Adding a new folder corresponding to the low-level part of the pretyper

together with the tactic monad.

The move is not complete yet, because some file candidates for this directory
have almost useless dependencies in other ones that should not be moved.

1 files changed, 1769 insertions, 0 deletions

diff --git a/engine/evd.ml b/engine/evd.ml
new file mode 100644
index 0000000000..454c51195b
--- /dev/null
+++ b/engine/evd.ml
@@ -0,0 +1,1769 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+open Pp
+open Errors
+open Util
+open Names
+open Nameops
+open Term
+open Vars
+open Termops
+open Environ
+open Globnames
+
+(** Generic filters *)
+module Filter :
+sig
+  type t
+  val equal : t -> t -> bool
+  val identity : t
+  val filter_list : t -> 'a list -> 'a list
+  val filter_array : t -> 'a array -> 'a array
+  val extend : int -> t -> t
+  val compose : t -> t -> t
+  val apply_subfilter : t -> bool list -> t
+  val restrict_upon : t -> int -> (int -> bool) -> t option
+  val map_along : (bool -> 'a -> bool) -> t -> 'a list -> t
+  val make : bool list -> t
+  val repr :  t -> bool list option
+end =
+struct
+  type t = bool list option
+  (** We guarantee through the interface that if a filter is [Some _] then it
+      contains at least one [false] somewhere. *)
+
+  let identity = None
+
+  let rec equal l1 l2 = match l1, l2 with
+  | [], [] -> true
+  | h1 :: l1, h2 :: l2 ->
+    (if h1 then h2 else not h2) && equal l1 l2
+  | _ -> false
+
+  let equal l1 l2 = match l1, l2 with
+  | None, None -> true
+  | Some _, None | None, Some _ -> false
+  | Some l1, Some l2 -> equal l1 l2
+
+  let rec is_identity = function
+  | [] -> true
+  | true :: l -> is_identity l
+  | false :: _ -> false
+
+  let normalize f = if is_identity f then None else Some f
+
+  let filter_list f l = match f with
+  | None -> l
+  | Some f -> CList.filter_with f l
+
+  let filter_array f v = match f with
+  | None -> v
+  | Some f -> CArray.filter_with f v
+
+  let rec extend n l =
+    if n = 0 then l
+    else extend (pred n) (true :: l)
+
+  let extend n = function
+  | None -> None
+  | Some f -> Some (extend n f)
+
+  let compose f1 f2 = match f1 with
+  | None -> f2
+  | Some f1 ->
+    match f2 with
+    | None -> None
+    | Some f2 -> normalize (CList.filter_with f1 f2)
+
+  let apply_subfilter_array filter subfilter =
+    (** In both cases we statically know that the argument will contain at
+        least one [false] *)
+    match filter with
+    | None -> Some (Array.to_list subfilter)
+    | Some f ->
+    let len = Array.length subfilter in
+    let fold b (i, ans) =
+      if b then
+        let () = assert (0 <= i) in
+        (pred i, Array.unsafe_get subfilter i :: ans)
+      else
+        (i, false :: ans)
+    in
+    Some (snd (List.fold_right fold f (pred len, [])))
+
+  let apply_subfilter filter subfilter =
+    apply_subfilter_array filter (Array.of_list subfilter)
+
+  let restrict_upon f len p =
+    let newfilter = Array.init len p in
+    if Array.for_all (fun id -> id) newfilter then None
+    else
+      Some (apply_subfilter_array f newfilter)
+
+  let map_along f flt l =
+    let ans = match flt with
+    | None -> List.map (fun x -> f true x) l
+    | Some flt -> List.map2 f flt l
+    in
+    normalize ans
+
+  let make l = normalize l
+
+  let repr f = f
+
+end
+
+(* The kinds of existential variables are now defined in [Evar_kinds] *)
+
+(* The type of mappings for existential variables *)
+
+module Dummy = struct end
+module Store = Store.Make(Dummy)
+
+type evar = Term.existential_key
+
+let string_of_existential evk = "?X" ^ string_of_int (Evar.repr evk)
+
+type evar_body =
+  | Evar_empty
+  | Evar_defined of constr
+
+type evar_info = {
+  evar_concl : constr;
+  evar_hyps : named_context_val;
+  evar_body : evar_body;
+  evar_filter : Filter.t;
+  evar_source : Evar_kinds.t Loc.located;
+  evar_candidates : constr list option; (* if not None, list of allowed instances *)
+  evar_extra : Store.t }
+
+let make_evar hyps ccl = {
+  evar_concl = ccl;
+  evar_hyps = hyps;
+  evar_body = Evar_empty;
+  evar_filter = Filter.identity;
+  evar_source = (Loc.ghost,Evar_kinds.InternalHole);
+  evar_candidates = None;
+  evar_extra = Store.empty
+}
+
+let instance_mismatch () =
+  anomaly (Pp.str "Signature and its instance do not match")
+
+let evar_concl evi = evi.evar_concl
+
+let evar_filter evi = evi.evar_filter
+
+let evar_body evi = evi.evar_body
+
+let evar_context evi = named_context_of_val evi.evar_hyps
+
+let evar_filtered_context evi =
+  Filter.filter_list (evar_filter evi) (evar_context evi)
+
+let evar_hyps evi = evi.evar_hyps
+
+let evar_filtered_hyps evi = match Filter.repr (evar_filter evi) with
+| None -> evar_hyps evi
+| Some filter ->
+  let rec make_hyps filter ctxt = match filter, ctxt with
+  | [], [] -> empty_named_context_val
+  | false :: filter, _ :: ctxt -> make_hyps filter ctxt
+  | true :: filter, decl :: ctxt ->
+    let hyps = make_hyps filter ctxt in
+    push_named_context_val decl hyps
+  | _ -> instance_mismatch ()
+  in
+  make_hyps filter (evar_context evi)
+
+let evar_env evi = Global.env_of_context evi.evar_hyps
+
+let evar_filtered_env evi = match Filter.repr (evar_filter evi) with
+| None -> evar_env evi
+| Some filter ->
+  let rec make_env filter ctxt = match filter, ctxt with
+  | [], [] -> reset_context (Global.env ())
+  | false :: filter, _ :: ctxt -> make_env filter ctxt
+  | true :: filter, decl :: ctxt ->
+    let env = make_env filter ctxt in
+    push_named decl env
+  | _ -> instance_mismatch ()
+  in
+  make_env filter (evar_context evi)
+
+let map_evar_body f = function
+  | Evar_empty -> Evar_empty
+  | Evar_defined d -> Evar_defined (f d)
+
+let map_evar_info f evi =
+  {evi with
+    evar_body = map_evar_body f evi.evar_body;
+    evar_hyps = map_named_val f evi.evar_hyps;
+    evar_concl = f evi.evar_concl;
+    evar_candidates = Option.map (List.map f) evi.evar_candidates }
+
+let evar_ident_info evi =
+  match evi.evar_source with
+  | _,Evar_kinds.ImplicitArg (c,(n,Some id),b) -> id
+  | _,Evar_kinds.VarInstance id -> id
+  | _,Evar_kinds.GoalEvar -> Id.of_string "Goal"
+  | _ ->
+      let env = reset_with_named_context evi.evar_hyps (Global.env()) in
+      Namegen.id_of_name_using_hdchar env evi.evar_concl Anonymous
+
+(* This exception is raised by *.existential_value *)
+exception NotInstantiatedEvar
+
+(* Note: let-in contributes to the instance *)
+
+let evar_instance_array test_id info args =
+  let len = Array.length args in
+  let rec instrec filter ctxt i = match filter, ctxt with
+  | [], [] ->
+    if Int.equal i len then []
+    else instance_mismatch ()
+  | false :: filter, _ :: ctxt ->
+    instrec filter ctxt i
+  | true :: filter, (id,_,_ as d) :: ctxt ->
+    if i < len then
+      let c = Array.unsafe_get args i in
+      if test_id d c then instrec filter ctxt (succ i)
+      else (id, c) :: instrec filter ctxt (succ i)
+    else instance_mismatch ()
+  | _ -> instance_mismatch ()
+  in
+  match Filter.repr (evar_filter info) with
+  | None ->
+    let map i (id,_,_ as d) =
+      if (i < len) then
+        let c = Array.unsafe_get args i in
+        if test_id d c then None else Some (id,c)
+      else instance_mismatch ()
+    in
+    List.map_filter_i map (evar_context info)
+  | Some filter ->
+    instrec filter (evar_context info) 0
+
+let make_evar_instance_array info args =
+  evar_instance_array (fun (id,_,_) -> isVarId id) info args
+
+let instantiate_evar_array info c args =
+  let inst = make_evar_instance_array info args in
+  match inst with
+  | [] -> c
+  | _ -> replace_vars inst c
+
+module StringOrd = struct type t = string let compare = String.compare end
+module UNameMap = struct
+    
+  include Map.Make(StringOrd)
+    
+  let union s t = 
+    if s == t then s
+    else
+      merge (fun k l r -> 
+	match l, r with
+	| Some _, _ -> l
+	| _, _ -> r) s t
+end
+
+(* 2nd part used to check consistency on the fly. *)
+type evar_universe_context = 
+ { uctx_names : Univ.Level.t UNameMap.t * string Univ.LMap.t;
+   uctx_local : Univ.universe_context_set; (** The local context of variables *)
+    uctx_univ_variables : Universes.universe_opt_subst;
+      (** The local universes that are unification variables *)
+    uctx_univ_algebraic : Univ.universe_set; 
+    (** The subset of unification variables that
+	can be instantiated with algebraic universes as they appear in types 
+	and universe instances only. *)
+    uctx_universes : Univ.universes; (** The current graph extended with the local constraints *)
