[vernac] Split `command.ml` into separate files.

Over the time, `Command` grew organically and it has become now one of
the most complex files in the codebase; however, its functionality is
well separated into 4 key components that have little to do with each
other.

We thus split the file, and also document the interfaces. Some parts
of `Command` export tricky internals to use by other plugins, and it
is common that plugin writers tend to get confused, so we are more
explicit about these parts now.

This patch depends on #6413.

16 files changed, 1723 insertions, 1546 deletions

diff --git a/vernac/classes.ml b/vernac/classes.ml
index efaf6c0c0..3d9c7defa 100644
--- a/vernac/classes.ml
+++ b/vernac/classes.ml
@@ -411,7 +411,7 @@ let context poly l =
       in
       let nstatus = match b with
       | None ->
-        pi3 (Command.declare_assumption false decl (t, univs) Universes.empty_binders [] impl
+        pi3 (ComAssumption.declare_assumption false decl (t, univs) Universes.empty_binders [] impl
           Vernacexpr.NoInline (Loc.tag id))
       | Some b ->
         let decl = (Discharge, poly, Definition) in
diff --git a/vernac/comAssumption.ml b/vernac/comAssumption.ml
new file mode 100644
index 000000000..5d7adb24a
--- /dev/null
+++ b/vernac/comAssumption.ml
@@ -0,0 +1,182 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+open Pp
+open CErrors
+open Util
+open Vars
+open Environ
+open Declare
+open Names
+open Globnames
+open Constrexpr_ops
+open Constrintern
+open Impargs
+open Decl_kinds
+open Pretyping
+open Vernacexpr
+open Entries
+
+(* 2| Variable/Hypothesis/Parameter/Axiom declarations *)
+
+let axiom_into_instance = ref false
+
+let _ =
+  let open Goptions in
+  declare_bool_option
+    { optdepr = false;
+      optname = "automatically declare axioms whose type is a typeclass as instances";
+      optkey = ["Typeclasses";"Axioms";"Are";"Instances"];
+      optread = (fun _ -> !axiom_into_instance);
+      optwrite = (:=) axiom_into_instance; }
+
+let should_axiom_into_instance = function
+  | Discharge ->
+    (* The typeclass behaviour of Variable and Context doesn't depend
+       on section status *)
+    true
+  | Global | Local -> !axiom_into_instance
+
+let declare_assumption is_coe (local,p,kind) (c,ctx) pl imps impl nl (_,ident) =
+match local with
+| Discharge when Lib.sections_are_opened () ->
+  let ctx = match ctx with
+    | Monomorphic_const_entry ctx -> ctx
+    | Polymorphic_const_entry ctx -> Univ.ContextSet.of_context ctx
+  in
+  let decl = (Lib.cwd(), SectionLocalAssum ((c,ctx),p,impl), IsAssumption kind) in
+  let _ = declare_variable ident decl in
+  let () = assumption_message ident in
+  let () =
+    if not !Flags.quiet && Proof_global.there_are_pending_proofs () then
+    Feedback.msg_info (str"Variable" ++ spc () ++ Id.print ident ++
+    strbrk " is not visible from current goals")
+  in
+  let r = VarRef ident in
+  let () = Typeclasses.declare_instance None true r in
+  let () = if is_coe then Class.try_add_new_coercion r ~local:true false in
+  (r,Univ.Instance.empty,true)
+
+| Global | Local | Discharge ->
+  let do_instance = should_axiom_into_instance local in
+  let local = DeclareDef.get_locality ident ~kind:"axiom" local in
+  let inl = match nl with
+    | NoInline -> None
+    | DefaultInline -> Some (Flags.get_inline_level())
+    | InlineAt i -> Some i
+  in
+  let decl = (ParameterEntry (None,(c,ctx),inl), IsAssumption kind) in
+  let kn = declare_constant ident ~local decl in
+  let gr = ConstRef kn in
+  let () = maybe_declare_manual_implicits false gr imps in
+  let () = Declare.declare_univ_binders gr pl in
+  let () = assumption_message ident in
+  let () = if do_instance then Typeclasses.declare_instance None false gr in
+  let () = if is_coe then Class.try_add_new_coercion gr ~local p in
+  let inst = match ctx with
+    | Polymorphic_const_entry ctx -> Univ.UContext.instance ctx
+    | Monomorphic_const_entry _ -> Univ.Instance.empty
+  in
+    (gr,inst,Lib.is_modtype_strict ())
+
+let interp_assumption sigma env impls bl c =
+  let c = mkCProdN ?loc:(local_binders_loc bl) bl c in
+  let sigma, (ty, impls) = interp_type_evars_impls env sigma ~impls c in
+  let ty = EConstr.Unsafe.to_constr ty in
+  sigma, (ty, impls)
+
+(* When monomorphic the universe constraints are declared with the first declaration only. *)
+let next_uctx =
+  let empty_uctx = Monomorphic_const_entry Univ.ContextSet.empty in
+  function
+  | Polymorphic_const_entry _ as uctx -> uctx
+  | Monomorphic_const_entry _ -> empty_uctx
+
+let declare_assumptions idl is_coe k (c,uctx) pl imps nl =
+  let refs, status, _ =
+    List.fold_left (fun (refs,status,uctx) id ->
+      let ref',u',status' =
+        declare_assumption is_coe k (c,uctx) pl imps false nl id in
+      (ref',u')::refs, status' && status, next_uctx uctx)
+      ([],true,uctx) idl
+  in
+  List.rev refs, status
+
+
+let maybe_error_many_udecls = function
+  | ((loc,id), Some _) ->
+    user_err ?loc ~hdr:"many_universe_declarations"
+      Pp.(str "When declaring multiple axioms in one command, " ++
+          str "only the first is allowed a universe binder " ++
+          str "(which will be shared by the whole block).")
+  | (_, None) -> ()
+
+let process_assumptions_udecls kind l =
+  let udecl, first_id = match l with
+    | (coe, ((id, udecl)::rest, c))::rest' ->
+      List.iter maybe_error_many_udecls rest;
+      List.iter (fun (coe, (idl, c)) -> List.iter maybe_error_many_udecls idl) rest';
+      udecl, id
+    | (_, ([], _))::_ | [] -> assert false
+  in
+  let () = match kind, udecl with
+    | (Discharge, _, _), Some _ when Lib.sections_are_opened () ->
+      let loc = fst first_id in
+      let msg = Pp.str "Section variables cannot be polymorphic." in
+      user_err ?loc  msg
+    | _ -> ()
+  in
+  udecl, List.map (fun (coe, (idl, c)) -> coe, (List.map fst idl, c)) l
+
+let do_assumptions kind nl l =
+  let open Context.Named.Declaration in
+  let env = Global.env () in
+  let udecl, l = process_assumptions_udecls kind l in
+  let sigma, udecl = Univdecls.interp_univ_decl_opt env udecl in
+  let l =
+    if pi2 kind (* poly *) then
+      (* Separate declarations so that A B : Type puts A and B in different levels. *)
+      List.fold_right (fun (is_coe,(idl,c)) acc ->
+        List.fold_right (fun id acc ->
+          (is_coe, ([id], c)) :: acc) idl acc)
+        l []
+    else l
+  in
+  (* We intepret all declarations in the same evar_map, i.e. as a telescope. *)
+  let (sigma,_,_),l = List.fold_left_map (fun (sigma,env,ienv) (is_coe,(idl,c)) ->
+    let sigma,(t,imps) = interp_assumption sigma env ienv [] c in
+    let env =
+      push_named_context (List.map (fun (_,id) -> LocalAssum (id,t)) idl) env in
+    let ienv = List.fold_right (fun (_,id) ienv ->
+      let impls = compute_internalization_data env Variable t imps in
+      Id.Map.add id impls ienv) idl ienv in
+      ((sigma,env,ienv),((is_coe,idl),t,imps)))
+    (sigma,env,empty_internalization_env) l
+  in
+  let sigma = solve_remaining_evars all_and_fail_flags env sigma Evd.empty in
+  (* The universe constraints come from the whole telescope. *)
+  let sigma = Evd.nf_constraints sigma in
+  let nf_evar c = EConstr.to_constr sigma (EConstr.of_constr c) in
+  let uvars, l = List.fold_left_map (fun uvars (coe,t,imps) ->
+      let t = nf_evar t in
+      let uvars = Univ.LSet.union uvars (Univops.universes_of_constr env t) in
+      uvars, (coe,t,imps))
+      Univ.LSet.empty l
+  in
+  let sigma = Evd.restrict_universe_context sigma uvars in
+  let uctx = Evd.check_univ_decl ~poly:(pi2 kind) sigma udecl in
+  let ubinders = Evd.universe_binders sigma in
+  pi2 (List.fold_left (fun (subst,status,uctx) ((is_coe,idl),t,imps) ->
+      let t = replace_vars subst t in
+      let refs, status' = declare_assumptions idl is_coe kind (t,uctx) ubinders imps nl in
+      let subst' = List.map2
+          (fun (_,id) (c,u) -> (id, Universes.constr_of_global_univ (c,u)))
+          idl refs
+      in
+      subst'@subst, status' && status, next_uctx uctx)
+    ([], true, uctx) l)
diff --git a/vernac/comAssumption.mli b/vernac/comAssumption.mli
new file mode 100644
index 000000000..2fa156abd
--- /dev/null
+++ b/vernac/comAssumption.mli
@@ -0,0 +1,34 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+open Names
+open Constr
+open Entries
+open Globnames
+open Vernacexpr
+open Constrexpr
+open Decl_kinds
+
+(** {6 Parameters/Assumptions} *)
+
+val do_assumptions : locality * polymorphic * assumption_object_kind ->
+  Vernacexpr.inline -> (Vernacexpr.ident_decl list * constr_expr) with_coercion list -> bool
+
+(************************************************************************)
+(** Internal API  *)
+(************************************************************************)
+
+(** Exported for Classes *)
+
+(** returns [false] if the assumption is neither local to a section,
+    nor in a module type and meant to be instantiated. *)
+val declare_assumption : coercion_flag -> assumption_kind ->
+  types in_constant_universes_entry ->
+  Universes.universe_binders -> Impargs.manual_implicits ->
+  bool (** implicit *) -> Vernacexpr.inline -> variable Loc.located ->
+  global_reference * Univ.Instance.t * bool
diff --git a/vernac/comDefinition.ml b/vernac/comDefinition.ml
new file mode 100644
index 000000000..c8b289c9d
--- /dev/null
+++ b/vernac/comDefinition.ml
@@ -0,0 +1,131 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2018     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+open Pp
+open Util
+open Constr
+open Environ
+open Entries
+open Termops
+open Redexpr
+open Declare
+open Constrintern
+open Pretyping
+
+open Context.Rel.Declaration
+
+(* Commands of the interface: Constant definitions *)
+
+let rec under_binders env sigma f n c =
+  if Int.equal n 0 then f env sigma (EConstr.of_constr c) else
+    match Constr.kind c with
+      | Lambda (x,t,c) ->
+          mkLambda (x,t,under_binders (push_rel (LocalAssum (x,t)) env) sigma f (n-1) c)
+      | LetIn (x,b,t,c) ->
+          mkLetIn (x,b,t,under_binders (push_rel (LocalDef (x,b,t)) env) sigma f (n-1) c)
+      | _ -> assert false
+
+let red_constant_entry n ce sigma = function
+  | None -> ce
+  | Some red ->
+      let proof_out = ce.const_entry_body in
+      let env = Global.env () in
+      let (redfun, _) = reduction_of_red_expr env red in
+      let redfun env sigma c =
+        let (_, c) = redfun env sigma c in
+        EConstr.Unsafe.to_constr c
+      in
+      { ce with const_entry_body = Future.chain proof_out
+        (fun ((body,ctx),eff) -> (under_binders env sigma redfun n body,ctx),eff) }
+
+let warn_implicits_in_term =
+  CWarnings.create ~name:"implicits-in-term" ~category:"implicits"
+         (fun () ->
+          strbrk "Implicit arguments declaration relies on type." ++ spc () ++
+            strbrk "The term declares more implicits than the type here.")
+
+let interp_definition pl bl poly red_option c ctypopt =
+  let env = Global.env() in
+  let evd, decl = Univdecls.interp_univ_decl_opt env pl in
+  let evd, (impls, ((env_bl, ctx), imps1)) = interp_context_evars env evd bl in
+  let ctx = List.map (fun d -> map_rel_decl EConstr.Unsafe.to_constr d) ctx in
+  let nb_args = Context.Rel.nhyps ctx in
+  let evd,imps,ce =
+    match ctypopt with
+      None ->
+        let evd, subst = Evd.nf_univ_variables evd in
+        let ctx = Context.Rel.map (Vars.subst_univs_constr subst) ctx in
+        let env_bl = push_rel_context ctx env in
+        let evd, (c, imps2) = interp_constr_evars_impls ~impls env_bl evd c in
+        let c = EConstr.Unsafe.to_constr c in
+        let evd,nf = Evarutil.nf_evars_and_universes evd in
+        let body = nf (it_mkLambda_or_LetIn c ctx) in
+        let vars = EConstr.universes_of_constr env evd (EConstr.of_constr body) in
+        let evd = Evd.restrict_universe_context evd vars in
+        let uctx = Evd.check_univ_decl ~poly evd decl in
+        evd, imps1@(Impargs.lift_implicits nb_args imps2),
+          definition_entry ~univs:uctx body
+    | Some ctyp ->
+        let evd, (ty, impsty) = interp_type_evars_impls ~impls env_bl evd ctyp in
+        let evd, subst = Evd.nf_univ_variables evd in
+        let ctx = Context.Rel.map (Vars.subst_univs_constr subst) ctx in
+        let env_bl = push_rel_context ctx env in
+        let evd, (c, imps2) = interp_casted_constr_evars_impls ~impls env_bl evd c ty in
+        let c = EConstr.Unsafe.to_constr c in
+        let evd, nf = Evarutil.nf_evars_and_universes evd in
+        let body = nf (it_mkLambda_or_LetIn c ctx) in
+        let ty = EConstr.Unsafe.to_constr ty in
+        let typ = nf (Term.it_mkProd_or_LetIn ty ctx) in
+        let beq b1 b2 = if b1 then b2 else not b2 in
+        let impl_eq (x,y,z) (x',y',z') = beq x x' && beq y y' && beq z z' in
+        (* Check that all implicit arguments inferable from the term
+           are inferable from the type *)
+        let chk (key,va) =
+          impl_eq (List.assoc_f Pervasives.(=) key impsty) va (* FIXME *)
+        in
+        if not (try List.for_all chk imps2 with Not_found -> false)
+        then warn_implicits_in_term ();
+        let bodyvars = EConstr.universes_of_constr env evd (EConstr.of_constr body) in
+        let tyvars = EConstr.universes_of_constr env evd (EConstr.of_constr ty) in
+        let vars = Univ.LSet.union bodyvars tyvars in
+        let evd = Evd.restrict_universe_context evd vars in
+        let uctx = Evd.check_univ_decl ~poly evd decl in
+        evd, imps1@(Impargs.lift_implicits nb_args impsty),
+          definition_entry ~types:typ ~univs:uctx body
+  in
+  (red_constant_entry (Context.Rel.length ctx) ce evd red_option, evd, decl, imps)
+
+let check_definition (ce, evd, _, imps) =
+  check_evars_are_solved (Global.env ()) evd Evd.empty;
+  ce
+
+let do_definition ident k univdecl bl red_option c ctypopt hook =
+  let (ce, evd, univdecl, imps as def) =
+    interp_definition univdecl bl (pi2 k) red_option c ctypopt
+  in
+    if Flags.is_program_mode () then
+      let env = Global.env () in
+      let (c,ctx), sideff = Future.force ce.const_entry_body in
+      assert(Safe_typing.empty_private_constants = sideff);
+      assert(Univ.ContextSet.is_empty ctx);
+      let typ = match ce.const_entry_type with
+        | Some t -> t
+        | None -> EConstr.to_constr evd (Retyping.get_type_of env evd (EConstr.of_constr c))
+      in
+      Obligations.check_evars env evd;
+      let obls, _, c, cty =
+        Obligations.eterm_obligations env ident evd 0 c typ
+      in
+      let ctx = Evd.evar_universe_context evd in
+      let hook = Lemmas.mk_hook (fun l r _ -> Lemmas.call_hook (fun exn -> exn) hook l r) in
+      ignore(Obligations.add_definition
+          ident ~term:c cty ctx ~univdecl ~implicits:imps ~kind:k ~hook obls)
+    else let ce = check_definition def in
+      ignore(DeclareDef.declare_definition ident k ce (Evd.universe_binders evd) imps
+        (Lemmas.mk_hook
+          (fun l r -> Lemmas.call_hook (fun exn -> exn) hook l r;r)))
diff --git a/vernac/comDefinition.mli b/vernac/comDefinition.mli
new file mode 100644
index 000000000..8dcd31f25
--- /dev/null
+++ b/vernac/comDefinition.mli
@@ -0,0 +1,29 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2018     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+open Names
+open Entries
+open Decl_kinds
+open Redexpr
+open Constrexpr
+
+(** {6 Definitions/Let} *)
+
+val do_definition : Id.t -> definition_kind -> Vernacexpr.universe_decl_expr option ->
+  local_binder_expr list -> red_expr option -> constr_expr ->
+  constr_expr option -> unit Lemmas.declaration_hook -> unit
+
+(************************************************************************)
+(** Internal API  *)
+(************************************************************************)
+
+(** Not used anywhere. *)
+val interp_definition :
+  Vernacexpr.universe_decl_expr option -> local_binder_expr list -> polymorphic -> red_expr option -> constr_expr ->
+  constr_expr option -> Safe_typing.private_constants definition_entry * Evd.evar_map *
+                        Univdecls.universe_decl * Impargs.manual_implicits
diff --git a/vernac/comFixpoint.ml b/vernac/comFixpoint.ml
new file mode 100644
index 000000000..d648e293a
--- /dev/null
+++ b/vernac/comFixpoint.ml
@@ -0,0 +1,356 @@
+open Pp
+open CErrors
+open Util
+open Constr
+open Vars
+open Termops
+open Declare
+open Names
+open Constrexpr
+open Constrexpr_ops
+open Constrintern
+open Decl_kinds
+open Pretyping
+open Evarutil
+open Evarconv
+open Misctypes
+open Vernacexpr
+
+module RelDecl = Context.Rel.Declaration
+
+(* 3c| Fixpoints and co-fixpoints *)
+
+(* An (unoptimized) function that maps preorders to partial orders...
