From 61dc740ed1c3780cccaec00d059a28f0d31d0052 Mon Sep 17 00:00:00 2001
From: Stephane Glondu <steph@glondu.net>
Date: Mon, 4 Jun 2012 12:07:52 +0200
Subject: Imported Upstream version 8.4~gamma0+really8.4beta2

---
 kernel/declarations.mli |   4 ++
 kernel/mod_typing.ml    |  82 +++++++++++++++++------------------
 kernel/safe_typing.ml   |  56 +++++++++++++++---------
 kernel/safe_typing.mli  |   2 +-
 kernel/subtyping.ml     |  74 +++++++++++++++++---------------
 kernel/term.ml          |   1 +
 kernel/term.mli         |   6 +--
 kernel/univ.ml          | 111 +++++++++++++++++++++++++++++-------------------
 kernel/univ.mli         |   4 ++
 9 files changed, 195 insertions(+), 145 deletions(-)

(limited to 'kernel')

diff --git a/kernel/declarations.mli b/kernel/declarations.mli
index 5b800ede..7cf74ba3 100644
--- a/kernel/declarations.mli
+++ b/kernel/declarations.mli
@@ -192,6 +192,10 @@ type structure_field_body =
   | SFBmodule of module_body
   | SFBmodtype of module_type_body
 
+(** NB: we may encounter now (at most) twice the same label in
+    a [structure_body], once for a module ([SFBmodule] or [SFBmodtype])
+    and once for an object ([SFBconst] or [SFBmind]) *)
+
 and structure_body = (label * structure_field_body) list
 
 and struct_expr_body =
diff --git a/kernel/mod_typing.ml b/kernel/mod_typing.ml
index a384c836..bfc6f3c7 100644
--- a/kernel/mod_typing.ml
+++ b/kernel/mod_typing.ml
@@ -35,10 +35,14 @@ let rec mp_from_mexpr = function
   | MSEfunctor (_,_,expr) -> mp_from_mexpr expr
   | MSEwith (expr,_) -> mp_from_mexpr expr
 
-let rec list_split_assoc k rev_before = function
+let is_modular = function
+  | SFBmodule _ | SFBmodtype _ -> true
+  | SFBconst _ | SFBmind _ -> false
+
+let rec list_split_assoc ((k,m) as km) rev_before = function
   | [] -> raise Not_found
-  | (k',b)::after when k=k' -> rev_before,b,after
-  | h::tail -> list_split_assoc k (h::rev_before) tail
+  | (k',b)::after when k=k' && is_modular b = m -> rev_before,b,after
+  | h::tail -> list_split_assoc km (h::rev_before) tail
 
 let discr_resolver env mtb =
      match mtb.typ_expr with
@@ -54,35 +58,34 @@ let rec rebuild_mp mp l =
 	
 let rec check_with env sign with_decl alg_sign mp equiv = 
   let sign,wd,equiv,cst= match with_decl with
-    | With_Definition (id,_) ->
-	let sign,cb,cst = check_with_aux_def env sign with_decl mp equiv in
-	  sign,With_definition_body(id,cb),equiv,cst
-    | With_Module (id,mp1) -> 
-	let sign,equiv,cst = 
-	  check_with_aux_mod env sign with_decl mp equiv in
-	  sign,With_module_body(id,mp1),equiv,cst in
+    | With_Definition (idl,c) ->
+	let sign,cb,cst = check_with_def env sign (idl,c) mp equiv in
+	sign,With_definition_body(idl,cb),equiv,cst
+    | With_Module (idl,mp1) ->
+	let sign,equiv,cst = check_with_mod env sign (idl,mp1) mp equiv in
+	sign,With_module_body(idl,mp1),equiv,cst
+  in
     if alg_sign = None then
       sign,None,equiv,cst
     else
       sign,Some (SEBwith(Option.get(alg_sign),wd)),equiv,cst
 	    
