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+(************************************************************************)
+(*         *   The Coq Proof Assistant / The Coq Development Team       *)
+(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2019       *)
+(* <O___,, *       (see CREDITS file for the list of authors)           *)
+(*   \VV/  **************************************************************)
+(*    //   *    This file is distributed under the terms of the         *)
+(*         *     GNU Lesser General Public License Version 2.1          *)
+(*         *     (see LICENSE file for the text of the license)         *)
+(************************************************************************)
+
+open Util
+open Names
+open Univ
+
+module NamedDecl = Context.Named.Declaration
+
+type _ section_kind =
+| SecMono : [ `mono ] section_kind
+| SecPoly : [ `poly ] section_kind
+
+type _ section_universes =
+| SecMonoUniv : [ `mono ] section_universes
+| SecPolyUniv : Name.t array * UContext.t -> [ `poly ] section_universes
+
+type section_entry =
+| SecDefinition of Constant.t
+| SecInductive of MutInd.t
+
+type 'a entry_map = 'a Cmap.t * 'a Mindmap.t
+
+type 'a section = {
+  sec_context : int;
+  (** Length of the named context suffix that has been introduced locally *)
+  sec_universes : 'a section_universes;
+  (** Universes local to the section *)
+  sec_entries : section_entry list;
+  (** Definitions introduced in the section *)
+  sec_data : 'a section_universes entry_map;
+}
+
+(** Sections can be nested with the proviso that no monomorphic section can be
+    opened inside a polymorphic one. The reverse is allowed. *)
+type t = {
+  sec_poly : [ `poly ] section list;
+  sec_mono : [ `mono ] section list;
+}
+
+let empty = {
+  sec_poly = [];
+  sec_mono = [];
+}
+
+let is_empty s =
+  List.is_empty s.sec_poly && List.is_empty s.sec_mono
+
+let is_polymorphic s =
+  not (List.is_empty s.sec_poly)
+
+let find_emap e (cmap, imap) = match e with
+| SecDefinition con -> Cmap.find con cmap
+| SecInductive ind -> Mindmap.find ind imap
+
+let add_emap e v (cmap, imap) = match e with
+| SecDefinition con -> (Cmap.add con v cmap, imap)
+| SecInductive ind -> (cmap, Mindmap.add ind v imap)
+
+type on_sec = { on_sec : 'a. 'a section_kind -> 'a section -> 'a section }
+
+let on_last_section f { sec_poly; sec_mono } = match sec_poly, sec_mono with
+| [], [] -> CErrors.user_err (Pp.str "No opened section")
+| sec :: rem, _ ->
+  let sec_poly = f.on_sec SecPoly sec :: rem in
+  { sec_mono; sec_poly }
+| [], sec :: rem ->
+  let sec_mono = f.on_sec SecMono sec :: rem in
+  { sec_mono; sec_poly }
+
+type 'r with_sec = { with_sec : 'a. ('a section_kind * 'a section) option -> 'r }
+
+let with_last_section f { sec_poly; sec_mono } = match sec_poly, sec_mono with
+| [], [] -> f.with_sec None
+| sec :: _, _ -> f.with_sec (Some (SecPoly, sec))
+| [], sec :: _ -> f.with_sec (Some (SecMono, sec))
+
+let push_local s =
+  let on_sec _ sec = { sec with sec_context = sec.sec_context + 1 } in
+  on_last_section { on_sec } s
+
+let push_context (nas, ctx) s =
+  let on_sec (type a) (kind : a section_kind) (sec : a section) : a section = match kind with
+  | SecMono ->
+    CErrors.anomaly (Pp.str "Adding polymorphic constraints to monomorphic section")
+  | SecPoly ->
+    let SecPolyUniv (snas, sctx) = sec.sec_universes in
+    let sec_universes = SecPolyUniv (Array.append snas nas, UContext.union sctx ctx) in
+    { sec with sec_universes }
+  in
+  on_last_section { on_sec } s
+
+let open_section ~poly sections =
+  if poly then
+    let sec = {
+      sec_context = 0;
+      sec_universes = SecPolyUniv ([||], Univ.UContext.empty);
+      sec_entries = [];
+      sec_data = (Cmap.empty, Mindmap.empty);
+    } in
+    { sections with sec_poly = sec :: sections.sec_poly }
+  else if List.is_empty sections.sec_poly then
+    let sec = {
+      sec_context = 0;
+      sec_universes = SecMonoUniv;
+      sec_entries = [];
+      sec_data = (Cmap.empty, Mindmap.empty);
+    } in
+    { sections with sec_mono = sec :: sections.sec_mono }
+  else
+    CErrors.user_err (Pp.str "Cannot open a monomorphic section inside a polymorphic one")
+
+let close_section sections =
+  (* TODO: implement me correctly when discharging in kernel *)
+  match sections.sec_poly, sections.sec_mono with
+  | _sec :: psecs, _ ->
+    let sections = { sections with sec_poly = psecs } in
+    sections
+  | [], _sec :: msecs ->
+    let sections = { sections with sec_mono = msecs } in
+    sections
+  | [], [] ->
+    CErrors.user_err (Pp.str "No opened section.")
