in
+    let uctx = CumulativityInfo.univ_context cumi in
+    let new_levels = Array.init (UContext.size uctx)
+        (fun i -> Level.(make (UGlobal.make DirPath.empty i)))
+    in
+    let lmap = Array.fold_left2 (fun lmap u u' -> LMap.add u u' lmap)
+        LMap.empty (Instance.to_array @@ UContext.instance uctx) new_levels
+    in
+    let dosubst = subst_univs_level_constr lmap in
+    let instance_other = Instance.of_array new_levels in
+    let constraints_other = Univ.subst_univs_level_constraints lmap (Univ.UContext.constraints uctx) in
+    let uctx_other = Univ.UContext.make (instance_other, constraints_other) in
+    let env = Environ.push_context uctx_other env_ar in
+    let subtyp_constraints =
+      CumulativityInfo.leq_constraints cumi
+        (UContext.instance uctx) instance_other
+        Constraint.empty
+    in
+    let env = Environ.add_constraints subtyp_constraints env in
+    (* process individual inductive types: *)
+    Array.iter (fun (_id,_cn,lc,(_sign,arity)) ->
+      match arity with
+        | RegularArity (_, full_arity, _) ->
+           check_subtyping_arity_constructor env dosubst full_arity numparams true;
+           Array.iter (fun cnt -> check_subtyping_arity_constructor env dosubst cnt numparams false) lc
+        | TemplateArity _ ->
+          anomaly ~label:"check_subtyping"
+            Pp.(str "template polymorphism and cumulative polymorphism are not compatible")
+    ) inds
+
+(* Type-check an inductive definition. Does not check positivity
+   conditions. *)
+(* TODO check that we don't overgeneralize construcors/inductive arities with
+   universes that are absent from them. Is it possible?
+*)
+let typecheck_inductive env mie =
+  let () = match mie.mind_entry_inds with
+  | [] -> anomaly (Pp.str "empty inductive types declaration.")
+  | _ -> ()
+  in
+  (* Check unicity of names *)
+  mind_check_names mie;
+  (* Params are typed-checked here *)
+  let env' =
+    match mie.mind_entry_universes with
+    | Monomorphic_ind_entry ctx -> push_context_set ctx env
+    | Polymorphic_ind_entry (_, ctx) -> push_context ctx env
+    | Cumulative_ind_entry (_, cumi) -> push_context (Univ.CumulativityInfo.univ_context cumi) env
+  in
+  let env_params = check_context env' mie.mind_entry_params in
+  let paramsctxt = mie.mind_entry_params in
+  (* We first type arity of each inductive definition *)
+  (* This allows building the environment of arities and to share *)
+  (* the set of constraints *)
+  let env_arities, rev_arity_list =
+    List.fold_left
+      (fun (env_ar,l) ind ->
+         (* Arities (without params) are typed-checked here *)
+         let template = ind.mind_entry_template in
+         let arity =
+           if isArity ind.mind_entry_arity then
+             let (ctx,s) = dest_arity env_params ind.mind_entry_arity in
+               match s with
+               | Type u when Univ.universe_level u = None ->
+                 (** We have an algebraic universe as the conclusion of the arity,
+                     typecheck the dummy Π ctx, Prop and do a special case for the conclusion.