-and check_with_aux_def env sign with_decl mp equiv = 
+and check_with_def env sign (idl,c) mp equiv =
   let sig_b = match sign with 
     | SEBstruct(sig_b) -> sig_b
     | _ -> error_signature_expected sign
   in
-  let id,idl = match with_decl with
-    | With_Definition (id::idl,_) | With_Module (id::idl,_) -> id,idl
-    | With_Definition ([],_) | With_Module ([],_) -> assert false
+  let id,idl = match idl with
+    | [] -> assert false
+    | id::idl -> id,idl
   in
   let l = label_of_id id in
     try
-      let rev_before,spec,after = list_split_assoc l [] sig_b in
+      let rev_before,spec,after = list_split_assoc (l,(idl<>[])) [] sig_b in
       let before = List.rev rev_before in
       let env' = Modops.add_signature mp before equiv env in
-	match with_decl with
-          | With_Definition ([],_) -> assert false
-	  | With_Definition ([id],c) ->
+      if idl = [] then
+	      (* Toplevel definition *)
 	      let cb = match spec with
 		| SFBconst cb -> cb
 		| _ -> error_not_a_constant l
@@ -115,8 +118,9 @@ and check_with_aux_def env sign with_decl mp equiv =
 		    Cemitcodes.from_val (compile_constant_body env' def);
 		  const_constraints = cst }
 	      in
-	      SEBstruct(before@((l,SFBconst(cb'))::after)),cb',cst
-	  | With_Definition (_::_,c) ->
+	      SEBstruct(before@(l,SFBconst(cb'))::after),cb',cst
+      else
+	      (* Definition inside a sub-module *)
 	      let old = match spec with
 		| SFBmodule msb -> msb
 		| _ -> error_not_a_module (string_of_label l)
@@ -124,43 +128,36 @@ and check_with_aux_def env sign with_decl mp equiv =
 		begin
 		  match old.mod_expr with
                     | None ->
-			let new_with_decl = With_Definition (idl,c) in 
 			let sign,cb,cst = 
-			  check_with_aux_def env' old.mod_type new_with_decl 
+			  check_with_def env' old.mod_type (idl,c)
 			    (MPdot(mp,l)) old.mod_delta in
 			let new_spec = SFBmodule({old with
 						    mod_type = sign;
 						    mod_type_alg = None}) in
-			  SEBstruct(before@((l,new_spec)::after)),cb,cst
+			  SEBstruct(before@(l,new_spec)::after),cb,cst
                     | Some msb ->
 			error_generative_module_expected l
 		end
-	  | _ -> anomaly "Modtyping:incorrect use of with"
     with
       | Not_found -> error_no_such_label l
       | Reduction.NotConvertible -> error_incorrect_with_constraint l
 
-and check_with_aux_mod env sign with_decl mp equiv = 
+and check_with_mod env sign (idl,mp1) mp equiv = 
   let sig_b = match sign with 
     | SEBstruct(sig_b) ->sig_b
     | _ -> error_signature_expected sign
   in
-  let id,idl = match with_decl with
-    | With_Definition (id::idl,_) | With_Module (id::idl,_) -> id,idl
-    | With_Definition ([],_) | With_Module ([],_) -> assert false
+  let id,idl = match idl with
+    | [] -> assert false
+    | id::idl -> id,idl
   in
   let l = label_of_id id in
     try
-      let rev_before,spec,after = list_split_assoc l [] sig_b in
+      let rev_before,spec,after = list_split_assoc (l,true) [] sig_b in
       let before = List.rev rev_before in
-      let rec mp_rec = function
-	| [] -> mp
-	| i::r -> MPdot(mp_rec r,label_of_id i)
-      in
       let env' = Modops.add_signature mp before equiv env in
-	match with_decl with
-          | With_Module ([],_) -> assert false
-	  | With_Module ([id], mp1) ->
+      if idl = [] then
+	      (* Toplevel module definition *)
 	      let old = match spec with
 		  SFBmodule msb -> msb
 		| _ -> error_not_a_module (string_of_label l)
@@ -194,7 +191,8 @@ and check_with_aux_mod env sign with_decl mp equiv =
 	      let id_subst = map_mp (MPdot(mp,l)) (MPdot(mp,l)) new_mb.mod_delta in
 		SEBstruct(before@(l,new_spec)::subst_signature id_subst after),
 	      add_delta_resolver equiv new_mb.mod_delta,cst
-          | With_Module (idc,mp1) -> 
+      else
+	      (* Module definition of a sub-module *)
 	      let old = match spec with
 		  SFBmodule msb -> msb
 		| _ -> error_not_a_module (string_of_label l)
@@ -202,10 +200,9 @@ and check_with_aux_mod env sign with_decl mp equiv =
 	      begin
 		match old.mod_expr with
 		    None ->
-		      let new_with_decl = With_Module (idl,mp1) in
 		      let sign,equiv',cst =
-			check_with_aux_mod env'
-			  old.mod_type new_with_decl (MPdot(mp,l)) old.mod_delta in
+			check_with_mod env'
+			  old.mod_type (idl,mp1) (MPdot(mp,l)) old.mod_delta in
 		      let new_equiv = add_delta_resolver equiv equiv' in
 		      let new_spec = SFBmodule {old with 
 						  mod_type = sign;
@@ -223,7 +220,6 @@ and check_with_aux_mod env sign with_decl mp equiv =
 		  | _ ->
 		      error_generative_module_expected l
               end
-	  | _ -> anomaly "Modtyping:incorrect use of with"
     with
 	Not_found -> error_no_such_label l
       | Reduction.NotConvertible -> error_incorrect_with_constraint l
@@ -368,7 +364,7 @@ let rec add_struct_expr_constraints env = function
 