+
+   Input:  a list of associations (x,[y1;...;yn]), all yi distincts
+           and different of x, meaning x<=y1, ..., x<=yn
+
+   Output: a list of associations (x,Inr [y1;...;yn]), collecting all
+           distincts yi greater than x, _or_, (x, Inl y) meaning that
+           x is in the same class as y (in which case, x occurs
+           nowhere else in the association map)
+
+   partial_order : ('a * 'a list) list -> ('a * ('a,'a list) union) list
+*)
+
+let rec partial_order cmp = function
+  | [] -> []
+  | (x,xge)::rest ->
+    let rec browse res xge' = function
+    | [] ->
+        let res = List.map (function
+          | (z, Inr zge) when List.mem_f cmp x zge ->
+            (z, Inr (List.union cmp zge xge'))
+          | r -> r) res in
+        (x,Inr xge')::res
+    | y::xge ->
+      let rec link y =
+        try match List.assoc_f cmp y res with
+        | Inl z -> link z
+        | Inr yge ->
+          if List.mem_f cmp x yge then
+            let res = List.remove_assoc_f cmp y res in
+            let res = List.map (function
+              | (z, Inl t) ->
+                  if cmp t y then (z, Inl x) else (z, Inl t)
+              | (z, Inr zge) ->
+                  if List.mem_f cmp y zge then
+                    (z, Inr (List.add_set cmp x (List.remove cmp y zge)))
+                  else
+                    (z, Inr zge)) res in
+            browse ((y,Inl x)::res) xge' (List.union cmp xge (List.remove cmp x yge))
+          else
+            browse res (List.add_set cmp y (List.union cmp xge' yge)) xge
+        with Not_found -> browse res (List.add_set cmp y xge') xge
+      in link y
+    in browse (partial_order cmp rest) [] xge
+
+let non_full_mutual_message x xge y yge isfix rest =
+  let reason =
+    if Id.List.mem x yge then
+      Id.print y ++ str " depends on " ++ Id.print x ++ strbrk " but not conversely"
+    else if Id.List.mem y xge then
+      Id.print x ++ str " depends on " ++ Id.print y ++ strbrk " but not conversely"
+    else
+      Id.print y ++ str " and " ++ Id.print x ++ strbrk " are not mutually dependent" in
+  let e = if List.is_empty rest then reason else strbrk "e.g., " ++ reason in
+  let k = if isfix then "fixpoint" else "cofixpoint" in
+  let w =
+    if isfix
+    then strbrk "Well-foundedness check may fail unexpectedly." ++ fnl()
+    else mt () in
+  strbrk "Not a fully mutually defined " ++ str k ++ fnl () ++
+  str "(" ++ e ++ str ")." ++ fnl () ++ w
+
+let warn_non_full_mutual =
+  CWarnings.create ~name:"non-full-mutual" ~category:"fixpoints"
+         (fun (x,xge,y,yge,isfix,rest) ->
+          non_full_mutual_message x xge y yge isfix rest)
+
+let check_mutuality env evd isfix fixl =
+  let names = List.map fst fixl in
+  let preorder =
+    List.map (fun (id,def) ->
+      (id, List.filter (fun id' -> not (Id.equal id id') && occur_var env evd id' (EConstr.of_constr def)) names))
+      fixl in
+  let po = partial_order Id.equal preorder in
+  match List.filter (function (_,Inr _) -> true | _ -> false) po with
+    | (x,Inr xge)::(y,Inr yge)::rest ->
+       warn_non_full_mutual (x,xge,y,yge,isfix,rest)
+    | _ -> ()
+
+type structured_fixpoint_expr = {
+  fix_name : Id.t;
+  fix_univs : universe_decl_expr option;
+  fix_annot : Id.t Loc.located option;
+  fix_binders : local_binder_expr list;
+  fix_body : constr_expr option;
+  fix_type : constr_expr
+}
+
+let interp_fix_context ~cofix env sigma fix =
+  let before, after = if not cofix then split_at_annot fix.fix_binders fix.fix_annot else [], fix.fix_binders in
+  let sigma, (impl_env, ((env', ctx), imps)) = interp_context_evars env sigma before in
+  let sigma, (impl_env', ((env'', ctx'), imps')) = interp_context_evars ~impl_env ~shift:(Context.Rel.nhyps ctx) env' sigma after in
+  let annot = Option.map (fun _ -> List.length (assums_of_rel_context ctx)) fix.fix_annot in
+  sigma, ((env'', ctx' @ ctx), (impl_env',imps @ imps'), annot)
+
+let interp_fix_ccl sigma impls (env,_) fix =
+  interp_type_evars_impls ~impls env sigma fix.fix_type
+
+let interp_fix_body env_rec sigma impls (_,ctx) fix ccl =
+  let open EConstr in
+  Option.cata (fun body ->
+    let env = push_rel_context ctx env_rec in
+    let sigma, body = interp_casted_constr_evars env sigma ~impls body ccl in
+    sigma, Some (it_mkLambda_or_LetIn body ctx)) (sigma, None) fix.fix_body
+
+let build_fix_type (_,ctx) ccl = EConstr.it_mkProd_or_LetIn ccl ctx
+
+let prepare_recursive_declaration fixnames fixtypes fixdefs =
+  let defs = List.map (subst_vars (List.rev fixnames)) fixdefs in
+  let names = List.map (fun id -> Name id) fixnames in
+  (Array.of_list names, Array.of_list fixtypes, Array.of_list defs)
+
+(* Jump over let-bindings. *)
+
+let compute_possible_guardness_evidences (ctx,_,recindex) =
+  (* A recursive index is characterized by the number of lambdas to
+     skip before finding the relevant inductive argument *)
+  match recindex with
+  | Some i -> [i]
+  | None ->
+      (* If recursive argument was not given by user, we try all args.
+         An earlier approach was to look only for inductive arguments,
+         but doing it properly involves delta-reduction, and it finally
+         doesn't seem to worth the effort (except for huge mutual
+         fixpoints ?) *)
+      List.interval 0 (Context.Rel.nhyps ctx - 1)
+
+type recursive_preentry =
+  Id.t list * constr option list * types list
+
+(* Wellfounded definition *)
+
+let contrib_name = "Program"
+let subtac_dir = [contrib_name]
+let tactics_module = subtac_dir @ ["Tactics"]
+
+let init_constant dir s sigma =
+  Evarutil.new_global sigma (Coqlib.coq_reference "Command" dir s)
+
+let fix_proto = init_constant tactics_module "fix_proto"
+
+let interp_recursive ~program_mode ~cofix fixl notations =
+  let open Context.Named.Declaration in
+  let open EConstr in
+  let env = Global.env() in
+  let fixnames = List.map (fun fix -> fix.fix_name) fixl in
+
+  (* Interp arities allowing for unresolved types *)
+  let all_universes =
+    List.fold_right (fun sfe acc ->
+        match sfe.fix_univs , acc with
+        | None , acc -> acc
+        | x , None -> x
+        | Some ls , Some us ->
+           let lsu = ls.univdecl_instance and usu = us.univdecl_instance in
+           if not (CList.for_all2eq (fun x y -> Id.equal (snd x) (snd y)) lsu usu) then
+             user_err Pp.(str "(co)-recursive definitions should all have the same universe binders");
+           Some us) fixl None in
+  let sigma, decl = Univdecls.interp_univ_decl_opt env all_universes in
+  let sigma, (fixctxs, fiximppairs, fixannots) =
+    on_snd List.split3 @@
+      List.fold_left_map (fun sigma -> interp_fix_context env sigma ~cofix) sigma fixl in
+  let fixctximpenvs, fixctximps = List.split fiximppairs in
+  let sigma, (fixccls,fixcclimps) =
+    on_snd List.split @@
+      List.fold_left3_map interp_fix_ccl sigma fixctximpenvs fixctxs fixl in
+  let fixtypes = List.map2 build_fix_type fixctxs fixccls in
+  let fixtypes = List.map (fun c -> nf_evar sigma c) fixtypes in
+  let fiximps = List.map3
+    (fun ctximps cclimps (_,ctx) -> ctximps@(Impargs.lift_implicits (Context.Rel.nhyps ctx) cclimps))
+    fixctximps fixcclimps fixctxs in
+  let sigma, rec_sign =
+    List.fold_left2
+      (fun (sigma, env') id t ->
+         if program_mode then
+           let sigma, sort = Typing.type_of ~refresh:true env sigma t in
+           let sigma, fixprot =
+             try
+               let sigma, h_term = fix_proto sigma in
+               let app = mkApp (h_term, [|sort; t|]) in
+               let _evd = ref sigma in
+               let res = Typing.e_solve_evars env _evd app in
+               !_evd, res
+             with e when CErrors.noncritical e -> sigma, t
+           in
+           sigma, LocalAssum (id,fixprot) :: env'
+         else sigma, LocalAssum (id,t) :: env')
+      (sigma,[]) fixnames fixtypes
+  in
+  let env_rec = push_named_context rec_sign env in
+
+  (* Get interpretation metadatas *)
+  let fixtypes = List.map EConstr.Unsafe.to_constr fixtypes in
+  let impls = compute_internalization_env env Recursive fixnames fixtypes fiximps in
+
+  (* Interp bodies with rollback because temp use of notations/implicit *)
+  let sigma, fixdefs =
+    Metasyntax.with_syntax_protection (fun () ->
+      List.iter (Metasyntax.set_notation_for_interpretation env_rec impls) notations;
+      List.fold_left4_map
+        (fun sigma fixctximpenv -> interp_fix_body env_rec sigma (Id.Map.fold Id.Map.add fixctximpenv impls))
+        sigma fixctximpenvs fixctxs fixl fixccls)
+      () in
+
+  (* Instantiate evars and check all are resolved *)
+  let sigma = solve_unif_constraints_with_heuristics env_rec sigma in
+  let sigma, nf = nf_evars_and_universes sigma in
+  let fixdefs = List.map (fun c -> Option.map EConstr.Unsafe.to_constr c) fixdefs in
+  let fixdefs = List.map (Option.map nf) fixdefs in
+  let fixtypes = List.map nf fixtypes in
+  let fixctxs = List.map (fun (_,ctx) -> ctx) fixctxs in
+
+  (* Build the fix declaration block *)
+  (env,rec_sign,decl,sigma), (fixnames,fixdefs,fixtypes), List.combine3 fixctxs fiximps fixannots
+
+let check_recursive isfix env evd (fixnames,fixdefs,_) =
+  check_evars_are_solved env evd Evd.empty;
+  if List.for_all Option.has_some fixdefs then begin
+    let fixdefs = List.map Option.get fixdefs in
+    check_mutuality env evd isfix (List.combine fixnames fixdefs)
+  end
+
+let interp_fixpoint ~cofix l ntns =
+  let (env,_,pl,evd),fix,info = interp_recursive ~program_mode:false ~cofix l ntns in
+  check_recursive true env evd fix;
+  (fix,pl,Evd.evar_universe_context evd,info)
+
+let declare_fixpoint local poly ((fixnames,fixdefs,fixtypes),pl,ctx,fiximps) indexes ntns =
+  if List.exists Option.is_empty fixdefs then
+    (* Some bodies to define by proof *)
+    let thms =
+      List.map3 (fun id t (ctx,imps,_) -> (id,(EConstr.of_constr t,(List.map RelDecl.get_name ctx,imps))))
+                fixnames fixtypes fiximps in
+    let init_tac =
+      Some (List.map (Option.cata (EConstr.of_constr %> Tactics.exact_no_check) Tacticals.New.tclIDTAC)
+        fixdefs) in
+    let evd = Evd.from_ctx ctx in
+    Lemmas.start_proof_with_initialization (Global,poly,DefinitionBody Fixpoint)
+      evd pl (Some(false,indexes,init_tac)) thms None (Lemmas.mk_hook (fun _ _ -> ()))
+  else begin
+    (* We shortcut the proof process *)
+    let fixdefs = List.map Option.get fixdefs in
+    let fixdecls = prepare_recursive_declaration fixnames fixtypes fixdefs in
+    let env = Global.env() in
+    let indexes = search_guard env indexes fixdecls in
+    let fiximps = List.map (fun (n,r,p) -> r) fiximps in
+    let vars = Univops.universes_of_constr env (mkFix ((indexes,0),fixdecls)) in
+    let fixdecls =
+      List.map_i (fun i _ -> mkFix ((indexes,i),fixdecls)) 0 fixnames in
+    let evd = Evd.from_ctx ctx in
+    let evd = Evd.restrict_universe_context evd vars in
+    let ctx = Evd.check_univ_decl ~poly evd pl in
+    let pl = Evd.universe_binders evd in
+    let fixdecls = List.map Safe_typing.mk_pure_proof fixdecls in
+    ignore (List.map4 (DeclareDef.declare_fix (local, poly, Fixpoint) pl ctx)
+              fixnames fixdecls fixtypes fiximps);
+    (* Declare the recursive definitions *)
+    fixpoint_message (Some indexes) fixnames;
+  end;
+  (* Declare notations *)
+  List.iter (Metasyntax.add_notation_interpretation (Global.env())) ntns
+
+let declare_cofixpoint local poly ((fixnames,fixdefs,fixtypes),pl,ctx,fiximps) ntns =
+  if List.exists Option.is_empty fixdefs then
+    (* Some bodies to define by proof *)
+    let thms =
+      List.map3 (fun id t (ctx,imps,_) -> (id,(EConstr.of_constr t,(List.map RelDecl.get_name ctx,imps))))
+                fixnames fixtypes fiximps in
+    let init_tac =
+      Some (List.map (Option.cata (EConstr.of_constr %> Tactics.exact_no_check) Tacticals.New.tclIDTAC)
+        fixdefs) in
+    let evd = Evd.from_ctx ctx in
+      Lemmas.start_proof_with_initialization (Global,poly, DefinitionBody CoFixpoint)
+      evd pl (Some(true,[],init_tac)) thms None (Lemmas.mk_hook (fun _ _ -> ()))
+  else begin
+    (* We shortcut the proof process *)
+    let fixdefs = List.map Option.get fixdefs in
+    let fixdecls = prepare_recursive_declaration fixnames fixtypes fixdefs in
+    let fixdecls = List.map_i (fun i _ -> mkCoFix (i,fixdecls)) 0 fixnames in
+    let env = Global.env () in
+    let vars = Univops.universes_of_constr env (List.hd fixdecls) in
+    let fixdecls = List.map Safe_typing.mk_pure_proof fixdecls in
+    let fiximps = List.map (fun (len,imps,idx) -> imps) fiximps in
+    let evd = Evd.from_ctx ctx in
+    let evd = Evd.restrict_universe_context evd vars in
+    let ctx = Evd.check_univ_decl ~poly evd pl in
+    let pl = Evd.universe_binders evd in
+    ignore (List.map4 (DeclareDef.declare_fix (local, poly, CoFixpoint) pl ctx)
+              fixnames fixdecls fixtypes fiximps);
+    (* Declare the recursive definitions *)
+    cofixpoint_message fixnames
+  end;
+  (* Declare notations *)
+  List.iter (Metasyntax.add_notation_interpretation (Global.env())) ntns
+
+let extract_decreasing_argument limit = function
+  | (na,CStructRec) -> na
+  | (na,_) when not limit -> na
+  | _ -> user_err Pp.(str
+      "Only structural decreasing is supported for a non-Program Fixpoint")
+
+let extract_fixpoint_components limit l =
+  let fixl, ntnl = List.split l in
+  let fixl = List.map (fun (((_,id),pl),ann,bl,typ,def) ->
+    let ann = extract_decreasing_argument limit ann in
+      {fix_name = id; fix_annot = ann; fix_univs = pl;
+       fix_binders = bl; fix_body = def; fix_type = typ}) fixl in
+  fixl, List.flatten ntnl
+
+let extract_cofixpoint_components l =
+  let fixl, ntnl = List.split l in
+  List.map (fun (((_,id),pl),bl,typ,def) ->
+            {fix_name = id; fix_annot = None; fix_univs = pl;
+             fix_binders = bl; fix_body = def; fix_type = typ}) fixl,
+  List.flatten ntnl
+
+let check_safe () =
+  let open Declarations in
+  let flags = Environ.typing_flags (Global.env ()) in
+  flags.check_universes && flags.check_guarded
+
+let do_fixpoint local poly l =
+  let fixl, ntns = extract_fixpoint_components true l in
+  let (_, _, _, info as fix) = interp_fixpoint ~cofix:false fixl ntns in
+  let possible_indexes =
+    List.map compute_possible_guardness_evidences info in
+  declare_fixpoint local poly fix possible_indexes ntns;
+  if not (check_safe ()) then Feedback.feedback Feedback.AddedAxiom else ()
+
+let do_cofixpoint local poly l =
+  let fixl,ntns = extract_cofixpoint_components l in
+  let cofix = interp_fixpoint ~cofix:true fixl ntns in
+  declare_cofixpoint local poly cofix ntns;
+  if not (check_safe ()) then Feedback.feedback Feedback.AddedAxiom else ()
diff --git a/vernac/comFixpoint.mli b/vernac/comFixpoint.mli
new file mode 100644
index 000000000..2c84bd84d
--- /dev/null
+++ b/vernac/comFixpoint.mli
@@ -0,0 +1,93 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2018     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+open Names
+open Constr
+open Decl_kinds
+open Constrexpr
+open Vernacexpr
+
+(** {6 Fixpoints and cofixpoints} *)
+
+(** Entry points for the vernacular commands Fixpoint and CoFixpoint *)
+
+val do_fixpoint :
+  (* When [false], assume guarded. *)
+  locality -> polymorphic -> (fixpoint_expr * decl_notation list) list -> unit
+
+val do_cofixpoint :
+  (* When [false], assume guarded. *)
+  locality -> polymorphic -> (cofixpoint_expr * decl_notation list) list -> unit
+
+(************************************************************************)
+(** Internal API  *)
+(************************************************************************)
+
+type structured_fixpoint_expr = {
+  fix_name : Id.t;
+  fix_univs : Vernacexpr.universe_decl_expr option;
+  fix_annot : Id.t Loc.located option;
+  fix_binders : local_binder_expr list;
+  fix_body : constr_expr option;
+  fix_type : constr_expr
+}
+
+(** Typing global fixpoints and cofixpoint_expr *)
+
+(** Exported for Program *)
+val interp_recursive :
+  (* Misc arguments *)
+  program_mode:bool -> cofix:bool ->
+  (* Notations of the fixpoint / should that be folded in the previous argument? *)
+  structured_fixpoint_expr list -> decl_notation list ->
+
+  (* env / signature / univs / evar_map *)
+  (Environ.env * EConstr.named_context * Univdecls.universe_decl * Evd.evar_map) *
+  (* names / defs / types *)
+  (Id.t list * Constr.constr option list * Constr.types list) *
+  (* ctx per mutual def / implicits / struct annotations *)
+  (EConstr.rel_context * Impargs.manual_explicitation list * int option) list
+
+(** Exported for Funind *)
+
+(** Extracting the semantical components out of the raw syntax of
+   (co)fixpoints declarations *)
+
+val extract_fixpoint_components : bool ->
+  (fixpoint_expr * decl_notation list) list ->
+    structured_fixpoint_expr list * decl_notation list
+
+val extract_cofixpoint_components :
+  (cofixpoint_expr * decl_notation list) list ->
+    structured_fixpoint_expr list * decl_notation list
+
+type recursive_preentry =
+  Id.t list * constr option list * types list
+
+val interp_fixpoint :
+  cofix:bool ->
+  structured_fixpoint_expr list -> decl_notation list ->
+  recursive_preentry * Univdecls.universe_decl * UState.t *
+  (EConstr.rel_context * Impargs.manual_implicits * int option) list
+
+(** Registering fixpoints and cofixpoints in the environment *)
+(** [Not used so far] *)
+val declare_fixpoint :
+  locality -> polymorphic ->
+  recursive_preentry * Univdecls.universe_decl * UState.t *
+  (Context.Rel.t * Impargs.manual_implicits * int option) list ->
+  Proof_global.lemma_possible_guards -> decl_notation list -> unit
+
+val declare_cofixpoint : locality -> polymorphic ->
+  recursive_preentry * Univdecls.universe_decl * UState.t *
+  (Context.Rel.t * Impargs.manual_implicits * int option) list ->
+  decl_notation list -> unit
+
+(** Very private function, do not use *)
+val compute_possible_guardness_evidences :
+  ('a, 'b) Context.Rel.pt * 'c * int option -> int list
diff --git a/vernac/comInductive.ml b/vernac/comInductive.ml
new file mode 100644
index 000000000..f3f50f41d
--- /dev/null
+++ b/vernac/comInductive.ml
@@ -0,0 +1,456 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+open Pp
+open CErrors
+open Sorts
+open Util
+open Constr
+open Termops
+open Environ
+open Declare
+open Names
+open Libnames
+open Globnames
+open Nameops
+open Constrexpr
+open Constrexpr_ops
+open Constrintern
+open Nametab
+open Impargs
+open Reductionops
+open Indtypes
+open Decl_kinds
+open Pretyping
+open Evarutil
+open Indschemes
+open Misctypes
+open Context.Rel.Declaration
+open Entries
+
+module RelDecl = Context.Rel.Declaration
+
+(* 3b| Mutual inductive definitions *)
+
+let rec complete_conclusion a cs = CAst.map_with_loc (fun ?loc -> function
+  | CProdN (bl,c) -> CProdN (bl,complete_conclusion a cs c)
+  | CLetIn (na,b,t,c) -> CLetIn (na,b,t,complete_conclusion a cs c)
+  | CHole (k, _, _) ->
+      let (has_no_args,name,params) = a in
+      if not has_no_args then
+        user_err ?loc
+         (strbrk"Cannot infer the non constant arguments of the conclusion of "
+          ++ Id.print cs ++ str ".");
+      let args = List.map (fun id -> CAst.make ?loc @@ CRef(Ident(loc,id),None)) params in
+      CAppExpl ((None,Ident(loc,name),None),List.rev args)
+  | c -> c
+  )
+
+let push_types env idl tl =
+  List.fold_left2 (fun env id t -> Environ.push_rel (LocalAssum (Name id,t)) env)
+    env idl tl
+
+type structured_one_inductive_expr = {
+  ind_name : Id.t;
+  ind_univs : Vernacexpr.universe_decl_expr option;
+  ind_arity : constr_expr;
+  ind_lc : (Id.t * constr_expr) list
+}
+
+type structured_inductive_expr =
+  local_binder_expr list * structured_one_inductive_expr list
+
+let minductive_message warn = function
+  | []  -> user_err Pp.(str "No inductive definition.")