+                 *)
+                 let proparity = infer_type env_params (mkArity (ctx, Sorts.prop)) in
+                 let (cctx, _) = destArity proparity.utj_val in
+                   (* Any universe is well-formed, we don't need to check [s] here *)
+                   mkArity (cctx, s)
+               | _ ->
+                 let arity = infer_type env_params ind.mind_entry_arity in
+                   arity.utj_val
+           else let arity = infer_type env_params ind.mind_entry_arity in
+                  arity.utj_val
+         in
+         let (sign, deflev) = dest_arity env_params arity in
+         let inflev =
+           (* The level of the inductive includes levels of indices if
+              in indices_matter mode *)
+             if indices_matter env
+             then Some (cumulate_arity_large_levels env_params sign)
+             else None
+         in
+         (* We do not need to generate the universe of full_arity; 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 full_arity = it_mkProd_or_LetIn arity paramsctxt in
+         let id = ind.mind_entry_typename in
+         let env_ar' =
+           push_rel (LocalAssum (Name id, full_arity)) env_ar in
+             (* (add_constraints cst2 env_ar) in *)
+           (env_ar', (id,full_arity,sign @ paramsctxt,template,deflev,inflev)::l))
+      (env',[])
+      mie.mind_entry_inds in
+
+  let arity_list = List.rev rev_arity_list in
+
+  (* builds the typing context "Gamma, I1:A1, ... In:An, params" *)
+  let env_ar_par = push_rel_context paramsctxt env_arities in
+
+  (* Now, we type the constructors (without params) *)
+  let inds =
+    List.fold_right2
+      (fun ind arity_data inds ->
+         let (lc',cstrs_univ) =
+           infer_constructor_packet env_ar_par paramsctxt ind.mind_entry_lc in
+         let consnames = ind.mind_entry_consnames in
+         let ind' = (arity_data,consnames,lc',cstrs_univ) in
+           ind'::inds)
+      mie.mind_entry_inds
+      arity_list
+    ([]) in
+
+  let inds = Array.of_list inds in
+
+  (* Compute/check the sorts of the inductive types *)
+
+  let inds =
+    Array.map (fun ((id,full_arity,sign,template,def_level,inf_level),cn,lc,clev)  ->
+      let infu =
+        (** Inferred level, with parameters and constructors. *)
+        match inf_level with
+        | Some alev -> Universe.sup clev alev
+        | None -> clev
+      in
+      let full_polymorphic () =
+        let defu = Sorts.univ_of_sort def_level in
+        let is_natural =
+          type_in_type env || (UGraph.check_leq (universes env') infu defu)
+        in
+        let _ =
+          (** Impredicative sort, always allow *)
+          if is_impredicative env defu then ()
+          else (** Predicative case: the inferred level must be lower or equal to the
+                   declared level. *)
+            if not is_natural then
+              anomaly ~label:"check_inductive"
+                (Pp.str"Incorrect universe " ++
+                   Universe.pr defu ++ Pp.str " declared for inductive type, inferred level is "
+                 ++ Universe.pr infu ++ Pp.str ".")
+        in
+          RegularArity (not is_natural,full_arity,defu)
+      in
+      let template_polymorphic () =
+        let _sign, s =
+          try dest_arity env full_arity
+          with NotArity -> raise (InductiveError (NotAnArity (env, full_arity)))
+        in
+        let u = Sorts.univ_of_sort s in
+        (* The polymorphic level is a function of the level of the *)
+        (* conclusions of the parameters *)
+        (* We enforce [u >= lev] in case [lev] has a strict upper *)
+        (* constraints over [u] *)
+        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 " ++
+             Universe.pr u ++ Pp.str " declared for inductive type, inferred level is "
+             ++ Universe.pr clev ++ Pp.str ".")
+        else
+          TemplateArity (param_ccls paramsctxt, infu)
+      in
+      let arity =
+        match mie.mind_entry_universes with
+        | Monomorphic_ind_entry _ ->
+          if template then template_polymorphic ()
+          else full_polymorphic ()
+        | Polymorphic_ind_entry _ | Cumulative_ind_entry _ ->
+          if template
+          then anomaly ~label:"polymorphic_template_ind"
+              Pp.(strbrk "Template polymorphism and full polymorphism are incompatible.")