   | SEBstruct (structure_body) ->
       List.fold_left
-        (fun env (l,item) -> add_struct_elem_constraints env item)
+        (fun env (_,item) -> add_struct_elem_constraints env item)
         env
         structure_body
 
@@ -413,7 +409,7 @@ let rec struct_expr_constraints cst = function
 
   | SEBstruct (structure_body) ->
       List.fold_left
-        (fun cst (l,item) -> struct_elem_constraints cst item)
+        (fun cst (_,item) -> struct_elem_constraints cst item)
         cst
         structure_body
 
diff --git a/kernel/safe_typing.ml b/kernel/safe_typing.ml
index c2d71ebb..d7a8b005 100644
--- a/kernel/safe_typing.ml
+++ b/kernel/safe_typing.ml
@@ -101,7 +101,8 @@ type safe_environment =
     { old : safe_environment;
       env : env;
       modinfo : module_info;
-      labset : Labset.t;
+      modlabels : Labset.t;
+      objlabels : Labset.t;
       revstruct : structure_body;
       univ : Univ.constraints;
       engagement : engagement option;
@@ -109,13 +110,16 @@ type safe_environment =
       loads : (module_path * module_body) list;
       local_retroknowledge : Retroknowledge.action list}
 
-let exists_label l senv = Labset.mem l senv.labset
+let exists_modlabel l senv = Labset.mem l senv.modlabels
+let exists_objlabel l senv = Labset.mem l senv.objlabels
 
-let check_label l senv =
-  if exists_label l senv then error_existing_label l
+let check_modlabel l senv =
+  if exists_modlabel l senv then error_existing_label l
+let check_objlabel l senv =
+  if exists_objlabel l senv then error_existing_label l
 
-let check_labels ls senv =
-  Labset.iter (fun l -> check_label l senv) ls
+let check_objlabels ls senv =
+  Labset.iter (fun l -> check_objlabel l senv) ls
 
 let labels_of_mib mib =
   let add,get =
@@ -140,7 +144,8 @@ let rec empty_environment =
       variant = NONE;
       resolver = empty_delta_resolver;
       resolver_of_param = empty_delta_resolver};
-    labset = Labset.empty;
+    modlabels = Labset.empty;
+    objlabels = Labset.empty;
     revstruct = [];
     univ = Univ.empty_constraint;
     engagement = None;
@@ -172,11 +177,15 @@ type generic_name =
   | M
 
 let add_field ((l,sfb) as field) gn senv =
-  let labels = match sfb with
-    | SFBmind mib -> labels_of_mib mib
-    | _ -> Labset.singleton l
+  let mlabs,olabs = match sfb with
+    | SFBmind mib ->
+      let l = labels_of_mib mib in
+      check_objlabels l senv; (Labset.empty,l)
+    | SFBconst _ ->
+      check_objlabel l senv; (Labset.empty, Labset.singleton l)
+    | SFBmodule _ | SFBmodtype _ ->
+      check_modlabel l senv; (Labset.singleton l, Labset.empty)
   in
-  check_labels labels senv;
   let senv = add_constraints (constraints_of_sfb sfb) senv in
   let env' = match sfb, gn with
     | SFBconst cb, C con -> Environ.add_constant con cb senv.env
@@ -187,7 +196,8 @@ let add_field ((l,sfb) as field) gn senv =
   in
   { senv with
     env = env';
-    labset = Labset.union labels senv.labset;
+    modlabels = Labset.union mlabs senv.modlabels;
+    objlabels = Labset.union olabs senv.objlabels;
     revstruct = field :: senv.revstruct }
 