+    uctx_initial_universes : Univ.universes; (** The graph at the creation of the evar_map *)
+  }
+  
+let empty_evar_universe_context = 
+  { uctx_names = UNameMap.empty, Univ.LMap.empty;
+    uctx_local = Univ.ContextSet.empty;
+    uctx_univ_variables = Univ.LMap.empty;
+    uctx_univ_algebraic = Univ.LSet.empty;
+    uctx_universes = Univ.initial_universes;
+    uctx_initial_universes = Univ.initial_universes }
+
+let evar_universe_context_from e = 
+  let u = universes e in
+    {empty_evar_universe_context with 
+      uctx_universes = u; uctx_initial_universes = u}
+
+let is_empty_evar_universe_context ctx =
+  Univ.ContextSet.is_empty ctx.uctx_local && 
+    Univ.LMap.is_empty ctx.uctx_univ_variables
+
+let union_evar_universe_context ctx ctx' =
+  if ctx == ctx' then ctx
+  else if is_empty_evar_universe_context ctx' then ctx
+  else
+    let local = Univ.ContextSet.union ctx.uctx_local ctx'.uctx_local in
+    let names = UNameMap.union (fst ctx.uctx_names) (fst ctx'.uctx_names) in
+    let names_rev = Univ.LMap.union (snd ctx.uctx_names) (snd ctx'.uctx_names) in
+      { uctx_names = (names, names_rev);
+	uctx_local = local;
+	uctx_univ_variables = 
+	  Univ.LMap.subst_union ctx.uctx_univ_variables ctx'.uctx_univ_variables;
+	uctx_univ_algebraic = 
+	  Univ.LSet.union ctx.uctx_univ_algebraic ctx'.uctx_univ_algebraic;
+	uctx_initial_universes = ctx.uctx_initial_universes;
+	uctx_universes = 
+	  if local == ctx.uctx_local then ctx.uctx_universes
+	  else
+	    let cstrsr = Univ.ContextSet.constraints ctx'.uctx_local in
+	      Univ.merge_constraints cstrsr ctx.uctx_universes }
+
+(* let union_evar_universe_context_key = Profile.declare_profile "union_evar_universe_context";; *)
+(* let union_evar_universe_context =  *)
+(*   Profile.profile2 union_evar_universe_context_key union_evar_universe_context;; *)
+
+type 'a in_evar_universe_context = 'a * evar_universe_context
+
+let evar_universe_context_set ctx = ctx.uctx_local
+let evar_universe_context_constraints ctx = snd ctx.uctx_local
+let evar_context_universe_context ctx = Univ.ContextSet.to_context ctx.uctx_local
+let evar_universe_context_of ctx = { empty_evar_universe_context with uctx_local = ctx }
+let evar_universe_context_subst ctx = ctx.uctx_univ_variables
+
+let instantiate_variable l b v =
+  (* let b = Univ.subst_large_constraint (Univ.Universe.make l) Univ.type0m_univ b in *)
+  (* if Univ.univ_depends (Univ.Universe.make l) b then  *)
+  (*   error ("Occur-check in universe variable instantiation") *)
+  (* else *) v := Univ.LMap.add l (Some b) !v
+
+exception UniversesDiffer
+
+let process_universe_constraints univs vars alg cstrs =
+  let vars = ref vars in
+  let normalize = Universes.normalize_universe_opt_subst vars in
+  let rec unify_universes fo l d r local =
+    let l = normalize l and r = normalize r in
+      if Univ.Universe.equal l r then local
+      else 
+	let varinfo x = 
+	  match Univ.Universe.level x with
+	  | None -> Inl x
+	  | Some l -> Inr (l, Univ.LMap.mem l !vars, Univ.LSet.mem l alg)
+	in
+	  if d == Universes.ULe then
+	    if Univ.check_leq univs l r then
+	      (** Keep Prop/Set <= var around if var might be instantiated by prop or set
+		  later. *)
+	      if Univ.Universe.is_level l then 
+		match Univ.Universe.level r with
+		| Some r ->
+		  Univ.Constraint.add (Option.get (Univ.Universe.level l),Univ.Le,r) local
+		| _ -> local
+	      else local
+	    else
+	      match Univ.Universe.level r with
+	      | None -> error ("Algebraic universe on the right")
+	      | Some rl ->
+		if Univ.Level.is_small rl then
+		  let levels = Univ.Universe.levels l in
+		    Univ.LSet.fold (fun l local ->
+		      if Univ.Level.is_small l || Univ.LMap.mem l !vars then
+			Univ.enforce_eq (Univ.Universe.make l) r local
+		      else raise (Univ.UniverseInconsistency (Univ.Le, Univ.Universe.make l, r, None)))
+		      levels local
+		else
+		  Univ.enforce_leq l r local
+	  else if d == Universes.ULub then
+	    match varinfo l, varinfo r with
+	    | (Inr (l, true, _), Inr (r, _, _)) 
+	    | (Inr (r, _, _), Inr (l, true, _)) -> 
+	      instantiate_variable l (Univ.Universe.make r) vars; 
+	      Univ.enforce_eq_level l r local
+	    | Inr (_, _, _), Inr (_, _, _) ->
+	      unify_universes true l Universes.UEq r local
+	    | _, _ -> assert false
+	  else (* d = Universes.UEq *)
+	    match varinfo l, varinfo r with
+	    | Inr (l', lloc, _), Inr (r', rloc, _) ->
+	      let () = 
+		if lloc then
+		  instantiate_variable l' r vars
+		else if rloc then 
+		  instantiate_variable r' l vars
+		else if not (Univ.check_eq univs l r) then
+		  (* Two rigid/global levels, none of them being local,
+		     one of them being Prop/Set, disallow *)
+		  if Univ.Level.is_small l' || Univ.Level.is_small r' then
+		    raise (Univ.UniverseInconsistency (Univ.Eq, l, r, None))
+		  else
+		    if fo then 
+		      raise UniversesDiffer
+	      in
+	        Univ.enforce_eq_level l' r' local
+           | _, _ (* One of the two is algebraic or global *) -> 
+	     if Univ.check_eq univs l r then local
+	     else raise (Univ.UniverseInconsistency (Univ.Eq, l, r, None))
+  in
+  let local = 
+    Universes.Constraints.fold (fun (l,d,r) local -> unify_universes false l d r local)
+      cstrs Univ.Constraint.empty
+  in
+    !vars, local
+
+let add_constraints_context ctx cstrs =
+  let univs, local = ctx.uctx_local in
+  let cstrs' = Univ.Constraint.fold (fun (l,d,r) acc -> 
+    let l = Univ.Universe.make l and r = Univ.Universe.make r in
+    let cstr' = 
+      if d == Univ.Lt then (Univ.Universe.super l, Universes.ULe, r)
+      else (l, (if d == Univ.Le then Universes.ULe else Universes.UEq), r)
+    in Universes.Constraints.add cstr' acc)
+    cstrs Universes.Constraints.empty
+  in
+  let vars, local' =
+    process_universe_constraints ctx.uctx_universes
+      ctx.uctx_univ_variables ctx.uctx_univ_algebraic
+      cstrs'
+  in
+    { ctx with uctx_local = (univs, Univ.Constraint.union local local');
+      uctx_univ_variables = vars;
+      uctx_universes = Univ.merge_constraints cstrs ctx.uctx_universes }
+
+(* let addconstrkey = Profile.declare_profile "add_constraints_context";; *)
+(* let add_constraints_context = Profile.profile2 addconstrkey add_constraints_context;; *)
+
+let add_universe_constraints_context ctx cstrs =
+  let univs, local = ctx.uctx_local in
+  let vars, local' = 
+    process_universe_constraints ctx.uctx_universes 
+      ctx.uctx_univ_variables ctx.uctx_univ_algebraic 
+      cstrs 
+  in
+    { ctx with uctx_local = (univs, Univ.Constraint.union local local');
+      uctx_univ_variables = vars;
+      uctx_universes = Univ.merge_constraints local' ctx.uctx_universes }
+
+(* let addunivconstrkey = Profile.declare_profile "add_universe_constraints_context";; *)
+(* let add_universe_constraints_context =  *)
+(*   Profile.profile2 addunivconstrkey add_universe_constraints_context;; *)
+(*******************************************************************)
+(* Metamaps *)
+
+(*******************************************************************)
+(*            Constraints for existential variables                *)
+(*******************************************************************)
+
+type 'a freelisted = {
+  rebus : 'a;
+  freemetas : Int.Set.t }
+
+(* Collects all metavars appearing in a constr *)
+let metavars_of c =
+  let rec collrec acc c =
+    match kind_of_term c with
+      | Meta mv -> Int.Set.add mv acc
+      | _         -> fold_constr collrec acc c
+  in
+  collrec Int.Set.empty c
+
+let mk_freelisted c =
+  { rebus = c; freemetas = metavars_of c }
+
+let map_fl f cfl = { cfl with rebus=f cfl.rebus }
+
+(* Status of an instance found by unification wrt to the meta it solves:
+  - a supertype of the meta (e.g. the solution to ?X <= T is a supertype of ?X)
+  - a subtype of the meta (e.g. the solution to T <= ?X is a supertype of ?X)
+  - a term that can be eta-expanded n times while still being a solution
+    (e.g. the solution [P] to [?X u v = P u v] can be eta-expanded twice)
+*)
+
+type instance_constraint = IsSuperType | IsSubType | Conv
+
+let eq_instance_constraint c1 c2 = c1 == c2
+
+(* Status of the unification of the type of an instance against the type of
+     the meta it instantiates:
+   - CoerceToType means that the unification of types has not been done
+     and that a coercion can still be inserted: the meta should not be
+     substituted freely (this happens for instance given via the
+     "with" binding clause).