+  | [x] -> (Id.print x ++ str " is defined" ++
+            if warn then str " as a non-primitive record" else mt())
+  | l   -> hov 0  (prlist_with_sep pr_comma Id.print l ++
+                     spc () ++ str "are defined")
+
+let check_all_names_different indl =
+  let ind_names = List.map (fun ind -> ind.ind_name) indl in
+  let cstr_names = List.map_append (fun ind -> List.map fst ind.ind_lc) indl in
+  let l = List.duplicates Id.equal ind_names in
+  let () = match l with
+  | [] -> ()
+  | t :: _ -> raise (InductiveError (SameNamesTypes t))
+  in
+  let l = List.duplicates Id.equal cstr_names in
+  let () = match l with
+  | [] -> ()
+  | c :: _ -> raise (InductiveError (SameNamesConstructors (List.hd l)))
+  in
+  let l = List.intersect Id.equal ind_names cstr_names in
+  match l with
+  | [] -> ()
+  | _ -> raise (InductiveError (SameNamesOverlap l))
+
+let mk_mltype_data sigma env assums arity indname =
+  let is_ml_type = is_sort env sigma (EConstr.of_constr arity) in
+  (is_ml_type,indname,assums)
+
+let prepare_param = function
+  | LocalAssum (na,t) -> Name.get_id na, LocalAssumEntry t
+  | LocalDef (na,b,_) -> Name.get_id na, LocalDefEntry b
+
+(** Make the arity conclusion flexible to avoid generating an upper bound universe now,
+    only if the universe does not appear anywhere else.
+    This is really a hack to stay compatible with the semantics of template polymorphic
+    inductives which are recognized when a "Type" appears at the end of the conlusion in
+    the source syntax. *)
+
+let rec check_anonymous_type ind =
+  let open Glob_term in
+    match DAst.get ind with
+    | GSort (GType []) -> true
+    | GProd ( _, _, _, e)
+    | GLetIn (_, _, _, e)
+    | GLambda (_, _, _, e)
+    | GApp (e, _)
+    | GCast (e, _) -> check_anonymous_type e
+    | _ -> false
+
+let make_conclusion_flexible sigma ty poly =
+  if poly && Term.isArity ty then
+    let _, concl = Term.destArity ty in
+      match concl with
+      | Type u ->
+        (match Univ.universe_level u with
+        | Some u ->
+          Evd.make_flexible_variable sigma ~algebraic:true u
+        | None -> sigma)
+      | _ -> sigma
+  else sigma
+
+let is_impredicative env u =
+  u = Prop Null || (is_impredicative_set env && u = Prop Pos)
+
+let interp_ind_arity env sigma ind =
+  let c = intern_gen IsType env ind.ind_arity in
+  let impls = Implicit_quantifiers.implicits_of_glob_constr ~with_products:true c in
+  let sigma,t = understand_tcc env sigma ~expected_type:IsType c in
+  let pseudo_poly = check_anonymous_type c in
+  let () = if not (Reductionops.is_arity env sigma t) then
+    user_err ?loc:(constr_loc ind.ind_arity) (str "Not an arity")
+  in
+  let t = EConstr.Unsafe.to_constr t in
+  sigma, (t, pseudo_poly, impls)
+
+let interp_cstrs env sigma impls mldata arity ind =
+  let cnames,ctyps = List.split ind.ind_lc in
+  (* Complete conclusions of constructor types if given in ML-style syntax *)
+  let ctyps' = List.map2 (complete_conclusion mldata) cnames ctyps in
+  (* Interpret the constructor types *)
+  let sigma, (ctyps'', cimpls) =
+    on_snd List.split @@
+    List.fold_left_map (fun sigma l ->
+        on_snd (on_fst EConstr.Unsafe.to_constr) @@
+        interp_type_evars_impls env sigma ~impls l) sigma ctyps' in
+  sigma, (cnames, ctyps'', cimpls)
+
+let sign_level env evd sign =
+  fst (List.fold_right
+    (fun d (lev,env) ->
+      match d with
+      | LocalDef _ -> lev, push_rel d env
+      | LocalAssum _ ->
+        let s = destSort (Reduction.whd_all env
+                            (EConstr.Unsafe.to_constr (nf_evar evd (Retyping.get_type_of env evd (EConstr.of_constr (RelDecl.get_type d))))))
+        in
+        let u = univ_of_sort s in
+          (Univ.sup u lev, push_rel d env))
+    sign (Univ.type0m_univ,env))
+
+let sup_list min = List.fold_left Univ.sup min
+
+let extract_level env evd min tys =
+  let sorts = List.map (fun ty ->
+    let ctx, concl = Reduction.dest_prod_assum env ty in
+      sign_level env evd (LocalAssum (Anonymous, concl) :: ctx)) tys
+  in sup_list min sorts
+
+let is_flexible_sort evd u =
+  match Univ.Universe.level u with
+  | Some l -> Evd.is_flexible_level evd l
+  | None -> false
+
+let inductive_levels env evd poly arities inds =
+  let destarities = List.map (fun x -> x, Reduction.dest_arity env x) arities in
+  let levels = List.map (fun (x,(ctx,a)) ->
+    if a = Prop Null then None
+    else Some (univ_of_sort a)) destarities
+  in
+  let cstrs_levels, min_levels, sizes =
+    CList.split3
+      (List.map2 (fun (_,tys,_) (arity,(ctx,du)) ->
+        let len = List.length tys in
+        let minlev = Sorts.univ_of_sort du in
+        let minlev =
+          if len > 1 && not (is_impredicative env du) then
+            Univ.sup minlev Univ.type0_univ
+          else minlev
+        in
+        let minlev =
+          (** Indices contribute. *)
+          if Indtypes.is_indices_matter () && List.length ctx > 0 then (
+            let ilev = sign_level env evd ctx in
+              Univ.sup ilev minlev)
+          else minlev
+        in
+        let clev = extract_level env evd minlev tys in
+          (clev, minlev, len)) inds destarities)
+  in
+  (* Take the transitive closure of the system of constructors *)
+  (* level constraints and remove the recursive dependencies *)
+  let levels' = Universes.solve_constraints_system (Array.of_list levels)
+    (Array.of_list cstrs_levels) (Array.of_list min_levels)
+  in
+  let evd, arities =
+    CList.fold_left3 (fun (evd, arities) cu (arity,(ctx,du)) len ->
+      if is_impredicative env du then
+        (** Any product is allowed here. *)
+        evd, arity :: arities
+      else (** If in a predicative sort, or asked to infer the type,
+               we take the max of:
+               - indices (if in indices-matter mode)
+               - constructors
+               - Type(1) if there is more than 1 constructor
+           *)
+        (** Constructors contribute. *)
+        let evd =
+          if Sorts.is_set du then
+            if not (Evd.check_leq evd cu Univ.type0_univ) then
+              raise (Indtypes.InductiveError Indtypes.LargeNonPropInductiveNotInType)
+            else evd
+          else evd
+            (* Evd.set_leq_sort env evd (Type cu) du *)
+        in
+        let evd =
+          if len >= 2 && Univ.is_type0m_univ cu then
+           (** "Polymorphic" type constraint and more than one constructor,
+               should not land in Prop. Add constraint only if it would
+               land in Prop directly (no informative arguments as well). *)
+            Evd.set_leq_sort env evd (Prop Pos) du
+          else evd
+        in
+        let duu = Sorts.univ_of_sort du in
+        let evd =
+          if not (Univ.is_small_univ duu) && Univ.Universe.equal cu duu then
+            if is_flexible_sort evd duu && not (Evd.check_leq evd Univ.type0_univ duu) then
+              Evd.set_eq_sort env evd (Prop Null) du
+            else evd
+          else Evd.set_eq_sort env evd (Type cu) du
+        in
+          (evd, arity :: arities))
+    (evd,[]) (Array.to_list levels') destarities sizes
+  in evd, List.rev arities
+
+let check_named (loc, na) = match na with
+| Name _ -> ()
+| Anonymous ->
+  let msg = str "Parameters must be named." in
+  user_err ?loc  msg
+
+
+let check_param = function
+| CLocalDef (na, _, _) -> check_named na
+| CLocalAssum (nas, Default _, _) -> List.iter check_named nas
+| CLocalAssum (nas, Generalized _, _) -> ()
+| CLocalPattern (loc,_) ->
+    Loc.raise ?loc (Stream.Error "pattern with quote not allowed here.")
+
+let interp_mutual_inductive (paramsl,indl) notations cum poly prv finite =
+  check_all_names_different indl;
+  List.iter check_param paramsl;
+  let env0 = Global.env() in
+  let pl = (List.hd indl).ind_univs in
+  let sigma, decl = Univdecls.interp_univ_decl_opt env0 pl in
+  let sigma, (impls, ((env_params, ctx_params), userimpls)) =
+    interp_context_evars env0 sigma paramsl
+  in
+  let ctx_params = List.map (fun d -> map_rel_decl EConstr.Unsafe.to_constr d) ctx_params in
+  let indnames = List.map (fun ind -> ind.ind_name) indl in
+
+  (* Names of parameters as arguments of the inductive type (defs removed) *)
+  let assums = List.filter is_local_assum ctx_params in
+  let params = List.map (RelDecl.get_name %> Name.get_id) assums in
+
+  (* Interpret the arities *)
+  let sigma, arities = List.fold_left_map (fun sigma -> interp_ind_arity env_params sigma) sigma indl in
+
+  let fullarities = List.map (fun (c, _, _) -> Term.it_mkProd_or_LetIn c ctx_params) arities in
+  let env_ar = push_types env0 indnames fullarities in
+  let env_ar_params = push_rel_context ctx_params env_ar in
+
+  (* Compute interpretation metadatas *)
+  let indimpls = List.map (fun (_, _, impls) -> userimpls @
+    lift_implicits (Context.Rel.nhyps ctx_params) impls) arities in
+  let arities = List.map pi1 arities and aritypoly = List.map pi2 arities in
+  let impls = compute_internalization_env env0 ~impls (Inductive (params,true)) indnames fullarities indimpls in
+  let ntn_impls = compute_internalization_env env0 (Inductive (params,true)) indnames fullarities indimpls in
+  let mldatas = List.map2 (mk_mltype_data sigma env_params params) arities indnames in
+
+  let sigma, constructors =
+    Metasyntax.with_syntax_protection (fun () ->
+     (* Temporary declaration of notations and scopes *)
+     List.iter (Metasyntax.set_notation_for_interpretation env_params ntn_impls) notations;
+     (* Interpret the constructor types *)
+     List.fold_left3_map (fun sigma -> interp_cstrs env_ar_params sigma impls) sigma mldatas arities indl)
+     () in
+
+  (* Try further to solve evars, and instantiate them *)
+  let sigma = solve_remaining_evars all_and_fail_flags env_params sigma Evd.empty in
+  (* Compute renewed arities *)
+  let sigma, nf = nf_evars_and_universes sigma in
+  let arities = List.map nf arities in
+  let constructors = List.map (fun (idl,cl,impsl) -> (idl,List.map nf cl,impsl)) constructors in
+  let sigma = List.fold_left2 (fun sigma ty poly -> make_conclusion_flexible sigma ty poly) sigma arities aritypoly in
+  let sigma, arities = inductive_levels env_ar_params sigma poly arities constructors in
+  let sigma, nf' = nf_evars_and_universes sigma in
+  let nf x = nf' (nf x) in
+  let arities = List.map nf' arities in
+  let constructors = List.map (fun (idl,cl,impsl) -> (idl,List.map nf' cl,impsl)) constructors in
+  let ctx_params = Context.Rel.map nf ctx_params in
+  let uctx = Evd.check_univ_decl ~poly sigma decl in
+  List.iter (fun c -> check_evars env_params Evd.empty sigma (EConstr.of_constr c)) arities;
+  Context.Rel.iter (fun c -> check_evars env0 Evd.empty sigma (EConstr.of_constr c)) ctx_params;
+  List.iter (fun (_,ctyps,_) ->
+    List.iter (fun c -> check_evars env_ar_params Evd.empty sigma (EConstr.of_constr c)) ctyps)
+    constructors;
+
+  (* Build the inductive entries *)
+  let entries = List.map4 (fun ind arity template (cnames,ctypes,cimpls) -> {
+    mind_entry_typename = ind.ind_name;
+    mind_entry_arity = arity;
+    mind_entry_template = template;
+    mind_entry_consnames = cnames;
+    mind_entry_lc = ctypes
+  }) indl arities aritypoly constructors in
+  let impls =
+    let len = Context.Rel.nhyps ctx_params in
+      List.map2 (fun indimpls (_,_,cimpls) ->
+        indimpls, List.map (fun impls ->
+          userimpls @ (lift_implicits len impls)) cimpls) indimpls constructors
+  in
+  let univs =
+    match uctx with
+    | Polymorphic_const_entry uctx ->
+      if cum then
+        Cumulative_ind_entry (Universes.univ_inf_ind_from_universe_context uctx)
+      else Polymorphic_ind_entry uctx
+    | Monomorphic_const_entry uctx ->
+      Monomorphic_ind_entry uctx
+  in
+  (* Build the mutual inductive entry *)
+  let mind_ent =
+    { mind_entry_params = List.map prepare_param ctx_params;
+      mind_entry_record = None;
+      mind_entry_finite = finite;
+      mind_entry_inds = entries;
+      mind_entry_private = if prv then Some false else None;
+      mind_entry_universes = univs;
+    }
+  in
+  (if poly && cum then
+      Inductiveops.infer_inductive_subtyping env_ar sigma mind_ent
+   else mind_ent), Evd.universe_binders sigma, impls
+
+(* Very syntactical equality *)
+let eq_local_binders bl1 bl2 =
+  List.equal local_binder_eq bl1 bl2
+
+let extract_coercions indl =
+  let mkqid (_,((_,id),_)) = qualid_of_ident id in
+  let extract lc = List.filter (fun (iscoe,_) -> iscoe) lc in
+  List.map mkqid (List.flatten(List.map (fun (_,_,_,lc) -> extract lc) indl))
+
+let extract_params indl =
+  let paramsl = List.map (fun (_,params,_,_) -> params) indl in
+  match paramsl with
+  | [] -> anomaly (Pp.str "empty list of inductive types.")
+  | params::paramsl ->
+      if not (List.for_all (eq_local_binders params) paramsl) then user_err Pp.(str
+        "Parameters should be syntactically the same for each inductive type.");
+      params
+
+let extract_inductive indl =
+  List.map (fun (((_,indname),pl),_,ar,lc) -> {
+    ind_name = indname; ind_univs = pl;
+    ind_arity = Option.cata (fun x -> x) (CAst.make @@ CSort (GType [])) ar;
+    ind_lc = List.map (fun (_,((_,id),t)) -> (id,t)) lc
+  }) indl
+
+let extract_mutual_inductive_declaration_components indl =
+  let indl,ntnl = List.split indl in
+  let params = extract_params indl in
+  let coes = extract_coercions indl in
+  let indl = extract_inductive indl in
+  (params,indl), coes, List.flatten ntnl
+
+let is_recursive mie =
+  let rec is_recursive_constructor lift typ =
+    match Constr.kind typ with
+    | Prod (_,arg,rest) ->
+        not (EConstr.Vars.noccurn Evd.empty (** FIXME *) lift (EConstr.of_constr arg)) ||
+        is_recursive_constructor (lift+1) rest
+    | LetIn (na,b,t,rest) -> is_recursive_constructor (lift+1) rest
+    | _ -> false
+  in
+  match mie.mind_entry_inds with
+  | [ind] ->
+      let nparams = List.length mie.mind_entry_params in
+      List.exists (fun t -> is_recursive_constructor (nparams+1) t) ind.mind_entry_lc
+  | _ -> false
+
+let declare_mutual_inductive_with_eliminations mie pl impls =
+  (* spiwack: raises an error if the structure is supposed to be non-recursive,
+        but isn't *)
+  begin match mie.mind_entry_finite with
+  | BiFinite when is_recursive mie ->
+      if Option.has_some mie.mind_entry_record then
+        user_err Pp.(str "Records declared with the keywords Record or Structure cannot be recursive. You can, however, define recursive records using the Inductive or CoInductive command.")
+      else
+        user_err Pp.(str ("Types declared with the keyword Variant cannot be recursive. Recursive types are defined with the Inductive and CoInductive command."))