 (* Applying a certain function to the resolver of a safe environment *)
@@ -320,7 +330,7 @@ let add_module l me inl senv =
 (* Interactive modules *)
 
 let start_module l senv =
-  check_label l senv;
+  check_modlabel l senv;
  let mp = MPdot(senv.modinfo.modpath, l) in
  let modinfo = { modpath = mp;
 		 label = l;
@@ -331,7 +341,8 @@ let start_module l senv =
    mp, { old = senv;
 	 env = senv.env;
 	 modinfo = modinfo;
-	 labset = Labset.empty;
+	 modlabels = Labset.empty;
+	 objlabels = Labset.empty;
 	 revstruct = [];
          univ = Univ.empty_constraint;
          engagement = None;
@@ -415,7 +426,8 @@ let end_module l restype senv =
     mp,resolver,{ old = oldsenv.old;
 		  env = newenv;
 		  modinfo = modinfo;
-		  labset = Labset.add l oldsenv.labset;
+		  modlabels = Labset.add l oldsenv.modlabels;
+		  objlabels = oldsenv.objlabels;
 		  revstruct = (l,SFBmodule mb)::oldsenv.revstruct;
 		  univ = Univ.union_constraints senv'.univ oldsenv.univ;
 		  (* engagement is propagated to the upper level *)
@@ -510,7 +522,8 @@ let add_module_parameter mbid mte inl senv =
 				   variant = new_variant;
 				   resolver_of_param = add_delta_resolver
 			      resolver_of_param senv.modinfo.resolver_of_param};
-		     labset = senv.labset;
+		     modlabels = senv.modlabels;
+		     objlabels = senv.objlabels;
 		     revstruct = [];
 		     univ = senv.univ;
 		     engagement = senv.engagement;
@@ -522,7 +535,7 @@ let add_module_parameter mbid mte inl senv =
 (* Interactive module types *)
 
 let start_modtype l senv =
-  check_label l senv;
+  check_modlabel l senv;
  let mp = MPdot(senv.modinfo.modpath, l) in
  let modinfo = { modpath = mp;
 		 label = l;
@@ -533,7 +546,8 @@ let start_modtype l senv =
   mp, { old = senv;
 	env = senv.env;
 	modinfo = modinfo;
-	labset = Labset.empty;
+	modlabels = Labset.empty;
+	objlabels = Labset.empty;
 	revstruct = [];
         univ = Univ.empty_constraint;
         engagement = None;
@@ -584,7 +598,8 @@ let end_modtype l senv =
     mp, { old = oldsenv.old;
 	  env = newenv;
 	  modinfo = oldsenv.modinfo;
-	  labset = Labset.add l oldsenv.labset;
+	  modlabels = Labset.add l oldsenv.modlabels;
+	  objlabels = oldsenv.objlabels;
 	  revstruct = (l,SFBmodtype mtb)::oldsenv.revstruct;
           univ = Univ.union_constraints senv.univ oldsenv.univ;
           engagement = senv.engagement;
@@ -643,7 +658,8 @@ let start_library dir senv =
   mp, { old = senv;
 	env = senv.env;
 	modinfo = modinfo;
-	labset = Labset.empty;
+	modlabels = Labset.empty;
+	objlabels = Labset.empty;
 	revstruct = [];
         univ = Univ.empty_constraint;
         engagement = None;
diff --git a/kernel/safe_typing.mli b/kernel/safe_typing.mli
index 6f46a45b..ad275d49 100644
--- a/kernel/safe_typing.mli
+++ b/kernel/safe_typing.mli
@@ -138,7 +138,7 @@ val typing : safe_environment -> constr -> judgment
 
 (** {7 Query } *)
 
-val exists_label : label -> safe_environment -> bool
+val exists_objlabel : label -> safe_environment -> bool
 