+   - TypeProcessed means that the information obtainable from the
+     unification of types has been extracted.
+   - TypeNotProcessed means that the unification of types has not been
+     done but it is known that no coercion may be inserted: the meta
+     can be substituted freely.
+*)
+
+type instance_typing_status =
+    CoerceToType | TypeNotProcessed | TypeProcessed
+
+(* Status of an instance together with the status of its type unification *)
+
+type instance_status = instance_constraint * instance_typing_status
+
+(* Clausal environments *)
+
+type clbinding =
+  | Cltyp of Name.t * constr freelisted
+  | Clval of Name.t * (constr freelisted * instance_status) * constr freelisted
+
+let map_clb f = function
+  | Cltyp (na,cfl) -> Cltyp (na,map_fl f cfl)
+  | Clval (na,(cfl1,pb),cfl2) -> Clval (na,(map_fl f cfl1,pb),map_fl f cfl2)
+
+(* name of defined is erased (but it is pretty-printed) *)
+let clb_name = function
+    Cltyp(na,_) -> (na,false)
+  | Clval (na,_,_) -> (na,true)
+
+(***********************)
+
+module Metaset = Int.Set
+
+module Metamap = Int.Map
+
+let metamap_to_list m =
+  Metamap.fold (fun n v l -> (n,v)::l) m []
+
+(*************************)
+(* Unification state *)
+
+type conv_pb = Reduction.conv_pb
+type evar_constraint = conv_pb * Environ.env * constr * constr
+
+module EvMap = Evar.Map
+
+type evar_map = {
+  (** Existential variables *)
+  defn_evars : evar_info EvMap.t;
+  undf_evars : evar_info EvMap.t;
+  evar_names : Id.t EvMap.t * existential_key Idmap.t;
+  (** Universes *)
+  universes  : evar_universe_context;
+  (** Conversion problems *)
+  conv_pbs   : evar_constraint list;
+  last_mods  : Evar.Set.t;
+  (** Metas *)
+  metas      : clbinding Metamap.t;
+  (** Interactive proofs *)
+  effects    : Declareops.side_effects;
+  future_goals : Evar.t list; (** list of newly created evars, to be
+                                  eventually turned into goals if not solved.*)
+  principal_future_goal : Evar.t option; (** if [Some e], [e] must be
+                                             contained
+                                             [future_goals]. The evar
+                                             [e] will inherit
+                                             properties (now: the
+                                             name) of the evar which
+                                             will be instantiated with
+                                             a term containing [e]. *)
+}
+
+(*** Lifting primitive from Evar.Map. ***)
+
+let add_name_newly_undefined naming evk evi (evtoid,idtoev) =
+  let id = match naming with
+  | Misctypes.IntroAnonymous ->
+      let id = evar_ident_info evi in
+      Namegen.next_ident_away_from id (fun id -> Idmap.mem id idtoev)
+  | Misctypes.IntroIdentifier id ->
+      let id' =
+        Namegen.next_ident_away_from id (fun id -> Idmap.mem id idtoev) in
+      if not (Names.Id.equal id id') then
+        user_err_loc
+          (Loc.ghost,"",str "Already an existential evar of name " ++ pr_id id);
+      id'
+  | Misctypes.IntroFresh id ->
+      Namegen.next_ident_away_from id (fun id -> Idmap.mem id idtoev) in
+  (EvMap.add evk id evtoid, Idmap.add id evk idtoev)
+
+let add_name_undefined naming evk evi (evtoid,idtoev as evar_names) =
+  if EvMap.mem evk evtoid then
+    evar_names
+  else
+    add_name_newly_undefined naming evk evi evar_names
+
+let remove_name_defined evk (evtoid,idtoev) =
+  let id = EvMap.find evk evtoid in
+  (EvMap.remove evk evtoid, Idmap.remove id idtoev)
+
+let remove_name_possibly_already_defined evk evar_names =
+  try remove_name_defined evk evar_names
+  with Not_found -> evar_names
+
+let rename evk id evd =
+  let (evtoid,idtoev) = evd.evar_names in
+  let id' = EvMap.find evk evtoid in
+  if Idmap.mem id idtoev then anomaly (str "Evar name already in use");
+  { evd with evar_names =
+      (EvMap.add evk id evtoid (* overwrite old name *),
+       Idmap.add id evk (Idmap.remove id' idtoev)) }
+
+let reassign_name_defined evk evk' (evtoid,idtoev) =
+  let id = EvMap.find evk evtoid in
+  (EvMap.add evk' id (EvMap.remove evk evtoid),
+   Idmap.add id evk' (Idmap.remove id idtoev))
+
+let add d e i = match i.evar_body with
+| Evar_empty ->
+  let evar_names = add_name_undefined Misctypes.IntroAnonymous e i d.evar_names in
+  { d with undf_evars = EvMap.add e i d.undf_evars; evar_names }
+| Evar_defined _ ->
+  let evar_names = remove_name_possibly_already_defined e d.evar_names in
+  { d with defn_evars = EvMap.add e i d.defn_evars; evar_names }
+
+let remove d e =
+  let undf_evars = EvMap.remove e d.undf_evars in
+  let defn_evars = EvMap.remove e d.defn_evars in
+  { d with undf_evars; defn_evars; }
+
+let find d e =
+  try EvMap.find e d.undf_evars
+  with Not_found -> EvMap.find e d.defn_evars
+
+let find_undefined d e = EvMap.find e d.undf_evars
+
+let mem d e = EvMap.mem e d.undf_evars || EvMap.mem e d.defn_evars
+
+(* spiwack: this function loses information from the original evar_map
+   it might be an idea not to export it. *)
+let to_list d =
+  (* Workaround for change in Map.fold behavior in ocaml 3.08.4 *)
+  let l = ref [] in
+  EvMap.iter (fun evk x -> l := (evk,x)::!l) d.defn_evars;
+  EvMap.iter (fun evk x -> l := (evk,x)::!l) d.undf_evars;
+  !l
+
+let undefined_map d = d.undf_evars
+
+let drop_all_defined d = { d with defn_evars = EvMap.empty }
+
+(* spiwack: not clear what folding over an evar_map, for now we shall
+    simply fold over the inner evar_map. *)
+let fold f d a =
+  EvMap.fold f d.defn_evars (EvMap.fold f d.undf_evars a)
+
+let fold_undefined f d a = EvMap.fold f d.undf_evars a
+
+let raw_map f d =
+  let f evk info =
+    let ans = f evk info in
+    let () = match info.evar_body, ans.evar_body with
+    | Evar_defined _, Evar_empty
+    | Evar_empty, Evar_defined _ ->
+      anomaly (str "Unrespectful mapping function.")
+    | _ -> ()
+    in
+    ans
+  in
+  let defn_evars = EvMap.smartmapi f d.defn_evars in
+  let undf_evars = EvMap.smartmapi f d.undf_evars in
+  { d with defn_evars; undf_evars; }
+
+let raw_map_undefined f d =
+  let f evk info =
+    let ans = f evk info in
+    let () = match ans.evar_body with
+    | Evar_defined _ ->
+      anomaly (str "Unrespectful mapping function.")