+  | _ -> ()
+  end;
+  let names = List.map (fun e -> e.mind_entry_typename) mie.mind_entry_inds in
+  let (_, kn), prim = declare_mind mie in
+  let mind = Global.mind_of_delta_kn kn in
+  List.iteri (fun i (indimpls, constrimpls) ->
+              let ind = (mind,i) in
+              let gr = IndRef ind in
+              maybe_declare_manual_implicits false gr indimpls;
+              Declare.declare_univ_binders gr pl;
+              List.iteri
+                (fun j impls ->
+                 maybe_declare_manual_implicits false
+                    (ConstructRef (ind, succ j)) impls)
+                constrimpls)
+      impls;
+  let warn_prim = match mie.mind_entry_record with Some (Some _) -> not prim | _ -> false in
+  Flags.if_verbose Feedback.msg_info (minductive_message warn_prim names);
+  if mie.mind_entry_private == None
+  then declare_default_schemes mind;
+  mind
+
+type one_inductive_impls =
+  Impargs.manual_explicitation list (* for inds *)*
+  Impargs.manual_explicitation list list (* for constrs *)
+
+let do_mutual_inductive indl cum poly prv finite =
+  let indl,coes,ntns = extract_mutual_inductive_declaration_components indl in
+  (* Interpret the types *)
+  let mie,pl,impls = interp_mutual_inductive indl ntns cum poly prv finite in
+  (* Declare the mutual inductive block with its associated schemes *)
+  ignore (declare_mutual_inductive_with_eliminations mie pl impls);
+  (* Declare the possible notations of inductive types *)
+  List.iter (Metasyntax.add_notation_interpretation (Global.env ())) ntns;
+  (* Declare the coercions *)
+  List.iter (fun qid -> Class.try_add_new_coercion (locate qid) ~local:false poly) coes;
+  (* If positivity is assumed declares itself as unsafe. *)
+  if Environ.deactivated_guard (Global.env ()) then Feedback.feedback Feedback.AddedAxiom else ()
diff --git a/vernac/comInductive.mli b/vernac/comInductive.mli
new file mode 100644
index 000000000..82ea131e1
--- /dev/null
+++ b/vernac/comInductive.mli
@@ -0,0 +1,65 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+open Names
+open Entries
+open Libnames
+open Vernacexpr
+open Constrexpr
+open Decl_kinds
+
+(** {6 Inductive and coinductive types} *)
+
+(** Entry points for the vernacular commands Inductive and CoInductive *)
+
+val do_mutual_inductive :
+  (one_inductive_expr * decl_notation list) list -> cumulative_inductive_flag ->
+  polymorphic -> private_flag -> Declarations.recursivity_kind -> unit
+
+(************************************************************************)
+(** Internal API  *)
+(************************************************************************)
+
+(** Exported for Record and Funind *)
+
+(** Registering a mutual inductive definition together with its
+   associated schemes *)
+
+type one_inductive_impls =
+  Impargs.manual_implicits (** for inds *)*
+  Impargs.manual_implicits list (** for constrs *)
+
+val declare_mutual_inductive_with_eliminations :
+  mutual_inductive_entry -> Universes.universe_binders -> one_inductive_impls list ->
+  MutInd.t
+
+(** Exported for Funind *)
+
+(** Extracting the semantical components out of the raw syntax of mutual
+   inductive declarations *)
+
+type structured_one_inductive_expr = {
+  ind_name : Id.t;
+  ind_univs : Vernacexpr.universe_decl_expr option;
+  ind_arity : constr_expr;
+  ind_lc : (Id.t * constr_expr) list
+}
+
+type structured_inductive_expr =
+  local_binder_expr list * structured_one_inductive_expr list
+
+val extract_mutual_inductive_declaration_components :
+  (one_inductive_expr * decl_notation list) list ->
+    structured_inductive_expr * (*coercions:*) qualid list * decl_notation list
+
+(** Typing mutual inductive definitions *)
+
+val interp_mutual_inductive :
+  structured_inductive_expr -> decl_notation list -> cumulative_inductive_flag ->
+  polymorphic -> private_flag -> Declarations.recursivity_kind ->
+  mutual_inductive_entry * Universes.universe_binders * one_inductive_impls list
diff --git a/vernac/comProgramFixpoint.ml b/vernac/comProgramFixpoint.ml
new file mode 100644
index 000000000..a9a91e304
--- /dev/null
+++ b/vernac/comProgramFixpoint.ml
@@ -0,0 +1,342 @@
+open Pp
+open CErrors
+open Util
+open Constr
+open Entries
+open Vars
+open Declare
+open Names
+open Libnames
+open Globnames
+open Nameops
+open Constrexpr
+open Constrexpr_ops
+open Constrintern
+open Decl_kinds
+open Evarutil
+open Context.Rel.Declaration
+open ComFixpoint
+
+module RelDecl = Context.Rel.Declaration
+
+(* Wellfounded definition *)
+
+open Coqlib
+
+let contrib_name = "Program"
+let subtac_dir = [contrib_name]
+let fixsub_module = subtac_dir @ ["Wf"]
+(* let tactics_module = subtac_dir @ ["Tactics"] *)
+
+let init_reference dir s () = Coqlib.coq_reference "Command" dir s
+let init_constant dir s sigma =
+  Evarutil.new_global sigma (Coqlib.coq_reference "Command" dir s)
+
+let make_ref l s = init_reference l s
+(* let fix_proto = init_constant tactics_module "fix_proto" *)
+let fix_sub_ref = make_ref fixsub_module "Fix_sub"
+let measure_on_R_ref = make_ref fixsub_module "MR"
+let well_founded = init_constant ["Init"; "Wf"] "well_founded"
+let mkSubset sigma name typ prop =
+  let open EConstr in
+  let sigma, app_h = Evarutil.new_global sigma (delayed_force build_sigma).typ in
+  sigma, mkApp (app_h, [| typ; mkLambda (name, typ, prop) |])
+
+let sigT = Lazy.from_fun build_sigma_type
+
+let make_qref s = Qualid (Loc.tag @@ qualid_of_string s)
+let lt_ref = make_qref "Init.Peano.lt"
+
+let rec telescope sigma l =
+  let open EConstr in
+  let open Vars in
+  match l with
+  | [] -> assert false
+  | [LocalAssum (n, t)] ->
+    sigma, t, [LocalDef (n, mkRel 1, t)], mkRel 1
+  | LocalAssum (n, t) :: tl ->
+      let sigma, ty, tys, (k, constr) =
+        List.fold_left
+          (fun (sigma, ty, tys, (k, constr)) decl ->
+            let t = RelDecl.get_type decl in
+            let pred = mkLambda (RelDecl.get_name decl, t, ty) in
+            let sigma, ty = Evarutil.new_global sigma (Lazy.force sigT).typ in
+            let sigma, intro = Evarutil.new_global sigma (Lazy.force sigT).intro in
+            let sigty = mkApp (ty, [|t; pred|]) in
+            let intro = mkApp (intro, [|lift k t; lift k pred; mkRel k; constr|]) in
+              (sigma, sigty, pred :: tys, (succ k, intro)))
+          (sigma, t, [], (2, mkRel 1)) tl
+      in
+      let sigma, last, subst = List.fold_right2
+        (fun pred decl (sigma, prev, subst) ->
+          let t = RelDecl.get_type decl in
+          let sigma, p1 = Evarutil.new_global sigma (Lazy.force sigT).proj1 in
+          let sigma, p2 = Evarutil.new_global sigma (Lazy.force sigT).proj2 in
+          let proj1 = applist (p1, [t; pred; prev]) in
+          let proj2 = applist (p2, [t; pred; prev]) in
+            (sigma, lift 1 proj2, LocalDef (get_name decl, proj1, t) :: subst))
+        (List.rev tys) tl (sigma, mkRel 1, [])
+      in sigma, ty, (LocalDef (n, last, t) :: subst), constr
+
+  | LocalDef (n, b, t) :: tl ->
+    let sigma, ty, subst, term = telescope sigma tl in
+    sigma, ty, (LocalDef (n, b, t) :: subst), lift 1 term
+
+let nf_evar_context sigma ctx =
+  List.map (map_constr (fun c -> Evarutil.nf_evar sigma c)) ctx
+
+let build_wellfounded (recname,pl,n,bl,arityc,body) poly r measure notation =
+  let open EConstr in
+  let open Vars in
+  let lift_rel_context n l = Termops.map_rel_context_with_binders (liftn n) l in
+  Coqlib.check_required_library ["Coq";"Program";"Wf"];
+  let env = Global.env() in
+  let sigma, decl = Univdecls.interp_univ_decl_opt env pl in
+  let sigma, (_, ((env', binders_rel), impls)) = interp_context_evars env sigma bl in
+  let len = List.length binders_rel in
+  let top_env = push_rel_context binders_rel env in
+  let sigma, top_arity = interp_type_evars top_env sigma arityc in
+  let full_arity = it_mkProd_or_LetIn top_arity binders_rel in
+  let sigma, argtyp, letbinders, make = telescope sigma binders_rel in
+  let argname = Id.of_string "recarg" in
+  let arg = LocalAssum (Name argname, argtyp) in
+  let binders = letbinders @ [arg] in
+  let binders_env = push_rel_context binders_rel env in
+  let sigma, (rel, _) = interp_constr_evars_impls env sigma r in
+  let relty = Typing.unsafe_type_of env sigma rel in
+  let relargty =
+    let error () =
+      user_err ?loc:(constr_loc r)
+               ~hdr:"Command.build_wellfounded"
+                    (Printer.pr_econstr_env env sigma rel ++ str " is not an homogeneous binary relation.")
+    in
+      try
+        let ctx, ar = Reductionops.splay_prod_n env sigma 2 relty in
+          match ctx, EConstr.kind sigma ar with
+          | [LocalAssum (_,t); LocalAssum (_,u)], Sort s
+              when Sorts.is_prop (ESorts.kind sigma s) && Reductionops.is_conv env sigma t u -> t
+          | _, _ -> error ()
+      with e when CErrors.noncritical e -> error ()
+  in
+  let sigma, measure = interp_casted_constr_evars binders_env sigma measure relargty in
+  let sigma, wf_rel, wf_rel_fun, measure_fn =
+    let measure_body, measure =
+      it_mkLambda_or_LetIn measure letbinders,
+      it_mkLambda_or_LetIn measure binders
+    in
+    let sigma, comb = Evarutil.new_global sigma (delayed_force measure_on_R_ref) in
+    let wf_rel = mkApp (comb, [| argtyp; relargty; rel; measure |]) in
+    let wf_rel_fun x y =
+      mkApp (rel, [| subst1 x measure_body;
+                     subst1 y measure_body |])
+    in sigma, wf_rel, wf_rel_fun, measure
+  in
+  let sigma, wf_term = well_founded sigma in
+  let wf_proof = mkApp (wf_term, [| argtyp ; wf_rel |]) in
+  let argid' = Id.of_string (Id.to_string argname ^ "'") in
+  let wfarg sigma len =
+    let sigma, ss_term = mkSubset sigma (Name argid') argtyp (wf_rel_fun (mkRel 1) (mkRel (len + 1))) in
+    sigma, LocalAssum (Name argid', ss_term)
+  in
+  let sigma, intern_bl =
+    let sigma, wfa = wfarg sigma 1 in
+    sigma, wfa :: [arg]
+  in
+  let _intern_env = push_rel_context intern_bl env in
+  let sigma, proj = Evarutil.new_global sigma (delayed_force build_sigma).Coqlib.proj1 in
+  let wfargpred = mkLambda (Name argid', argtyp, wf_rel_fun (mkRel 1) (mkRel 3)) in
+  let projection = (* in wfarg :: arg :: before *)
+    mkApp (proj, [| argtyp ; wfargpred ; mkRel 1 |])
+  in
+  let top_arity_let = it_mkLambda_or_LetIn top_arity letbinders in
+  let intern_arity = substl [projection] top_arity_let in
+  (* substitute the projection of wfarg for something,
+     now intern_arity is in wfarg :: arg *)
+  let sigma, wfa = wfarg sigma 1 in
+  let intern_fun_arity_prod = it_mkProd_or_LetIn intern_arity [wfa] in
+  let intern_fun_binder = LocalAssum (Name (add_suffix recname "'"), intern_fun_arity_prod) in
+  let sigma, curry_fun =
+    let wfpred = mkLambda (Name argid', argtyp, wf_rel_fun (mkRel 1) (mkRel (2 * len + 4))) in
+    let sigma, intro = Evarutil.new_global sigma (delayed_force build_sigma).Coqlib.intro in
+    let arg = mkApp (intro, [| argtyp; wfpred; lift 1 make; mkRel 1 |]) in
+    let app = mkApp (mkRel (2 * len + 2 (* recproof + orig binders + current binders *)), [| arg |]) in
+    let rcurry = mkApp (rel, [| measure; lift len measure |]) in
+    let lam = LocalAssum (Name (Id.of_string "recproof"), rcurry) in
+    let body = it_mkLambda_or_LetIn app (lam :: binders_rel) in
+    let ty = it_mkProd_or_LetIn (lift 1 top_arity) (lam :: binders_rel) in
+    sigma, LocalDef (Name recname, body, ty)
+  in
+  let fun_bl = intern_fun_binder :: [arg] in
+  let lift_lets = lift_rel_context 1 letbinders in
+  let sigma, intern_body =
+    let ctx = LocalAssum (Name recname, get_type curry_fun) :: binders_rel in
+    let (r, l, impls, scopes) =
+      Constrintern.compute_internalization_data env
+        Constrintern.Recursive (EConstr.Unsafe.to_constr full_arity) impls
+    in
+    let newimpls = Id.Map.singleton recname
+        (r, l, impls @ [(Some (Id.of_string "recproof", Impargs.Manual, (true, false)))],
+         scopes @ [None]) in
+    interp_casted_constr_evars (push_rel_context ctx env) sigma
+      ~impls:newimpls body (lift 1 top_arity)
+  in
+  let intern_body_lam = it_mkLambda_or_LetIn intern_body (curry_fun :: lift_lets @ fun_bl) in
+  let prop = mkLambda (Name argname, argtyp, top_arity_let) in
+  (* XXX: Previous code did parallel evdref update, so possible old
+     weak ordering semantics may bite here. *)
+  let sigma, def =
+    let sigma, h_a_term = Evarutil.new_global sigma (delayed_force fix_sub_ref) in
+    let sigma, h_e_term = Evarutil.new_evar env sigma
+        ~src:(Loc.tag @@ Evar_kinds.QuestionMark (Evar_kinds.Define false,Anonymous)) wf_proof in
+    sigma, mkApp (h_a_term, [| argtyp ; wf_rel ; h_e_term; prop |])
+  in
+  let _evd = ref sigma in
+  let def = Typing.e_solve_evars env _evd def in
+  let sigma = !_evd in
+  let sigma = Evarutil.nf_evar_map sigma in
+  let def = mkApp (def, [|intern_body_lam|]) in
+  let binders_rel = nf_evar_context sigma binders_rel in
+  let binders = nf_evar_context sigma binders in
+  let top_arity = Evarutil.nf_evar sigma top_arity in
+  let hook, recname, typ =
+    if List.length binders_rel > 1 then
+      let name = add_suffix recname "_func" in
+      (* XXX: Mutating the evar_map in the hook! *)
+      (* XXX: Likely the sigma is out of date when the hook is called .... *)
+      let hook sigma l gr _ =
+        let sigma, h_body = Evarutil.new_global sigma gr in
+        let body = it_mkLambda_or_LetIn (mkApp (h_body, [|make|])) binders_rel in
+        let ty = it_mkProd_or_LetIn top_arity binders_rel in
+        let ty = EConstr.Unsafe.to_constr ty in
+        let univs = Evd.check_univ_decl ~poly sigma decl in
+        (*FIXME poly? *)
+        let ce = definition_entry ~types:ty ~univs (EConstr.to_constr sigma body) in
+        (** FIXME: include locality *)
+        let c = Declare.declare_constant recname (DefinitionEntry ce, IsDefinition Definition) in
+        let gr = ConstRef c in
+        let () = Universes.register_universe_binders gr (Evd.universe_binders sigma) in
+        if Impargs.is_implicit_args () || not (List.is_empty impls) then
+          Impargs.declare_manual_implicits false gr [impls]
+      in
+      let typ = it_mkProd_or_LetIn top_arity binders in
+      hook, name, typ
+    else
+      let typ = it_mkProd_or_LetIn top_arity binders_rel in
+      let hook sigma l gr _ =
+        if Impargs.is_implicit_args () || not (List.is_empty impls) then
+          Impargs.declare_manual_implicits false gr [impls]
+      in hook, recname, typ
+  in
+  (* XXX: Capturing sigma here... bad bad *)
+  let hook = Lemmas.mk_hook (hook sigma) in
+  let fullcoqc = EConstr.to_constr sigma def in
+  let fullctyp = EConstr.to_constr sigma typ in
+  Obligations.check_evars env sigma;
+  let evars, _, evars_def, evars_typ =
+    Obligations.eterm_obligations env recname sigma 0 fullcoqc fullctyp
+  in
+  let ctx = Evd.evar_universe_context sigma in
+    ignore(Obligations.add_definition recname ~term:evars_def ~univdecl:decl
+             evars_typ ctx evars ~hook)
+
+let out_def = function
+  | Some def -> def
+  | None -> user_err Pp.(str "Program Fixpoint needs defined bodies.")
+
+let collect_evars_of_term evd c ty =
+  let evars = Evar.Set.union (Evd.evars_of_term c) (Evd.evars_of_term ty) in
+  Evar.Set.fold (fun ev acc -> Evd.add acc ev (Evd.find_undefined evd ev))
+  evars (Evd.from_ctx (Evd.evar_universe_context evd))
+
+let do_program_recursive local poly fixkind fixl ntns =
+  let cofix = fixkind = Obligations.IsCoFixpoint in
+  let (env, rec_sign, pl, evd), fix, info =
+    interp_recursive ~cofix ~program_mode:true fixl ntns
+  in
+    (* Program-specific code *)
+    (* Get the interesting evars, those that were not instanciated *)
+  let evd = Typeclasses.resolve_typeclasses ~filter:Typeclasses.no_goals ~fail:true env evd in
+    (* Solve remaining evars *)
+  let evd = nf_evar_map_undefined evd in
+  let collect_evars id def typ imps =
+    (* Generalize by the recursive prototypes  *)
+    let def =
+      EConstr.to_constr evd (Termops.it_mkNamedLambda_or_LetIn (EConstr.of_constr def) rec_sign)
+    and typ =
+      EConstr.to_constr evd (Termops.it_mkNamedProd_or_LetIn (EConstr.of_constr typ) rec_sign)
+    in
+    let evm = collect_evars_of_term evd def typ in
+    let evars, _, def, typ =
+      Obligations.eterm_obligations env id evm
+        (List.length rec_sign) def typ
+    in (id, def, typ, imps, evars)
+  in
+  let (fixnames,fixdefs,fixtypes) = fix in
+  let fiximps = List.map pi2 info in
+  let fixdefs = List.map out_def fixdefs in
+  let defs = List.map4 collect_evars fixnames fixdefs fixtypes fiximps in
+  let () = if not cofix then begin
+      let possible_indexes = List.map ComFixpoint.compute_possible_guardness_evidences info in
+      let fixdecls = Array.of_list (List.map (fun x -> Name x) fixnames),
+        Array.of_list fixtypes,
+        Array.of_list (List.map (subst_vars (List.rev fixnames)) fixdefs)
+      in
+      let indexes =
+        Pretyping.search_guard (Global.env ()) possible_indexes fixdecls in
+      List.iteri (fun i _ ->
+          Inductive.check_fix env
+                              ((indexes,i),fixdecls))
+        fixl
+  end in
+  let ctx = Evd.evar_universe_context evd in
+  let kind = match fixkind with
+  | Obligations.IsFixpoint _ -> (local, poly, Fixpoint)
+  | Obligations.IsCoFixpoint -> (local, poly, CoFixpoint)
+  in
+  Obligations.add_mutual_definitions defs ~kind ~univdecl:pl ctx ntns fixkind
+
+let do_program_fixpoint local poly l =
+  let g = List.map (fun ((_,wf,_,_,_),_) -> wf) l in
+    match g, l with
+    | [(n, CWfRec r)], [((((_,id),pl),_,bl,typ,def),ntn)] ->
+        let recarg =
+          match n with
+          | Some n -> mkIdentC (snd n)
+          | None ->
+              user_err ~hdr:"do_program_fixpoint"
+                (str "Recursive argument required for well-founded fixpoints")
+        in build_wellfounded (id, pl, n, bl, typ, out_def def) poly r recarg ntn
+
+    | [(n, CMeasureRec (m, r))], [((((_,id),pl),_,bl,typ,def),ntn)] ->
+        build_wellfounded (id, pl, n, bl, typ, out_def def) poly
+          (Option.default (CAst.make @@ CRef (lt_ref,None)) r) m ntn
+
+    | _, _ when List.for_all (fun (n, ro) -> ro == CStructRec) g ->
+        let fixl,ntns = extract_fixpoint_components true l in
+        let fixkind = Obligations.IsFixpoint g in
+          do_program_recursive local poly fixkind fixl ntns
+
+    | _, _ ->
+        user_err ~hdr:"do_program_fixpoint"
+          (str "Well-founded fixpoints not allowed in mutually recursive blocks")
+
+let extract_cofixpoint_components l =
+  let fixl, ntnl = List.split l in
+  List.map (fun (((_,id),pl),bl,typ,def) ->
+            {fix_name = id; fix_annot = None; fix_univs = pl;
+             fix_binders = bl; fix_body = def; fix_type = typ}) fixl,
+  List.flatten ntnl
+
+let check_safe () =
+  let open Declarations in
+  let flags = Environ.typing_flags (Global.env ()) in
+  flags.check_universes && flags.check_guarded
+
+let do_fixpoint local poly l =
+  do_program_fixpoint local poly l;
+  if not (check_safe ()) then Feedback.feedback Feedback.AddedAxiom else ()
+
+let do_cofixpoint local poly l =
+  let fixl,ntns = extract_cofixpoint_components l in
+  do_program_recursive local poly Obligations.IsCoFixpoint fixl ntns;
+  if not (check_safe ()) then Feedback.feedback Feedback.AddedAxiom else ()
diff --git a/vernac/comProgramFixpoint.mli b/vernac/comProgramFixpoint.mli
new file mode 100644
index 000000000..943cb8efe
--- /dev/null
+++ b/vernac/comProgramFixpoint.mli
@@ -0,0 +1,12 @@
+open Decl_kinds
+open Vernacexpr
+
+(** Special Fixpoint handling when command is activated. *)
+
+val do_fixpoint :
+  (* When [false], assume guarded. *)
+  locality -> polymorphic -> (fixpoint_expr * decl_notation list) list -> unit
+
+val do_cofixpoint :
+  (* When [false], assume guarded. *)
+  locality -> polymorphic -> (cofixpoint_expr * decl_notation list) list -> unit
diff --git a/vernac/command.ml b/vernac/command.ml
deleted file mode 100644
index 837785ff0..000000000
--- a/vernac/command.ml
+++ /dev/null
@@ -1,1374 +0,0 @@
-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017     *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-
-open Pp
-open CErrors
-open Sorts
-open Util
-open Constr
-open Vars
-open Termops
-open Environ
-open Redexpr
-open Declare
-open Names
-open Libnames
-open Globnames
-open Nameops
-open Constrexpr
-open Constrexpr_ops
-open Constrintern
-open Nametab
-open Impargs
-open Reductionops
-open Indtypes
-open Decl_kinds
-open Pretyping
-open Evarutil
-open Evarconv
-open Indschemes
-open Misctypes
-open Vernacexpr
-open Context.Rel.Declaration
-open Entries
-
-module RelDecl = Context.Rel.Declaration
-
-let do_universe poly l = Declare.do_universe poly l
-let do_constraint poly l = Declare.do_constraint poly l
-
-let rec under_binders env sigma f n c =
-  if Int.equal n 0 then f env sigma (EConstr.of_constr c) else
-    match Constr.kind c with
-      | Lambda (x,t,c) ->
-	  mkLambda (x,t,under_binders (push_rel (LocalAssum (x,t)) env) sigma f (n-1) c)
-      | LetIn (x,b,t,c) ->
-	  mkLetIn (x,b,t,under_binders (push_rel (LocalDef (x,b,t)) env) sigma f (n-1) c)
-      | _ -> assert false
-
-let rec complete_conclusion a cs = CAst.map_with_loc (fun ?loc -> function
-  | CProdN (bl,c) -> CProdN (bl,complete_conclusion a cs c)
-  | CLetIn (na,b,t,c) -> CLetIn (na,b,t,complete_conclusion a cs c)
-  | CHole (k, _, _) ->
-      let (has_no_args,name,params) = a in
-      if not has_no_args then
-	user_err ?loc
-	 (strbrk"Cannot infer the non constant arguments of the conclusion of "
-	  ++ Id.print cs ++ str ".");
-      let args = List.map (fun id -> CAst.make ?loc @@ CRef(Ident(loc,id),None)) params in
-      CAppExpl ((None,Ident(loc,name),None),List.rev args)
-  | c -> c
-  )
-
-(* Commands of the interface *)
-
-(* 1| Constant definitions *)
-
-let red_constant_entry n ce sigma = function
-  | None -> ce
-  | Some red ->
-      let proof_out = ce.const_entry_body in
-      let env = Global.env () in
-      let (redfun, _) = reduction_of_red_expr env red in
-      let redfun env sigma c =
-        let (_, c) = redfun env sigma c in
-        EConstr.Unsafe.to_constr c
-      in
-      { ce with const_entry_body = Future.chain proof_out
-        (fun ((body,ctx),eff) -> (under_binders env sigma redfun n body,ctx),eff) }
-
-let warn_implicits_in_term =
-  CWarnings.create ~name:"implicits-in-term" ~category:"implicits"
-         (fun () ->
-          strbrk "Implicit arguments declaration relies on type." ++ spc () ++
-            strbrk "The term declares more implicits than the type here.")
