diff --git a/Makefile b/Makefile
index ec9028ac01..cf444c32cc 100644
--- a/Makefile
+++ b/Makefile
@@ -58,7 +58,8 @@ FLOCQ=\
 VLIB=Axioms.v Coqlib.v Intv.v Maps.v Heaps.v Lattice.v Ordered.v \
   Iteration.v Integers.v Archi.v Fappli_IEEE_extra.v Floats.v \
   Parmov.v UnionFind.v Wfsimpl.v \
-  Postorder.v FSetAVLplus.v IntvSets.v Decidableplus.v BoolEqual.v
+  Postorder.v FSetAVLplus.v IntvSets.v Decidableplus.v BoolEqual.v \
+  Symbols.v
 
 # Parts common to the front-ends and the back-end (in common/)
 
diff --git a/Makefile.extr b/Makefile.extr
index a1c2ef7c0a..e0697efc4f 100644
--- a/Makefile.extr
+++ b/Makefile.extr
@@ -50,6 +50,7 @@ INCLUDES=$(patsubst %,-I %, $(DIRS))
 # Control of warnings:
 
 WARNINGS=-w +a-4-9-27 -strict-sequence -safe-string -warn-error +a #Deprication returns with ocaml 4.03
+extraction/%.cmi: WARNINGS +=-w -20-27-32..34-39-41-44..45
 extraction/%.cmx: WARNINGS +=-w -20-27-32..34-39-41-44..45
 extraction/%.cmo: WARNINGS +=-w -20-27-32..34-39-41-44..45
 cparser/pre_parser.cmx: WARNINGS += -w -41
diff --git a/arm/AsmToJSON.ml b/arm/AsmToJSON.ml
index 49cca9298e..a6084b8a8e 100644
--- a/arm/AsmToJSON.ml
+++ b/arm/AsmToJSON.ml
@@ -37,7 +37,7 @@ let mnemonic_names = [ "Padc"; "Padd"; "Padds"; "Pand";"Pannot"; "Pasr"; "Pb"; "
 
 type instruction_arg =
   | ALabel of positive
-  | Atom of positive
+  | Atom of ident
   | Data32 of Integers.Int.int
   | Data64 of Integers.Int64.int
   | DFreg of freg
diff --git a/backend/Asmexpandaux.mli b/backend/Asmexpandaux.mli
index 797eb10c6d..b903453fae 100644
--- a/backend/Asmexpandaux.mli
+++ b/backend/Asmexpandaux.mli
@@ -13,7 +13,6 @@
 
 open Asm
 open AST
-open BinNums
 
 (** Auxiliary functions for builtin expansion *)
 
@@ -31,6 +30,6 @@ val set_current_function: coq_function -> unit
   (* Set the current function *)
 val get_current_function: unit -> coq_function
   (* Get the current function *)
-val expand_debug: positive -> int -> (preg -> int) -> (instruction -> unit) -> instruction list -> unit
+val expand_debug: ident -> int -> (preg -> int) -> (instruction -> unit) -> instruction list -> unit
   (* Expand builtin debug function. Takes the function id, the register number of the stackpointer, a
      function to get the dwarf mapping of varibale names  and for the expansion of simple instructions *)
diff --git a/backend/Cminor.v b/backend/Cminor.v
index 11941da31a..c1a29fac47 100644
--- a/backend/Cminor.v
+++ b/backend/Cminor.v
@@ -185,7 +185,7 @@ Definition funsig (fd: fundef) :=
 *)
 
 Definition genv := Genv.t fundef unit.
-Definition env := PTree.t val.
+Definition env := ATree.t val.
 
 (** The following functions build the initial local environment at
   function entry, binding parameters to the provided arguments and
@@ -193,21 +193,21 @@ Definition env := PTree.t val.
 
 Fixpoint set_params (vl: list val) (il: list ident) {struct il} : env :=
   match il, vl with
-  | i1 :: is, v1 :: vs => PTree.set i1 v1 (set_params vs is)
-  | i1 :: is, nil => PTree.set i1 Vundef (set_params nil is)
-  | _, _ => PTree.empty val
+  | i1 :: is, v1 :: vs => ATree.set i1 v1 (set_params vs is)
+  | i1 :: is, nil => ATree.set i1 Vundef (set_params nil is)
+  | _, _ => ATree.empty val
   end.
 
 Fixpoint set_locals (il: list ident) (e: env) {struct il} : env :=
   match il with
   | nil => e
-  | i1 :: is => PTree.set i1 Vundef (set_locals is e)
+  | i1 :: is => ATree.set i1 Vundef (set_locals is e)
   end.
 
 Definition set_optvar (optid: option ident) (v: val) (e: env) : env :=
   match optid with
   | None => e
-  | Some id => PTree.set id v e
+  | Some id => ATree.set id v e
   end.
 
 (** Continuations *)
@@ -359,7 +359,7 @@ Variable m: mem.
 
 Inductive eval_expr: expr -> val -> Prop :=
   | eval_Evar: forall id v,
-      PTree.get id e = Some v ->
+      ATree.get id e = Some v ->
       eval_expr (Evar id) v
   | eval_Econst: forall cst v,
       eval_constant sp cst = Some v ->
@@ -447,7 +447,7 @@ Inductive step: state -> trace -> state -> Prop :=
   | step_assign: forall f id a k sp e m v,
       eval_expr sp e m a v ->
       step (State f (Sassign id a) k sp e m)
-        E0 (State f Sskip k sp (PTree.set id v e) m)
+        E0 (State f Sskip k sp (ATree.set id v e) m)
 
   | step_store: forall f chunk addr a k sp e m vaddr v m',
       eval_expr sp e m addr vaddr ->
@@ -673,7 +673,7 @@ with exec_stmt:
   | exec_Sassign:
       forall f sp e m id a v,
       eval_expr ge sp e m a v ->
-      exec_stmt f sp e m (Sassign id a) E0 (PTree.set id v e) m Out_normal
+      exec_stmt f sp e m (Sassign id a) E0 (ATree.set id v e) m Out_normal
   | exec_Sstore:
       forall f sp e m chunk addr a vaddr v m',
       eval_expr ge sp e m addr vaddr ->
@@ -948,7 +948,7 @@ Proof.
   constructor.
 
 (* assign *)
-  exists (State f Sskip k sp (PTree.set id v e) m); split.
+  exists (State f Sskip k sp (ATree.set id v e) m); split.
   apply star_one. constructor. auto.
   constructor.
 
diff --git a/backend/CminorSel.v b/backend/CminorSel.v
index 96cb8ae662..bab806a228 100644
--- a/backend/CminorSel.v
+++ b/backend/CminorSel.v
@@ -165,7 +165,7 @@ Variable m: mem.
 
 Inductive eval_expr: letenv -> expr -> val -> Prop :=
   | eval_Evar: forall le id v,
-      PTree.get id e = Some v ->
+      ATree.get id e = Some v ->
       eval_expr le (Evar id) v
   | eval_Eop: forall le op al vl v,
       eval_exprlist le al vl ->
@@ -284,7 +284,7 @@ End EVAL_EXPR.
 
 Definition set_builtin_res (res: builtin_res ident) (v: val) (e: env) : env :=
   match res with
-  | BR id => PTree.set id v e
+  | BR id => ATree.set id v e
   | _ => e
   end.
 
@@ -348,7 +348,7 @@ Inductive step: state -> trace -> state -> Prop :=
   | step_assign: forall f id a k sp e m v,
       eval_expr sp e m nil a v ->
       step (State f (Sassign id a) k sp e m)
-        E0 (State f Sskip k sp (PTree.set id v e) m)
+        E0 (State f Sskip k sp (ATree.set id v e) m)
 
   | step_store: forall f chunk addr al b k sp e m vl v vaddr m',
       eval_exprlist sp e m nil al vl ->
diff --git a/backend/Debugvar.v b/backend/Debugvar.v
index 1f36103017..4a4da6ea65 100644
--- a/backend/Debugvar.v
+++ b/backend/Debugvar.v
@@ -74,7 +74,7 @@ Fixpoint set_state (v: ident) (i: debuginfo) (s: avail) : avail :=
   match s with
   | nil => (v, i) :: nil
   | (v', i') as vi' :: s' =>
-      match Pos.compare v v' with
+      match Ident.compare v v' with
       | Eq => (v, i) :: s'
       | Lt => (v, i) :: s
       | Gt => vi' :: set_state v i s'
@@ -85,7 +85,7 @@ Fixpoint remove_state (v: ident) (s: avail) : avail :=
   match s with
   | nil => nil
   | (v', i') as vi' :: s' =>
-      match Pos.compare v v' with
+      match Ident.compare v v' with
       | Eq => s'
       | Lt => s
       | Gt => vi' :: remove_state v s'
@@ -157,7 +157,7 @@ Fixpoint join (s1: avail) (s2: avail) {struct s1} : avail :=
         match s2 with
         | nil => nil
         | (v2, i2) as vi2 :: s2' =>
-            match Pos.compare v1 v2 with
+            match Ident.compare v1 v2 with
             | Eq => if eq_debuginfo i1 i2 then vi1 :: join s1' s2' else join s1' s2'
             | Lt => join s1' s2
             | Gt => join2 s2'
@@ -296,7 +296,7 @@ Fixpoint diff (s1 s2: avail) {struct s1} : avail :=
         match s2 with
         | nil => s1
         | (v2, i2) :: s2' =>
-            match Pos.compare v1 v2 with
+            match Ident.compare v1 v2 with
             | Eq => if eq_debuginfo i1 i2 then diff s1' s2' else vi1 :: diff s1' s2'
             | Lt => vi1 :: diff s1' s2
             | Gt => diff2 s2'
diff --git a/backend/Debugvarproof.v b/backend/Debugvarproof.v
index d31c63ec74..cb4b69cf87 100644
--- a/backend/Debugvarproof.v
+++ b/backend/Debugvarproof.v
@@ -41,7 +41,8 @@ Remark diff_same:
 Proof.
   induction s as [ | [v i] s]; simpl.
   auto.
-  rewrite Pos.compare_refl. rewrite dec_eq_true. auto.
+  destruct (Ident.compare_spec v v); try solve [eelim Ident.lt_not_eq; eauto].
+  rewrite dec_eq_true. auto.
 Qed.
 
 Remark delta_state_same:
@@ -117,7 +118,7 @@ Qed.
     but establish some confidence in the availability analysis. *)
 
 Definition avail_above (v: ident) (s: avail) : Prop :=
-  forall v' i', In (v', i') s -> Plt v v'.
+  forall v' i', In (v', i') s -> Ident.lt v v'.
 
 Inductive wf_avail: avail -> Prop :=
   | wf_avail_nil:
@@ -132,7 +133,7 @@ Lemma set_state_1:
 Proof.
   induction s as [ | [v' i'] s]; simpl.
 - auto.
-- destruct (Pos.compare v v'); simpl; auto.
+- destruct (Ident.compare v v'); simpl; auto.
 Qed.
 