+    | _ -> ()
+    in
+    ans
+  in
+  { d with undf_evars = EvMap.smartmapi f d.undf_evars; }
+
+let is_evar = mem
+
+let is_defined d e = EvMap.mem e d.defn_evars
+
+let is_undefined d e = EvMap.mem e d.undf_evars
+
+let existential_value d (n, args) =
+  let info = find d n in
+  match evar_body info with
+  | Evar_defined c ->
+    instantiate_evar_array info c args
+  | Evar_empty ->
+    raise NotInstantiatedEvar
+
+let existential_opt_value d ev =
+  try Some (existential_value d ev)
+  with NotInstantiatedEvar -> None
+
+let existential_type d (n, args) =
+  let info =
+    try find d n
+    with Not_found ->
+      anomaly (str "Evar " ++ str (string_of_existential n) ++ str " was not declared") in
+  instantiate_evar_array info info.evar_concl args
+
+let add_constraints d c =
+  { d with universes = add_constraints_context d.universes c }
+
+let add_universe_constraints d c = 
+  { d with universes = add_universe_constraints_context d.universes c }
+
+(*** /Lifting... ***)
+
+(* evar_map are considered empty disregarding histories *)
+let is_empty d =
+  EvMap.is_empty d.defn_evars &&
+  EvMap.is_empty d.undf_evars &&
+  List.is_empty d.conv_pbs &&
+  Metamap.is_empty d.metas
+
+let cmap f evd = 
+  { evd with
+      metas = Metamap.map (map_clb f) evd.metas;
+      defn_evars = EvMap.map (map_evar_info f) evd.defn_evars;
+      undf_evars = EvMap.map (map_evar_info f) evd.defn_evars
+  }
+
+(* spiwack: deprecated *)
+let create_evar_defs sigma = { sigma with
+  conv_pbs=[]; last_mods=Evar.Set.empty; metas=Metamap.empty }
+(* spiwack: tentatively deprecated *)
+let create_goal_evar_defs sigma = { sigma with
+   (* conv_pbs=[]; last_mods=Evar.Set.empty; metas=Metamap.empty } *)
+  metas=Metamap.empty } 
+
+let empty = {
+  defn_evars = EvMap.empty;
+  undf_evars = EvMap.empty;
+  universes  = empty_evar_universe_context;
+  conv_pbs   = [];
+  last_mods  = Evar.Set.empty;
+  metas      = Metamap.empty;
+  effects    = Declareops.no_seff;
+  evar_names = (EvMap.empty,Idmap.empty); (* id<->key for undefined evars *)
+  future_goals = [];
+  principal_future_goal = None;
+}
+
+let from_env ?ctx e = 
+  match ctx with
+  | None -> { empty with universes = evar_universe_context_from e }
+  | Some ctx -> { empty with universes = ctx }
+
+let has_undefined evd = not (EvMap.is_empty evd.undf_evars)
+
+let evars_reset_evd ?(with_conv_pbs=false) ?(with_univs=true) evd d =
+  let conv_pbs = if with_conv_pbs then evd.conv_pbs else d.conv_pbs in
+  let last_mods = if with_conv_pbs then evd.last_mods else d.last_mods in
+  let universes = 
+    if not with_univs then evd.universes
+    else union_evar_universe_context evd.universes d.universes
+  in
+  { evd with
+    metas = d.metas;
+    last_mods; conv_pbs; universes }
+
+let merge_universe_context evd uctx' =
+  { evd with universes = union_evar_universe_context evd.universes uctx' }
+
+let set_universe_context evd uctx' =
+  { evd with universes = uctx' }
+
+let add_conv_pb ?(tail=false) pb d =
+  if tail then {d with conv_pbs = d.conv_pbs @ [pb]}
+  else {d with conv_pbs = pb::d.conv_pbs}
+
+let evar_source evk d = (find d evk).evar_source
+
+let evar_ident evk evd =
+  try EvMap.find evk (fst evd.evar_names)
+  with Not_found ->
+    (* Unnamed (non-dependent) evar *)
+    add_suffix (Id.of_string "X") (string_of_int (Evar.repr evk))
+
+let evar_key id evd =
+  Idmap.find id (snd evd.evar_names)
+
+let define_aux def undef evk body =
+  let oldinfo =
+    try EvMap.find evk undef
+    with Not_found ->
+      if EvMap.mem evk def then
+        anomaly ~label:"Evd.define" (Pp.str "cannot define an evar twice")
+      else
+        anomaly ~label:"Evd.define" (Pp.str "cannot define undeclared evar")
+  in
+  let () = assert (oldinfo.evar_body == Evar_empty) in
+  let newinfo = { oldinfo with evar_body = Evar_defined body } in
+  EvMap.add evk newinfo def, EvMap.remove evk undef
+
+(* define the existential of section path sp as the constr body *)
+let define evk body evd =
+  let (defn_evars, undf_evars) = define_aux evd.defn_evars evd.undf_evars evk body in
+  let last_mods = match evd.conv_pbs with
+  | [] ->  evd.last_mods
+  | _ -> Evar.Set.add evk evd.last_mods
+  in
+  let evar_names = remove_name_defined evk evd.evar_names in
+  { evd with defn_evars; undf_evars; last_mods; evar_names }
+
+let evar_declare hyps evk ty ?(src=(Loc.ghost,Evar_kinds.InternalHole)) 
+    ?(filter=Filter.identity) ?candidates ?(store=Store.empty)
+    ?(naming=Misctypes.IntroAnonymous) evd =
+  let () = match Filter.repr filter with
+  | None -> ()
+  | Some filter ->
+    assert (Int.equal (List.length filter) (List.length (named_context_of_val hyps)))
+  in
+  let evar_info = {
+    evar_hyps = hyps;
+    evar_concl = ty;
+    evar_body = Evar_empty;
+    evar_filter = filter;
+    evar_source = src;
+    evar_candidates = candidates;
+    evar_extra = store; }
+  in
+  let evar_names = add_name_newly_undefined naming evk evar_info evd.evar_names in
+  { evd with undf_evars = EvMap.add evk evar_info evd.undf_evars; evar_names }
+
+let restrict evk evk' filter ?candidates evd =
+  let evar_info = EvMap.find evk evd.undf_evars in
+  let evar_info' =
+    { evar_info with evar_filter = filter;
+      evar_candidates = candidates;
+      evar_extra = Store.empty } in
+  let evar_names = reassign_name_defined evk evk' evd.evar_names in
+  let ctxt = Filter.filter_list filter (evar_context evar_info) in
+  let id_inst = Array.map_of_list (fun (id,_,_) -> mkVar id) ctxt in
+  let body = mkEvar(evk',id_inst) in
+  let (defn_evars, undf_evars) = define_aux evd.defn_evars evd.undf_evars evk body in
+  { evd with undf_evars = EvMap.add evk' evar_info' undf_evars;
+    defn_evars; evar_names }
+
+let downcast evk ccl evd =
+  let evar_info = EvMap.find evk evd.undf_evars in
+  let evar_info' = { evar_info with evar_concl = ccl } in
+  { evd with undf_evars = EvMap.add evk evar_info' evd.undf_evars }
+
+(* extracts conversion problems that satisfy predicate p *)
+(* Note: conv_pbs not satisying p are stored back in reverse order *)
+let extract_conv_pbs evd p =
+  let (pbs,pbs1) =
+    List.fold_left
+      (fun (pbs,pbs1) pb ->
+    	 if p pb then
+	   (pb::pbs,pbs1)
+         else
+	   (pbs,pb::pbs1))
+      ([],[])
+      evd.conv_pbs
+  in
+  {evd with conv_pbs = pbs1; last_mods = Evar.Set.empty},
+  pbs
+
+let extract_changed_conv_pbs evd p =
+  extract_conv_pbs evd (fun pb -> p evd.last_mods pb)
+
+let extract_all_conv_pbs evd =
+  extract_conv_pbs evd (fun _ -> true)
+
+let loc_of_conv_pb evd (pbty,env,t1,t2) =
+  match kind_of_term (fst (decompose_app t1)) with
+  | Evar (evk1,_) -> fst (evar_source evk1 evd)
+  | _ ->
+  match kind_of_term (fst (decompose_app t2)) with
+  | Evar (evk2,_) -> fst (evar_source evk2 evd)
+  | _ -> Loc.ghost
+
+(** The following functions return the set of evars immediately
+    contained in the object *)
+
+(* excluding defined evars *)
+
+let evar_list c =
+  let rec evrec acc c =
+    match kind_of_term c with
+    | Evar (evk, _ as ev) -> ev :: acc
+    | _ -> fold_constr evrec acc c in
+  evrec [] c
+
+let evars_of_term c =
+  let rec evrec acc c =
+    match kind_of_term c with
+    | Evar (n, l) -> Evar.Set.add n (Array.fold_left evrec acc l)
+    | _ -> fold_constr evrec acc c
+  in
+  evrec Evar.Set.empty c
+
+let evars_of_named_context nc =
+  List.fold_right (fun (_, b, t) s ->
+    Option.fold_left (fun s t ->
+      Evar.Set.union s (evars_of_term t))
+      (Evar.Set.union s (evars_of_term t)) b)
+    nc Evar.Set.empty
+
+let evars_of_filtered_evar_info evi =
+  Evar.Set.union (evars_of_term evi.evar_concl)
+    (Evar.Set.union
+	(match evi.evar_body with
+	| Evar_empty -> Evar.Set.empty
+	| Evar_defined b -> evars_of_term b)
+	(evars_of_named_context (evar_filtered_context evi)))
+
+(**********************************************************)
+(* Side effects *)
+
+let emit_side_effects eff evd =
+  { evd with effects = Declareops.union_side_effects eff evd.effects; }
+
+let drop_side_effects evd =
+  { evd with effects = Declareops.no_seff; }
+
+let eval_side_effects evd = evd.effects
+
+(* Future goals *)
+let declare_future_goal evk evd =
+  { evd with future_goals = evk::evd.future_goals }
+
+let declare_principal_goal evk evd =
+  match evd.principal_future_goal with
+  | None -> { evd with
+    future_goals = evk::evd.future_goals;
+    principal_future_goal=Some evk; }
+  | Some _ -> Errors.error "Only one main subgoal per instantiation."