 (*spiwack: safe retroknowledge functionalities *)
 
diff --git a/kernel/subtyping.ml b/kernel/subtyping.ml
index c141a02a..08ee67b4 100644
--- a/kernel/subtyping.ml
+++ b/kernel/subtyping.ml
@@ -32,15 +32,18 @@ type namedobject =
   | Constant of constant_body
   | IndType of inductive * mutual_inductive_body
   | IndConstr of constructor * mutual_inductive_body
+
+type namedmodule =
   | Module of module_body
   | Modtype of module_type_body
 
 (* adds above information about one mutual inductive: all types and
    constructors *)
 
-let add_nameobjects_of_mib ln mib map =
-  let add_nameobjects_of_one j oib map =
-    let ip = (ln,j) in
+let add_mib_nameobjects mp l mib map =
+  let ind = make_mind mp empty_dirpath l in
+  let add_mip_nameobjects j oib map =
+    let ip = (ind,j) in
     let map =
       array_fold_right_i
       (fun i id map ->
@@ -50,22 +53,33 @@ let add_nameobjects_of_mib ln mib map =
     in
       Labmap.add (label_of_id oib.mind_typename) (IndType (ip, mib)) map
   in
-    array_fold_right_i add_nameobjects_of_one mib.mind_packets map
+  array_fold_right_i add_mip_nameobjects mib.mind_packets map
+
+
+(* creates (namedobject/namedmodule) map for the whole signature *)
+
+type labmap = { objs : namedobject Labmap.t; mods : namedmodule Labmap.t }
 
+let empty_labmap = { objs = Labmap.empty; mods = Labmap.empty }
 
-(* creates namedobject map for the whole signature *)
+let get_obj mp map l =
+  try Labmap.find l map.objs
+  with Not_found -> error_no_such_label_sub l (string_of_mp mp)
 
-let make_label_map mp list =
+let get_mod mp map l =
+  try Labmap.find l map.mods
+  with Not_found -> error_no_such_label_sub l (string_of_mp mp)
+
+let make_labmap mp list =
   let add_one (l,e) map =
-   let add_map obj = Labmap.add l obj map in
    match e with
-    | SFBconst cb -> add_map (Constant cb)
-    | SFBmind mib ->
-       add_nameobjects_of_mib (make_mind mp empty_dirpath l) mib map
-    | SFBmodule mb -> add_map (Module mb)
-    | SFBmodtype mtb -> add_map (Modtype mtb)
+    | SFBconst cb -> { map with objs = Labmap.add l (Constant cb) map.objs }
+    | SFBmind mib -> { map with objs = add_mib_nameobjects mp l mib map.objs }
+    | SFBmodule mb -> { map with mods = Labmap.add l (Module mb) map.mods }
+    | SFBmodtype mtb -> { map with mods = Labmap.add l (Modtype mtb) map.mods }
   in
-    List.fold_right add_one list Labmap.empty
+  List.fold_right add_one list empty_labmap
+
 
 let check_conv_error error why cst f env a1 a2 =
   try
@@ -299,7 +313,6 @@ let check_constant cst env mp1 l info1 cb2 spec2 subst1 subst2 =
       let ty1 = type_of_constructor cstr (mind1,mind1.mind_packets.(i)) in
       let ty2 = Typeops.type_of_constant_type env cb2.const_type in
        check_conv NotConvertibleTypeField cst conv env ty1 ty2
-   | _ -> error DefinitionFieldExpected
 
 let rec check_modules cst env msb1 msb2 subst1 subst2 =
   let mty1 = module_type_of_module None msb1 in
@@ -308,33 +321,24 @@ let rec check_modules cst env msb1 msb2 subst1 subst2 =
     cst
 