-        
-let interp_definition pl bl poly red_option c ctypopt =
-  let env = Global.env() in
-  let evd, decl = Univdecls.interp_univ_decl_opt env pl in
-  let evd, (impls, ((env_bl, ctx), imps1)) = interp_context_evars env evd bl in
-  let ctx = List.map (fun d -> map_rel_decl EConstr.Unsafe.to_constr d) ctx in
-  let nb_args = Context.Rel.nhyps ctx in
-  let evd,imps,ce =
-    match ctypopt with
-      None ->
-        let evd, subst = Evd.nf_univ_variables evd in
-	let ctx = Context.Rel.map (Vars.subst_univs_constr subst) ctx in
-	let env_bl = push_rel_context ctx env in
-        let evd, (c, imps2) = interp_constr_evars_impls ~impls env_bl evd c in
-	let c = EConstr.Unsafe.to_constr c in
-        let evd,nf = Evarutil.nf_evars_and_universes evd in
-        let body = nf (it_mkLambda_or_LetIn c ctx) in
-        let vars = EConstr.universes_of_constr env evd (EConstr.of_constr body) in
-        let evd = Evd.restrict_universe_context evd vars in
-        let uctx = Evd.check_univ_decl ~poly evd decl in
-        evd, imps1@(Impargs.lift_implicits nb_args imps2),
-          definition_entry ~univs:uctx body
-    | Some ctyp ->
-        let evd, (ty, impsty) = interp_type_evars_impls ~impls env_bl evd ctyp in
-        let evd, subst = Evd.nf_univ_variables evd in
-	let ctx = Context.Rel.map (Vars.subst_univs_constr subst) ctx in
-	let env_bl = push_rel_context ctx env in
-        let evd, (c, imps2) = interp_casted_constr_evars_impls ~impls env_bl evd c ty in
-	let c = EConstr.Unsafe.to_constr c in
-        let evd, nf = Evarutil.nf_evars_and_universes evd in
-	let body = nf (it_mkLambda_or_LetIn c ctx) in
-	let ty = EConstr.Unsafe.to_constr ty in
-	let typ = nf (Term.it_mkProd_or_LetIn ty ctx) in
-        let beq b1 b2 = if b1 then b2 else not b2 in
-        let impl_eq (x,y,z) (x',y',z') = beq x x' && beq y y' && beq z z' in
-	(* Check that all implicit arguments inferable from the term
-           are inferable from the type *)
-        let chk (key,va) =
-          impl_eq (List.assoc_f Pervasives.(=) key impsty) va (* FIXME *)
-        in
-	if not (try List.for_all chk imps2 with Not_found -> false)
-	then warn_implicits_in_term ();
-        let bodyvars = EConstr.universes_of_constr env evd (EConstr.of_constr body) in
-        let tyvars = EConstr.universes_of_constr env evd (EConstr.of_constr ty) in
-        let vars = Univ.LSet.union bodyvars tyvars in
-        let evd = Evd.restrict_universe_context evd vars in
-        let uctx = Evd.check_univ_decl ~poly evd decl in
-        evd, imps1@(Impargs.lift_implicits nb_args impsty),
-          definition_entry ~types:typ ~univs:uctx body
-  in
-  (red_constant_entry (Context.Rel.length ctx) ce evd red_option, evd, decl, imps)
-
-let check_definition (ce, evd, _, imps) =
-  check_evars_are_solved (Global.env ()) evd Evd.empty;
-  ce
-
-let do_definition ident k univdecl bl red_option c ctypopt hook =
-  let (ce, evd, univdecl, imps as def) =
-    interp_definition univdecl bl (pi2 k) red_option c ctypopt
-  in
-    if Flags.is_program_mode () then
-      let env = Global.env () in
-      let (c,ctx), sideff = Future.force ce.const_entry_body in
-      assert(Safe_typing.empty_private_constants = sideff);
-      assert(Univ.ContextSet.is_empty ctx);
-      let typ = match ce.const_entry_type with 
-	| Some t -> t
-	| None -> EConstr.to_constr evd (Retyping.get_type_of env evd (EConstr.of_constr c))
-      in 
-      Obligations.check_evars env evd;
-      let obls, _, c, cty = 
-	Obligations.eterm_obligations env ident evd 0 c typ
-      in
-      let ctx = Evd.evar_universe_context evd in
-      let hook = Lemmas.mk_hook (fun l r _ -> Lemmas.call_hook (fun exn -> exn) hook l r) in
-      ignore(Obligations.add_definition
-          ident ~term:c cty ctx ~univdecl ~implicits:imps ~kind:k ~hook obls)
-    else let ce = check_definition def in
-      ignore(DeclareDef.declare_definition ident k ce (Evd.universe_binders evd) imps
-        (Lemmas.mk_hook
-          (fun l r -> Lemmas.call_hook (fun exn -> exn) hook l r;r)))
-
-(* 2| Variable/Hypothesis/Parameter/Axiom declarations *)
-
-let axiom_into_instance = ref false
-
-let _ =
-  let open Goptions in
-  declare_bool_option
-    { optdepr = false;
-      optname = "automatically declare axioms whose type is a typeclass as instances";
-      optkey = ["Typeclasses";"Axioms";"Are";"Instances"];
-      optread = (fun _ -> !axiom_into_instance);
-      optwrite = (:=) axiom_into_instance; }
-
-let should_axiom_into_instance = function
-  | Discharge ->
-    (* The typeclass behaviour of Variable and Context doesn't depend
-       on section status *)
-    true
-  | Global | Local -> !axiom_into_instance
-
-let declare_assumption is_coe (local,p,kind) (c,ctx) pl imps impl nl (_,ident) =
-match local with
-| Discharge when Lib.sections_are_opened () ->
-  let ctx = match ctx with
-    | Monomorphic_const_entry ctx -> ctx
-    | Polymorphic_const_entry ctx -> Univ.ContextSet.of_context ctx
-  in
-  let decl = (Lib.cwd(), SectionLocalAssum ((c,ctx),p,impl), IsAssumption kind) in
-  let _ = declare_variable ident decl in
-  let () = assumption_message ident in
-  let () =
-    if not !Flags.quiet && Proof_global.there_are_pending_proofs () then
-    Feedback.msg_info (str"Variable" ++ spc () ++ Id.print ident ++
-    strbrk " is not visible from current goals")
-  in
-  let r = VarRef ident in
-  let () = Typeclasses.declare_instance None true r in
-  let () = if is_coe then Class.try_add_new_coercion r ~local:true false in
-  (r,Univ.Instance.empty,true)
-
-| Global | Local | Discharge ->
-  let do_instance = should_axiom_into_instance local in
-  let local = DeclareDef.get_locality ident ~kind:"axiom" local in
-  let inl = match nl with
-    | NoInline -> None
-    | DefaultInline -> Some (Flags.get_inline_level())
-    | InlineAt i -> Some i
-  in
-  let decl = (ParameterEntry (None,(c,ctx),inl), IsAssumption kind) in
-  let kn = declare_constant ident ~local decl in
-  let gr = ConstRef kn in
-  let () = maybe_declare_manual_implicits false gr imps in
-  let () = Declare.declare_univ_binders gr pl in
-  let () = assumption_message ident in
-  let () = if do_instance then Typeclasses.declare_instance None false gr in
-  let () = if is_coe then Class.try_add_new_coercion gr ~local p in
-  let inst = match ctx with
-    | Polymorphic_const_entry ctx -> Univ.UContext.instance ctx
-    | Monomorphic_const_entry _ -> Univ.Instance.empty
-  in
-    (gr,inst,Lib.is_modtype_strict ())
-
-let interp_assumption sigma env impls bl c =
-  let c = mkCProdN ?loc:(local_binders_loc bl) bl c in
-  let sigma, (ty, impls) = interp_type_evars_impls env sigma ~impls c in
-  let ty = EConstr.Unsafe.to_constr ty in
-  sigma, (ty, impls)
-
-(* When monomorphic the universe constraints are declared with the first declaration only. *)
-let next_uctx =
-  let empty_uctx = Monomorphic_const_entry Univ.ContextSet.empty in
-  function
-  | Polymorphic_const_entry _ as uctx -> uctx
-  | Monomorphic_const_entry _ -> empty_uctx
-
-let declare_assumptions idl is_coe k (c,uctx) pl imps nl =
-  let refs, status, _ =
-    List.fold_left (fun (refs,status,uctx) id ->
-      let ref',u',status' =
-        declare_assumption is_coe k (c,uctx) pl imps false nl id in
-      (ref',u')::refs, status' && status, next_uctx uctx)
-      ([],true,uctx) idl
-  in
-  List.rev refs, status
-
-
-let maybe_error_many_udecls = function
-  | ((loc,id), Some _) ->
-    user_err ?loc ~hdr:"many_universe_declarations"
-      Pp.(str "When declaring multiple axioms in one command, " ++
-          str "only the first is allowed a universe binder " ++
-          str "(which will be shared by the whole block).")
-  | (_, None) -> ()
-
-let process_assumptions_udecls kind l =
-  let udecl, first_id = match l with
-    | (coe, ((id, udecl)::rest, c))::rest' ->
-      List.iter maybe_error_many_udecls rest;
-      List.iter (fun (coe, (idl, c)) -> List.iter maybe_error_many_udecls idl) rest';
-      udecl, id
-    | (_, ([], _))::_ | [] -> assert false
-  in
-  let () = match kind, udecl with
-    | (Discharge, _, _), Some _ when Lib.sections_are_opened () ->
-      let loc = fst first_id in
-      let msg = Pp.str "Section variables cannot be polymorphic." in
-      user_err ?loc  msg
-    | _ -> ()
-  in
-  udecl, List.map (fun (coe, (idl, c)) -> coe, (List.map fst idl, c)) l
-
-let do_assumptions kind nl l =
-  let open Context.Named.Declaration in
-  let env = Global.env () in
-  let udecl, l = process_assumptions_udecls kind l in
-  let sigma, udecl = Univdecls.interp_univ_decl_opt env udecl in
-  let l =
-    if pi2 kind (* poly *) then
-      (* Separate declarations so that A B : Type puts A and B in different levels. *)
-      List.fold_right (fun (is_coe,(idl,c)) acc ->
-        List.fold_right (fun id acc ->
-          (is_coe, ([id], c)) :: acc) idl acc)
-        l []
-    else l
-  in
-  (* We intepret all declarations in the same evar_map, i.e. as a telescope. *)
-  let (sigma,_,_),l = List.fold_left_map (fun (sigma,env,ienv) (is_coe,(idl,c)) ->
-    let sigma,(t,imps) = interp_assumption sigma env ienv [] c in
-    let env =
-      push_named_context (List.map (fun (_,id) -> LocalAssum (id,t)) idl) env in
-    let ienv = List.fold_right (fun (_,id) ienv ->
-      let impls = compute_internalization_data env Variable t imps in
-      Id.Map.add id impls ienv) idl ienv in
-      ((sigma,env,ienv),((is_coe,idl),t,imps)))
-    (sigma,env,empty_internalization_env) l
-  in
-  let sigma = solve_remaining_evars all_and_fail_flags env sigma Evd.empty in
-  (* The universe constraints come from the whole telescope. *)
-  let sigma = Evd.nf_constraints sigma in
-  let nf_evar c = EConstr.to_constr sigma (EConstr.of_constr c) in
-  let uvars, l = List.fold_left_map (fun uvars (coe,t,imps) ->
-      let t = nf_evar t in
-      let uvars = Univ.LSet.union uvars (Univops.universes_of_constr env t) in
-      uvars, (coe,t,imps))
-      Univ.LSet.empty l
-  in
-  let sigma = Evd.restrict_universe_context sigma uvars in
-  let uctx = Evd.check_univ_decl ~poly:(pi2 kind) sigma udecl in
-  let ubinders = Evd.universe_binders sigma in
-  pi2 (List.fold_left (fun (subst,status,uctx) ((is_coe,idl),t,imps) ->
-      let t = replace_vars subst t in
-      let refs, status' = declare_assumptions idl is_coe kind (t,uctx) ubinders imps nl in
-      let subst' = List.map2
-          (fun (_,id) (c,u) -> (id, Universes.constr_of_global_univ (c,u)))
-          idl refs
-      in
-      subst'@subst, status' && status, next_uctx uctx)
-    ([], true, uctx) l)
-
-(* 3a| Elimination schemes for mutual inductive definitions *)
-
-(* 3b| Mutual inductive definitions *)
-
-let push_types env idl tl =
-  List.fold_left2 (fun env id t -> Environ.push_rel (LocalAssum (Name id,t)) env)
-    env idl tl
-
-type structured_one_inductive_expr = {
-  ind_name : Id.t;
-  ind_univs : Vernacexpr.universe_decl_expr option;
-  ind_arity : constr_expr;
-  ind_lc : (Id.t * constr_expr) list
-}
-
-type structured_inductive_expr =
-  local_binder_expr list * structured_one_inductive_expr list
-
-let minductive_message warn = function
-  | []  -> user_err Pp.(str "No inductive definition.")
-  | [x] -> (Id.print x ++ str " is defined" ++ 
-	    if warn then str " as a non-primitive record" else mt())
-  | l   -> hov 0  (prlist_with_sep pr_comma Id.print l ++
-		     spc () ++ str "are defined")
-
-let check_all_names_different indl =
-  let ind_names = List.map (fun ind -> ind.ind_name) indl in
-  let cstr_names = List.map_append (fun ind -> List.map fst ind.ind_lc) indl in
-  let l = List.duplicates Id.equal ind_names in
-  let () = match l with
-  | [] -> ()
-  | t :: _ -> raise (InductiveError (SameNamesTypes t))
-  in
-  let l = List.duplicates Id.equal cstr_names in
-  let () = match l with
-  | [] -> ()
-  | c :: _ -> raise (InductiveError (SameNamesConstructors (List.hd l)))
-  in
-  let l = List.intersect Id.equal ind_names cstr_names in
-  match l with
-  | [] -> ()
-  | _ -> raise (InductiveError (SameNamesOverlap l))
-
-let mk_mltype_data sigma env assums arity indname =
-  let is_ml_type = is_sort env sigma (EConstr.of_constr arity) in
-  (is_ml_type,indname,assums)
-
-let prepare_param = function
-  | LocalAssum (na,t) -> Name.get_id na, LocalAssumEntry t
-  | LocalDef (na,b,_) -> Name.get_id na, LocalDefEntry b
-
-(** Make the arity conclusion flexible to avoid generating an upper bound universe now,
-    only if the universe does not appear anywhere else.