+          else full_polymorphic ()
+      in
+        (id,cn,lc,(sign,arity)))
+    inds
+  in
+  (* Check that the subtyping information inferred for inductive types in the block is correct. *)
+  (* This check produces a value of the unit type if successful or raises an anomaly if check fails. *)
+  let () =
+    match mie.mind_entry_universes with
+    | Monomorphic_ind_entry _ -> ()
+    | Polymorphic_ind_entry _ -> ()
+    | Cumulative_ind_entry (_, cumi) -> check_subtyping cumi paramsctxt env_arities inds
+  in (env_arities, env_ar_par, paramsctxt, inds)
diff --git a/kernel/indTyping.mli b/kernel/indTyping.mli
new file mode 100644
index 0000000000..b16ada5ee8
--- /dev/null
+++ b/kernel/indTyping.mli
@@ -0,0 +1,24 @@
+(************************************************************************)
+(*         *   The Coq Proof Assistant / The Coq Development Team       *)
+(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
+(* <O___,, *       (see CREDITS file for the list of authors)           *)
+(*   \VV/  **************************************************************)
+(*    //   *    This file is distributed under the terms of the         *)
+(*         *     GNU Lesser General Public License Version 2.1          *)
+(*         *     (see LICENSE file for the text of the license)         *)
+(************************************************************************)
+
+open Names
+open Constr
+open Environ
+
+val typecheck_inductive :
+  env ->
+  Entries.mutual_inductive_entry ->
+  env * env * rel_context *
+  (Id.t * Id.t list * types array *
+   (rel_context *
+    (bool * types * Univ.Universe.t,
+     Univ.Level.t option list * Univ.Universe.t)
+      Declarations.declaration_arity))
+    array
diff --git a/kernel/indtypes.ml b/kernel/indtypes.ml
index e0f60a3731..16ba6e81fa 100644
--- a/kernel/indtypes.ml
+++ b/kernel/indtypes.ml
@@ -11,7 +11,6 @@
 open CErrors
 open Util
 open Names
-open Univ
 open Term
 open Constr
 open Vars
@@ -20,9 +19,7 @@ open Declareops
 open Inductive
 open Environ
 open Reduction
-open Typeops
 open Entries
-open Pp
 open Context.Rel.Declaration
 
 (* Terminology:
@@ -49,9 +46,6 @@ let weaker_noccur_between env x nvars t =
    if noccur_between x nvars t' then Some t'
    else None
 
-let is_constructor_head t =
-  isRel(fst(decompose_app t))
-
 (************************************************************************)
 (* Various well-formedness check for inductive declarations            *)
 
@@ -68,341 +62,7 @@ type inductive_error = Type_errors.inductive_error =
   | BadEntry
   | LargeNonPropInductiveNotInType
 
-exception InductiveError of inductive_error
-
-(* [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 =
-  let rec check idset = function
-    | [] -> idset
-    | c::cl ->
-	if Id.Set.mem c idset then
-	  raise (InductiveError (SameNamesConstructors c))
-	else
-	  check (Id.Set.add c idset) cl
-  in
-  check
-
-(* [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 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 (SameNamesTypes id))
-	else
-	  let cstset' = check_constructors_names 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. *)
-
-(************************************************************************)
-(************************************************************************)
-
-(* Typing the arities and constructor types *)
-
-let infos_and_sort env t =
-  let rec aux env t max =
-    let t = whd_all env t in
-      match kind t with
-      | Prod (name,c1,c2) ->
-        let varj = infer_type env c1 in
-	let env1 = Environ.push_rel (LocalAssum (name,varj.utj_val)) env in
-        let max = Universe.sup max (Sorts.univ_of_sort varj.utj_type) in
-	  aux env1 c2 max
-    | _ when is_constructor_head t -> max
-    | _ -> (* don't fail if not positive, it is tested later *) max
-  in aux env t Universe.type0m
-
-(* Computing the levels of polymorphic inductive types
-
-   For each inductive type of a block that is of level u_i, we have
-   the constraints that u_i >= v_i where v_i is the type level of the
-   types of the constructors of this inductive type. Each v_i depends
-   of some of the u_i and of an extra (maybe non variable) universe,