 Lemma set_state_2:
@@ -141,7 +142,7 @@ Lemma set_state_2:
 Proof.
   induction s as [ | [v1 i1] s]; simpl; intros.
 - contradiction.
-- destruct (Pos.compare_spec v v1); simpl.
+- destruct (Ident.compare_spec v v1); simpl.
 + subst v1. destruct H0. congruence. auto.
 + auto.
 + destruct H0; auto.
@@ -155,14 +156,14 @@ Lemma set_state_3:
 Proof.
   induction 1; simpl; intros.
 - intuition congruence.
-- destruct (Pos.compare_spec v v0); simpl in H1.
+- destruct (Ident.compare_spec v v0); simpl in H1.
 + subst v0. destruct H1. inv H1; auto. right; split.
-  apply not_eq_sym. apply Plt_ne. eapply H; eauto.
+  apply not_eq_sym. apply Ident.lt_not_eq. eapply H; eauto.
   auto.
 + destruct H1. inv H1; auto.
-  destruct H1. inv H1. right; split; auto. apply not_eq_sym. apply Plt_ne. auto.
-  right; split; auto. apply not_eq_sym. apply Plt_ne. apply Plt_trans with v0; eauto.
-+ destruct H1. inv H1. right; split; auto. apply Plt_ne. auto.
+  destruct H1. inv H1. right; split; auto. apply not_eq_sym. apply Ident.lt_not_eq. auto.
+  right; split; auto. apply not_eq_sym. apply Ident.lt_not_eq. apply Ident.lt_trans with v0; eauto.
++ destruct H1. inv H1. right; split; auto. apply Ident.lt_not_eq. auto.
   destruct IHwf_avail as [A | [A B]]; auto.
 Qed.
 
@@ -171,11 +172,11 @@ Lemma wf_set_state:
 Proof.
   induction 1; simpl.
 - constructor. red; simpl; tauto. constructor.
-- destruct (Pos.compare_spec v v0).
+- destruct (Ident.compare_spec v v0).
 + subst v0. constructor; auto.
 + constructor.
   red; simpl; intros. destruct H2.
-  inv H2. auto. apply Plt_trans with v0; eauto.
+  inv H2. auto. apply Ident.lt_trans with v0; eauto.
   constructor; auto.
 + constructor.
   red; intros. exploit set_state_3. eexact H0. eauto. intros [[A B] | [A B]]; subst; eauto.
@@ -187,11 +188,11 @@ Lemma remove_state_1:
 Proof.
   induction 1; simpl; red; intros.
 - auto.
-- destruct (Pos.compare_spec v v0); simpl in *.
-+ subst v0. elim (Plt_strict v); eauto.
-+ destruct H1. inv H1.  elim (Plt_strict v); eauto.
-  elim (Plt_strict v). apply Plt_trans with v0; eauto.
-+ destruct H1. inv H1. elim (Plt_strict v); eauto.  tauto.
+- destruct (Ident.compare_spec v v0); simpl in *.
++ subst v0. elim (Ident.lt_not_eq v v); eauto.
++ destruct H1. inv H1.  elim (Ident.lt_not_eq v v); eauto.
+  elim (Ident.lt_not_eq v v); eauto. apply Ident.lt_trans with v0; eauto.
++ destruct H1. inv H1. elim (Ident.lt_not_eq v v); eauto.  tauto.
 Qed.
 
 Lemma remove_state_2:
@@ -199,7 +200,7 @@ Lemma remove_state_2:
 Proof.
   induction s as [ | [v1 i1] s]; simpl; intros.
 - auto.
-- destruct (Pos.compare_spec v v1); simpl.
+- destruct (Ident.compare_spec v v1); simpl.
 + subst v1. destruct H0. congruence. auto.
 + auto.
 + destruct H0; auto.
@@ -210,11 +211,11 @@ Lemma remove_state_3:
 Proof.
   induction 1; simpl; intros.
 - contradiction.
-- destruct (Pos.compare_spec v v0); simpl in H1.
-+ subst v0. split; auto. apply not_eq_sym; apply Plt_ne; eauto.
-+ destruct H1. inv H1. split; auto. apply not_eq_sym; apply Plt_ne; eauto.
-  split; auto. apply not_eq_sym; apply Plt_ne. apply Plt_trans with v0; eauto.
-+ destruct H1. inv H1. split; auto. apply Plt_ne; auto.
+- destruct (Ident.compare_spec v v0); simpl in H1.
++ subst v0. split; auto. apply not_eq_sym; apply Ident.lt_not_eq; eauto.
++ destruct H1. inv H1. split; auto. apply not_eq_sym; apply Ident.lt_not_eq; eauto.
+  split; auto. apply not_eq_sym; apply Ident.lt_not_eq. apply Ident.lt_trans with v0; eauto.
++ destruct H1. inv H1. split; auto. apply Ident.lt_not_eq; auto.
   destruct IHwf_avail as [A B] ; auto.
 Qed.
 
@@ -223,7 +224,7 @@ Lemma wf_remove_state:
 Proof.
   induction 1; simpl.
 - constructor.
-- destruct (Pos.compare_spec v v0).
+- destruct (Ident.compare_spec v v0).
 + auto.
 + constructor; auto.
 + constructor; auto. red; intros.
@@ -246,12 +247,22 @@ Lemma join_1:
 Proof.
   induction 1; simpl; try tauto; induction 1; simpl; intros I1 I2; auto.
   destruct I1, I2.
-- inv H3; inv H4. rewrite Pos.compare_refl. rewrite dec_eq_true; auto with coqlib.
+- inv H3; inv H4.
+  destruct (Ident.compare_spec v v); try solve [eelim Ident.lt_not_eq; eauto].
+  rewrite dec_eq_true; auto with coqlib.
 - inv H3.
-  assert (L: Plt v1 v) by eauto. apply Pos.compare_gt_iff in L. rewrite L. auto.
+  assert (L: Ident.lt v1 v) by eauto.
+  destruct (Ident.compare_spec v v1).
+  + eelim Ident.lt_not_eq; eauto.
+  + elim (Ident.lt_not_eq v v); eauto using Ident.lt_trans.
+  + auto.
 - inv H4.
-  assert (L: Plt v0 v) by eauto. apply Pos.compare_lt_iff in L. rewrite L. apply IHwf_avail. constructor; auto. auto. auto with coqlib.
-- destruct (Pos.compare v0 v1).
+  assert (L: Ident.lt v0 v) by eauto.
+  destruct (Ident.compare_spec v0 v).
+  + eelim Ident.lt_not_eq; eauto.
+  + apply IHwf_avail. constructor; auto. auto. auto with coqlib.
+  + elim (Ident.lt_not_eq v v); eauto using Ident.lt_trans.
+- destruct (Ident.compare v0 v1).
 + destruct (eq_debuginfo i0 i1); auto with coqlib.
 + apply IHwf_avail; auto with coqlib. constructor; auto.
 + eauto.
@@ -262,7 +273,7 @@ Lemma join_2:
   In (v, i) (join s1 s2) -> In (v, i) s1 /\ In (v, i) s2.
 Proof.
   induction 1; simpl; try tauto; induction 1; simpl; intros I; try tauto.
-  destruct (Pos.compare_spec v0 v1).
+  destruct (Ident.compare_spec v0 v1).
 - subst v1. destruct (eq_debuginfo i0 i1).
   + subst i1. destruct I. auto. exploit IHwf_avail; eauto. tauto.
   + exploit IHwf_avail; eauto. tauto.
@@ -275,7 +286,7 @@ Lemma wf_join:
   forall s1, wf_avail s1 -> forall s2, wf_avail s2 -> wf_avail (join s1 s2).
 Proof.
   induction 1; simpl; induction 1; simpl; try constructor.
-  destruct (Pos.compare_spec v v0).
+  destruct (Ident.compare_spec v v0).
 - subst v0. destruct (eq_debuginfo i i0); auto. constructor; auto.
   red; intros. apply join_2 in H3; auto. destruct H3. eauto.
 - apply IHwf_avail. constructor; auto.
diff --git a/backend/Inlining.v b/backend/Inlining.v
index f7ee416640..faf61d5713 100644
--- a/backend/Inlining.v
+++ b/backend/Inlining.v
@@ -23,9 +23,9 @@ Require Import Op Registers RTL.
   inlining, as determined by the external heuristic
   [should_inline]. *)
 
-Definition funenv : Type := PTree.t function.
+Definition funenv : Type := ATree.t function.
 
-Definition size_fenv (fenv: funenv) := PTree_Properties.cardinal fenv.
+Definition size_fenv (fenv: funenv) := ATree_Properties.cardinal fenv.
 
 Parameter inlining_info: Type.  (* abstract type, implemented on the Caml side *)
 
@@ -37,15 +37,15 @@ Definition add_globdef (io: inlining_info) (fenv: funenv) (idg: ident * globdef
   match idg with
   | (id, Gfun (Internal f)) =>
       if should_inline io id f
-      then PTree.set id f fenv
-      else PTree.remove id fenv
+      then ATree.set id f fenv
+      else ATree.remove id fenv
   | (id, _) =>
-      PTree.remove id fenv
+      ATree.remove id fenv
   end.
 
 Definition funenv_program (p: program) : funenv :=
   let io := inlining_analysis p in
-  List.fold_left (add_globdef io) p.(prog_defs) (PTree.empty function).
+  List.fold_left (add_globdef io) p.(prog_defs) (ATree.empty function).
 
 (** State monad *)
 
@@ -291,12 +291,12 @@ Variable rec: forall fenv', (size_fenv fenv' < size_fenv fenv)%nat -> context ->
 
 Inductive inline_decision (ros: reg + ident) : Type :=
   | Cannot_inline
-  | Can_inline (id: ident) (f: function) (P: ros = inr reg id) (Q: fenv!id = Some f).
+  | Can_inline (id: ident) (f: function) (P: ros = inr reg id) (Q: fenv$id = Some f).
 
 Program Definition can_inline (ros: reg + ident): inline_decision ros :=
   match ros with
   | inl r => Cannot_inline _
-  | inr id => match fenv!id with Some f => Can_inline _ id f _ _ | None => Cannot_inline _ end
+  | inr id => match fenv$id with Some f => Can_inline _ id f _ _ | None => Cannot_inline _ end
   end.
 