 and check_signatures cst env mp1 sig1 mp2 sig2 subst1 subst2 reso1 reso2= 
-  let map1 = make_label_map mp1 sig1 in
+  let map1 = make_labmap mp1 sig1 in
   let check_one_body cst (l,spec2) =
-    let info1 =
-      try
-	Labmap.find l map1
-      with
-	  Not_found -> error_no_such_label_sub l
-	    (string_of_mp mp1)
-    in
-      match spec2 with
+    match spec2 with
 	| SFBconst cb2 ->
-	    check_constant cst env mp1 l info1 cb2 spec2 subst1 subst2
+	    check_constant cst env mp1 l (get_obj mp1 map1 l)
+	      cb2 spec2 subst1 subst2
 	| SFBmind mib2 ->
-	    check_inductive cst env
-	      mp1 l info1 mp2 mib2 spec2 subst1 subst2 reso1 reso2
+	    check_inductive cst env mp1 l (get_obj mp1 map1 l)
+	      mp2 mib2 spec2 subst1 subst2 reso1 reso2
 	| SFBmodule msb2 ->
-	    begin
-	      match info1 with
-		| Module msb -> check_modules cst env msb msb2 
-		    subst1 subst2
-		| _ -> error_signature_mismatch l spec2 ModuleFieldExpected
+	    begin match get_mod mp1 map1 l with
+	      | Module msb -> check_modules cst env msb msb2 subst1 subst2
+	      | _ -> error_signature_mismatch l spec2 ModuleFieldExpected
 	    end
 	| SFBmodtype mtb2 ->
-	    let mtb1 =
-	      match info1 with
-		| Modtype mtb -> mtb
-		| _ -> error_signature_mismatch l spec2 ModuleTypeFieldExpected
+	    let mtb1 = match get_mod mp1 map1 l with
+	      | Modtype mtb -> mtb
+	      | _ -> error_signature_mismatch l spec2 ModuleTypeFieldExpected
 	    in
 	    let env = add_module (module_body_of_type mtb2.typ_mp mtb2)
 	      (add_module (module_body_of_type mtb1.typ_mp mtb1) env) in
diff --git a/kernel/term.ml b/kernel/term.ml
index dcb63cf7..46bc7c56 100644
--- a/kernel/term.ml
+++ b/kernel/term.ml
@@ -322,6 +322,7 @@ let isCast c = match kind_of_term c with Cast _ -> true | _ -> false
 
 (* Tests if a de Bruijn index *)
 let isRel c = match kind_of_term c with Rel _ -> true | _ -> false
+let isRelN n c = match kind_of_term c with Rel n' -> n = n' | _ -> false
 
 (* Tests if a variable *)
 let isVar c = match kind_of_term c with Var _ -> true | _ -> false
diff --git a/kernel/term.mli b/kernel/term.mli
index d5899f18..e83be6d6 100644
--- a/kernel/term.mli
+++ b/kernel/term.mli
@@ -229,8 +229,9 @@ val kind_of_type : types -> (constr, types) kind_of_type
 (** {6 Simple term case analysis. } *)
 
 val isRel  : constr -> bool
+val isRelN : int -> constr -> bool
 val isVar  : constr -> bool
-val isVarId  : identifier -> constr -> bool
+val isVarId : identifier -> constr -> bool
 val isInd  : constr -> bool
 val isEvar : constr -> bool
 val isMeta : constr -> bool
@@ -435,8 +436,7 @@ val it_mkProd_or_LetIn : types -> rel_context -> types
 (** {6 Other term destructors. } *)
 
 (** Transforms a product term {% $ %}(x_1:T_1)..(x_n:T_n)T{% $ %} into the pair
-   {% $ %}([(x_n,T_n);...;(x_1,T_1)],T){% $ %}, where {% $ %}T{% $ %} is not a product.
-   It includes also local definitions *)
+   {% $ %}([(x_n,T_n);...;(x_1,T_1)],T){% $ %}, where {% $ %}T{% $ %} is not a product. *)
 val decompose_prod : constr -> (name*constr) list * constr
 
 (** Transforms a lambda term {% $ %}[x_1:T_1]..[x_n:T_n]T{% $ %} into the pair
diff --git a/kernel/univ.ml b/kernel/univ.ml
index a8934544..0193542a 100644
--- a/kernel/univ.ml
+++ b/kernel/univ.ml
@@ -260,46 +260,62 @@ type order = EQ | LT | LE | NLE
 
 (** [compare_neq] : is [arcv] in the transitive upward closure of [arcu] ?
 