-    This is really a hack to stay compatible with the semantics of template polymorphic 
-    inductives which are recognized when a "Type" appears at the end of the conlusion in
-    the source syntax. *)
-    
-let rec check_anonymous_type ind =
-  let open Glob_term in
-    match DAst.get ind with
-    | GSort (GType []) -> true
-    | GProd ( _, _, _, e) 
-    | GLetIn (_, _, _, e)
-    | GLambda (_, _, _, e)
-    | GApp (e, _)
-    | GCast (e, _) -> check_anonymous_type e
-    | _ -> false
-
-let make_conclusion_flexible sigma ty poly =
-  if poly && Term.isArity ty then
-    let _, concl = Term.destArity ty in
-      match concl with
-      | Type u -> 
-        (match Univ.universe_level u with
-        | Some u -> 
-          Evd.make_flexible_variable sigma ~algebraic:true u
-        | None -> sigma)
-      | _ -> sigma
-  else sigma
-
-let is_impredicative env u =
-  u = Prop Null || (is_impredicative_set env && u = Prop Pos)
-
-let interp_ind_arity env sigma ind =
-  let c = intern_gen IsType env ind.ind_arity in
-  let impls = Implicit_quantifiers.implicits_of_glob_constr ~with_products:true c in
-  let sigma,t = understand_tcc env sigma ~expected_type:IsType c in
-  let pseudo_poly = check_anonymous_type c in
-  let () = if not (Reductionops.is_arity env sigma t) then
-    user_err ?loc:(constr_loc ind.ind_arity) (str "Not an arity")
-  in
-  let t = EConstr.Unsafe.to_constr t in
-  sigma, (t, pseudo_poly, impls)
-
-let interp_cstrs env sigma impls mldata arity ind =
-  let cnames,ctyps = List.split ind.ind_lc in
-  (* Complete conclusions of constructor types if given in ML-style syntax *)
-  let ctyps' = List.map2 (complete_conclusion mldata) cnames ctyps in
-  (* Interpret the constructor types *)
-  let sigma, (ctyps'', cimpls) =
-    on_snd List.split @@
-    List.fold_left_map (fun sigma l ->
-        on_snd (on_fst EConstr.Unsafe.to_constr) @@
-        interp_type_evars_impls env sigma ~impls l) sigma ctyps' in
-  sigma, (cnames, ctyps'', cimpls)
-
-let sign_level env evd sign =
-  fst (List.fold_right
-    (fun d (lev,env) ->
-      match d with
-      | LocalDef _ -> lev, push_rel d env
-      | LocalAssum _ ->
-	let s = destSort (Reduction.whd_all env 
-			    (EConstr.Unsafe.to_constr (nf_evar evd (Retyping.get_type_of env evd (EConstr.of_constr (RelDecl.get_type d))))))
-	in
-	let u = univ_of_sort s in
-	  (Univ.sup u lev, push_rel d env))
-    sign (Univ.type0m_univ,env))
-
-let sup_list min = List.fold_left Univ.sup min
-
-let extract_level env evd min tys = 
-  let sorts = List.map (fun ty -> 
-    let ctx, concl = Reduction.dest_prod_assum env ty in
-      sign_level env evd (LocalAssum (Anonymous, concl) :: ctx)) tys
-  in sup_list min sorts
-
-let is_flexible_sort evd u =
-  match Univ.Universe.level u with
-  | Some l -> Evd.is_flexible_level evd l
-  | None -> false
-
-let inductive_levels env evd poly arities inds =
-  let destarities = List.map (fun x -> x, Reduction.dest_arity env x) arities in
-  let levels = List.map (fun (x,(ctx,a)) -> 
-    if a = Prop Null then None
-    else Some (univ_of_sort a)) destarities
-  in
-  let cstrs_levels, min_levels, sizes = 
-    CList.split3
-      (List.map2 (fun (_,tys,_) (arity,(ctx,du)) -> 
-	let len = List.length tys in
-	let minlev = Sorts.univ_of_sort du in
-	let minlev =
-	  if len > 1 && not (is_impredicative env du) then
-	    Univ.sup minlev Univ.type0_univ
-	  else minlev
-	in
-	let minlev =
-	  (** Indices contribute. *)
-	  if Indtypes.is_indices_matter () && List.length ctx > 0 then (
-            let ilev = sign_level env evd ctx in
-	      Univ.sup ilev minlev)
-	  else minlev
-	in
-        let clev = extract_level env evd minlev tys in
-	  (clev, minlev, len)) inds destarities)
-  in
-  (* Take the transitive closure of the system of constructors *)
-  (* level constraints and remove the recursive dependencies *)
-  let levels' = Universes.solve_constraints_system (Array.of_list levels)
-    (Array.of_list cstrs_levels) (Array.of_list min_levels)
-  in
-  let evd, arities =
-    CList.fold_left3 (fun (evd, arities) cu (arity,(ctx,du)) len ->
-      if is_impredicative env du then
-	(** Any product is allowed here. *)
-	evd, arity :: arities
-      else (** If in a predicative sort, or asked to infer the type,
-	       we take the max of:
-	       - indices (if in indices-matter mode)
-	       - constructors
-	       - Type(1) if there is more than 1 constructor
-	   *)
-        (** Constructors contribute. *)
-	let evd = 
-	  if Sorts.is_set du then
-	    if not (Evd.check_leq evd cu Univ.type0_univ) then 
-	      raise (Indtypes.InductiveError Indtypes.LargeNonPropInductiveNotInType)
-	    else evd
-	  else evd
-	    (* Evd.set_leq_sort env evd (Type cu) du *)
-	in
-	let evd = 
-	  if len >= 2 && Univ.is_type0m_univ cu then 
-	   (** "Polymorphic" type constraint and more than one constructor, 
-	       should not land in Prop. Add constraint only if it would
-	       land in Prop directly (no informative arguments as well). *)
-	    Evd.set_leq_sort env evd (Prop Pos) du
-	  else evd
-	in
-	let duu = Sorts.univ_of_sort du in
-	let evd =
-	  if not (Univ.is_small_univ duu) && Univ.Universe.equal cu duu then
-	    if is_flexible_sort evd duu && not (Evd.check_leq evd Univ.type0_univ duu) then
-	      Evd.set_eq_sort env evd (Prop Null) du
-	    else evd
-	  else Evd.set_eq_sort env evd (Type cu) du
-	in
-	  (evd, arity :: arities))
-    (evd,[]) (Array.to_list levels') destarities sizes
-  in evd, List.rev arities
-
-let check_named (loc, na) = match na with
-| Name _ -> ()
-| Anonymous ->
-  let msg = str "Parameters must be named." in
-  user_err ?loc  msg
-
-
-let check_param = function
-| CLocalDef (na, _, _) -> check_named na
-| CLocalAssum (nas, Default _, _) -> List.iter check_named nas
-| CLocalAssum (nas, Generalized _, _) -> ()
-| CLocalPattern (loc,_) ->
-    Loc.raise ?loc (Stream.Error "pattern with quote not allowed here.")
-
-let interp_mutual_inductive (paramsl,indl) notations cum poly prv finite =
-  check_all_names_different indl;
-  List.iter check_param paramsl;
-  let env0 = Global.env() in
-  let pl = (List.hd indl).ind_univs in
-  let sigma, decl = Univdecls.interp_univ_decl_opt env0 pl in
-  let sigma, (impls, ((env_params, ctx_params), userimpls)) =
-    interp_context_evars env0 sigma paramsl
-  in
-  let ctx_params = List.map (fun d -> map_rel_decl EConstr.Unsafe.to_constr d) ctx_params in
-  let indnames = List.map (fun ind -> ind.ind_name) indl in
-
-  (* Names of parameters as arguments of the inductive type (defs removed) *)
-  let assums = List.filter is_local_assum ctx_params in
-  let params = List.map (RelDecl.get_name %> Name.get_id) assums in
-
-  (* Interpret the arities *)
-  let sigma, arities = List.fold_left_map (fun sigma -> interp_ind_arity env_params sigma) sigma indl in
-
-  let fullarities = List.map (fun (c, _, _) -> Term.it_mkProd_or_LetIn c ctx_params) arities in
-  let env_ar = push_types env0 indnames fullarities in
-  let env_ar_params = push_rel_context ctx_params env_ar in
-
-  (* Compute interpretation metadatas *)
-  let indimpls = List.map (fun (_, _, impls) -> userimpls @ 
-    lift_implicits (Context.Rel.nhyps ctx_params) impls) arities in
-  let arities = List.map pi1 arities and aritypoly = List.map pi2 arities in
-  let impls = compute_internalization_env env0 ~impls (Inductive (params,true)) indnames fullarities indimpls in
-  let ntn_impls = compute_internalization_env env0 (Inductive (params,true)) indnames fullarities indimpls in
-  let mldatas = List.map2 (mk_mltype_data sigma env_params params) arities indnames in
-
-  let sigma, constructors =
-    Metasyntax.with_syntax_protection (fun () ->
-     (* Temporary declaration of notations and scopes *)
-     List.iter (Metasyntax.set_notation_for_interpretation env_params ntn_impls) notations;
-     (* Interpret the constructor types *)
-     List.fold_left3_map (fun sigma -> interp_cstrs env_ar_params sigma impls) sigma mldatas arities indl)
-     () in
-
-  (* Try further to solve evars, and instantiate them *)
-  let sigma = solve_remaining_evars all_and_fail_flags env_params sigma Evd.empty in
-  (* Compute renewed arities *)
-  let sigma, nf = nf_evars_and_universes sigma in
-  let arities = List.map nf arities in
-  let constructors = List.map (fun (idl,cl,impsl) -> (idl,List.map nf cl,impsl)) constructors in
-  let sigma = List.fold_left2 (fun sigma ty poly -> make_conclusion_flexible sigma ty poly) sigma arities aritypoly in
-  let sigma, arities = inductive_levels env_ar_params sigma poly arities constructors in
-  let sigma, nf' = nf_evars_and_universes sigma in
-  let nf x = nf' (nf x) in
-  let arities = List.map nf' arities in
-  let constructors = List.map (fun (idl,cl,impsl) -> (idl,List.map nf' cl,impsl)) constructors in
-  let ctx_params = Context.Rel.map nf ctx_params in
-  let uctx = Evd.check_univ_decl ~poly sigma decl in
-  List.iter (fun c -> check_evars env_params Evd.empty sigma (EConstr.of_constr c)) arities;
-  Context.Rel.iter (fun c -> check_evars env0 Evd.empty sigma (EConstr.of_constr c)) ctx_params;
-  List.iter (fun (_,ctyps,_) ->
-    List.iter (fun c -> check_evars env_ar_params Evd.empty sigma (EConstr.of_constr c)) ctyps)
-    constructors;
-
-  (* Build the inductive entries *)
-  let entries = List.map4 (fun ind arity template (cnames,ctypes,cimpls) -> {
-    mind_entry_typename = ind.ind_name;
-    mind_entry_arity = arity;
-    mind_entry_template = template;
-    mind_entry_consnames = cnames;
-    mind_entry_lc = ctypes
-  }) indl arities aritypoly constructors in
-  let impls =
-    let len = Context.Rel.nhyps ctx_params in
-      List.map2 (fun indimpls (_,_,cimpls) ->
-	indimpls, List.map (fun impls ->
-	  userimpls @ (lift_implicits len impls)) cimpls) indimpls constructors
-  in
-  let univs =
-    match uctx with
-    | Polymorphic_const_entry uctx ->
-      if cum then
-        Cumulative_ind_entry (Universes.univ_inf_ind_from_universe_context uctx)
-      else Polymorphic_ind_entry uctx
-    | Monomorphic_const_entry uctx ->
-      Monomorphic_ind_entry uctx
-  in
-  (* Build the mutual inductive entry *)
-  let mind_ent =
-    { mind_entry_params = List.map prepare_param ctx_params;
-      mind_entry_record = None;
-      mind_entry_finite = finite;
-      mind_entry_inds = entries;
-      mind_entry_private = if prv then Some false else None;
-      mind_entry_universes = univs;
-    }
-  in
-  (if poly && cum then
-      Inductiveops.infer_inductive_subtyping env_ar sigma mind_ent
-   else mind_ent), Evd.universe_binders sigma, impls
-
-(* Very syntactical equality *)
-let eq_local_binders bl1 bl2 =
-  List.equal local_binder_eq bl1 bl2
-
-let extract_coercions indl =
-  let mkqid (_,((_,id),_)) = qualid_of_ident id in
-  let extract lc = List.filter (fun (iscoe,_) -> iscoe) lc in
-  List.map mkqid (List.flatten(List.map (fun (_,_,_,lc) -> extract lc) indl))
-
-let extract_params indl =
-  let paramsl = List.map (fun (_,params,_,_) -> params) indl in
-  match paramsl with
-  | [] -> anomaly (Pp.str "empty list of inductive types.")
-  | params::paramsl ->
-      if not (List.for_all (eq_local_binders params) paramsl) then user_err Pp.(str
-	"Parameters should be syntactically the same for each inductive type.");
-      params
-
-let extract_inductive indl =
-  List.map (fun (((_,indname),pl),_,ar,lc) -> {
-    ind_name = indname; ind_univs = pl;
-    ind_arity = Option.cata (fun x -> x) (CAst.make @@ CSort (GType [])) ar;
-    ind_lc = List.map (fun (_,((_,id),t)) -> (id,t)) lc
-  }) indl
-
-let extract_mutual_inductive_declaration_components indl =
-  let indl,ntnl = List.split indl in
-  let params = extract_params indl in
-  let coes = extract_coercions indl in
-  let indl = extract_inductive indl in
-  (params,indl), coes, List.flatten ntnl
-
-let is_recursive mie =
-  let rec is_recursive_constructor lift typ =
-    match Constr.kind typ with
-    | Prod (_,arg,rest) ->
-        not (EConstr.Vars.noccurn Evd.empty (** FIXME *) lift (EConstr.of_constr arg)) ||
-        is_recursive_constructor (lift+1) rest
-    | LetIn (na,b,t,rest) -> is_recursive_constructor (lift+1) rest
-    | _ -> false
-  in
-  match mie.mind_entry_inds with
-  | [ind] ->
-      let nparams = List.length mie.mind_entry_params in
-      List.exists (fun t -> is_recursive_constructor (nparams+1) t) ind.mind_entry_lc
-  | _ -> false
-
-let declare_mutual_inductive_with_eliminations mie pl impls =
-  (* spiwack: raises an error if the structure is supposed to be non-recursive,
-        but isn't *)
-  begin match mie.mind_entry_finite with
-  | BiFinite when is_recursive mie ->
-      if Option.has_some mie.mind_entry_record then
-        user_err Pp.(str "Records declared with the keywords Record or Structure cannot be recursive. You can, however, define recursive records using the Inductive or CoInductive command.")
-      else
-        user_err Pp.(str ("Types declared with the keyword Variant cannot be recursive. Recursive types are defined with the Inductive and CoInductive command."))
-  | _ -> ()
-  end;
-  let names = List.map (fun e -> e.mind_entry_typename) mie.mind_entry_inds in
-  let (_, kn), prim = declare_mind mie in
-  let mind = Global.mind_of_delta_kn kn in
-  List.iteri (fun i (indimpls, constrimpls) ->
-	      let ind = (mind,i) in
-	      let gr = IndRef ind in
-	      maybe_declare_manual_implicits false gr indimpls;
-              Declare.declare_univ_binders gr pl;
-	      List.iteri
-		(fun j impls ->
-		 maybe_declare_manual_implicits false
-		    (ConstructRef (ind, succ j)) impls)
-		constrimpls)
-      impls;
-  let warn_prim = match mie.mind_entry_record with Some (Some _) -> not prim | _ -> false in
-  Flags.if_verbose Feedback.msg_info (minductive_message warn_prim names);
-  if mie.mind_entry_private == None
-  then declare_default_schemes mind;
-  mind
-
-type one_inductive_impls =
-  Impargs.manual_explicitation list (* for inds *)*
-  Impargs.manual_explicitation list list (* for constrs *)
-
-let do_mutual_inductive indl cum poly prv finite =
-  let indl,coes,ntns = extract_mutual_inductive_declaration_components indl in
-  (* Interpret the types *)
-  let mie,pl,impls = interp_mutual_inductive indl ntns cum poly prv finite in
-  (* Declare the mutual inductive block with its associated schemes *)
-  ignore (declare_mutual_inductive_with_eliminations mie pl impls);
-  (* Declare the possible notations of inductive types *)
-  List.iter (Metasyntax.add_notation_interpretation (Global.env ())) ntns;
-  (* Declare the coercions *)
-  List.iter (fun qid -> Class.try_add_new_coercion (locate qid) ~local:false poly) coes;
-  (* If positivity is assumed declares itself as unsafe. *)
-  if Environ.deactivated_guard (Global.env ()) then Feedback.feedback Feedback.AddedAxiom else ()
-
-(* 3c| Fixpoints and co-fixpoints *)
-
-(* An (unoptimized) function that maps preorders to partial orders...
-
-   Input:  a list of associations (x,[y1;...;yn]), all yi distincts
-           and different of x, meaning x<=y1, ..., x<=yn
-
-   Output: a list of associations (x,Inr [y1;...;yn]), collecting all
-           distincts yi greater than x, _or_, (x, Inl y) meaning that
-           x is in the same class as y (in which case, x occurs
-           nowhere else in the association map)
-
-   partial_order : ('a * 'a list) list -> ('a * ('a,'a list) union) list
-*)
-
-let rec partial_order cmp = function
-  | [] -> []
-  | (x,xge)::rest ->
-    let rec browse res xge' = function
-    | [] ->
-	let res = List.map (function
-	  | (z, Inr zge) when List.mem_f cmp x zge ->
-            (z, Inr (List.union cmp zge xge'))
-	  | r -> r) res in
-	(x,Inr xge')::res
-    | y::xge ->
-      let rec link y =
-	try match List.assoc_f cmp y res with
-	| Inl z -> link z
-	| Inr yge ->
-	  if List.mem_f cmp x yge then
-	    let res = List.remove_assoc_f cmp y res in
-	    let res = List.map (function
-	      | (z, Inl t) ->
-		  if cmp t y then (z, Inl x) else (z, Inl t)
-	      | (z, Inr zge) ->
-		  if List.mem_f cmp y zge then
-		    (z, Inr (List.add_set cmp x (List.remove cmp y zge)))
-		  else
-		    (z, Inr zge)) res in
-	    browse ((y,Inl x)::res) xge' (List.union cmp xge (List.remove cmp x yge))
-	  else
-	    browse res (List.add_set cmp y (List.union cmp xge' yge)) xge
-	with Not_found -> browse res (List.add_set cmp y xge') xge
-      in link y
-    in browse (partial_order cmp rest) [] xge
-
-let non_full_mutual_message x xge y yge isfix rest =
-  let reason =
-    if Id.List.mem x yge then
-      Id.print y ++ str " depends on " ++ Id.print x ++ strbrk " but not conversely"
-    else if Id.List.mem y xge then
-      Id.print x ++ str " depends on " ++ Id.print y ++ strbrk " but not conversely"
-    else
-      Id.print y ++ str " and " ++ Id.print x ++ strbrk " are not mutually dependent" in
-  let e = if List.is_empty rest then reason else strbrk "e.g., " ++ reason in
-  let k = if isfix then "fixpoint" else "cofixpoint" in
-  let w =
-    if isfix
-    then strbrk "Well-foundedness check may fail unexpectedly." ++ fnl()
-    else mt () in
-  strbrk "Not a fully mutually defined " ++ str k ++ fnl () ++
-  str "(" ++ e ++ str ")." ++ fnl () ++ w
-
-let warn_non_full_mutual =
-  CWarnings.create ~name:"non-full-mutual" ~category:"fixpoints"
-         (fun (x,xge,y,yge,isfix,rest) ->
-          non_full_mutual_message x xge y yge isfix rest)
-
-let check_mutuality env evd isfix fixl =
-  let names = List.map fst fixl in
-  let preorder =
-    List.map (fun (id,def) ->
-      (id, List.filter (fun id' -> not (Id.equal id id') && occur_var env evd id' (EConstr.of_constr def)) names))
-      fixl in
-  let po = partial_order Id.equal preorder in
-  match List.filter (function (_,Inr _) -> true | _ -> false) po with
-    | (x,Inr xge)::(y,Inr yge)::rest ->
-       warn_non_full_mutual (x,xge,y,yge,isfix,rest)
-    | _ -> ()
-
-type structured_fixpoint_expr = {
-  fix_name : Id.t;
-  fix_univs : universe_decl_expr option;
-  fix_annot : Id.t Loc.located option;
-  fix_binders : local_binder_expr list;
-  fix_body : constr_expr option;
-  fix_type : constr_expr
-}
-
-let interp_fix_context env sigma isfix fix =
-  let before, after = if isfix then split_at_annot fix.fix_binders fix.fix_annot else [], fix.fix_binders in
-  let sigma, (impl_env, ((env', ctx), imps)) = interp_context_evars env sigma before in
-  let sigma, (impl_env', ((env'', ctx'), imps')) = interp_context_evars ~impl_env ~shift:(Context.Rel.nhyps ctx) env' sigma after in
-  let annot = Option.map (fun _ -> List.length (assums_of_rel_context ctx)) fix.fix_annot in
-  sigma, ((env'', ctx' @ ctx), (impl_env',imps @ imps'), annot)
-
-let interp_fix_ccl sigma impls (env,_) fix =
-  interp_type_evars_impls ~impls env sigma fix.fix_type
-
-let interp_fix_body env_rec sigma impls (_,ctx) fix ccl =
-  let open EConstr in
-  Option.cata (fun body ->
-    let env = push_rel_context ctx env_rec in
-    let sigma, body = interp_casted_constr_evars env sigma ~impls body ccl in
-    sigma, Some (it_mkLambda_or_LetIn body ctx)) (sigma, None) fix.fix_body
-
-let build_fix_type (_,ctx) ccl = EConstr.it_mkProd_or_LetIn ccl ctx
-
-let prepare_recursive_declaration fixnames fixtypes fixdefs =
-  let defs = List.map (subst_vars (List.rev fixnames)) fixdefs in
-  let names = List.map (fun id -> Name id) fixnames in
-  (Array.of_list names, Array.of_list fixtypes, Array.of_list defs)
-
-(* Jump over let-bindings. *)
-
-let compute_possible_guardness_evidences (ctx,_,recindex) =
-  (* A recursive index is characterized by the number of lambdas to
-     skip before finding the relevant inductive argument *)
-  match recindex with
-  | Some i -> [i]
-  | None ->
-      (* If recursive argument was not given by user, we try all args.