 (** Inlining of a call to function [f].  An appropriate context is
@@ -304,7 +304,7 @@ Program Definition can_inline (ros: reg + ident): inline_decision ros :=
   are inserted to copy the arguments of the call to the parameters of [f]. *)
 
 Definition inline_function (ctx: context) (id: ident) (f: function)
-                           (P: PTree.get id fenv = Some f)
+                           (P: ATree.get id fenv = Some f)
                            (args: list reg)
                            (retpc: node) (retreg: reg) : mon node :=
   let npc := max_pc_function f in
@@ -312,21 +312,21 @@ Definition inline_function (ctx: context) (id: ident) (f: function)
   do dpc <- reserve_nodes npc;
   do dreg <- reserve_regs nreg;
   let ctx' := callcontext ctx dpc dreg nreg f.(fn_stacksize) retpc retreg in
-  do x <- rec (PTree.remove id fenv) (PTree_Properties.cardinal_remove P) ctx' f;
+  do x <- rec (ATree.remove id fenv) (ATree_Properties.cardinal_remove P) ctx' f;
   add_moves (sregs ctx args) (sregs ctx' f.(fn_params)) (spc ctx' f.(fn_entrypoint)).
 
 (** Inlining of a tail call to function [f].  Similar to [inline_function],
   but the new context is different. *)
 
 Definition inline_tail_function (ctx: context) (id: ident) (f: function)
-                               (P: PTree.get id fenv = Some f)
+                               (P: ATree.get id fenv = Some f)
                                (args: list reg): mon node :=
   let npc := max_pc_function f in
   let nreg := max_reg_function f in
   do dpc <- reserve_nodes npc;
   do dreg <- reserve_regs nreg;
   let ctx' := tailcontext ctx dpc dreg nreg f.(fn_stacksize) in
-  do x <- rec (PTree.remove id fenv) (PTree_Properties.cardinal_remove P) ctx' f;
+  do x <- rec (ATree.remove id fenv) (ATree_Properties.cardinal_remove P) ctx' f;
   add_moves (sregs ctx args) (sregs ctx' f.(fn_params)) (spc ctx' f.(fn_entrypoint)).
 
 (** The instruction generated for a [Ireturn] instruction found in an
diff --git a/backend/Inliningaux.ml b/backend/Inliningaux.ml
index 842e0c9310..c145d00821 100644
--- a/backend/Inliningaux.ml
+++ b/backend/Inliningaux.ml
@@ -15,38 +15,38 @@ open Datatypes
 open FSetAVL
 open Maps
 open Op
-open Ordered
+open Symbols
 open !RTL
 
-module PSet = Make(OrderedPositive)
+module ASet = Make(OrderedIdent)
 
 type inlining_info = {
-  call_cnt : int PTree.t; (* Count the number of direct calls to a function *)
-  addr_taken : PSet.t; (* The set of globals which have their address taken *)
+  call_cnt : int ATree.t; (* Count the number of direct calls to a function *)
+  addr_taken : ASet.t; (* The set of globals which have their address taken *)
 }
 
 let empty_inlining_info = {
-  call_cnt = PTree.empty;
-  addr_taken = PSet.empty;
+  call_cnt = ATree.empty;
+  addr_taken = ASet.empty;
 }
 
 let call_count id io =
-  match PTree.get id io.call_cnt with
+  match ATree.get id io.call_cnt with
   | Some cnt -> cnt
   | None -> 0
 
 let called id io =
-  let call_cnt = PTree.set id (1 + call_count id io) io.call_cnt in
+  let call_cnt = ATree.set id (1 + call_count id io) io.call_cnt in
   { io with call_cnt = call_cnt }
 
 let address_taken id io =
-  PSet.mem id io.addr_taken
+  ASet.mem id io.addr_taken
 
 let rec used_id io ids =
   match ids with
   | [] -> io
   | id::ids ->
-     used_id {io with addr_taken = PSet.add id io.addr_taken} ids
+     used_id {io with addr_taken = ASet.add id io.addr_taken} ids
 
 let used_in_globvar io gv =
   let used_in_init_data io = function
diff --git a/backend/Inliningproof.v b/backend/Inliningproof.v
index 2dcb895687..3c2cf0e1d1 100644
--- a/backend/Inliningproof.v
+++ b/backend/Inliningproof.v
@@ -392,7 +392,7 @@ Lemma find_inlined_function:
   forall fenv id rs fd f,
   fenv_compat prog fenv ->
   find_function ge (inr id) rs = Some fd ->
-  fenv!id = Some f ->
+  fenv$id = Some f ->
   fd = Internal f.
 Proof.
   intros.
diff --git a/backend/Inliningspec.v b/backend/Inliningspec.v
index c345c94260..22015601e0 100644
--- a/backend/Inliningspec.v
+++ b/backend/Inliningspec.v
@@ -24,39 +24,39 @@ Require Import Inlining.
 
 Definition fenv_compat (p: program) (fenv: funenv) : Prop :=
   forall id f,
-  fenv!id = Some f -> (prog_defmap p)!id = Some (Gfun (Internal f)).
+  fenv$id = Some f -> (prog_defmap p)$id = Some (Gfun (Internal f)).
 
 Lemma funenv_program_compat:
   forall p, fenv_compat p (funenv_program p).
 Proof.
-  set (P := fun (dm: PTree.t (globdef fundef unit)) (fenv: funenv) =>
+  set (P := fun (dm: ATree.t (globdef fundef unit)) (fenv: funenv) =>
               forall id f,
-              fenv!id = Some f -> dm!id = Some (Gfun (Internal f))).
+              fenv$id = Some f -> dm$id = Some (Gfun (Internal f))).
   assert (REMOVE: forall dm fenv id g,
              P dm fenv ->
-             P (PTree.set id g dm) (PTree.remove id fenv)).
-  { unfold P; intros. rewrite PTree.grspec in H0. destruct (PTree.elt_eq id0 id).
+             P (ATree.set id g dm) (ATree.remove id fenv)).
+  { unfold P; intros. rewrite ATree.grspec in H0. destruct (ATree.elt_eq id0 id).
     discriminate.
-    rewrite PTree.gso; auto.
+    rewrite ATree.gso; auto.
   }
   assert (ADD: forall io dm fenv idg,
              P dm fenv ->
-             P (PTree.set (fst idg) (snd idg) dm) (add_globdef io fenv idg)).
+             P (ATree.set (fst idg) (snd idg) dm) (add_globdef io fenv idg)).
   { intros io dm fenv [id g]; simpl; intros.
     destruct g as [ [f|ef] | v]; auto.
     destruct (should_inline io id f); auto.
-    red; intros. rewrite ! PTree.gsspec in *.
-    destruct (peq id0 id); auto. inv H0; auto.
+    red; intros. rewrite ! ATree.gsspec in *.
+    destruct (ATree.elt_eq id0 id); auto. inv H0; auto.
   }
   assert (REC: forall p l dm fenv,
             P dm fenv ->
-            P (fold_left (fun x idg => PTree.set (fst idg) (snd idg) x) l dm)
+            P (fold_left (fun x idg => ATree.set (fst idg) (snd idg) x) l dm)
               (fold_left (add_globdef p) l fenv)).
   { induction l; simpl; intros.
   - auto.
   - apply IHl. apply ADD; auto.
   }
-  intros. apply REC. red; intros.  rewrite PTree.gempty in H; discriminate.
+  intros. apply REC. red; intros.  rewrite ATree.gempty in H; discriminate.
 Qed.
 
 Lemma fenv_compat_linkorder:
@@ -283,7 +283,7 @@ Inductive tr_instr: context -> node -> instruction -> code -> Prop :=
       tr_instr ctx pc (Icall sg ros args res s) c
   | tr_call_inlined:forall ctx pc sg id args res s c f pc1 ctx',
       Ple res ctx.(mreg) ->
-      fenv!id = Some f ->
+      fenv$id = Some f ->
       c!(spc ctx pc) = Some(Inop pc1) ->
       tr_moves c pc1 (sregs ctx args) (sregs ctx' f.(fn_params)) (spc ctx' f.(fn_entrypoint)) ->
       tr_funbody ctx' f c ->
@@ -300,7 +300,7 @@ Inductive tr_instr: context -> node -> instruction -> code -> Prop :=
       ctx.(retinfo) = Some(s, res) ->
       tr_instr ctx pc (Itailcall sg ros args) c
   | tr_tailcall_inlined: forall ctx pc sg id args c f pc1 ctx',
-      fenv!id = Some f ->
+      fenv$id = Some f ->
       c!(spc ctx pc) = Some(Inop pc1) ->
       tr_moves c pc1 (sregs ctx args) (sregs ctx' f.(fn_params)) (spc ctx' f.(fn_entrypoint)) ->
       tr_funbody ctx' f c ->
@@ -337,7 +337,7 @@ with tr_funbody: context -> function -> code -> Prop :=
       tr_funbody ctx f c.
 
 Definition fenv_agree (fe: funenv) : Prop :=
-  forall id f, fe!id = Some f -> fenv!id = Some f.
+  forall id f, fe$id = Some f -> fenv$id = Some f.
 
 Section EXPAND_INSTR.
 
@@ -504,7 +504,7 @@ Proof.
     intros. rewrite S1. eapply set_instr_other; eauto. unfold node; xomega.
     xomega. xomega.
   eapply rec_spec; eauto.
-    red; intros. rewrite PTree.grspec in H. destruct (PTree.elt_eq id0 id); try discriminate. auto.
+    red; intros. rewrite ATree.grspec in H. destruct (ATree.elt_eq id0 id); try discriminate. auto.
     simpl. subst s2; simpl in *; xomega.
     simpl. subst s3; simpl in *; xomega.
     simpl. xomega.
@@ -534,7 +534,7 @@ Proof.
   eapply add_moves_spec; eauto.
     intros. rewrite S1. eapply set_instr_other; eauto. unfold node; xomega. xomega. xomega.
   eapply rec_spec; eauto.
-    red; intros. rewrite PTree.grspec in H. destruct (PTree.elt_eq id0 id); try discriminate. auto.
+    red; intros. rewrite ATree.grspec in H. destruct (ATree.elt_eq id0 id); try discriminate. auto.
     simpl. subst s3; simpl in *. subst s2; simpl in *. xomega.
     simpl. subst s3; simpl in *; xomega.
     simpl. xomega.
diff --git a/backend/NeedDomain.v b/backend/NeedDomain.v
index d431f3d8c3..a507855add 100644
--- a/backend/NeedDomain.v
+++ b/backend/NeedDomain.v
@@ -1093,7 +1093,7 @@ Qed.
 
 Inductive nmem : Type :=
   | NMemDead
-  | NMem (stk: ISet.t) (gl: PTree.t ISet.t).
+  | NMem (stk: ISet.t) (gl: ATree.t ISet.t).
 
 (** Interpretation of [nmem]:
 - [NMemDead]: all memory locations are unused (dead).  Acts as bottom.
@@ -1112,19 +1112,19 @@ Inductive nlive: nmem -> block -> Z -> Prop :=
       (STK: b = sp -> ~ISet.In ofs stk)
       (GL: forall id iv,
            Genv.find_symbol ge id = Some b ->
-           gl!id = Some iv ->
+           gl$id = Some iv ->
            ~ISet.In ofs iv),
       nlive (NMem stk gl) b ofs.
 