-   say w_i that summarize all the other constraints. Typically, for
-   three inductive types, we could have
-
-   u1,u2,u3,w1 <= u1
-   u1       w2 <= u2
-      u2,u3,w3 <= u3
-
-   From this system of inequations, we shall deduce
-
-   w1,w2,w3 <= u1
-   w1,w2 <= u2
-   w1,w2,w3 <= u3
-*)
-
-(* 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 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 -> Term.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) lc 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
-  (lc'', level)
-
-(* If indices matter *)
-let cumulate_arity_large_levels env sign =
-  fst (List.fold_right
-    (fun d (lev,env) ->
-     match d with
-     | LocalAssum (_,t) ->
-	let tj = infer_type env t in
-        let u = Sorts.univ_of_sort tj.utj_type in
-	  (Universe.sup u 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 && 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 paramsctxt =
-  let fold acc = function
-    | (LocalAssum (_, p)) ->
-      (let c = Term.strip_prod_assum p in
-      match kind c with
-        | Sort (Type u) -> Univ.Universe.level u
-        | _ -> None) :: acc
-    | LocalDef _ -> acc
-  in
-  List.fold_left fold [] paramsctxt
-
-(* Check arities and constructors *)
-let check_subtyping_arity_constructor env (subst : constr -> constr) (arcn : types) numparams is_arity =
-  let numchecked = ref 0 in
-  let basic_check ev tp =
-    if !numchecked < numparams then () else conv_leq ev tp (subst tp);
-    numchecked := !numchecked + 1
-  in
-  let check_typ typ typ_env =
-    match typ with
-    | LocalAssum (_, typ') ->
-      begin
-       try
-          basic_check typ_env typ'; Environ.push_rel typ typ_env
-        with NotConvertible -> 
-          anomaly ~label:"bad inductive subtyping relation" (Pp.str "Invalid subtyping relation")
-      end
-    | _ -> anomaly (Pp.str "")
-  in
-  let typs, codom = dest_prod env arcn in
-  let last_env = Context.Rel.fold_outside check_typ typs ~init:env in
-  if not is_arity then basic_check last_env codom else ()
-
-(* Check that the subtyping information inferred for inductive types in the block is correct. *)
-(* This check produces a value of the unit type if successful or raises an anomaly if check fails. *)
-let check_subtyping cumi paramsctxt env_ar inds = 
-    let numparams = Context.Rel.nhyps paramsctxt in
-    let uctx = CumulativityInfo.univ_context cumi in
-    let new_levels = Array.init (UContext.size uctx)
-        (fun i -> Level.make (Level.UGlobal.make DirPath.empty i))
-    in
-    let lmap = Array.fold_left2 (fun lmap u u' -> LMap.add u u' lmap)
-        LMap.empty (Instance.to_array @@ UContext.instance uctx) new_levels
-    in
-    let dosubst = subst_univs_level_constr lmap in
-    let instance_other = Instance.of_array new_levels in
-    let constraints_other = Univ.subst_univs_level_constraints lmap (Univ.UContext.constraints uctx) in
-    let uctx_other = Univ.UContext.make (instance_other, constraints_other) in
-    let env = Environ.push_context uctx_other env_ar in
-    let subtyp_constraints =
-      CumulativityInfo.leq_constraints cumi
-        (UContext.instance uctx) instance_other
-        Constraint.empty
-    in
-    let env = Environ.add_constraints subtyp_constraints env in
-    (* process individual inductive types: *)
-    Array.iter (fun (_id,_cn,lc,(_sign,arity)) ->
-      match arity with
-        | RegularArity (_, full_arity, _) ->
-           check_subtyping_arity_constructor env dosubst full_arity numparams true;
-           Array.iter (fun cnt -> check_subtyping_arity_constructor env dosubst cnt numparams false) lc
-        | TemplateArity _ ->
-          anomaly ~label:"check_subtyping"
-            Pp.(str "template polymorphism and cumulative polymorphism are not compatible")
-    ) inds
-
-(* Type-check an inductive definition. Does not check positivity
-   conditions. *)
-(* TODO check that we don't overgeneralize construcors/inductive arities with
-   universes that are absent from them. Is it possible? 
-*)
-let typecheck_inductive env mie =
-  let () = match mie.mind_entry_inds with
-  | [] -> anomaly (Pp.str "empty inductive types declaration.")