-	 An earlier approach was to look only for inductive arguments,
-	 but doing it properly involves delta-reduction, and it finally
-         doesn't seem to worth the effort (except for huge mutual
-	 fixpoints ?) *)
-      List.interval 0 (Context.Rel.nhyps ctx - 1)
-
-type recursive_preentry =
-  Id.t list * constr option list * types list
-
-(* Wellfounded definition *)
-
-open Coqlib
-
-let contrib_name = "Program"
-let subtac_dir = [contrib_name]
-let fixsub_module = subtac_dir @ ["Wf"]
-let tactics_module = subtac_dir @ ["Tactics"]
-
-let init_reference dir s () = Coqlib.coq_reference "Command" dir s
-let init_constant dir s sigma =
-  Evarutil.new_global sigma (Coqlib.coq_reference "Command" dir s)
-
-let make_ref l s = init_reference l s
-let fix_proto = init_constant tactics_module "fix_proto"
-let fix_sub_ref = make_ref fixsub_module "Fix_sub"
-let measure_on_R_ref = make_ref fixsub_module "MR"
-let well_founded = init_constant ["Init"; "Wf"] "well_founded"
-let mkSubset sigma name typ prop =
-  let open EConstr in
-  let sigma, h_term = Evarutil.new_global sigma (delayed_force build_sigma).typ in
-  sigma, mkApp (h_term, [| typ; mkLambda (name, typ, prop) |])
-
-let sigT = Lazy.from_fun build_sigma_type
-
-let make_qref s = Qualid (Loc.tag @@ qualid_of_string s)
-let lt_ref = make_qref "Init.Peano.lt"
-
-let rec telescope sigma l =
-  let open EConstr in
-  let open Vars in
-  match l with
-  | [] -> assert false
-  | [LocalAssum (n, t)] ->
-    sigma, t, [LocalDef (n, mkRel 1, t)], mkRel 1
-  | LocalAssum (n, t) :: tl ->
-      let sigma, ty, tys, (k, constr) =
-	List.fold_left
-          (fun (sigma, ty, tys, (k, constr)) decl ->
-            let t = RelDecl.get_type decl in
-            let pred = mkLambda (RelDecl.get_name decl, t, ty) in
-            let sigma, ty = Evarutil.new_global sigma (Lazy.force sigT).typ in
-            let sigma, intro = Evarutil.new_global sigma (Lazy.force sigT).intro in
-	    let sigty = mkApp (ty, [|t; pred|]) in
-	    let intro = mkApp (intro, [|lift k t; lift k pred; mkRel k; constr|]) in
-              (sigma, sigty, pred :: tys, (succ k, intro)))
-          (sigma, t, [], (2, mkRel 1)) tl
-      in
-      let sigma, last, subst = List.fold_right2
-        (fun pred decl (sigma, prev, subst) ->
-          let t = RelDecl.get_type decl in
-          let sigma, p1 = Evarutil.new_global sigma (Lazy.force sigT).proj1 in
-          let sigma, p2 = Evarutil.new_global sigma (Lazy.force sigT).proj2 in
-	  let proj1 = applist (p1, [t; pred; prev]) in
-	  let proj2 = applist (p2, [t; pred; prev]) in
-            (sigma, lift 1 proj2, LocalDef (get_name decl, proj1, t) :: subst))
-        (List.rev tys) tl (sigma, mkRel 1, [])
-      in sigma, ty, (LocalDef (n, last, t) :: subst), constr
-
-  | LocalDef (n, b, t) :: tl ->
-    let sigma, ty, subst, term = telescope sigma tl in
-    sigma, ty, (LocalDef (n, b, t) :: subst), lift 1 term
-
-let nf_evar_context sigma ctx =
-  List.map (map_constr (fun c -> Evarutil.nf_evar sigma c)) ctx
-
-let build_wellfounded (recname,pl,n,bl,arityc,body) poly r measure notation =
-  let open EConstr in
-  let open Vars in
-  let lift_rel_context n l = Termops.map_rel_context_with_binders (liftn n) l in
-  Coqlib.check_required_library ["Coq";"Program";"Wf"];
-  let env = Global.env() in
-  let sigma, decl = Univdecls.interp_univ_decl_opt env pl in
-  let sigma, (_, ((env', binders_rel), impls)) = interp_context_evars env sigma bl in
-  let len = List.length binders_rel in
-  let top_env = push_rel_context binders_rel env in
-  let sigma, top_arity = interp_type_evars top_env sigma arityc in
-  let full_arity = it_mkProd_or_LetIn top_arity binders_rel in
-  let sigma, argtyp, letbinders, make = telescope sigma binders_rel in
-  let argname = Id.of_string "recarg" in
-  let arg = LocalAssum (Name argname, argtyp) in
-  let binders = letbinders @ [arg] in
-  let binders_env = push_rel_context binders_rel env in
-  let sigma, (rel, _) = interp_constr_evars_impls env sigma r in
-  let relty = Typing.unsafe_type_of env sigma rel in
-  let relargty =
-    let error () =
-      user_err ?loc:(constr_loc r)
-               ~hdr:"Command.build_wellfounded"
-                    (Printer.pr_econstr_env env sigma rel ++ str " is not an homogeneous binary relation.")
-    in
-      try
-        let ctx, ar = Reductionops.splay_prod_n env sigma 2 relty in
-          match ctx, EConstr.kind sigma ar with
-	  | [LocalAssum (_,t); LocalAssum (_,u)], Sort s
-              when Sorts.is_prop (ESorts.kind sigma s) && Reductionops.is_conv env sigma t u -> t
-	  | _, _ -> error ()
-      with e when CErrors.noncritical e -> error ()
-  in
-  let sigma, measure = interp_casted_constr_evars binders_env sigma measure relargty in
-  let sigma, wf_rel, wf_rel_fun, measure_fn =
-    let measure_body, measure =
-      it_mkLambda_or_LetIn measure letbinders,
-      it_mkLambda_or_LetIn measure binders
-    in
-    let sigma, comb = Evarutil.new_global sigma (delayed_force measure_on_R_ref) in
-    let wf_rel = mkApp (comb, [| argtyp; relargty; rel; measure |]) in
-    let wf_rel_fun x y =
-      mkApp (rel, [| subst1 x measure_body;
- 		     subst1 y measure_body |])
-    in sigma, wf_rel, wf_rel_fun, measure
-  in
-  let sigma, wf_term = well_founded sigma in
-  let wf_proof = mkApp (wf_term, [| argtyp ; wf_rel |]) in
-  let argid' = Id.of_string (Id.to_string argname ^ "'") in
-  let wfarg sigma len =
-    let sigma, ss_term = mkSubset sigma (Name argid') argtyp (wf_rel_fun (mkRel 1) (mkRel (len + 1))) in
-    sigma, LocalAssum (Name argid', ss_term)
-  in
-  let sigma, intern_bl =
-    let sigma, wfa = wfarg sigma 1 in
-    sigma, wfa :: [arg]
-  in
-  let _intern_env = push_rel_context intern_bl env in
-  let sigma, proj = Evarutil.new_global sigma (delayed_force build_sigma).Coqlib.proj1 in
-  let wfargpred = mkLambda (Name argid', argtyp, wf_rel_fun (mkRel 1) (mkRel 3)) in
-  let projection = (* in wfarg :: arg :: before *)
-    mkApp (proj, [| argtyp ; wfargpred ; mkRel 1 |])
-  in
-  let top_arity_let = it_mkLambda_or_LetIn top_arity letbinders in
-  let intern_arity = substl [projection] top_arity_let in
-  (* substitute the projection of wfarg for something,
-     now intern_arity is in wfarg :: arg *)
-  let sigma, wfa = wfarg sigma 1 in
-  let intern_fun_arity_prod = it_mkProd_or_LetIn intern_arity [wfa] in
-  let intern_fun_binder = LocalAssum (Name (add_suffix recname "'"), intern_fun_arity_prod) in
-  let sigma, curry_fun =
-    let wfpred = mkLambda (Name argid', argtyp, wf_rel_fun (mkRel 1) (mkRel (2 * len + 4))) in
-    let sigma, intro = Evarutil.new_global sigma (delayed_force build_sigma).Coqlib.intro in
-    let arg = mkApp (intro, [| argtyp; wfpred; lift 1 make; mkRel 1 |]) in
-    let app = mkApp (mkRel (2 * len + 2 (* recproof + orig binders + current binders *)), [| arg |]) in
-    let rcurry = mkApp (rel, [| measure; lift len measure |]) in
-    let lam = LocalAssum (Name (Id.of_string "recproof"), rcurry) in
-    let body = it_mkLambda_or_LetIn app (lam :: binders_rel) in
-    let ty = it_mkProd_or_LetIn (lift 1 top_arity) (lam :: binders_rel) in
-    sigma, LocalDef (Name recname, body, ty)
-  in
-  let fun_bl = intern_fun_binder :: [arg] in
-  let lift_lets = lift_rel_context 1 letbinders in
-  let sigma, intern_body =
-    let ctx = LocalAssum (Name recname, get_type curry_fun) :: binders_rel in
-    let (r, l, impls, scopes) =
-      Constrintern.compute_internalization_data env
-	Constrintern.Recursive (EConstr.Unsafe.to_constr full_arity) impls 
-    in
-    let newimpls = Id.Map.singleton recname
-        (r, l, impls @ [(Some (Id.of_string "recproof", Impargs.Manual, (true, false)))],
-         scopes @ [None]) in
-    interp_casted_constr_evars (push_rel_context ctx env) sigma
-      ~impls:newimpls body (lift 1 top_arity)
-  in
-  let intern_body_lam = it_mkLambda_or_LetIn intern_body (curry_fun :: lift_lets @ fun_bl) in
-  let prop = mkLambda (Name argname, argtyp, top_arity_let) in
-  (* XXX: Previous code did parallel evdref update, so possible old
-     weak ordering semantics may bite here. *)
-  let sigma, def =
-    let sigma, h_a_term = Evarutil.new_global sigma (delayed_force fix_sub_ref) in
-    let sigma, h_e_term = Evarutil.new_evar env sigma
-        ~src:(Loc.tag @@ Evar_kinds.QuestionMark (Evar_kinds.Define false,Anonymous)) wf_proof in
-    sigma, mkApp (h_a_term, [| argtyp ; wf_rel ; h_e_term; prop |])
-  in
-  let _evd = ref sigma in
-  let def = Typing.e_solve_evars env _evd def in
-  let sigma = !_evd in
-  let sigma = Evarutil.nf_evar_map sigma in
-  let def = mkApp (def, [|intern_body_lam|]) in
-  let binders_rel = nf_evar_context sigma binders_rel in
-  let binders = nf_evar_context sigma binders in
-  let top_arity = Evarutil.nf_evar sigma top_arity in
-  let hook, recname, typ =
-    if List.length binders_rel > 1 then
-      let name = add_suffix recname "_func" in
-      (* XXX: Mutating the evar_map in the hook! *)
-      (* XXX: Likely the sigma is out of date when the hook is called .... *)
-      let hook sigma l gr _ =
-        let sigma, h_body = Evarutil.new_global sigma gr in
-        let body = it_mkLambda_or_LetIn (mkApp (h_body, [|make|])) binders_rel in
-        let ty = it_mkProd_or_LetIn top_arity binders_rel in
-        let ty = EConstr.Unsafe.to_constr ty in
-        let univs = Evd.check_univ_decl ~poly sigma decl in
-        (*FIXME poly? *)
-        let ce = definition_entry ~types:ty ~univs (EConstr.to_constr sigma body) in
-        (** FIXME: include locality *)
-        let c = Declare.declare_constant recname (DefinitionEntry ce, IsDefinition Definition) in
-        let gr = ConstRef c in
-        let () = Universes.register_universe_binders gr (Evd.universe_binders sigma) in
-        if Impargs.is_implicit_args () || not (List.is_empty impls) then
-          Impargs.declare_manual_implicits false gr [impls]
-      in
-      let typ = it_mkProd_or_LetIn top_arity binders in
-      hook, name, typ
-    else
-      let typ = it_mkProd_or_LetIn top_arity binders_rel in
-      let hook sigma l gr _ =
-	if Impargs.is_implicit_args () || not (List.is_empty impls) then
-	  Impargs.declare_manual_implicits false gr [impls]
-      in hook, recname, typ
-  in
-  (* XXX: Capturing sigma here... bad bad *)
-  let hook = Lemmas.mk_hook (hook sigma) in
-  let fullcoqc = EConstr.to_constr sigma def in
-  let fullctyp = EConstr.to_constr sigma typ in
-  Obligations.check_evars env sigma;
-  let evars, _, evars_def, evars_typ =
-    Obligations.eterm_obligations env recname sigma 0 fullcoqc fullctyp
-  in
-  let ctx = Evd.evar_universe_context sigma in
-    ignore(Obligations.add_definition recname ~term:evars_def ~univdecl:decl
-	     evars_typ ctx evars ~hook)
-
-let interp_recursive isfix fixl notations =
-  let open Context.Named.Declaration in
-  let open EConstr in
-  let env = Global.env() in
-  let fixnames = List.map (fun fix -> fix.fix_name) fixl in
-
-  (* Interp arities allowing for unresolved types *)
-  let all_universes =
-    List.fold_right (fun sfe acc ->
-        match sfe.fix_univs , acc with
-        | None , acc -> acc
-        | x , None -> x
-        | Some ls , Some us ->
-           let lsu = ls.univdecl_instance and usu = us.univdecl_instance in
-	   if not (CList.for_all2eq (fun x y -> Id.equal (snd x) (snd y)) lsu usu) then
-	     user_err Pp.(str "(co)-recursive definitions should all have the same universe binders");
-	   Some us) fixl None in
-  let sigma, decl = Univdecls.interp_univ_decl_opt env all_universes in
-  let sigma, (fixctxs, fiximppairs, fixannots) =
-    on_snd List.split3 @@
-      List.fold_left_map (fun sigma -> interp_fix_context env sigma isfix) sigma fixl in
-  let fixctximpenvs, fixctximps = List.split fiximppairs in
-  let sigma, (fixccls,fixcclimps) =
-    on_snd List.split @@
-      List.fold_left3_map interp_fix_ccl sigma fixctximpenvs fixctxs fixl in
-  let fixtypes = List.map2 build_fix_type fixctxs fixccls in
-  let fixtypes = List.map (fun c -> nf_evar sigma c) fixtypes in
-  let fiximps = List.map3
-    (fun ctximps cclimps (_,ctx) -> ctximps@(Impargs.lift_implicits (Context.Rel.nhyps ctx) cclimps))
-    fixctximps fixcclimps fixctxs in
-  let sigma, rec_sign =
-    List.fold_left2
-      (fun (sigma, env') id t ->
-         if Flags.is_program_mode () then
-           let sigma, sort = Typing.type_of ~refresh:true env sigma t in
-           let sigma, fixprot =
-             try
-               let sigma, h_term = fix_proto sigma in
-               let app = mkApp (h_term, [|sort; t|]) in
-               let _evd = ref sigma in
-               let res = Typing.e_solve_evars env _evd app in
-               !_evd, res
-             with e when CErrors.noncritical e -> sigma, t
-           in
-           sigma, LocalAssum (id,fixprot) :: env'
-         else sigma, LocalAssum (id,t) :: env')
-      (sigma,[]) fixnames fixtypes
-  in
-  let env_rec = push_named_context rec_sign env in
-
-  (* Get interpretation metadatas *)
-  let fixtypes = List.map EConstr.Unsafe.to_constr fixtypes in
-  let impls = compute_internalization_env env Recursive fixnames fixtypes fiximps in
-
-  (* Interp bodies with rollback because temp use of notations/implicit *)
-  let sigma, fixdefs =
-    Metasyntax.with_syntax_protection (fun () ->
-      List.iter (Metasyntax.set_notation_for_interpretation env_rec impls) notations;
-      List.fold_left4_map
-        (fun sigma fixctximpenv -> interp_fix_body env_rec sigma (Id.Map.fold Id.Map.add fixctximpenv impls))
-        sigma fixctximpenvs fixctxs fixl fixccls)
-      () in
-
-  (* Instantiate evars and check all are resolved *)
-  let sigma = solve_unif_constraints_with_heuristics env_rec sigma in
-  let sigma, nf = nf_evars_and_universes sigma in
-  let fixdefs = List.map (fun c -> Option.map EConstr.Unsafe.to_constr c) fixdefs in
-  let fixdefs = List.map (Option.map nf) fixdefs in
-  let fixtypes = List.map nf fixtypes in
-  let fixctxs = List.map (fun (_,ctx) -> ctx) fixctxs in
-
-  (* Build the fix declaration block *)
-  (env,rec_sign,decl,sigma), (fixnames,fixdefs,fixtypes), List.combine3 fixctxs fiximps fixannots
-
-let check_recursive isfix env evd (fixnames,fixdefs,_) =
-  check_evars_are_solved env evd Evd.empty;
-  if List.for_all Option.has_some fixdefs then begin
-    let fixdefs = List.map Option.get fixdefs in
-    check_mutuality env evd isfix (List.combine fixnames fixdefs)
-  end
-
-let interp_fixpoint l ntns =
-  let (env,_,pl,evd),fix,info = interp_recursive true l ntns in
-  check_recursive true env evd fix;
-  (fix,pl,Evd.evar_universe_context evd,info)
-
-let interp_cofixpoint l ntns =
-  let (env,_,pl,evd),fix,info = interp_recursive false l ntns in
-  check_recursive false env evd fix;
-  (fix,pl,Evd.evar_universe_context evd,info)
-    
-let declare_fixpoint local poly ((fixnames,fixdefs,fixtypes),pl,ctx,fiximps) indexes ntns =
-  if List.exists Option.is_empty fixdefs then
-    (* Some bodies to define by proof *)
-    let thms =
-      List.map3 (fun id t (ctx,imps,_) -> (id,(EConstr.of_constr t,(List.map RelDecl.get_name ctx,imps))))
-		fixnames fixtypes fiximps in
-    let init_tac =
-      Some (List.map (Option.cata (EConstr.of_constr %> Tactics.exact_no_check) Tacticals.New.tclIDTAC)
-        fixdefs) in
-    let evd = Evd.from_ctx ctx in
-    Lemmas.start_proof_with_initialization (Global,poly,DefinitionBody Fixpoint)
-      evd pl (Some(false,indexes,init_tac)) thms None (Lemmas.mk_hook (fun _ _ -> ()))
-  else begin
-    (* We shortcut the proof process *)
-    let fixdefs = List.map Option.get fixdefs in
-    let fixdecls = prepare_recursive_declaration fixnames fixtypes fixdefs in
-    let env = Global.env() in
-    let indexes = search_guard env indexes fixdecls in
-    let fiximps = List.map (fun (n,r,p) -> r) fiximps in
-    let vars = Univops.universes_of_constr env (mkFix ((indexes,0),fixdecls)) in
-    let fixdecls =
-      List.map_i (fun i _ -> mkFix ((indexes,i),fixdecls)) 0 fixnames in
-    let evd = Evd.from_ctx ctx in
-    let evd = Evd.restrict_universe_context evd vars in
-    let ctx = Evd.check_univ_decl ~poly evd pl in
-    let pl = Evd.universe_binders evd in
-    let fixdecls = List.map Safe_typing.mk_pure_proof fixdecls in
-    ignore (List.map4 (DeclareDef.declare_fix (local, poly, Fixpoint) pl ctx)
-	      fixnames fixdecls fixtypes fiximps);
-    (* Declare the recursive definitions *)
-    fixpoint_message (Some indexes) fixnames;
-  end;
-  (* Declare notations *)
-  List.iter (Metasyntax.add_notation_interpretation (Global.env())) ntns
-
-let declare_cofixpoint local poly ((fixnames,fixdefs,fixtypes),pl,ctx,fiximps) ntns =
-  if List.exists Option.is_empty fixdefs then
-    (* Some bodies to define by proof *)
-    let thms =
-      List.map3 (fun id t (ctx,imps,_) -> (id,(EConstr.of_constr t,(List.map RelDecl.get_name ctx,imps))))
-		fixnames fixtypes fiximps in
-    let init_tac =
-      Some (List.map (Option.cata (EConstr.of_constr %> Tactics.exact_no_check) Tacticals.New.tclIDTAC)
-        fixdefs) in
-    let evd = Evd.from_ctx ctx in
-      Lemmas.start_proof_with_initialization (Global,poly, DefinitionBody CoFixpoint)
-      evd pl (Some(true,[],init_tac)) thms None (Lemmas.mk_hook (fun _ _ -> ()))
-  else begin
-    (* We shortcut the proof process *)
-    let fixdefs = List.map Option.get fixdefs in
-    let fixdecls = prepare_recursive_declaration fixnames fixtypes fixdefs in
-    let fixdecls = List.map_i (fun i _ -> mkCoFix (i,fixdecls)) 0 fixnames in
-    let env = Global.env () in
-    let vars = Univops.universes_of_constr env (List.hd fixdecls) in
-    let fixdecls = List.map Safe_typing.mk_pure_proof fixdecls in
-    let fiximps = List.map (fun (len,imps,idx) -> imps) fiximps in
-    let evd = Evd.from_ctx ctx in
-    let evd = Evd.restrict_universe_context evd vars in
-    let ctx = Evd.check_univ_decl ~poly evd pl in
-    let pl = Evd.universe_binders evd in
-    ignore (List.map4 (DeclareDef.declare_fix (local, poly, CoFixpoint) pl ctx)
-	      fixnames fixdecls fixtypes fiximps);
-    (* Declare the recursive definitions *)
-    cofixpoint_message fixnames
-  end;
-  (* Declare notations *)
-  List.iter (Metasyntax.add_notation_interpretation (Global.env())) ntns
-
-let extract_decreasing_argument limit = function
-  | (na,CStructRec) -> na
-  | (na,_) when not limit -> na
-  | _ -> user_err Pp.(str 
-      "Only structural decreasing is supported for a non-Program Fixpoint")
-
-let extract_fixpoint_components limit l =
-  let fixl, ntnl = List.split l in
-  let fixl = List.map (fun (((_,id),pl),ann,bl,typ,def) ->
-    let ann = extract_decreasing_argument limit ann in
-      {fix_name = id; fix_annot = ann; fix_univs = pl;
-       fix_binders = bl; fix_body = def; fix_type = typ}) fixl in
-  fixl, List.flatten ntnl
-
-let extract_cofixpoint_components l =
-  let fixl, ntnl = List.split l in
-  List.map (fun (((_,id),pl),bl,typ,def) ->
-	    {fix_name = id; fix_annot = None; fix_univs = pl;
-	     fix_binders = bl; fix_body = def; fix_type = typ}) fixl,
-  List.flatten ntnl
-
-let out_def = function
-  | Some def -> def
-  | None -> user_err Pp.(str "Program Fixpoint needs defined bodies.")