 (** All locations are live *)
 
-Definition nmem_all := NMem ISet.empty (PTree.empty _).
+Definition nmem_all := NMem ISet.empty (ATree.empty _).
 
 Lemma nlive_all: forall b ofs, nlive nmem_all b ofs.
 Proof.
   intros; constructor; intros.
   apply ISet.In_empty.
-  rewrite PTree.gempty in H0; discriminate.
+  rewrite ATree.gempty in H0; discriminate.
 Qed.
 
 (** Add a range of live locations to [nm].  The range starts at
@@ -1136,12 +1136,12 @@ Definition nmem_add (nm: nmem) (p: aptr) (sz: Z) : nmem :=
   | NMem stk gl =>
       match p with
       | Gl id ofs =>
-          match gl!id with
-          | Some iv => NMem stk (PTree.set id (ISet.remove (Ptrofs.unsigned ofs) (Ptrofs.unsigned ofs + sz) iv) gl)
+          match gl$id with
+          | Some iv => NMem stk (ATree.set id (ISet.remove (Ptrofs.unsigned ofs) (Ptrofs.unsigned ofs + sz) iv) gl)
           | None => nm
           end
       | Glo id =>
-          NMem stk (PTree.remove id gl)
+          NMem stk (ATree.remove id gl)
       | Stk ofs =>
           NMem (ISet.remove (Ptrofs.unsigned ofs) (Ptrofs.unsigned ofs + sz) stk) gl
       | Stack =>
@@ -1162,11 +1162,11 @@ Proof.
   inv H1; try (apply nlive_all).
   - (* Gl id ofs *)
     assert (Genv.find_symbol ge id = Some b) by (eapply H; eauto).
-    destruct gl!id as [iv|] eqn:NG.
+    destruct gl$id as [iv|] eqn:NG.
   + constructor; simpl; intros.
     congruence.
     assert (id0 = id) by (eapply Genv.genv_vars_inj; eauto). subst id0.
-    rewrite PTree.gss in H5. inv H5. rewrite ISet.In_remove.
+    rewrite ATree.gss in H5. inv H5. rewrite ISet.In_remove.
     intros [A B]. elim A; auto.
   + constructor; simpl; intros.
     congruence.
@@ -1177,7 +1177,7 @@ Proof.
     constructor; simpl; intros.
     congruence.
     assert (id0 = id) by (eapply Genv.genv_vars_inj; eauto). subst id0.
-    rewrite PTree.grs in H5. congruence.
+    rewrite ATree.grs in H5. congruence.
   - (* Stk ofs *)
     constructor; simpl; intros.
     rewrite ISet.In_remove. intros [A B]. elim A; auto.
@@ -1194,14 +1194,14 @@ Lemma incl_nmem_add:
 Proof.
   intros. inversion H; subst. unfold nmem_add; destruct p; try (apply nlive_all).
 - (* Gl id ofs *)
-  destruct gl!id as [iv|] eqn:NG.
+  destruct gl$id as [iv|] eqn:NG.
   + split; simpl; intros. auto.
-    rewrite PTree.gsspec in H1. destruct (peq id0 id); eauto. inv H1.
+    rewrite ATree.gsspec in H1. destruct (ATree.elt_eq id0 id); eauto. inv H1.
     rewrite ISet.In_remove. intros [P Q]. eelim GL; eauto.
   + auto.
 - (* Glo id *)
   split; simpl; intros. auto.
-  rewrite PTree.grspec in H1. destruct (PTree.elt_eq id0 id). congruence. eauto.
+  rewrite ATree.grspec in H1. destruct (ATree.elt_eq id0 id). congruence. eauto.
 - (* Stk ofs *)
   split; simpl; intros.
   rewrite ISet.In_remove. intros [P Q]. eelim STK; eauto.
@@ -1222,11 +1222,11 @@ Definition nmem_remove (nm: nmem) (p: aptr) (sz: Z) : nmem :=
     match p with
     | Gl id ofs =>
         let iv' :=
-        match gl!id with
+        match gl$id with
         | Some iv => ISet.add (Ptrofs.unsigned ofs) (Ptrofs.unsigned ofs + sz) iv
         | None    => ISet.interval (Ptrofs.unsigned ofs) (Ptrofs.unsigned ofs + sz)
         end in
-        NMem stk (PTree.set id iv' gl)
+        NMem stk (ATree.set id iv' gl)
     | Stk ofs =>
         NMem (ISet.add (Ptrofs.unsigned ofs) (Ptrofs.unsigned ofs + sz) stk) gl
     | _ => nm
@@ -1244,7 +1244,7 @@ Lemma nlive_remove:
 Proof.
   intros. inversion H2; subst. unfold nmem_remove; inv H1; auto.
 - (* Gl id ofs *)
-  set (iv' := match gl!id with
+  set (iv' := match gl$id with
                   | Some iv =>
                       ISet.add (Ptrofs.unsigned ofs) (Ptrofs.unsigned ofs + sz) iv
                   | None =>
@@ -1253,8 +1253,8 @@ Proof.
               end).
   assert (Genv.find_symbol ge id = Some b) by (eapply H; eauto).
   split; simpl; auto; intros.
-  rewrite PTree.gsspec in H6. destruct (peq id0 id).
-+ inv H6. destruct H3. congruence. destruct gl!id as [iv0|] eqn:NG.
+  rewrite ATree.gsspec in H6. destruct (ATree.elt_eq id0 id).
++ inv H6. destruct H3. congruence. destruct gl$id as [iv0|] eqn:NG.
   unfold iv'; rewrite ISet.In_add. intros [P|P]. omega. eelim GL; eauto.
   unfold iv'; rewrite ISet.In_interval. omega.
 + eauto.
@@ -1273,7 +1273,7 @@ Definition nmem_contains (nm: nmem) (p: aptr) (sz: Z) :=
   | NMem stk gl =>
       match p with
       | Gl id ofs =>
-          match gl!id with
+          match gl$id with
           | Some iv => negb (ISet.contains (Ptrofs.unsigned ofs) (Ptrofs.unsigned ofs + sz) iv)
           | None => true
           end
@@ -1296,7 +1296,7 @@ Proof.
   inv H1; try discriminate.
 - (* Gl id ofs *)
   assert (Genv.find_symbol ge id = Some b) by (eapply H; eauto).
-  destruct gl!id as [iv|] eqn:HG; inv H2.
+  destruct gl$id as [iv|] eqn:HG; inv H2.
   destruct (ISet.contains (Ptrofs.unsigned ofs) (Ptrofs.unsigned ofs + sz) iv) eqn:IC; try discriminate.
   rewrite ISet.contains_spec in IC. eelim GL; eauto.
 - (* Stk ofs *)
@@ -1309,14 +1309,14 @@ Qed.
   a [Ireturn] or [Itailcall] instruction. *)
 
 Definition nmem_dead_stack (sz: Z) :=
-  NMem (ISet.interval 0 sz) (PTree.empty _).
+  NMem (ISet.interval 0 sz) (ATree.empty _).
 
 Lemma nlive_dead_stack:
   forall sz b' i, b' <> sp \/ ~(0 <= i < sz) -> nlive (nmem_dead_stack sz) b' i.
 Proof.
   intros; constructor; simpl; intros.
 - rewrite ISet.In_interval. intuition.
-- rewrite PTree.gempty in H1; discriminate.
+- rewrite ATree.gempty in H1; discriminate.
 Qed.
 
 (** Least upper bound *)
@@ -1327,7 +1327,7 @@ Definition nmem_lub (nm1 nm2: nmem) : nmem :=
   | _, NMemDead => nm1
   | NMem stk1 gl1, NMem stk2 gl2 =>
       NMem (ISet.inter stk1 stk2)
-           (PTree.combine
+           (ATree.combine
                 (fun o1 o2 =>
                   match o1, o2 with
                   | Some iv1, Some iv2 => Some(ISet.inter iv1 iv2)
@@ -1342,9 +1342,9 @@ Proof.
   intros. inversion H; subst. destruct nm2; simpl. auto.
   constructor; simpl; intros.
 - rewrite ISet.In_inter. intros [P Q]. eelim STK; eauto.
-- rewrite PTree.gcombine in H1 by auto.
-  destruct gl!id as [iv1|] eqn:NG1; try discriminate;
-  destruct gl0!id as [iv2|] eqn:NG2; inv H1.
+- rewrite ATree.gcombine in H1 by auto.
+  destruct gl$id as [iv1|] eqn:NG1; try discriminate;
+  destruct gl0$id as [iv2|] eqn:NG2; inv H1.
   rewrite ISet.In_inter. intros [P Q]. eelim GL; eauto.
 Qed.
 
@@ -1354,9 +1354,9 @@ Proof.
   intros. inversion H; subst. destruct nm1; simpl. auto.
   constructor; simpl; intros.
 - rewrite ISet.In_inter. intros [P Q]. eelim STK; eauto.
-- rewrite PTree.gcombine in H1 by auto.
-  destruct gl0!id as [iv1|] eqn:NG1; try discriminate;
-  destruct gl!id as [iv2|] eqn:NG2; inv H1.
+- rewrite ATree.gcombine in H1 by auto.
+  destruct gl0$id as [iv1|] eqn:NG1; try discriminate;
+  destruct gl$id as [iv2|] eqn:NG2; inv H1.
   rewrite ISet.In_inter. intros [P Q]. eelim GL; eauto.
 Qed.
 
@@ -1365,7 +1365,7 @@ Qed.
 Definition nmem_beq (nm1 nm2: nmem) : bool :=
   match nm1, nm2 with
   | NMemDead, NMemDead => true
-  | NMem stk1 gl1, NMem stk2 gl2 => ISet.beq stk1 stk2 && PTree.beq ISet.beq gl1 gl2
+  | NMem stk1 gl1, NMem stk2 gl2 => ISet.beq stk1 stk2 && ATree.beq ISet.beq gl1 gl2
   | _, _ => false
   end.
 