+
+let future_goals evd = evd.future_goals
+
+let principal_future_goal evd = evd.principal_future_goal
+
+let reset_future_goals evd =
+  { evd with future_goals = [] ; principal_future_goal=None }
+
+let restore_future_goals evd gls pgl =
+  { evd with future_goals = gls ; principal_future_goal = pgl }
+
+(**********************************************************)
+(* Sort variables *)
+
+type rigid = 
+  | UnivRigid
+  | UnivFlexible of bool (** Is substitution by an algebraic ok? *)
+
+let univ_rigid = UnivRigid
+let univ_flexible = UnivFlexible false
+let univ_flexible_alg = UnivFlexible true
+
+let evar_universe_context d = d.universes
+
+let universe_context_set d = d.universes.uctx_local
+
+let universe_context evd =
+  Univ.ContextSet.to_context evd.universes.uctx_local
+
+let universe_subst evd =
+  evd.universes.uctx_univ_variables
+
+let merge_uctx rigid uctx ctx' =
+  let open Univ in
+  let uctx = 
+    match rigid with
+    | UnivRigid -> uctx
+    | UnivFlexible b ->
+      let levels = ContextSet.levels ctx' in
+      let fold u accu =
+        if LMap.mem u accu then accu
+        else LMap.add u None accu
+      in
+      let uvars' = LSet.fold fold levels uctx.uctx_univ_variables in
+	if b then
+	  { uctx with uctx_univ_variables = uvars';
+	  uctx_univ_algebraic = LSet.union uctx.uctx_univ_algebraic levels }
+	else { uctx with uctx_univ_variables = uvars' }
+  in
+  let uctx_local = ContextSet.append ctx' uctx.uctx_local in
+  let uctx_universes = merge_constraints (ContextSet.constraints ctx') uctx.uctx_universes in
+  { uctx with uctx_local; uctx_universes }
+
+let merge_context_set rigid evd ctx' = 
+  {evd with universes = merge_uctx rigid evd.universes ctx'}
+
+let merge_uctx_subst uctx s =
+  { uctx with uctx_univ_variables = Univ.LMap.subst_union uctx.uctx_univ_variables s }
+      
+let merge_universe_subst evd subst = 
+  {evd with universes = merge_uctx_subst evd.universes subst }
+
+let with_context_set rigid d (a, ctx) = 
+  (merge_context_set rigid d ctx, a)
+
+let add_uctx_names s l (names, names_rev) =
+    (UNameMap.add s l names, Univ.LMap.add l s names_rev)
+
+let uctx_new_univ_variable rigid name
+  ({ uctx_local = ctx; uctx_univ_variables = uvars; uctx_univ_algebraic = avars} as uctx) =
+  let u = Universes.new_univ_level (Global.current_dirpath ()) in
+  let ctx' = Univ.ContextSet.add_universe u ctx in
+  let uctx' = 
+    match rigid with
+    | UnivRigid -> uctx
+    | UnivFlexible b -> 
+      let uvars' = Univ.LMap.add u None uvars in
+	if b then {uctx with uctx_univ_variables = uvars';
+	  uctx_univ_algebraic = Univ.LSet.add u avars}
+	else {uctx with uctx_univ_variables = Univ.LMap.add u None uvars} in
+  let names = 
+    match name with
+    | Some n -> add_uctx_names n u uctx.uctx_names
+    | None -> uctx.uctx_names
+  in
+    {uctx' with uctx_names = names; uctx_local = ctx';
+      uctx_universes = Univ.add_universe u uctx.uctx_universes}, u
+
+let new_univ_level_variable ?name rigid evd =
+  let uctx', u = uctx_new_univ_variable rigid name evd.universes in
+    ({evd with universes = uctx'}, u)
+
+let new_univ_variable ?name rigid evd =
+  let uctx', u = uctx_new_univ_variable rigid name evd.universes in
+    ({evd with universes = uctx'}, Univ.Universe.make u)
+
+let new_sort_variable ?name rigid d =
+  let (d', u) = new_univ_variable rigid ?name d in
+    (d', Type u)
+
+let make_flexible_variable evd b u =
+  let {uctx_univ_variables = uvars; uctx_univ_algebraic = avars} as ctx = evd.universes in
+  let uvars' = Univ.LMap.add u None uvars in
+  let avars' = 
+    if b then
+      let uu = Univ.Universe.make u in
+      let substu_not_alg u' v =
+	Option.cata (fun vu -> Univ.Universe.equal uu vu && not (Univ.LSet.mem u' avars)) false v
+      in
+	if not (Univ.LMap.exists substu_not_alg uvars)
+	then Univ.LSet.add u avars else avars 
+    else avars 
+  in
+    {evd with universes = {ctx with uctx_univ_variables = uvars'; 
+      uctx_univ_algebraic = avars'}}
+
+(****************************************)
+(* Operations on constants              *)
+(****************************************)
+
+let fresh_sort_in_family ?(rigid=univ_flexible) env evd s = 
+  with_context_set rigid evd (Universes.fresh_sort_in_family env s)
+
+let fresh_constant_instance env evd c =
+  with_context_set univ_flexible evd (Universes.fresh_constant_instance env c)
+
+let fresh_inductive_instance env evd i =
+  with_context_set univ_flexible evd (Universes.fresh_inductive_instance env i)
+
+let fresh_constructor_instance env evd c =
+  with_context_set univ_flexible evd (Universes.fresh_constructor_instance env c)
+
+let fresh_global ?(rigid=univ_flexible) ?names env evd gr =
+  with_context_set rigid evd (Universes.fresh_global_instance ?names env gr)
+
+let whd_sort_variable evd t = t
+
+let is_sort_variable evd s = 
+  match s with 
+  | Type u -> 
+    (match Univ.universe_level u with
+    | Some l as x -> 
+      let uctx = evd.universes in
+	if Univ.LSet.mem l (Univ.ContextSet.levels uctx.uctx_local) then x
+	else None
+    | None -> None)
+  | _ -> None
+
+let is_flexible_level evd l = 
+  let uctx = evd.universes in
+    Univ.LMap.mem l uctx.uctx_univ_variables
+
+let is_eq_sort s1 s2 =
+  if Sorts.equal s1 s2 then None
+  else
+    let u1 = univ_of_sort s1
+    and u2 = univ_of_sort s2 in
+      if Univ.Universe.equal u1 u2 then None
+      else Some (u1, u2)
+
+let normalize_universe evd =
+  let vars = ref evd.universes.uctx_univ_variables in
+  let normalize = Universes.normalize_universe_opt_subst vars in
+    normalize
+
+let normalize_universe_instance evd l =
+  let vars = ref evd.universes.uctx_univ_variables in
+  let normalize = Univ.level_subst_of (Universes.normalize_univ_variable_opt_subst vars) in
+    Univ.Instance.subst_fn normalize l
+
+let normalize_sort evars s =
+  match s with
+  | Prop _ -> s
+  | Type u -> 
+    let u' = normalize_universe evars u in
+    if u' == u then s else Type u'
+
+(* FIXME inefficient *)
+let set_eq_sort env d s1 s2 =
+  let s1 = normalize_sort d s1 and s2 = normalize_sort d s2 in
+  match is_eq_sort s1 s2 with
+  | None -> d
+  | Some (u1, u2) ->
+    if not (type_in_type env) then
+      add_universe_constraints d
+        (Universes.Constraints.singleton (u1,Universes.UEq,u2))
+    else
+      d
+
+let has_lub evd u1 u2 =
+  (* let normalize = Universes.normalize_universe_opt_subst (ref univs.uctx_univ_variables) in *)
+  (* (\* let dref, norm = memo_normalize_universe d in *\) *)
+  (* let u1 = normalize u1 and u2 = normalize u2 in *)
+    if Univ.Universe.equal u1 u2 then evd
+    else add_universe_constraints evd
+      (Universes.Constraints.singleton (u1,Universes.ULub,u2))
+
+let set_eq_level d u1 u2 =
+  add_constraints d (Univ.enforce_eq_level u1 u2 Univ.Constraint.empty)
+
+let set_leq_level d u1 u2 =
+  add_constraints d (Univ.enforce_leq_level u1 u2 Univ.Constraint.empty)
+
+let set_eq_instances ?(flex=false) d u1 u2 =
+  add_universe_constraints d
+    (Universes.enforce_eq_instances_univs flex u1 u2 Universes.Constraints.empty)
+
+let set_leq_sort env evd s1 s2 =
+  let s1 = normalize_sort evd s1 
+  and s2 = normalize_sort evd s2 in
+  match is_eq_sort s1 s2 with
+  | None -> evd
+  | Some (u1, u2) ->
+    (* if Univ.is_type0_univ u2 then *)
+    (*   if Univ.is_small_univ u1 then evd *)
+    (*   else raise (Univ.UniverseInconsistency (Univ.Le, u1, u2, [])) *)
+    (* else if Univ.is_type0m_univ u2 then  *)
+    (*   raise (Univ.UniverseInconsistency (Univ.Le, u1, u2, [])) *)
+    (* else  *)
+      if not (type_in_type env) then
+      add_universe_constraints evd (Universes.Constraints.singleton (u1,Universes.ULe,u2))
+      else evd
+	    
+let check_eq evd s s' =
+  Univ.check_eq evd.universes.uctx_universes s s'
+
+let check_leq evd s s' =
+  Univ.check_leq evd.universes.uctx_universes s s'
+
+let subst_univs_context_with_def def usubst (ctx, cst) =