-  We try to avoid visiting unneeded parts of this transitive closure,
-  by stopping as soon as [arcv] is encountered. During the recursive
-  traversal, [lt_done] and [le_done] are universes we have already
-  visited, they do not contain [arcv]. The 3rd arg is
-  [(lt_todo,le_todo)], two lists of universes not yet considered,
-  known to be above [arcu], strictly or not.
+  In [strict] mode, we fully distinguish between LE and LT, while in
+  non-strict mode, we simply answer LE for both situations.
+
+  If [arcv] is encountered in a LT part, we could directly answer
+  without visiting unneeded parts of this transitive closure.
+  In [strict] mode, if [arcv] is encountered in a LE part, we could only
+  change the default answer (1st arg [c]) from NLE to LE, since a strict
+  constraint may appear later. During the recursive traversal,
+  [lt_done] and [le_done] are universes we have already visited,
+  they do not contain [arcv]. The 4rd arg is [(lt_todo,le_todo)],
+  two lists of universes not yet considered, known to be above [arcu],
+  strictly or not.
 
   We use depth-first search, but the presence of [arcv] in [new_lt]
   is checked as soon as possible : this seems to be slightly faster
   on a test.
 *)
 
-let compare_neq g arcu arcv =
-  let rec cmp lt_done le_done = function
-  | [],[] -> NLE
+let compare_neq strict g arcu arcv =
+  let rec cmp c lt_done le_done = function
+  | [],[] -> c
   | arc::lt_todo, le_todo ->
     if List.memq arc lt_done then
-      cmp lt_done le_done (lt_todo,le_todo)
+      cmp c lt_done le_done (lt_todo,le_todo)
     else
       let lt_new = can g (arc.lt@arc.le) in
-      if List.memq arcv lt_new then LT
-      else cmp (arc::lt_done) le_done (lt_new@lt_todo,le_todo)
+      if List.memq arcv lt_new then
+	if strict then LT else LE
+      else cmp c (arc::lt_done) le_done (lt_new@lt_todo,le_todo)
   | [], arc::le_todo ->
-    if arc == arcv then LE
-    (* No need to continue inspecting universes above arc:
-       if arcv is strictly above arc, then we would have a cycle *)
+    if arc == arcv then
+      (* No need to continue inspecting universes above arc:
+	 if arcv is strictly above arc, then we would have a cycle.
+         But we cannot answer LE yet, a stronger constraint may
+	 come later from [le_todo]. *)
+      if strict then cmp LE lt_done le_done ([],le_todo) else LE
     else
       if (List.memq arc lt_done) || (List.memq arc le_done) then
-	cmp lt_done le_done ([],le_todo)
+	cmp c lt_done le_done ([],le_todo)
       else
 	let lt_new = can g arc.lt in
-	if List.memq arcv lt_new then LT
+	if List.memq arcv lt_new then
+	  if strict then LT else LE
 	else
 	  let le_new = can g arc.le in
-	  cmp lt_done (arc::le_done) (lt_new, le_new@le_todo)
+	  cmp c lt_done (arc::le_done) (lt_new, le_new@le_todo)
   in
-  cmp [] [] ([],[arcu])
+  cmp NLE [] [] ([],[arcu])
 
 let compare g arcu arcv =
-  if arcu == arcv then EQ else compare_neq g arcu arcv
+  if arcu == arcv then EQ else compare_neq true g arcu arcv
+
+let is_leq g arcu arcv =
+  arcu == arcv || (compare_neq false g arcu arcv = LE)
+
+let is_lt g arcu arcv = (compare g arcu arcv = LT)
 
 (* Invariants : compare(u,v) = EQ <=> compare(v,u) = EQ
                 compare(u,v) = LT or LE => compare(v,u) = NLE
@@ -337,11 +353,11 @@ let rec check_eq g u v =
 let compare_greater g strict u v =
   let g, arcu = safe_repr g u in
   let g, arcv = safe_repr g v in
-  if not strict && arcv == snd (safe_repr g UniverseLevel.Set) then true else
-  match compare g arcv arcu with
-    | (EQ|LE) -> not strict
-    | LT -> true
-    | NLE -> false
+  if strict then
+    is_lt g arcv arcu
+  else
+    arcv == snd (safe_repr g UniverseLevel.Set) || is_leq g arcv arcu
+
 (*
 let compare_greater g strict u v =
   let b = compare_greater g strict u v in
@@ -368,9 +384,8 @@ let setlt g arcu arcv =
 (* checks that non-redundant *)
 let setlt_if (g,arcu) v =
   let arcv = repr g v in
-  match compare g arcu arcv with
-  | LT -> g, arcu
-  | _ -> setlt g arcu arcv
+  if is_lt g arcu arcv then g, arcu
+  else setlt g arcu arcv
 