@@ -1377,13 +1377,13 @@ Proof.
   unfold nmem_beq; intros.
   destruct nm1 as [ | stk1 gl1]; destruct nm2 as [ | stk2 gl2]; try discriminate.
 - split; intros L; inv L.
-- InvBooleans. rewrite ISet.beq_spec in H0. rewrite PTree.beq_correct in H1.
+- InvBooleans. rewrite ISet.beq_spec in H0. rewrite ATree.beq_correct in H1.
   split; intros L; inv L; constructor; intros.
 + rewrite <- H0. eauto.
-+ specialize (H1 id). rewrite H2 in H1. destruct gl1!id as [iv1|] eqn: NG; try contradiction.
++ specialize (H1 id). rewrite H2 in H1. destruct gl1$id as [iv1|] eqn: NG; try contradiction.
   rewrite ISet.beq_spec in H1. rewrite <- H1. eauto.
 + rewrite H0. eauto.
-+ specialize (H1 id). rewrite H2 in H1. destruct gl2!id as [iv2|] eqn: NG; try contradiction.
++ specialize (H1 id). rewrite H2 in H1. destruct gl2$id as [iv2|] eqn: NG; try contradiction.
   rewrite ISet.beq_spec in H1. rewrite H1. eauto.
 Qed.
 
diff --git a/backend/PrintAsmaux.ml b/backend/PrintAsmaux.ml
index d985d5a41d..73b5462516 100644
--- a/backend/PrintAsmaux.ml
+++ b/backend/PrintAsmaux.ml
@@ -25,10 +25,10 @@ module type TARGET =
       val print_prologue: out_channel -> unit
       val print_epilogue: out_channel -> unit
       val print_align: out_channel -> int -> unit
-      val print_comm_symb:  out_channel -> Z.t -> P.t -> int -> unit
-      val print_var_info: out_channel -> P.t -> unit
-      val print_fun_info: out_channel -> P.t -> unit
-      val get_section_names: P.t -> section_name * section_name * section_name
+      val print_comm_symb:  out_channel -> Z.t -> ident -> int -> unit
+      val print_var_info: out_channel -> ident -> unit
+      val print_fun_info: out_channel -> ident -> unit
+      val get_section_names: ident -> section_name * section_name * section_name
       val print_file_line: out_channel -> string -> int -> unit
       val print_optional_fun_info: out_channel -> unit
       val cfi_startproc: out_channel -> unit
@@ -39,7 +39,7 @@ module type TARGET =
       val section: out_channel -> section_name -> unit
       val name_of_section: section_name -> string
       val comment: string
-      val symbol: out_channel -> P.t -> unit
+      val symbol: out_channel -> ident -> unit
       val default_falignment: int
       val label: out_channel -> int -> unit
       val address: string
diff --git a/backend/RTLgen.v b/backend/RTLgen.v
index 9d7a850699..cdb5c0ddb4 100644
--- a/backend/RTLgen.v
+++ b/backend/RTLgen.v
@@ -36,7 +36,7 @@ Local Open Scope string_scope.
   during translation of expressions, when crossing a [Elet] binding. *)
 
 Record mapping: Type := mkmapping {
-  map_vars: PTree.t reg;
+  map_vars: ATree.t reg;
   map_letvars: list reg
 }.
 
@@ -290,11 +290,11 @@ Definition new_reg : mon reg :=
 (** ** Operations on mappings *)
 
 Definition init_mapping : mapping :=
-  mkmapping (PTree.empty reg) nil.
+  mkmapping (ATree.empty reg) nil.
 
 Definition add_var (map: mapping) (name: ident) : mon (reg * mapping) :=
   do r <- new_reg;
-     ret (r, mkmapping (PTree.set name r map.(map_vars))
+     ret (r, mkmapping (ATree.set name r map.(map_vars))
                        map.(map_letvars)).
 
 Fixpoint add_vars (map: mapping) (names: list ident)
@@ -308,7 +308,7 @@ Fixpoint add_vars (map: mapping) (names: list ident)
   end.
 
 Definition find_var (map: mapping) (name: ident) : mon reg :=
-  match PTree.get name map.(map_vars) with
+  match ATree.get name map.(map_vars) with
   | None => error (Errors.MSG "RTLgen: unbound variable " :: Errors.CTX name :: nil)
   | Some r => ret r
   end.
@@ -551,7 +551,7 @@ Parameter more_likely: condexpr -> stmt -> stmt -> bool.
   [nlist] if it terminates by an [exit n] construct.  [rret] is the
   register where the return value of the function must be stored, if any. *)
 
-Definition labelmap : Type := PTree.t node.
+Definition labelmap : Type := ATree.t node.
 
 Fixpoint transl_stmt (map: mapping) (s: stmt) (nd: node)
                      (nexits: list node) (ngoto: labelmap) (nret: node) (rret: option reg)
@@ -628,7 +628,7 @@ Fixpoint transl_stmt (map: mapping) (s: stmt) (nd: node)
       end
   | Slabel lbl s' =>
       do ns <- transl_stmt map s' nd nexits ngoto nret rret;
-      match ngoto!lbl with
+      match ngoto$lbl with
       | None => error (Errors.msg "RTLgen: unbound label")
       | Some n =>
           do xx <-
@@ -638,7 +638,7 @@ Fixpoint transl_stmt (map: mapping) (s: stmt) (nd: node)
           ret ns
       end
   | Sgoto lbl =>
-      match ngoto!lbl with
+      match ngoto$lbl with
       | None => error (Errors.MSG "Undefined defined label " ::
                        Errors.CTX lbl :: nil)
       | Some n => ret n
@@ -650,7 +650,7 @@ Fixpoint transl_stmt (map: mapping) (s: stmt) (nd: node)
 Definition alloc_label (lbl: Cminor.label) (maps: labelmap * state) : labelmap * state :=
   let (map, s) := maps in
   let n := s.(st_nextnode) in
-  (PTree.set lbl n map,
+  (ATree.set lbl n map,
    mkstate s.(st_nextreg) (Pos.succ s.(st_nextnode)) s.(st_code) (reserve_instr_wf s)).
 
 Fixpoint reserve_labels (s: stmt) (ms: labelmap * state)
@@ -682,7 +682,7 @@ Definition transl_fun (f: CminorSel.function) (ngoto: labelmap): mon (node * lis
   ret (nentry, rparams).
 
 Definition transl_function (f: CminorSel.function) : Errors.res RTL.function :=
-  let (ngoto, s0) := reserve_labels f.(fn_body) (PTree.empty node, init_state) in
+  let (ngoto, s0) := reserve_labels f.(fn_body) (ATree.empty node, init_state) in
   match transl_fun f ngoto s0 with
   | Error msg => Errors.Error msg
   | OK (nentry, rparams) s i =>
diff --git a/backend/RTLgenproof.v b/backend/RTLgenproof.v
index 072db1387a..f507accace 100644
--- a/backend/RTLgenproof.v
+++ b/backend/RTLgenproof.v
@@ -30,17 +30,17 @@ Record map_wf (m: mapping) : Prop :=
   mk_map_wf {
     map_wf_inj:
       (forall id1 id2 r,
-         m.(map_vars)!id1 = Some r -> m.(map_vars)!id2 = Some r -> id1 = id2);
+         m.(map_vars)$id1 = Some r -> m.(map_vars)$id2 = Some r -> id1 = id2);
      map_wf_disj:
       (forall id r,
-         m.(map_vars)!id = Some r -> In r m.(map_letvars) -> False)
+         m.(map_vars)$id = Some r -> In r m.(map_letvars) -> False)
   }.
 
 Lemma init_mapping_wf:
   map_wf init_mapping.
 Proof.
   unfold init_mapping; split; simpl.
-  intros until r. rewrite PTree.gempty. congruence.
+  intros until r. rewrite ATree.gempty. congruence.
   tauto.
 Qed.
 
@@ -51,8 +51,8 @@ Lemma add_var_wf:
 Proof.
   intros. monadInv H.
   apply mk_map_wf; simpl.
-  intros until r0. repeat rewrite PTree.gsspec.
-  destruct (peq id1 name); destruct (peq id2 name).
+  intros until r0. repeat rewrite ATree.gsspec.
+  destruct (ATree.elt_eq id1 name); destruct (ATree.elt_eq id2 name).
   congruence.
   intros. inv H. elimtype False.
   apply valid_fresh_absurd with r0 s1.
@@ -63,8 +63,8 @@ Proof.
   apply H1. left; exists id1; auto.
   eauto with rtlg.
   inv H0. eauto.
-  intros until r0. rewrite PTree.gsspec.
-  destruct (peq id name).
+  intros until r0. rewrite ATree.gsspec.
+  destruct (ATree.elt_eq id name).
   intros. inv H.
   apply valid_fresh_absurd with r0 s1.
   apply H1. right; auto.
@@ -103,7 +103,7 @@ Record match_env
   mk_match_env {
     me_vars:
       (forall id v,
-         e!id = Some v -> exists r, map.(map_vars)!id = Some r /\ Val.lessdef v rs#r);
+         e$id = Some v -> exists r, map.(map_vars)$id = Some r /\ Val.lessdef v rs#r);
     me_letvars:
       Val.lessdef_list le rs##(map.(map_letvars))
   }.
@@ -111,8 +111,8 @@ Record match_env
 Lemma match_env_find_var:
   forall map e le rs id v r,
   match_env map e le rs ->
-  e!id = Some v ->
-  map.(map_vars)!id = Some r ->
+  e$id = Some v ->
+  map.(map_vars)$id = Some r ->
   Val.lessdef v rs#r.
 Proof.
   intros. exploit me_vars; eauto. intros [r' [EQ' RS]].
@@ -176,12 +176,12 @@ Lemma match_env_update_var:
   forall map e le rs id r v tv,
   Val.lessdef v tv ->
   map_wf map ->
-  map.(map_vars)!id = Some r ->
+  map.(map_vars)$id = Some r ->
   match_env map e le rs ->
-  match_env map (PTree.set id v e) le (rs#r <- tv).
+  match_env map (ATree.set id v e) le (rs#r <- tv).
 Proof.
   intros. inversion H0. inversion H2. apply mk_match_env.
-  intros id' v'. rewrite PTree.gsspec. destruct (peq id' id); intros.
+  intros id' v'. rewrite ATree.gsspec. destruct (ATree.elt_eq id' id); intros.
   subst id'. inv H3. exists r; split. auto. rewrite PMap.gss. auto.
   exploit me_vars0; eauto. intros [r' [A B]].
   exists r'; split. auto. rewrite PMap.gso; auto.
@@ -249,10 +249,10 @@ Qed.
 Lemma match_env_empty:
   forall map,
   map.(map_letvars) = nil ->
-  match_env map (PTree.empty val) nil (Regmap.init Vundef).
+  match_env map (ATree.empty val) nil (Regmap.init Vundef).
 Proof.
   intros. apply mk_match_env.
-  intros. rewrite PTree.gempty in H0. discriminate.
+  intros. rewrite ATree.gempty in H0. discriminate.
   rewrite H. constructor.
 Qed.
 