+
+let same_poly (type a) ~poly (knd : a section_kind) = match knd with
+| SecPoly -> poly
+| SecMono -> not poly
+
+let push_global ~poly e s =
+  if is_empty s then s
+  else
+    let on_sec knd sec =
+      if same_poly ~poly knd then { sec with
+        sec_entries = e :: sec.sec_entries;
+        sec_data = add_emap e sec.sec_universes sec.sec_data;
+      } else
+        CErrors.user_err (Pp.str "Cannot mix universe polymorphic and \
+          monomorphic declarations in sections.")
+    in
+    on_last_section { on_sec } s
+
+let push_constant ~poly con s = push_global ~poly (SecDefinition con) s
+
+let push_inductive ~poly ind s = push_global ~poly (SecInductive ind) s
+
+type abstr_info = {
+  abstr_ctx : Constr.named_context;
+  abstr_subst : Univ.Instance.t;
+  abstr_uctx : Univ.AUContext.t;
+}
+
+let empty_segment = {
+  abstr_ctx = [];
+  abstr_subst = Instance.empty;
+  abstr_uctx = AUContext.empty;
+}
+
+let extract_hyps sec vars hyps =
+  (* FIXME: this code is fishy. It is supposed to check that declared section
+     variables are an ordered subset of the ambient ones, but it doesn't check
+     e.g. uniqueness of naming nor convertibility of the section data. *)
+  let rec aux ids hyps = match ids, hyps with
+  | id :: ids, decl :: hyps when Names.Id.equal id (NamedDecl.get_id decl) ->
+    decl :: aux ids hyps
+  | _ :: ids, hyps ->
+    aux ids hyps
+  | [], _ -> []
+  in
+  let ids = List.map NamedDecl.get_id @@ List.firstn sec.sec_context vars in
+  aux ids hyps
+
+let section_segment_of_entry vars e hyps sections =
+  (* [vars] are the named hypotheses, [hyps] the subset that is declared by the
+    global *)
+  let with_sec (type a) (s : (a section_kind * a section) option) = match s with
+  | None ->
+    CErrors.user_err (Pp.str "No opened section.")
+  | Some (knd, sec) ->
+    let hyps = extract_hyps sec vars hyps in
+    let inst, auctx = match knd, find_emap e sec.sec_data with
+    | SecMono, SecMonoUniv ->
+      Instance.empty, AUContext.empty
+    | SecPoly, SecPolyUniv (nas, ctx) ->
+      Univ.abstract_universes nas ctx
+    in
+    {
+      abstr_ctx = hyps;
+      abstr_subst = inst;
+      abstr_uctx = auctx;
+    }
+  in
+  with_last_section { with_sec } sections
+
+let segment_of_constant env con s =
+  let body = Environ.lookup_constant con env in
+  let vars = Environ.named_context env in
+  section_segment_of_entry vars (SecDefinition con) body.Declarations.const_hyps s
+
+let segment_of_inductive env mind s =
+  let mib = Environ.lookup_mind mind env in
+  let vars = Environ.named_context env in
+  section_segment_of_entry vars (SecInductive mind) mib.Declarations.mind_hyps s
+
+let instance_from_variable_context =
+  List.rev %> List.filter NamedDecl.is_local_assum %> List.map NamedDecl.get_id %> Array.of_list
+
+let extract_worklist info =
+  let args = instance_from_variable_context info.abstr_ctx in
+  info.abstr_subst, args
+
+let replacement_context env s =
+  let with_sec sec = match sec with
+  | None -> CErrors.user_err (Pp.str "No opened section.")
+  | Some (_, sec) ->
+    let cmap, imap = sec.sec_data in
+    let cmap = Cmap.mapi (fun con _ -> extract_worklist @@ segment_of_constant env con s) cmap in
+    let imap = Mindmap.mapi (fun ind _ -> extract_worklist @@ segment_of_inductive env ind s) imap in
+    (cmap, imap)
+  in
+  with_last_section { with_sec } s
+
+let is_in_section env gr s =
+  let with_sec sec = match sec with
+  | None -> false
+  | Some (_, sec) ->
+    let open GlobRef in
+    match gr with
+    | VarRef id ->
+      let vars = List.firstn sec.sec_context (Environ.named_context env) in
+      List.exists (fun decl -> Id.equal id (NamedDecl.get_id decl)) vars
+    | ConstRef con ->
+      Cmap.mem con (fst sec.sec_data)
+    | IndRef (ind, _) | ConstructRef ((ind, _), _) ->
+      Mindmap.mem ind (snd sec.sec_data)
+  in
+  with_last_section { with_sec } s
+
+let is_polymorphic_univ u s =
+  let check sec =
+    let SecPolyUniv (_, uctx) = sec.sec_universes in
+    Array.mem u (Instance.to_array (UContext.instance uctx))
+  in
+  List.exists check s.sec_poly