 (* setleq : UniverseLevel.t -> UniverseLevel.t -> unit *)
 (* forces u >= v *)
@@ -383,9 +398,8 @@ let setleq g arcu arcv =
 (* checks that non-redundant *)
 let setleq_if (g,arcu) v =
   let arcv = repr g v in
-  match compare g arcu arcv with
-  | NLE -> setleq g arcu arcv
-  | _ -> g, arcu
+  if is_leq g arcu arcv then g, arcu
+  else setleq g arcu arcv
 
 (* merge : UniverseLevel.t -> UniverseLevel.t -> unit *)
 (* we assume  compare(u,v) = LE *)
@@ -429,14 +443,12 @@ let error_inconsistency o u v = raise (UniverseInconsistency (o,Atom u,Atom v))
 let enforce_univ_leq u v g =
   let g,arcu = safe_repr g u in
   let g,arcv = safe_repr g v in
-  match compare g arcu arcv with
-    | NLE ->
-	(match compare g arcv arcu with
-           | LT -> error_inconsistency Le u v
-           | LE -> merge g arcv arcu
-           | NLE -> fst (setleq g arcu arcv)
-           | EQ -> anomaly "Univ.compare")
-    | _ -> g
+  if is_leq g arcu arcv then g
+  else match compare g arcv arcu with
+    | LT -> error_inconsistency Le u v
+    | LE -> merge g arcv arcu
+    | NLE -> fst (setleq g arcu arcv)
+    | EQ -> anomaly "Univ.compare"
 
 (* enforc_univ_eq : UniverseLevel.t -> UniverseLevel.t -> unit *)
 (* enforc_univ_eq u v will force u=v if possible, will fail otherwise *)
@@ -463,9 +475,8 @@ let enforce_univ_lt u v g =
     | LE -> fst (setlt g arcu arcv)
     | EQ -> error_inconsistency Lt u v
     | NLE ->
-	(match compare g arcv arcu with
-           | NLE -> fst (setlt g arcu arcv)
-           | _ -> error_inconsistency Lt u v)
+      if is_leq g arcv arcu then error_inconsistency Lt u v
+      else fst (setlt g arcu arcv)
 
 (* Constraints and sets of consrtaints. *)
 
@@ -480,7 +491,13 @@ let enforce_constraint cst g =
 module Constraint = Set.Make(
   struct
     type t = univ_constraint
-    let compare = Pervasives.compare
+    let compare (u,c,v) (u',c',v') =
+      let i = Pervasives.compare c c' in
+      if i <> 0 then i
+      else
+	let i' = UniverseLevel.compare u u' in
+	if i' <> 0 then i'
+	else UniverseLevel.compare v v'
   end)
 
 type constraints = Constraint.t
@@ -784,6 +801,14 @@ let no_upper_constraints u cst =
   | Atom u -> Constraint.for_all (fun (u1,_,_) -> u1 <> u) cst
   | Max _ -> anomaly "no_upper_constraints"
 
+(* Is u mentionned in v (or equals to v) ? *)
+
+let univ_depends u v =
+  match u, v with
+    | Atom u, Atom v -> u = v
+    | Atom u, Max (gel,gtl) -> List.mem u gel || List.mem u gtl
+    | _ -> anomaly "univ_depends given a non-atomic 1st arg"
+
 (* Pretty-printing *)
 
 let pr_arc = function
diff --git a/kernel/univ.mli b/kernel/univ.mli
index 8b3f6291..e4e66915 100644
--- a/kernel/univ.mli
+++ b/kernel/univ.mli
@@ -91,6 +91,10 @@ val subst_large_constraints :
 
 val no_upper_constraints : universe -> constraints -> bool
 
+(** Is u mentionned in v (or equals to v) ? *)
+
+val univ_depends : universe -> universe -> bool
+
 (** {6 Pretty-printing of universes. } *)
 
 val pr_uni_level : universe_level -> Pp.std_ppcmds
-- 
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