-
-let collect_evars_of_term evd c ty =
-  let evars = Evar.Set.union (Evd.evars_of_term c) (Evd.evars_of_term ty) in
-  Evar.Set.fold (fun ev acc -> Evd.add acc ev (Evd.find_undefined evd ev))
-  evars (Evd.from_ctx (Evd.evar_universe_context evd))
-
-let do_program_recursive local poly fixkind fixl ntns =
-  let isfix = fixkind != Obligations.IsCoFixpoint in
-  let (env, rec_sign, pl, evd), fix, info = 
-    interp_recursive isfix fixl ntns 
-  in
-    (* Program-specific code *)
-    (* Get the interesting evars, those that were not instanciated *)
-  let evd = Typeclasses.resolve_typeclasses ~filter:Typeclasses.no_goals ~fail:true env evd in
-    (* Solve remaining evars *)
-  let evd = nf_evar_map_undefined evd in
-  let collect_evars id def typ imps =
-    (* Generalize by the recursive prototypes  *)
-    let def =
-      EConstr.to_constr evd (Termops.it_mkNamedLambda_or_LetIn (EConstr.of_constr def) rec_sign)
-    and typ =
-      EConstr.to_constr evd (Termops.it_mkNamedProd_or_LetIn (EConstr.of_constr typ) rec_sign)
-    in
-    let evm = collect_evars_of_term evd def typ in
-    let evars, _, def, typ = 
-      Obligations.eterm_obligations env id evm
-	(List.length rec_sign) def typ
-    in (id, def, typ, imps, evars)
-  in
-  let (fixnames,fixdefs,fixtypes) = fix in
-  let fiximps = List.map pi2 info in
-  let fixdefs = List.map out_def fixdefs in
-  let defs = List.map4 collect_evars fixnames fixdefs fixtypes fiximps in
-  let () = if isfix then begin
-      let possible_indexes = List.map compute_possible_guardness_evidences info in
-      let fixdecls = Array.of_list (List.map (fun x -> Name x) fixnames),
-	Array.of_list fixtypes,
-	Array.of_list (List.map (subst_vars (List.rev fixnames)) fixdefs)
-      in
-      let indexes = 
-        Pretyping.search_guard (Global.env ()) possible_indexes fixdecls in
-      List.iteri (fun i _ ->
-          Inductive.check_fix env
-                              ((indexes,i),fixdecls))
-        fixl
-  end in
-  let ctx = Evd.evar_universe_context evd in
-  let kind = match fixkind with
-  | Obligations.IsFixpoint _ -> (local, poly, Fixpoint)
-  | Obligations.IsCoFixpoint -> (local, poly, CoFixpoint)
-  in
-  Obligations.add_mutual_definitions defs ~kind ~univdecl:pl ctx ntns fixkind
-
-let do_program_fixpoint local poly l =
-  let g = List.map (fun ((_,wf,_,_,_),_) -> wf) l in
-    match g, l with
-    | [(n, CWfRec r)], [((((_,id),pl),_,bl,typ,def),ntn)] ->
-	let recarg = 
-	  match n with
-	  | Some n -> mkIdentC (snd n)
-	  | None ->
-	      user_err ~hdr:"do_program_fixpoint"
-		(str "Recursive argument required for well-founded fixpoints")
-	in build_wellfounded (id, pl, n, bl, typ, out_def def) poly r recarg ntn
-	     
-    | [(n, CMeasureRec (m, r))], [((((_,id),pl),_,bl,typ,def),ntn)] ->
-	build_wellfounded (id, pl, n, bl, typ, out_def def) poly
-	  (Option.default (CAst.make @@ CRef (lt_ref,None)) r) m ntn
-	  
-    | _, _ when List.for_all (fun (n, ro) -> ro == CStructRec) g ->
-	let fixl,ntns = extract_fixpoint_components true l in
-	let fixkind = Obligations.IsFixpoint g in
-	  do_program_recursive local poly fixkind fixl ntns
-
-    | _, _ ->
-	user_err ~hdr:"do_program_fixpoint"
-	  (str "Well-founded fixpoints not allowed in mutually recursive blocks")
-
-let check_safe () =
-  let open Declarations in
-  let flags = Environ.typing_flags (Global.env ()) in
-  flags.check_universes && flags.check_guarded
-
-let do_fixpoint local poly l =
-  if Flags.is_program_mode () then do_program_fixpoint local poly l
-  else
-    let fixl, ntns = extract_fixpoint_components true l in
-    let (_, _, _, info as fix) = interp_fixpoint fixl ntns in
-    let possible_indexes =
-      List.map compute_possible_guardness_evidences info in
-    declare_fixpoint local poly fix possible_indexes ntns;
-    if not (check_safe ()) then Feedback.feedback Feedback.AddedAxiom else ()
-
-let do_cofixpoint local poly l =
-  let fixl,ntns = extract_cofixpoint_components l in
-    if Flags.is_program_mode () then
-      do_program_recursive local poly Obligations.IsCoFixpoint fixl ntns
-    else
-      let cofix = interp_cofixpoint fixl ntns in
-      declare_cofixpoint local poly cofix ntns;
-      if not (check_safe ()) then Feedback.feedback Feedback.AddedAxiom else ()
diff --git a/vernac/command.mli b/vernac/command.mli
deleted file mode 100644
index c7342e6da..000000000
--- a/vernac/command.mli
+++ /dev/null
@@ -1,163 +0,0 @@
-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017     *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-
-open Names
-open Constr
-open Entries
-open Libnames
-open Globnames
-open Vernacexpr
-open Constrexpr
-open Decl_kinds
-open Redexpr
-
-(** This file is about the interpretation of raw commands into typed
-    ones and top-level declaration of the main Gallina objects *)
-
-val do_universe : polymorphic -> Id.t Loc.located list -> unit
-val do_constraint : polymorphic ->
-  (Misctypes.glob_level * Univ.constraint_type * Misctypes.glob_level) list -> unit
-
-(** {6 Definitions/Let} *)
-
-val interp_definition :
-  Vernacexpr.universe_decl_expr option -> local_binder_expr list -> polymorphic -> red_expr option -> constr_expr ->
-  constr_expr option -> Safe_typing.private_constants definition_entry * Evd.evar_map * 
-                        Univdecls.universe_decl * Impargs.manual_implicits
-
-val do_definition : Id.t -> definition_kind -> Vernacexpr.universe_decl_expr option ->
-  local_binder_expr list -> red_expr option -> constr_expr ->
-  constr_expr option -> unit Lemmas.declaration_hook -> unit
-
-(** {6 Parameters/Assumptions} *)
-
-(* val interp_assumption : env -> evar_map ref -> *)
-(*   local_binder_expr list -> constr_expr ->  *)
-(*   types Univ.in_universe_context_set * Impargs.manual_implicits *)
-
-(** returns [false] if the assumption is neither local to a section,
-    nor in a module type and meant to be instantiated. *)
-val declare_assumption : coercion_flag -> assumption_kind -> 
-  types in_constant_universes_entry ->
-  Universes.universe_binders -> Impargs.manual_implicits ->
-  bool (** implicit *) -> Vernacexpr.inline -> variable Loc.located ->
-  global_reference * Univ.Instance.t * bool
-
-val do_assumptions : locality * polymorphic * assumption_object_kind ->
-  Vernacexpr.inline -> (Vernacexpr.ident_decl list * constr_expr) with_coercion list -> bool
-
-(* val declare_assumptions : variable Loc.located list -> *)
-(*   coercion_flag -> assumption_kind -> types Univ.in_universe_context_set ->  *)
-(*   Impargs.manual_implicits -> bool -> Vernacexpr.inline -> bool *)
-
-(** {6 Inductive and coinductive types} *)
-
-(** Extracting the semantical components out of the raw syntax of mutual
-   inductive declarations *)
-
-type structured_one_inductive_expr = {
-  ind_name : Id.t;
-  ind_univs : Vernacexpr.universe_decl_expr option;
-  ind_arity : constr_expr;
-  ind_lc : (Id.t * constr_expr) list
-}
-
-type structured_inductive_expr =
-  local_binder_expr list * structured_one_inductive_expr list
-
-val extract_mutual_inductive_declaration_components :
-  (one_inductive_expr * decl_notation list) list ->
-    structured_inductive_expr * (*coercions:*) qualid list * decl_notation list
-
-(** Typing mutual inductive definitions *)
-
-type one_inductive_impls =
-  Impargs.manual_implicits (** for inds *)*
-  Impargs.manual_implicits list (** for constrs *)
-
-val interp_mutual_inductive :
-  structured_inductive_expr -> decl_notation list -> cumulative_inductive_flag ->
-  polymorphic -> private_flag -> Declarations.recursivity_kind ->
-  mutual_inductive_entry * Universes.universe_binders * one_inductive_impls list
-
-(** Registering a mutual inductive definition together with its
-   associated schemes *)
-
-val declare_mutual_inductive_with_eliminations :
-  mutual_inductive_entry -> Universes.universe_binders -> one_inductive_impls list ->
-  MutInd.t
-
-(** Entry points for the vernacular commands Inductive and CoInductive *)
-
-val do_mutual_inductive :
-  (one_inductive_expr * decl_notation list) list -> cumulative_inductive_flag ->
-  polymorphic -> private_flag -> Declarations.recursivity_kind -> unit
-
-(** {6 Fixpoints and cofixpoints} *)
-
-type structured_fixpoint_expr = {
-  fix_name : Id.t;
-  fix_univs : Vernacexpr.universe_decl_expr option;
-  fix_annot : Id.t Loc.located option;
-  fix_binders : local_binder_expr list;
-  fix_body : constr_expr option;
-  fix_type : constr_expr
-}
-
-(** Extracting the semantical components out of the raw syntax of
-   (co)fixpoints declarations *)
-
-val extract_fixpoint_components : bool ->
-  (fixpoint_expr * decl_notation list) list ->
-    structured_fixpoint_expr list * decl_notation list
-
-val extract_cofixpoint_components :
-  (cofixpoint_expr * decl_notation list) list ->
-    structured_fixpoint_expr list * decl_notation list
-
-(** Typing global fixpoints and cofixpoint_expr *)
-
-type recursive_preentry =
-  Id.t list * constr option list * types list
-
-val interp_fixpoint :
-  structured_fixpoint_expr list -> decl_notation list ->
-    recursive_preentry * Univdecls.universe_decl * UState.t *
-    (EConstr.rel_context * Impargs.manual_implicits * int option) list
-
-val interp_cofixpoint :
-  structured_fixpoint_expr list -> decl_notation list ->
-    recursive_preentry * Univdecls.universe_decl * UState.t *
-    (EConstr.rel_context * Impargs.manual_implicits * int option) list
-
-(** Registering fixpoints and cofixpoints in the environment *)
-
-val declare_fixpoint :
-  locality -> polymorphic ->
-  recursive_preentry * Univdecls.universe_decl * UState.t *
-  (Context.Rel.t * Impargs.manual_implicits * int option) list ->
-  Proof_global.lemma_possible_guards -> decl_notation list -> unit
-
-val declare_cofixpoint : locality -> polymorphic -> 
-  recursive_preentry * Univdecls.universe_decl * UState.t *
-  (Context.Rel.t * Impargs.manual_implicits * int option) list ->
-  decl_notation list -> unit
-
-(** Entry points for the vernacular commands Fixpoint and CoFixpoint *)
-
-val do_fixpoint :
-  (* When [false], assume guarded. *)
-  locality -> polymorphic -> (fixpoint_expr * decl_notation list) list -> unit
-
-val do_cofixpoint :
-  (* When [false], assume guarded. *)
-  locality -> polymorphic -> (cofixpoint_expr * decl_notation list) list -> unit
-
-(** Utils *)
-
-val check_mutuality : Environ.env -> Evd.evar_map -> bool -> (Id.t * types) list -> unit
diff --git a/vernac/record.ml b/vernac/record.ml
index d97a5149d..114b55cb4 100644
--- a/vernac/record.ml
+++ b/vernac/record.ml
@@ -433,7 +433,7 @@ let declare_structure finite ubinders univs id idbuild paramimpls params arity t
     | Monomorphic_const_entry _ ->
        mie
   in
-  let kn = Command.declare_mutual_inductive_with_eliminations mie ubinders [(paramimpls,[])] in
+  let kn = ComInductive.declare_mutual_inductive_with_eliminations mie ubinders [(paramimpls,[])] in
   let rsp = (kn,0) in (* This is ind path of idstruc *)
   let cstr = (rsp,1) in
   let kinds,sp_projs = declare_projections rsp ctx ~kind binder_name coers ubinders fieldimpls fields in
diff --git a/vernac/vernac.mllib b/vernac/vernac.mllib
index 8673155e2..f001b572a 100644
--- a/vernac/vernac.mllib
+++ b/vernac/vernac.mllib
@@ -11,7 +11,11 @@ Search
 Indschemes
 DeclareDef
 Obligations
-Command
+ComDefinition
+ComAssumption
+ComInductive
+ComFixpoint
+ComProgramFixpoint
 Classes
 Record
 Assumptions
diff --git a/vernac/vernacentries.ml b/vernac/vernacentries.ml
index 63768d9b8..f6e812168 100644
--- a/vernac/vernacentries.ml
+++ b/vernac/vernacentries.ml
@@ -18,7 +18,6 @@ open Tacmach
 open Constrintern
 open Prettyp
 open Printer
-open Command
 open Goptions
 open Libnames
 open Globnames
@@ -489,7 +488,7 @@ let vernac_definition ~atts discharge kind ((loc,id as lid),pl) def =
           | Some r ->
             let sigma, env = Pfedit.get_current_context () in
             Some (snd (Hook.get f_interp_redexp env sigma r)) in
-        do_definition id (local, atts.polymorphic, kind) pl bl red_option c typ_opt hook)
+        ComDefinition.do_definition id (local, atts.polymorphic, kind) pl bl red_option c typ_opt hook)
 
 let vernac_start_proof ~atts kind l =
   let local = enforce_locality_exp atts.locality NoDischarge in
@@ -520,7 +519,7 @@ let vernac_assumption ~atts discharge kind l nl =
       List.iter (fun (lid, _) ->
 	if global then Dumpglob.dump_definition lid false "ax"
 	else Dumpglob.dump_definition lid true "var") idl) l;
-  let status = do_assumptions kind nl l in
+  let status = ComAssumption.do_assumptions kind nl l in
   if not status then Feedback.feedback Feedback.AddedAxiom
 
 let should_treat_as_cumulative cum poly =
@@ -592,18 +591,29 @@ let vernac_inductive ~atts cum lo finite indl =
       | _ -> user_err Pp.(str "Cannot handle mutually (co)inductive records.")
     in
     let indl = List.map unpack indl in
-    do_mutual_inductive indl is_cumulative atts.polymorphic lo finite
+    ComInductive.do_mutual_inductive indl is_cumulative atts.polymorphic lo finite
 
 let vernac_fixpoint ~atts discharge l =
   let local = enforce_locality_exp atts.locality discharge in
   if Dumpglob.dump () then
     List.iter (fun (((lid,_), _, _, _, _), _) -> Dumpglob.dump_definition lid false "def") l;
+  (* XXX: Switch to the attribute system and match on ~atts *)
+  let do_fixpoint = if Flags.is_program_mode () then
+      ComProgramFixpoint.do_fixpoint
+    else
+      ComFixpoint.do_fixpoint
+  in
   do_fixpoint local atts.polymorphic l
 
 let vernac_cofixpoint ~atts discharge l =
   let local = enforce_locality_exp atts.locality discharge in
   if Dumpglob.dump () then
     List.iter (fun (((lid,_), _, _, _), _) -> Dumpglob.dump_definition lid false "def") l;
+  let do_cofixpoint = if Flags.is_program_mode () then
+      ComProgramFixpoint.do_cofixpoint
+    else
+      ComFixpoint.do_cofixpoint
+  in
   do_cofixpoint local atts.polymorphic l
 
 let vernac_scheme l =
@@ -627,14 +637,14 @@ let vernac_universe ~atts l =
     user_err ?loc:atts.loc ~hdr:"vernac_universe"
 		 (str"Polymorphic universes can only be declared inside sections, " ++
 		  str "use Monomorphic Universe instead");
-  do_universe atts.polymorphic l
+  Declare.do_universe atts.polymorphic l
 
 let vernac_constraint ~atts l =
   if atts.polymorphic && not (Lib.sections_are_opened ()) then
     user_err ?loc:atts.loc ~hdr:"vernac_constraint"
 		 (str"Polymorphic universe constraints can only be declared"
 		  ++ str " inside sections, use Monomorphic Constraint instead");
-  do_constraint atts.polymorphic l
+  Declare.do_constraint atts.polymorphic l
 
 (**********************)
 (* Modules            *)