+  (Univ.LSet.diff ctx def, Univ.subst_univs_constraints usubst cst)
+
+let normalize_evar_universe_context_variables uctx =
+  let normalized_variables, undef, def, subst = 
+    Universes.normalize_univ_variables uctx.uctx_univ_variables 
+  in
+  let ctx_local = subst_univs_context_with_def def (Univ.make_subst subst) uctx.uctx_local in
+  let ctx_local', univs = Universes.refresh_constraints uctx.uctx_initial_universes ctx_local in
+    subst, { uctx with uctx_local = ctx_local';
+      uctx_univ_variables = normalized_variables;
+      uctx_universes = univs }
+
+(* let normvarsconstrkey = Profile.declare_profile "normalize_evar_universe_context_variables";; *)
+(* let normalize_evar_universe_context_variables = *)
+(*   Profile.profile1 normvarsconstrkey normalize_evar_universe_context_variables;; *)
+    
+let abstract_undefined_variables uctx =
+  let vars' = 
+    Univ.LMap.fold (fun u v acc ->
+      if v == None then Univ.LSet.remove u acc
+      else acc)
+    uctx.uctx_univ_variables uctx.uctx_univ_algebraic
+  in { uctx with uctx_local = Univ.ContextSet.empty;
+      uctx_univ_algebraic = vars' }
+
+
+let refresh_undefined_univ_variables uctx =
+  let subst, ctx' = Universes.fresh_universe_context_set_instance uctx.uctx_local in
+  let alg = Univ.LSet.fold (fun u acc -> Univ.LSet.add (Univ.subst_univs_level_level subst u) acc) 
+    uctx.uctx_univ_algebraic Univ.LSet.empty 
+  in
+  let vars = 
+    Univ.LMap.fold
+      (fun u v acc ->
+	Univ.LMap.add (Univ.subst_univs_level_level subst u) 
+          (Option.map (Univ.subst_univs_level_universe subst) v) acc)
+      uctx.uctx_univ_variables Univ.LMap.empty
+  in 
+  let uctx' = {uctx_names = uctx.uctx_names;
+	       uctx_local = ctx'; 
+	       uctx_univ_variables = vars; uctx_univ_algebraic = alg;
+	       uctx_universes = Univ.initial_universes;
+	       uctx_initial_universes = uctx.uctx_initial_universes } in
+    uctx', subst
+
+let refresh_undefined_universes evd =
+  let uctx', subst = refresh_undefined_univ_variables evd.universes in
+  let evd' = cmap (subst_univs_level_constr subst) {evd with universes = uctx'} in
+    evd', subst
+
+let normalize_evar_universe_context uctx = 
+  let rec fixpoint uctx = 
+    let ((vars',algs'), us') = 
+      Universes.normalize_context_set uctx.uctx_local uctx.uctx_univ_variables
+        uctx.uctx_univ_algebraic
+    in
+      if Univ.LSet.equal (fst us') (fst uctx.uctx_local) then 
+        uctx
+      else
+	let us', universes = Universes.refresh_constraints uctx.uctx_initial_universes us' in
+	let uctx' = 
+	  { uctx_names = uctx.uctx_names;
+	    uctx_local = us'; 
+	    uctx_univ_variables = vars'; 
+	    uctx_univ_algebraic = algs';
+	    uctx_universes = universes;
+	    uctx_initial_universes = uctx.uctx_initial_universes }
+	in fixpoint uctx'
+  in fixpoint uctx
+
+let nf_univ_variables evd = 
+  let subst, uctx' = normalize_evar_universe_context_variables evd.universes in
+  let evd' = {evd with universes = uctx'} in
+    evd', subst
+
+let nf_constraints evd =
+  let subst, uctx' = normalize_evar_universe_context_variables evd.universes in
+  let uctx' = normalize_evar_universe_context uctx' in
+    {evd with universes = uctx'}
+
+let nf_constraints = 
+  if Flags.profile then
+    let nfconstrkey = Profile.declare_profile "nf_constraints" in
+      Profile.profile1 nfconstrkey nf_constraints
+  else nf_constraints
+
+let universe_of_name evd s = 
+  UNameMap.find s (fst evd.universes.uctx_names)
+
+let add_universe_name evd s l =
+  let names' = add_uctx_names s l evd.universes.uctx_names in
+    {evd with universes = {evd.universes with uctx_names = names'}}
+
+let universes evd = evd.universes.uctx_universes
+
+(* Conversion w.r.t. an evar map and its local universes. *)
+
+let conversion_gen env evd pb t u =
+  match pb with 
+  | Reduction.CONV -> 
+    Reduction.trans_conv_universes 
+      full_transparent_state ~evars:(existential_opt_value evd) env 
+      evd.universes.uctx_universes t u
+  | Reduction.CUMUL -> Reduction.trans_conv_leq_universes
+     full_transparent_state ~evars:(existential_opt_value evd) env 
+    evd.universes.uctx_universes t u
+
+(* let conversion_gen_key = Profile.declare_profile "conversion_gen" *)
+(* let conversion_gen = Profile.profile5 conversion_gen_key conversion_gen *)
+
+let conversion env d pb t u =
+  conversion_gen env d pb t u; d
+
+let test_conversion env d pb t u =
+  try conversion_gen env d pb t u; true
+  with _ -> false
+
+let eq_constr_univs evd t u =
+  let b, c = Universes.eq_constr_univs_infer evd.universes.uctx_universes t u in
+    if b then 
+      try let evd' = add_universe_constraints evd c in evd', b
+      with Univ.UniverseInconsistency _ | UniversesDiffer -> evd, false
+    else evd, b
+
+let e_eq_constr_univs evdref t u =
+  let evd, b = eq_constr_univs !evdref t u in
+    evdref := evd; b
+
+let eq_constr_univs_test evd t u =
+  snd (eq_constr_univs evd t u)
+
+(**********************************************************)
+(* Accessing metas *)
+
+(** We use this function to overcome OCaml compiler limitations and to prevent
+    the use of costly in-place modifications. *)
+let set_metas evd metas = {
+  defn_evars = evd.defn_evars;
+  undf_evars = evd.undf_evars;
+  universes  = evd.universes;
+  conv_pbs = evd.conv_pbs;
+  last_mods = evd.last_mods;
+  metas;
+  effects = evd.effects;
+  evar_names = evd.evar_names;
+  future_goals = evd.future_goals;
+  principal_future_goal = evd.principal_future_goal;
+}
+
+let meta_list evd = metamap_to_list evd.metas
+
+let undefined_metas evd =
+  let filter = function
+    | (n,Clval(_,_,typ)) -> None
+    | (n,Cltyp (_,typ))  -> Some n
+  in
+  let m = List.map_filter filter (meta_list evd) in
+  List.sort Int.compare m
+
+let map_metas_fvalue f evd =
+  let map = function
+  | Clval(id,(c,s),typ) -> Clval(id,(mk_freelisted (f c.rebus),s),typ)
+  | x -> x
+  in
+  set_metas evd (Metamap.smartmap map evd.metas)
+
+let meta_opt_fvalue evd mv =
+  match Metamap.find mv evd.metas with
+    | Clval(_,b,_) -> Some b
+    | Cltyp _ -> None
+
+let meta_defined evd mv =
+  match Metamap.find mv evd.metas with
+    | Clval _ -> true
+    | Cltyp _ -> false
+
+let try_meta_fvalue evd mv =
+  match Metamap.find mv evd.metas with
+    | Clval(_,b,_) -> b
+    | Cltyp _ -> raise Not_found
+
+let meta_fvalue evd mv =
+  try try_meta_fvalue evd mv
+  with Not_found -> anomaly ~label:"meta_fvalue" (Pp.str "meta has no value")
+
+let meta_value evd mv =
+  (fst (try_meta_fvalue evd mv)).rebus
+
+let meta_ftype evd mv =
+  match Metamap.find mv evd.metas with
+    | Cltyp (_,b) -> b
+    | Clval(_,_,b) -> b
+
+let meta_type evd mv = (meta_ftype evd mv).rebus
+
+let meta_declare mv v ?(name=Anonymous) evd =
+  let metas = Metamap.add mv (Cltyp(name,mk_freelisted v)) evd.metas in
+  set_metas evd metas
+
+let meta_assign mv (v, pb) evd =
+  let modify _ = function
+  | Cltyp (na, ty) -> Clval (na, (mk_freelisted v, pb), ty)
+  | _ -> anomaly ~label:"meta_assign" (Pp.str "already defined")
+  in
+  let metas = Metamap.modify mv modify evd.metas in
+  set_metas evd metas
+
+let meta_reassign mv (v, pb) evd =
+  let modify _ = function
+  | Clval(na, _, ty) -> Clval (na, (mk_freelisted v, pb), ty)
+  | _ -> anomaly ~label:"meta_reassign" (Pp.str "not yet defined")
+  in
+  let metas = Metamap.modify mv modify evd.metas in
+  set_metas evd metas
+
+(* If the meta is defined then forget its name *)
+let meta_name evd mv =
+  try fst (clb_name (Metamap.find mv evd.metas)) with Not_found -> Anonymous
+
+let explain_no_such_bound_variable evd id =
+  let mvl =
+    List.rev (Metamap.fold (fun n clb l ->
+      let na = fst (clb_name clb) in
+      if na != Anonymous then out_name na :: l else l)
+    evd.metas []) in
+  errorlabstrm "Evd.meta_with_name"
+    (str"No such bound variable " ++ pr_id id ++
+     (if mvl == [] then str " (no bound variables at all in the expression)."