@@ -281,7 +281,7 @@ Proof.
   destruct (IHil _ _ _ _ nil nil _ EQ) as [ME UNDEF]. constructor. inv ME. split.
   replace (init_regs nil x) with (Regmap.init Vundef) in me_vars0, me_letvars0.
   constructor; simpl.
-  intros id v. repeat rewrite PTree.gsspec. destruct (peq id a); intros.
+  intros id v. repeat rewrite ATree.gsspec. destruct (ATree.elt_eq id a); intros.
   subst a. inv H. exists x1; split. auto. constructor.
   eauto.
   eauto.
@@ -290,7 +290,7 @@ Proof.
   (* vl = v1 :: vs *)
   destruct (IHil _ _ _ _ _ _ _ EQ H0) as [ME UNDEF]. inv ME. split.
   constructor; simpl.
-  intros id v. repeat rewrite PTree.gsspec. destruct (peq id a); intros.
+  intros id v. repeat rewrite ATree.gsspec. destruct (ATree.elt_eq id a); intros.
   subst a. inv H. inv H1. exists x1; split. auto. rewrite Regmap.gss. constructor.
   inv H1. eexists; eauto.
   exploit me_vars0; eauto. intros [r' [C D]].
@@ -321,8 +321,8 @@ Proof.
   exploit IHil; eauto. intro.
   monadInv EQ1.
   constructor.
-  intros id v. simpl. repeat rewrite PTree.gsspec.
-  destruct (peq id a). subst a. intro.
+  intros id v. simpl. repeat rewrite ATree.gsspec.
+  destruct (ATree.elt_eq id a). subst a. intro.
   exists x1. split. auto. inv H3. constructor.
   eauto with rtlg.
   intros. eapply me_vars; eauto.
@@ -398,7 +398,7 @@ Proof.
   intros until tf. unfold transl_fundef, transf_partial_fundef.
   case f; intro.
   unfold transl_function.
-  destruct (reserve_labels (fn_body f0) (PTree.empty node, init_state)) as [ngoto s0].
+  destruct (reserve_labels (fn_body f0) (ATree.empty node, init_state)) as [ngoto s0].
   case (transl_fun f0 ngoto s0); simpl; intros.
   discriminate.
   destruct p. simpl in H. inversion H. reflexivity.
@@ -516,8 +516,8 @@ Definition transl_condexpr_prop
   corresponding to the evaluations of sub-expressions or sub-statements. *)
 
 Lemma transl_expr_Evar_correct:
-  forall (le : letenv) (id : positive) (v: val),
-  e ! id = Some v ->
+  forall (le : letenv) (id : ident) (v: val),
+  e $ id = Some v ->
   transl_expr_prop le (Evar id) v.
 Proof.
   intros; red; intros. inv TE.
@@ -1263,7 +1263,7 @@ Qed.
 
 Lemma tr_find_label:
   forall c map lbl n (ngoto: labelmap) nret rret s' k' cs,
-  ngoto!lbl = Some n ->
+  ngoto$lbl = Some n ->
   forall s k ns1 nd1 nexits1,
   find_label lbl s k = Some (s', k') ->
   tr_stmt c map s ns1 nd1 nexits1 ngoto nret rret ->
diff --git a/backend/RTLgenspec.v b/backend/RTLgenspec.v
index 17022a7df5..c463bfa804 100644
--- a/backend/RTLgenspec.v
+++ b/backend/RTLgenspec.v
@@ -238,7 +238,7 @@ Hint Resolve regs_valid_incr: rtlg.
   local or let-bound variable. *)
 
 Definition reg_in_map (m: mapping) (r: reg) : Prop :=
-  (exists id, m.(map_vars)!id = Some r) \/ In r m.(map_letvars).
+  (exists id, m.(map_vars)$id = Some r) \/ In r m.(map_letvars).
 
 (** A compilation environment (mapping) is valid in a given state if
   the registers associated with Cminor local variables and let-bound variables
@@ -316,7 +316,7 @@ Lemma init_mapping_valid:
 Proof.
   unfold map_valid, init_mapping.
   intros s r [[id A] | B].
-  simpl in A. rewrite PTree.gempty in A; discriminate.
+  simpl in A. rewrite ATree.gempty in A; discriminate.
   simpl in B. tauto.
 Qed.
 
@@ -326,7 +326,7 @@ Lemma find_var_in_map:
   forall s1 s2 map name r i,
   find_var map name s1 = OK r s2 i -> reg_in_map map r.
 Proof.
-  intros until r. unfold find_var; caseEq (map.(map_vars)!name).
+  intros until r. unfold find_var; caseEq (ATree.get name map.(map_vars)).
   intros. inv H0. left; exists name; auto.
   intros. inv H0.
 Qed.
@@ -371,7 +371,7 @@ Proof.
   intros. monadInv H.
   split. eauto with rtlg.
   inversion EQ. subst. red. intros r' [[id A] | B].
-  simpl in A. rewrite PTree.gsspec in A. destruct (peq id name).
+  simpl in A. rewrite ATree.gsspec in A. destruct (ATree.elt_eq id name).
   inv A. eauto with rtlg.
   apply reg_valid_incr with s1. eauto with rtlg.
   apply H0. left; exists id; auto.
@@ -381,9 +381,9 @@ Qed.
 
 Lemma add_var_find:
   forall s1 s2 map name r map' i,
-  add_var map name s1 = OK (r,map') s2 i -> map'.(map_vars)!name = Some r.
+  add_var map name s1 = OK (r,map') s2 i -> map'.(map_vars)$name = Some r.
 Proof.
-  intros. monadInv H. simpl. apply PTree.gss.
+  intros. monadInv H. simpl. apply ATree.gss.
 Qed.
 
 Lemma add_vars_valid:
@@ -517,7 +517,7 @@ Qed.
 Inductive target_reg_ok (map: mapping) (pr: list reg): expr -> reg -> Prop :=
   | target_reg_var:
       forall id r,
-      map.(map_vars)!id = Some r ->
+      map.(map_vars)$id = Some r ->
       target_reg_ok map pr (Evar id) r
   | target_reg_letvar:
       forall idx r,
@@ -587,7 +587,7 @@ Proof.
   intros. unfold alloc_reg in H1. destruct a;
   try (eapply new_reg_target_ok; eauto; fail).
   (* Evar *)
-  generalize H1; unfold find_var. caseEq (map_vars map)!i0; intros.
+  generalize H1; unfold find_var. caseEq (map_vars map)$i0; intros.
   inv H3. constructor. auto. inv H3.
   (* Elet *)
   generalize H1; unfold find_letvar. caseEq (nth_error (map_letvars map) n); intros.
@@ -673,7 +673,7 @@ Inductive reg_map_ok: mapping -> reg -> option ident -> Prop :=
       ~reg_in_map map rd ->
       reg_map_ok map rd None
   | reg_map_ok_somevar: forall map rd id,
-      map.(map_vars)!id = Some rd ->
+      map.(map_vars)$id = Some rd ->
       reg_map_ok map rd (Some id).
 
 Hint Resolve reg_map_ok_novar: rtlg.
@@ -696,7 +696,7 @@ Hint Resolve reg_map_ok_novar: rtlg.
 Inductive tr_expr (c: code):
        mapping -> list reg -> expr -> node -> node -> reg -> option ident -> Prop :=
   | tr_Evar: forall map pr id ns nd r rd dst,
-      map.(map_vars)!id = Some r ->
+      map.(map_vars)$id = Some r ->
       ((rd = r /\ dst = None) \/ (reg_map_ok map rd dst /\ ~In rd pr)) ->
       tr_move c ns r nd rd ->
       tr_expr c map pr (Evar id) ns nd rd dst
@@ -811,7 +811,7 @@ Inductive tr_exitexpr (c: code):
 
 Inductive tr_builtin_res: mapping -> builtin_res ident -> builtin_res reg -> Prop :=
   | tr_builtin_res_var: forall map id r,
-      map.(map_vars)!id = Some r ->
+      map.(map_vars)$id = Some r ->
       tr_builtin_res map (BR id) (BR r)
   | tr_builtin_res_none: forall map,
       tr_builtin_res map BR_none BR_none
@@ -833,7 +833,7 @@ Inductive tr_stmt (c: code) (map: mapping):
   | tr_Sskip: forall ns nexits ngoto nret rret,
      tr_stmt c map Sskip ns ns nexits ngoto nret rret
   | tr_Sassign: forall id a ns nd nexits ngoto nret rret r,
-     map.(map_vars)!id = Some r ->
+     map.(map_vars)$id = Some r ->
      tr_expr c map nil a ns nd r (Some id) ->
      tr_stmt c map (Sassign id a) ns nd nexits ngoto nret rret
   | tr_Sstore: forall chunk addr al b ns nd nexits ngoto nret rret rd n1 rl n2,
@@ -895,12 +895,12 @@ Inductive tr_stmt (c: code) (map: mapping):
      tr_expr c map nil a ns nret rret None ->
      tr_stmt c map (Sreturn (Some a)) ns nd nexits ngoto nret (Some rret)
   | tr_Slabel: forall lbl s ns nd nexits ngoto nret rret n,
-     ngoto!lbl = Some n ->
+     ngoto$lbl = Some n ->
      c!n = Some (Inop ns) ->
      tr_stmt c map s ns nd nexits ngoto nret rret ->
      tr_stmt c map (Slabel lbl s) ns nd nexits ngoto nret rret
   | tr_Sgoto: forall lbl ns nd nexits ngoto nret rret,
-     ngoto!lbl = Some ns ->
+     ngoto$lbl = Some ns ->
      tr_stmt c map (Sgoto lbl) ns nd nexits ngoto nret rret.
 
 (** [tr_function f tf] specifies the RTL function [tf] that
@@ -1002,7 +1002,7 @@ with transl_condexpr_charact:
 Proof.
   induction a; intros; try (monadInv TR); saturateTrans.
   (* Evar *)
-  generalize EQ; unfold find_var. caseEq (map_vars map)!i; intros; inv EQ1.
+  generalize EQ; unfold find_var. caseEq (map_vars map)$i; intros; inv EQ1.
   econstructor; eauto.
   inv OK. left; split; congruence. right; eauto with rtlg.
   eapply add_move_charact; eauto.
@@ -1096,7 +1096,7 @@ Lemma transl_expr_assign_charact:
 Proof.
   induction a; intros; monadInv TR; saturateTrans.
   (* Evar *)
-  generalize EQ; unfold find_var. caseEq (map_vars map)!i; intros; inv EQ1.
+  generalize EQ; unfold find_var. caseEq (map_vars map)$i; intros; inv EQ1.
   econstructor; eauto.
   eapply add_move_charact; eauto.
   (* Eop *)
@@ -1140,7 +1140,7 @@ Lemma alloc_optreg_map_ok:
   reg_map_ok map r optid.
 Proof.
   unfold alloc_optreg; intros. destruct optid.
-  constructor. unfold find_var in H0. destruct (map_vars map)!i0; monadInv H0. auto.
+  constructor. unfold find_var in H0. destruct (map_vars map)$i0; monadInv H0. auto.
   constructor. eapply new_reg_not_in_map; eauto.
 Qed.
 