-  | _ -> ()
-  in
-  (* Check unicity of names *)
-  mind_check_names mie;
-  (* Params are typed-checked here *)
-  let env' =
-    match mie.mind_entry_universes with
-    | Monomorphic_ind_entry ctx -> push_context_set ctx env
-    | Polymorphic_ind_entry (_, ctx) -> push_context ctx env
-    | Cumulative_ind_entry (_, cumi) -> push_context (Univ.CumulativityInfo.univ_context cumi) env
-  in
-  let env_params = check_context env' mie.mind_entry_params in
-  let paramsctxt = mie.mind_entry_params in
-  (* We first type arity of each inductive definition *)
-  (* This allows building the environment of arities and to share *)
-  (* the set of constraints *)
-  let env_arities, rev_arity_list =
-    List.fold_left
-      (fun (env_ar,l) ind ->
-         (* Arities (without params) are typed-checked here *)
-         let template = ind.mind_entry_template in
-         let arity =
-	   if isArity ind.mind_entry_arity then
-	     let (ctx,s) = dest_arity env_params ind.mind_entry_arity in
-	       match s with
-	       | Type u when Univ.universe_level u = None ->
-	         (** We have an algebraic universe as the conclusion of the arity,
-		     typecheck the dummy Π ctx, Prop and do a special case for the conclusion.
-		 *)
-	         let proparity = infer_type env_params (mkArity (ctx, Sorts.prop)) in
-		 let (cctx, _) = destArity proparity.utj_val in
-		   (* Any universe is well-formed, we don't need to check [s] here *)
-		   mkArity (cctx, s)
-	       | _ -> 
-		 let arity = infer_type env_params ind.mind_entry_arity in
-		   arity.utj_val
-	   else let arity = infer_type env_params ind.mind_entry_arity in
-		  arity.utj_val
-	 in
-	 let (sign, deflev) = dest_arity env_params arity in
-	 let inflev = 
-	   (* The level of the inductive includes levels of indices if 
-	      in indices_matter mode *)
-             if indices_matter env
-	     then Some (cumulate_arity_large_levels env_params sign)
-	     else None
-	 in
-	 (* We do not need to generate the universe of full_arity; 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 full_arity = it_mkProd_or_LetIn arity paramsctxt in
-	 let id = ind.mind_entry_typename in
-	 let env_ar' =
-           push_rel (LocalAssum (Name id, full_arity)) env_ar in
-             (* (add_constraints cst2 env_ar) in *)
-           (env_ar', (id,full_arity,sign @ paramsctxt,template,deflev,inflev)::l))
-      (env',[])
-      mie.mind_entry_inds in
-
-  let arity_list = List.rev rev_arity_list in
-
-  (* builds the typing context "Gamma, I1:A1, ... In:An, params" *)
-  let env_ar_par = push_rel_context paramsctxt env_arities in
-
-  (* Now, we type the constructors (without params) *)
-  let inds =
-    List.fold_right2
-      (fun ind arity_data inds ->
-	 let (lc',cstrs_univ) =
-	   infer_constructor_packet env_ar_par paramsctxt ind.mind_entry_lc in
-	 let consnames = ind.mind_entry_consnames in
-	 let ind' = (arity_data,consnames,lc',cstrs_univ) in
-	   ind'::inds)
-      mie.mind_entry_inds
-      arity_list
-    ([]) in
-
-  let inds = Array.of_list inds in
-
-  (* Compute/check the sorts of the inductive types *)
-
-  let inds =
-    Array.map (fun ((id,full_arity,sign,template,def_level,inf_level),cn,lc,clev)  ->
-      let infu = 
-	(** Inferred level, with parameters and constructors. *)
-	match inf_level with
-	| Some alev -> Universe.sup clev alev
-	| None -> clev
-      in
-      let full_polymorphic () = 
-        let defu = Sorts.univ_of_sort def_level in
-	let is_natural =
-	  type_in_type env || (UGraph.check_leq (universes env') infu defu)
-	in
-	let _ =
-	  (** Impredicative sort, always allow *)
-	  if is_impredicative env defu then ()
-	  else (** Predicative case: the inferred level must be lower or equal to the
-		   declared level. *)
-	    if not is_natural then
-	      anomaly ~label:"check_inductive" 
-		(Pp.str"Incorrect universe " ++
-		   Universe.pr defu ++ Pp.str " declared for inductive type, inferred level is "
-		 ++ Universe.pr infu ++ Pp.str ".")