+      else
+        (str" (possible name" ++
+         str (if List.length mvl == 1 then " is: " else "s are: ") ++
+         pr_enum pr_id mvl ++ str").")))
+
+let meta_with_name evd id =
+  let na = Name id in
+  let (mvl,mvnodef) =
+    Metamap.fold
+      (fun n clb (l1,l2 as l) ->
+        let (na',def) = clb_name clb in
+        if Name.equal na na' then if def then (n::l1,l2) else (n::l1,n::l2)
+        else l)
+      evd.metas ([],[]) in
+  match mvnodef, mvl with
+    | _,[]  ->
+      explain_no_such_bound_variable evd id
+    | ([n],_|_,[n]) ->
+	n
+    | _  ->
+	errorlabstrm "Evd.meta_with_name"
+          (str "Binder name \"" ++ pr_id id ++
+           strbrk "\" occurs more than once in clause.")
+
+let clear_metas evd = {evd with metas = Metamap.empty}
+
+let meta_merge evd1 evd2 =
+  let metas = Metamap.fold Metamap.add evd1.metas evd2.metas in
+  let universes = union_evar_universe_context evd2.universes evd1.universes in
+  {evd2 with universes; metas; }
+
+type metabinding = metavariable * constr * instance_status
+
+let retract_coercible_metas evd =
+  let mc = ref [] in
+  let map n v = match v with
+  | Clval (na, (b, (Conv, CoerceToType as s)), typ) ->
+    let () = mc := (n, b.rebus, s) :: !mc in
+    Cltyp (na, typ)
+  | v -> v
+  in
+  let metas = Metamap.smartmapi map evd.metas in
+  !mc, set_metas evd metas
+
+let subst_defined_metas_evars (bl,el) c =
+  let rec substrec c = match kind_of_term c with
+    | Meta i ->
+      let select (j,_,_) = Int.equal i j in
+      substrec (pi2 (List.find select bl))
+    | Evar (evk,args) ->
+      let select (_,(evk',args'),_) = Evar.equal evk evk' && Array.equal Constr.equal args args' in
+      (try substrec (pi3 (List.find select el))
+       with Not_found -> map_constr substrec c)
+    | _ -> map_constr substrec c
+  in try Some (substrec c) with Not_found -> None
+
+let evar_source_of_meta mv evd =
+  match meta_name evd mv with
+  | Anonymous -> (Loc.ghost,Evar_kinds.GoalEvar)
+  | Name id -> (Loc.ghost,Evar_kinds.VarInstance id)
+
+let dependent_evar_ident ev evd =
+  let evi = find evd ev in
+  match evi.evar_source with
+  | (_,Evar_kinds.VarInstance id) -> id
+  | _ -> anomaly (str "Not an evar resulting of a dependent binding")
+
+(*******************************************************************)
+
+type pending = (* before: *) evar_map * (* after: *) evar_map
+
+type pending_constr = pending * constr
+
+type open_constr = evar_map * constr
+
+(*******************************************************************)
+(* The type constructor ['a sigma] adds an evar map to an object of
+  type ['a] *)
+type 'a sigma = {
+  it : 'a ;
+  sigma : evar_map
+}
+
+let sig_it x = x.it
+let sig_sig x = x.sigma
+let on_sig s f = 
+  let sigma', v = f s.sigma in
+    { s with sigma = sigma' }, v
+
+(*******************************************************************)
+(* The state monad with state an evar map. *)
+
+module MonadR =
+  Monad.Make (struct
+
+    type +'a t = evar_map -> evar_map * 'a
+
+    let return a = fun s -> (s,a)
+
+    let (>>=) x f = fun s ->
+      let (s',a) = x s in
+      f a s'
+
+    let (>>) x y = fun s ->
+      let (s',()) = x s in
+      y s'
+
+    let map f x = fun s ->
+      on_snd f (x s)
+
+  end)
+
+module Monad =
+  Monad.Make (struct
+
+    type +'a t = evar_map -> 'a * evar_map
+
+    let return a = fun s -> (a,s)
+
+    let (>>=) x f = fun s ->
+      let (a,s') = x s in
+      f a s'
+
+    let (>>) x y = fun s ->
+      let ((),s') = x s in
+      y s'
+
+    let map f x = fun s ->
+      on_fst f (x s)
+
+  end)
+
+(**********************************************************)
+(* Failure explanation *)
+
+type unsolvability_explanation = SeveralInstancesFound of int
+
+(**********************************************************)
+(* Pretty-printing *)
+
+let pr_existential_key sigma evk = str "?" ++ pr_id (evar_ident evk sigma)
+
+let pr_instance_status (sc,typ) =
+  begin match sc with
+  | IsSubType -> str " [or a subtype of it]"
+  | IsSuperType -> str " [or a supertype of it]"
+  | Conv -> mt ()
+  end ++
+  begin match typ with
+  | CoerceToType -> str " [up to coercion]"
+  | TypeNotProcessed -> mt ()
+  | TypeProcessed -> str " [type is checked]"
+  end
+
+let pr_meta_map mmap =
+  let pr_name = function
+      Name id -> str"[" ++ pr_id id ++ str"]"
+    | _ -> mt() in
+  let pr_meta_binding = function
+    | (mv,Cltyp (na,b)) ->
+      	hov 0
+	  (pr_meta mv ++ pr_name na ++ str " : " ++
+           print_constr b.rebus ++ fnl ())
+    | (mv,Clval(na,(b,s),t)) ->
+      	hov 0
+	  (pr_meta mv ++ pr_name na ++ str " := " ++
+           print_constr b.rebus ++
+	   str " : " ++ print_constr t.rebus ++
+	   spc () ++ pr_instance_status s ++ fnl ())
+  in
+  prlist pr_meta_binding (metamap_to_list mmap)
+
+let pr_decl ((id,b,_),ok) =
+  match b with
+  | None -> if ok then pr_id id else (str "{" ++ pr_id id ++ str "}")
+  | Some c -> str (if ok then "(" else "{") ++ pr_id id ++ str ":=" ++
+      print_constr c ++ str (if ok then ")" else "}")
+
+let rec pr_evar_source = function
+  | Evar_kinds.QuestionMark _ -> str "underscore"
+  | Evar_kinds.CasesType false -> str "pattern-matching return predicate"
+  | Evar_kinds.CasesType true ->
+      str "subterm of pattern-matching return predicate"
+  | Evar_kinds.BinderType (Name id) -> str "type of " ++ Nameops.pr_id id
+  | Evar_kinds.BinderType Anonymous -> str "type of anonymous binder"
+  | Evar_kinds.ImplicitArg (c,(n,ido),b) ->
+      let id = Option.get ido in
+      str "parameter " ++ pr_id id ++ spc () ++ str "of" ++
+      spc () ++ print_constr (printable_constr_of_global c)
+  | Evar_kinds.InternalHole -> str "internal placeholder"
+  | Evar_kinds.TomatchTypeParameter (ind,n) ->
+      pr_nth n ++ str " argument of type " ++ print_constr (mkInd ind)
+  | Evar_kinds.GoalEvar -> str "goal evar"
+  | Evar_kinds.ImpossibleCase -> str "type of impossible pattern-matching clause"
+  | Evar_kinds.MatchingVar _ -> str "matching variable"
+  | Evar_kinds.VarInstance id -> str "instance of " ++ pr_id id
+  | Evar_kinds.SubEvar evk ->
+      str "subterm of " ++ str (string_of_existential evk)
+
+let pr_evar_info evi =
+  let phyps =