@@ -1223,7 +1223,7 @@ Lemma convert_builtin_res_charact:
   tr_builtin_res map res res'.
 Proof.
   destruct res; simpl; intros.
-- monadInv TR. constructor.  unfold find_var in EQ. destruct (map_vars map)!x; inv EQ; auto.
+- monadInv TR. constructor.  unfold find_var in EQ. destruct (map_vars map)$x; inv EQ; auto.
 - destruct oty; monadInv TR.
 + constructor. eauto with rtlg.
 + constructor.
@@ -1241,7 +1241,7 @@ Proof.
   (* Sskip *)
   constructor.
   (* Sassign *)
-  revert EQ. unfold find_var. case_eq (map_vars map)!i; intros; monadInv EQ.
+  revert EQ. unfold find_var. case_eq (map_vars map)$i; intros; monadInv EQ.
   eapply tr_Sassign; eauto.
   eapply transl_expr_assign_charact; eauto with rtlg.
   constructor. auto.
@@ -1323,13 +1323,13 @@ Proof.
   constructor. auto. simpl; tauto.
   monadInv TR. constructor.
   (* Slabel *)
-  generalize EQ0; clear EQ0. case_eq (ngoto!l); intros; monadInv EQ0.
+  generalize EQ0; clear EQ0. case_eq (ngoto$l); intros; monadInv EQ0.
   generalize EQ1; clear EQ1. unfold handle_error.
   case_eq (update_instr n (Inop ns) s0); intros; inv EQ1.
   econstructor. eauto. eauto with rtlg.
   eapply tr_stmt_incr with s0; eauto with rtlg.
   (* Sgoto *)
-  generalize TR; clear TR. case_eq (ngoto!l); intros; monadInv TR.
+  generalize TR; clear TR. case_eq (ngoto$l); intros; monadInv TR.
   econstructor. auto.
 Qed.
 
@@ -1339,7 +1339,7 @@ Lemma transl_function_charact:
   tr_function f tf.
 Proof.
   intros until tf. unfold transl_function.
-  caseEq (reserve_labels (fn_body f) (PTree.empty node, init_state)).
+  caseEq (reserve_labels (fn_body f) (ATree.empty node, init_state)).
   intros ngoto s0 RESERVE.
   caseEq (transl_fun f ngoto s0). congruence.
   intros [nentry rparams] sfinal INCR TR E. inv E.
diff --git a/backend/Selection.v b/backend/Selection.v
index 4520cb0c54..c06bdace81 100644
--- a/backend/Selection.v
+++ b/backend/Selection.v
@@ -62,7 +62,7 @@ Definition store (chunk: memory_chunk) (e1 e2: expr) :=
 Section SELECTION.
 
 Definition globdef := AST.globdef Cminor.fundef unit.
-Variable defmap: PTree.t globdef.
+Variable defmap: ATree.t globdef.
 Context {hf: helper_functions}.
 
 Definition sel_constant (cst: Cminor.constant) : expr :=
@@ -192,7 +192,7 @@ Definition classify_call (e: Cminor.expr) : call_kind :=
   match expr_is_addrof_ident e with
   | None => Call_default
   | Some id =>
-      match defmap!id with
+      match defmap$id with
       | Some(Gfun(External ef)) => if ef_inline ef then Call_builtin ef else Call_imm id
       | _ => Call_imm id
       end
@@ -322,7 +322,7 @@ End SELECTION.
 
 (** Conversion of functions. *)
 
-Definition sel_function (dm: PTree.t globdef) (hf: helper_functions) (f: Cminor.function) : res function :=
+Definition sel_function (dm: ATree.t globdef) (hf: helper_functions) (f: Cminor.function) : res function :=
   do body' <- sel_stmt dm f.(Cminor.fn_body);
   OK (mkfunction
         f.(Cminor.fn_sig)
@@ -331,7 +331,7 @@ Definition sel_function (dm: PTree.t globdef) (hf: helper_functions) (f: Cminor.
         f.(Cminor.fn_stackspace)
         body').
 
-Definition sel_fundef (dm: PTree.t globdef) (hf: helper_functions) (f: Cminor.fundef) : res fundef :=
+Definition sel_fundef (dm: ATree.t globdef) (hf: helper_functions) (f: Cminor.fundef) : res fundef :=
   transf_partial_fundef (sel_function dm hf) f.
 
 (** Setting up the helper functions. *)
@@ -349,10 +349,10 @@ Definition globdef_of_interest (gd: globdef) : bool :=
   | _ => false
   end.
 
-Definition record_globdefs (defmap: PTree.t globdef) : PTree.t globdef :=
-  PTree.fold
-    (fun m id gd => if globdef_of_interest gd then PTree.set id gd m else m)
-    defmap (PTree.empty globdef).
+Definition record_globdefs (defmap: ATree.t globdef) : ATree.t globdef :=
+  ATree.fold
+    (fun m id gd => if globdef_of_interest gd then ATree.set id gd m else m)
+    defmap (ATree.empty globdef).
 
 Definition lookup_helper_aux
      (name: String.string) (sg: signature) (res: option ident)
@@ -365,16 +365,16 @@ Definition lookup_helper_aux
   | _ => res
   end.
 
-Definition lookup_helper (globs: PTree.t globdef)
+Definition lookup_helper (globs: ATree.t globdef)
                          (name: String.string) (sg: signature) : res ident :=
-  match PTree.fold (lookup_helper_aux name sg) globs None with
+  match ATree.fold (lookup_helper_aux name sg) globs None with
   | Some id => OK id
   | None    => Error (MSG name :: MSG ": missing or incorrect declaration" :: nil)
   end.
 
 Local Open Scope string_scope.
 
-Definition get_helpers (defmap: PTree.t globdef) : res helper_functions :=
+Definition get_helpers (defmap: ATree.t globdef) : res helper_functions :=
   let globs := record_globdefs defmap in
   do i64_dtos <- lookup_helper globs "__compcert_i64_dtos" sig_f_l ;
   do i64_dtou <- lookup_helper globs "__compcert_i64_dtou" sig_f_l ;
diff --git a/backend/Selectionproof.v b/backend/Selectionproof.v
index dc01ad20b3..3de8f75b8b 100644
--- a/backend/Selectionproof.v
+++ b/backend/Selectionproof.v
@@ -33,31 +33,31 @@ Definition match_prog (p: Cminor.program) (tp: CminorSel.program) :=
 (** Processing of helper functions *)
 
 Lemma record_globdefs_sound:
-  forall dm id gd, (record_globdefs dm)!id = Some gd -> dm!id = Some gd.
+  forall dm id gd, (record_globdefs dm)$id = Some gd -> dm$id = Some gd.
 Proof.
   intros.
-  set (f := fun m id gd => if globdef_of_interest gd then PTree.set id gd m else m) in *.
-  set (P := fun m m' => m'!id = Some gd -> m!id = Some gd).
-  assert (X: P dm (PTree.fold f dm (PTree.empty _))).
-  { apply PTree_Properties.fold_rec.
+  set (f := fun m id gd => if globdef_of_interest gd then ATree.set id gd m else m) in *.
+  set (P := fun m m' => m'$id = Some gd -> m$id = Some gd).
+  assert (X: P dm (ATree.fold f dm (ATree.empty _))).
+  { apply ATree_Properties.fold_rec.
   - unfold P; intros. rewrite <- H0; auto.
-  - red. rewrite ! PTree.gempty. auto.
-  - unfold P; intros. rewrite PTree.gsspec. unfold f in H3.
+  - red. rewrite ! ATree.gempty. auto.
+  - unfold P; intros. rewrite ATree.gsspec. unfold f in H3.
     destruct (globdef_of_interest v).
-    + rewrite PTree.gsspec in H3. destruct (peq id k); auto.
-    + apply H2 in H3. destruct (peq id k). congruence. auto. }
+    + rewrite ATree.gsspec in H3. destruct (ATree.elt_eq id k); auto.
+    + apply H2 in H3. destruct (ATree.elt_eq id k). congruence. auto. }
   apply X. auto.
 Qed.
 
 Lemma lookup_helper_correct_1:
   forall globs name sg id,
   lookup_helper globs name sg = OK id ->
-  globs!id = Some (Gfun (External (EF_runtime name sg))).
+  globs$id = Some (Gfun (External (EF_runtime name sg))).
 Proof.
   intros.
-  set (P := fun (m: PTree.t globdef) res => res = Some id -> m!id = Some(Gfun(External (EF_runtime name sg)))).
-  assert (P globs (PTree.fold (lookup_helper_aux name sg) globs None)).
-  { apply PTree_Properties.fold_rec; red; intros.
+  set (P := fun (m: ATree.t globdef) res => res = Some id -> m$id = Some(Gfun(External (EF_runtime name sg)))).
+  assert (P globs (ATree.fold (lookup_helper_aux name sg) globs None)).
+  { apply ATree_Properties.fold_rec; red; intros.
   - rewrite <- H0. apply H1; auto.
   - discriminate.
   - assert (EITHER: k = id /\ v = Gfun (External (EF_runtime name sg))
@@ -67,11 +67,11 @@ Proof.
       destruct (signature_eq sg sg0); auto.
       inversion H3. left; split; auto. repeat f_equal; auto. }
     destruct EITHER as [[X Y] | X].
-    subst k v. apply PTree.gss.
-    apply H2 in X. rewrite PTree.gso by congruence. auto.
+    subst k v. apply ATree.gss.
+    apply H2 in X. rewrite ATree.gso by congruence. auto.
   }
   red in H0. unfold lookup_helper in H.
-  destruct (PTree.fold (lookup_helper_aux name sg) globs None); inv H. auto.
+  destruct (ATree.fold (lookup_helper_aux name sg) globs None); inv H. auto.
 Qed.
 
 Lemma lookup_helper_correct:
@@ -357,7 +357,7 @@ Proof.
   destruct (Genv.find_symbol ge id) as [b|] eqn:FS; try discriminate.
   rewrite Genv.find_funct_find_funct_ptr in H1.
   assert (DFL: exists b1, Genv.find_symbol ge id = Some b1 /\ Vptr b Ptrofs.zero = Vptr b1 Ptrofs.zero) by (exists b; auto).
-  unfold globdef; destruct (prog_defmap unit)!id as [[[f|ef] |gv] |] eqn:G; auto.
+  unfold globdef; destruct (prog_defmap unit)$id as [[[f|ef] |gv] |] eqn:G; auto.
   destruct (ef_inline ef) eqn:INLINE; auto.
   destruct (prog_defmap_linkorder _ _ _ _ H G) as (gd & P & Q).
   inv Q. inv H2.
@@ -601,14 +601,14 @@ Qed.
 (** Relationship between the local environments. *)
 
 Definition env_lessdef (e1 e2: env) : Prop :=
-  forall id v1, e1!id = Some v1 -> exists v2, e2!id = Some v2 /\ Val.lessdef v1 v2.
+  forall id v1, e1$id = Some v1 -> exists v2, e2$id = Some v2 /\ Val.lessdef v1 v2.
 