-	in
-	  RegularArity (not is_natural,full_arity,defu)
-      in
-      let template_polymorphic () =
-        let _sign, s =
-          try dest_arity env full_arity
-          with NotArity -> raise (InductiveError (NotAnArity (env, full_arity)))
-        in
-        let u = Sorts.univ_of_sort s in
-        (* The polymorphic level is a function of the level of the *)
-        (* conclusions of the parameters *)
-        (* We enforce [u >= lev] in case [lev] has a strict upper *)
-        (* constraints over [u] *)
-        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 " ++
-             Universe.pr u ++ Pp.str " declared for inductive type, inferred level is "
-             ++ Universe.pr clev ++ Pp.str ".")
-        else
-          TemplateArity (param_ccls paramsctxt, infu)
-      in
-      let arity =
-        match mie.mind_entry_universes with
-        | Monomorphic_ind_entry _ ->
-          if template then template_polymorphic ()
-          else full_polymorphic ()
-        | Polymorphic_ind_entry _ | Cumulative_ind_entry _ ->
-          if template
-          then anomaly ~label:"polymorphic_template_ind"
-              Pp.(strbrk "Template polymorphism and full polymorphism are incompatible.")
-          else full_polymorphic ()
-      in
-	(id,cn,lc,(sign,arity)))
-    inds
-  in
-  (* Check that the subtyping information inferred for inductive types in the block is correct. *)
-  (* This check produces a value of the unit type if successful or raises an anomaly if check fails. *)
-  let () = 
-    match mie.mind_entry_universes with
-    | Monomorphic_ind_entry _ -> ()
-    | Polymorphic_ind_entry _ -> ()
-    | Cumulative_ind_entry (_, cumi) -> check_subtyping cumi paramsctxt env_arities inds
-  in (env_arities, env_ar_par, paramsctxt, inds)
+exception InductiveError = Type_errors.InductiveError
 
 (************************************************************************)
 (************************************************************************)
@@ -965,7 +625,7 @@ let build_inductive env prv iu env_ar paramsctxt kn isrecord isfinite inds nmr r
 
 let check_inductive env kn mie =
   (* First type-check the inductive definition *)
-  let (env_ar, env_ar_par, paramsctxt, inds) = typecheck_inductive env mie in
+  let (env_ar, env_ar_par, paramsctxt, inds) = IndTyping.typecheck_inductive env mie in
   (* Then check positivity conditions *)
   let chkpos = (Environ.typing_flags env).check_guarded in
   let (nmr,recargs) = check_positivity ~chkpos kn env_ar_par paramsctxt mie.mind_entry_finite inds in
diff --git a/kernel/indtypes.mli b/kernel/indtypes.mli
index b4879611a3..5e37df6976 100644
--- a/kernel/indtypes.mli
+++ b/kernel/indtypes.mli
@@ -16,13 +16,6 @@ open Entries
 
 (** Inductive type checking and errors *)
 
-(** The different kinds of errors that may result of a malformed inductive
-  definition. *)
-
-val infos_and_sort : env -> constr -> Univ.Universe.t
-
-val check_subtyping_arity_constructor : env -> (constr -> constr) -> types -> int -> bool -> unit
-
 val check_positivity : chkpos:bool ->
            Names.MutInd.t ->
            Environ.env ->
diff --git a/kernel/kernel.mllib b/kernel/kernel.mllib
index 54c239349d..0b10e788b6 100644
--- a/kernel/kernel.mllib
+++ b/kernel/kernel.mllib
@@ -39,6 +39,7 @@ Type_errors
 Modops
 Inductive
 Typeops
+IndTyping
 Indtypes
 Cooking
 Term_typing