+    try
+      let decls = match Filter.repr (evar_filter evi) with
+      | None -> List.map (fun c -> (c, true)) (evar_context evi)
+      | Some filter -> List.combine (evar_context evi) filter
+      in
+      prlist_with_sep spc pr_decl (List.rev decls)
+    with Invalid_argument _ -> str "Ill-formed filtered context" in
+  let pty = print_constr evi.evar_concl in
+  let pb =
+    match evi.evar_body with
+      | Evar_empty -> mt ()
+      | Evar_defined c -> spc() ++ str"=> "  ++ print_constr c
+  in
+  let candidates =
+    match evi.evar_body, evi.evar_candidates with
+      | Evar_empty, Some l ->
+           spc () ++ str "{" ++
+           prlist_with_sep (fun () -> str "|") print_constr l ++ str "}"
+      | _ ->
+          mt ()
+  in
+  let src = str "(" ++ pr_evar_source (snd evi.evar_source) ++ str ")" in
+  hov 2
+    (str"["  ++ phyps ++ spc () ++ str"|- "  ++ pty ++ pb ++ str"]" ++
+       candidates ++ spc() ++ src)
+
+let compute_evar_dependency_graph (sigma : evar_map) =
+  (* Compute the map binding ev to the evars whose body depends on ev *)
+  let fold evk evi acc =
+    let fold_ev evk' acc =
+      let tab =
+        try EvMap.find evk' acc
+        with Not_found -> Evar.Set.empty
+      in
+      EvMap.add evk' (Evar.Set.add evk tab) acc
+    in
+    match evar_body evi with
+    | Evar_empty -> assert false
+    | Evar_defined c -> Evar.Set.fold fold_ev (evars_of_term c) acc
+  in
+  EvMap.fold fold sigma.defn_evars EvMap.empty
+
+let evar_dependency_closure n sigma =
+  (** Create the DAG of depth [n] representing the recursive dependencies of
+      undefined evars. *)
+  let graph = compute_evar_dependency_graph sigma in
+  let rec aux n curr accu =
+    if Int.equal n 0 then Evar.Set.union curr accu
+    else
+      let fold evk accu =
+        try
+          let deps = EvMap.find evk graph in
+          Evar.Set.union deps accu
+        with Not_found -> accu
+      in
+      (** Consider only the newly added evars *)
+      let ncurr = Evar.Set.fold fold curr Evar.Set.empty in
+      (** Merge the others *)
+      let accu = Evar.Set.union curr accu in
+      aux (n - 1) ncurr accu
+  in
+  let undef = EvMap.domain (undefined_map sigma) in
+  aux n undef Evar.Set.empty
+
+let evar_dependency_closure n sigma =
+  let deps = evar_dependency_closure n sigma in
+  let map = EvMap.bind (fun ev -> find sigma ev) deps in
+  EvMap.bindings map
+
+let has_no_evar sigma =
+  EvMap.is_empty sigma.defn_evars && EvMap.is_empty sigma.undf_evars
+
+let pr_uctx_level uctx = 
+  let map, map_rev = uctx.uctx_names in 
+    fun l ->
+      try str(Univ.LMap.find l map_rev)
+      with Not_found -> 
+	Universes.pr_with_global_universes l
+
+let pr_evd_level evd = pr_uctx_level evd.universes
+
+let pr_evar_universe_context ctx =
+  let prl = pr_uctx_level ctx in
+  if is_empty_evar_universe_context ctx then mt ()
+  else
+    (str"UNIVERSES:"++brk(0,1)++ 
+       h 0 (Univ.pr_universe_context_set prl ctx.uctx_local) ++ fnl () ++
+     str"ALGEBRAIC UNIVERSES:"++brk(0,1)++
+     h 0 (Univ.LSet.pr prl ctx.uctx_univ_algebraic) ++ fnl() ++
+     str"UNDEFINED UNIVERSES:"++brk(0,1)++
+       h 0 (Universes.pr_universe_opt_subst ctx.uctx_univ_variables) ++ fnl())
+
+let print_env_short env =
+  let pr_body n = function
+  | None -> pr_name n
+  | Some b -> str "(" ++ pr_name n ++ str " := " ++ print_constr b ++ str ")" in
+  let pr_named_decl (n, b, _) = pr_body (Name n) b in
+  let pr_rel_decl (n, b, _) = pr_body n b in
+  let nc = List.rev (named_context env) in
+  let rc = List.rev (rel_context env) in
+    str "[" ++ pr_sequence pr_named_decl nc ++ str "]" ++ spc () ++
+    str "[" ++ pr_sequence pr_rel_decl rc ++ str "]"
+
+let pr_evar_constraints pbs =
+  let pr_evconstr (pbty, env, t1, t2) =
+    print_env_short env ++ spc () ++ str "|-" ++ spc () ++
+      print_constr_env env t1 ++ spc () ++
+      str (match pbty with
+            | Reduction.CONV -> "=="
+            | Reduction.CUMUL -> "<=") ++
+      spc () ++ print_constr_env env t2
+  in
+  prlist_with_sep fnl pr_evconstr pbs
+
+let pr_evar_map_gen with_univs pr_evars sigma =
+  let { universes = uvs } = sigma in
+  let evs = if has_no_evar sigma then mt () else pr_evars sigma ++ fnl ()
+  and svs = if with_univs then pr_evar_universe_context uvs else mt ()
+  and cstrs =
+    if List.is_empty sigma.conv_pbs then mt ()
+    else
+    str "CONSTRAINTS:" ++ brk (0, 1) ++
+      pr_evar_constraints sigma.conv_pbs ++ fnl ()
+  and metas =
+    if Metamap.is_empty sigma.metas then mt ()
+    else
+      str "METAS:" ++ brk (0, 1) ++ pr_meta_map sigma.metas
+  in
+  evs ++ svs ++ cstrs ++ metas
+
+let pr_evar_list sigma l =
+  let pr (ev, evi) =
+    h 0 (str (string_of_existential ev) ++
+      str "==" ++ pr_evar_info evi ++
+      (if evi.evar_body == Evar_empty
+       then str " {" ++ pr_id (evar_ident ev sigma) ++ str "}"
+       else mt ()))
+  in
+  h 0 (prlist_with_sep fnl pr l)
+
+let pr_evar_by_depth depth sigma = match depth with
+| None ->
+  (* Print all evars *)
+  str"EVARS:"++brk(0,1)++pr_evar_list sigma (to_list sigma)++fnl()
+| Some n ->
+  (* Print all evars *)
+  str"UNDEFINED EVARS:"++
+  (if Int.equal n 0 then mt() else str" (+level "++int n++str" closure):")++
+  brk(0,1)++
+  pr_evar_list sigma (evar_dependency_closure n sigma)++fnl()
+
+let pr_evar_by_filter filter sigma =
+  let defined = Evar.Map.filter filter sigma.defn_evars in
+  let undefined = Evar.Map.filter filter sigma.undf_evars in
+  let prdef =
+    if Evar.Map.is_empty defined then mt ()
+    else str "DEFINED EVARS:" ++ brk (0, 1) ++
+      pr_evar_list sigma (Evar.Map.bindings defined)
+  in
+  let prundef =
+    if Evar.Map.is_empty undefined then mt ()
+    else str "UNDEFINED EVARS:" ++ brk (0, 1) ++
+      pr_evar_list sigma (Evar.Map.bindings undefined)
+  in
+  prdef ++ prundef
+
+let pr_evar_map ?(with_univs=true) depth sigma =
+  pr_evar_map_gen with_univs (fun sigma -> pr_evar_by_depth depth sigma) sigma
+
+let pr_evar_map_filter ?(with_univs=true) filter sigma =
+  pr_evar_map_gen with_univs (fun sigma -> pr_evar_by_filter filter sigma) sigma
+
+let pr_metaset metas =
+  str "[" ++ pr_sequence pr_meta (Metaset.elements metas) ++ str "]"