 Lemma set_var_lessdef:
   forall e1 e2 id v1 v2,
   env_lessdef e1 e2 -> Val.lessdef v1 v2 ->
-  env_lessdef (PTree.set id v1 e1) (PTree.set id v2 e2).
+  env_lessdef (ATree.set id v1 e1) (ATree.set id v2 e2).
 Proof.
-  intros; red; intros. rewrite PTree.gsspec in *. destruct (peq id0 id).
+  intros; red; intros. rewrite ATree.gsspec in *. destruct (ATree.elt_eq id0 id).
   exists v2; split; congruence.
   auto.
 Qed.
@@ -627,7 +627,7 @@ Lemma set_params_lessdef:
   env_lessdef (set_params vl1 il) (set_params vl2 il).
 Proof.
   induction il; simpl; intros.
-  red; intros. rewrite PTree.gempty in H0; congruence.
+  red; intros. rewrite ATree.gempty in H0; congruence.
   inv H; apply set_var_lessdef; auto.
 Qed.
 
@@ -837,9 +837,9 @@ Remark match_call_cont_cont:
   forall k k', match_call_cont k k' -> exists cunit hf, match_cont cunit hf k k'.
 Proof.
   intros. simple refine (let cunit : Cminor.program := _ in _).
-  econstructor. apply nil. apply nil. apply xH.
+  econstructor. apply nil. apply nil. apply #"!dummy_main!".
   simple refine (let hf : helper_functions := _ in _).
-  econstructor; apply xH.
+  econstructor; apply #"!dummy_helper!".
   exists cunit, hf; auto.
 Qed.
 
diff --git a/backend/SplitLongproof.v b/backend/SplitLongproof.v
index f1e8b5904b..0239a3db8a 100644
--- a/backend/SplitLongproof.v
+++ b/backend/SplitLongproof.v
@@ -53,7 +53,7 @@ Axiom i64_helpers_correct :
  /\ (forall x y, external_implements "__compcert_i64_smulh" sig_ll_l (x::y::nil) (Val.mullhs x y)).
 
 Definition helper_declared {F V: Type} (p: AST.program (AST.fundef F) V) (id: ident) (name: string) (sg: signature) : Prop :=
-  (prog_defmap p)!id = Some (Gfun (External (EF_runtime name sg))).
+  (prog_defmap p)$id = Some (Gfun (External (EF_runtime name sg))).
 
 Definition helper_functions_declared {F V: Type} (p: AST.program (AST.fundef F) V) (hf: helper_functions) : Prop :=
      helper_declared p i64_dtos "__compcert_i64_dtos" sig_f_l
diff --git a/backend/Unusedglob.v b/backend/Unusedglob.v
index 916e111b06..2d064d8fa4 100644
--- a/backend/Unusedglob.v
+++ b/backend/Unusedglob.v
@@ -22,7 +22,7 @@ Local Open Scope string_scope.
 
 (** The working set *)
 
-Module IS := FSetAVL.Make(OrderedPositive).
+Module IS := FSetAVL.Make(OrderedIdent).
 
 Record workset := mk_workset {
   w_seen :> IS.t;
@@ -73,10 +73,10 @@ Definition add_ref_init_data (w: workset) (i: init_data) : workset :=
 Definition add_ref_globvar (gv: globvar unit) (w: workset): workset :=
   List.fold_left add_ref_init_data gv.(gvar_init) w.
 
-Definition prog_map : Type := PTree.t (globdef fundef unit).
+Definition prog_map : Type := ATree.t (globdef fundef unit).
 
 Definition add_ref_definition (pm: prog_map) (id: ident) (w: workset): workset :=
-  match pm!id with
+  match pm$id with
   | None => w
   | Some (Gfun (Internal f)) => add_ref_function f w
   | Some (Gfun (External ef)) => w
@@ -124,7 +124,7 @@ Fixpoint filter_globdefs (used: IS.t) (accu defs: list (ident * globdef fundef u
   the possible exception of the [prog_main] name. *)
 
 Definition global_defined (p: program) (pm: prog_map) (id: ident) : bool :=
-  match pm!id with Some _ => true | None => ident_eq id (prog_main p) end.
+  match pm$id with Some _ => true | None => ident_eq id (prog_main p) end.
 
 Definition transform_program (p: program) : res program :=
   let pm := prog_defmap p in
diff --git a/backend/Unusedglobproof.v b/backend/Unusedglobproof.v
index 7899a04cc9..ba6bd742de 100644
--- a/backend/Unusedglobproof.v
+++ b/backend/Unusedglobproof.v
@@ -34,7 +34,7 @@ Record match_prog_1 (u: IS.t) (p tp: program) : Prop := {
     tp.(prog_public) = p.(prog_public);
   match_prog_def:
     forall id,
-       (prog_defmap tp)!id = if IS.mem id u then (prog_defmap p)!id else None;
+       (prog_defmap tp)$id = if IS.mem id u then (prog_defmap p)$id else None;
   match_prog_unique:
     list_norepet (prog_defs_names tp)
 }.
@@ -59,7 +59,7 @@ Definition ref_def (gd: globdef fundef unit) (id: ident) : Prop :=
 
 Record valid_used_set (p: program) (u: IS.t) : Prop := {
   used_closed: forall id gd id',
-    IS.In id u -> (prog_defmap p)!id = Some gd -> ref_def gd id' ->
+    IS.In id u -> (prog_defmap p)$id = Some gd -> ref_def gd id' ->
     IS.In id' u;
   used_main:
     IS.In p.(prog_main) u;
@@ -148,7 +148,7 @@ Lemma add_ref_definition_incl:
   forall pm id w, workset_incl w (add_ref_definition pm id w).
 Proof.
   unfold add_ref_definition; intros.
-  destruct (pm!id) as [[[] | ? ] | ].
+  destruct (pm$id) as [[[] | ? ] | ].
   apply add_ref_function_incl.
   apply workset_incl_refl.
   apply add_ref_globvar_incl.
@@ -202,7 +202,7 @@ Qed.
 
 Lemma seen_add_ref_definition:
   forall pm id gd id' w,
-  pm!id = Some gd -> ref_def gd id' -> IS.In id' (add_ref_definition pm id w).
+  pm$id = Some gd -> ref_def gd id' -> IS.In id' (add_ref_definition pm id w).
 Proof.
   unfold add_ref_definition; intros. rewrite H. red in H0; destruct gd as [[f|ef]|gv].
   apply seen_add_ref_function; auto.
@@ -255,12 +255,12 @@ Let pm := prog_defmap p.
 
 Definition workset_invariant (w: workset) : Prop :=
   forall id gd id',
-  IS.In id w -> ~List.In id (w_todo w) -> pm!id = Some gd -> ref_def gd id' ->
+  IS.In id w -> ~List.In id (w_todo w) -> pm$id = Some gd -> ref_def gd id' ->
   IS.In id' w.
 
 Definition used_set_closed (u: IS.t) : Prop :=
   forall id gd id',
-  IS.In id u -> pm!id = Some gd -> ref_def gd id' -> IS.In id' u.
+  IS.In id u -> pm$id = Some gd -> ref_def gd id' -> IS.In id' u.
 
 Lemma iter_step_invariant:
   forall w,
@@ -320,7 +320,7 @@ Proof.
 - intros. eapply used_globals_incl; eauto. apply seen_public_initial_workset; auto.
 - intros. apply ISF.for_all_iff in H0.
 + red in H0. apply H0 in H1. unfold global_defined in H1.
-  destruct pm!id as [g|] eqn:E.
+  destruct pm$id as [g|] eqn:E.
 * left. change id with (fst (id,g)). apply in_map. apply in_prog_defmap; auto.
 * InvBooleans; auto.
 + hnf. simpl; intros; congruence.
@@ -335,7 +335,7 @@ Section TRANSFORMATION.
 Variable p: program.
 Variable used: IS.t.
 
-Let add_def (m: prog_map) idg := PTree.set (fst idg) (snd idg) m.
+Let add_def (m: prog_map) idg := ATree.set (fst idg) (snd idg) m.
 
 Remark filter_globdefs_accu:
   forall defs accu1 accu2 u,
@@ -357,14 +357,14 @@ Qed.
 Lemma filter_globdefs_map_1:
   forall id l u m1,
   IS.mem id u = false ->
-  m1!id = None ->
-  (fold_left add_def (filter_globdefs u nil l) m1)!id = None.
+  m1$id = None ->
+  (fold_left add_def (filter_globdefs u nil l) m1)$id = None.
 Proof.
   induction l as [ | [id1 gd1] l]; simpl; intros.
 - auto.
 - destruct (IS.mem id1 u) eqn:MEM.
 + rewrite filter_globdefs_nil. rewrite fold_left_app. simpl.
-  unfold add_def at 1. simpl. rewrite PTree.gso by congruence. eapply IHl; eauto.
+  unfold add_def at 1. simpl. rewrite ATree.gso by congruence. eapply IHl; eauto.
   rewrite ISF.remove_b. rewrite H; auto.
 + eapply IHl; eauto.
 Qed.
@@ -372,8 +372,8 @@ Qed.
 Lemma filter_globdefs_map_2:
   forall id l u m1 m2,
   IS.mem id u = true ->
-  m1!id = m2!id ->
-  (fold_left add_def (filter_globdefs u nil l) m1)!id = (fold_left add_def (List.rev l) m2)!id.
+  m1$id = m2$id ->
+  (fold_left add_def (filter_globdefs u nil l) m1)$id = (fold_left add_def (List.rev l) m2)$id.
 Proof.
   induction l as [ | [id1 gd1] l]; simpl; intros.
 - auto.
@@ -381,22 +381,22 @@ Proof.
   destruct (IS.mem id1 u) eqn:MEM.
 + rewrite filter_globdefs_nil. rewrite fold_left_app. simpl.
   unfold add_def at 1 3. simpl.
-  rewrite ! PTree.gsspec. destruct (peq id id1). auto.
+  rewrite ! ATree.gsspec. destruct (ATree.elt_eq id id1). auto.
   apply IHl; auto.
   apply IS.mem_1. apply IS.remove_2; auto. apply IS.mem_2; auto.
-+ unfold add_def at 2. simpl. rewrite PTree.gso by congruence. apply IHl; auto.
++ unfold add_def at 2. simpl. rewrite ATree.gso by congruence. apply IHl; auto.
 Qed.
 
 Lemma filter_globdefs_map:
   forall id u defs,
-  (PTree_Properties.of_list (filter_globdefs u nil (List.rev defs)))! id =
-  if IS.mem id u then (PTree_Properties.of_list defs)!id else None.
+  (ATree_Properties.of_list (filter_globdefs u nil (List.rev defs)))$ id =
+  if IS.mem id u then (ATree_Properties.of_list defs)$id else None.
 Proof.
-  intros. unfold PTree_Properties.of_list. fold prog_map. unfold PTree.elt. fold add_def.
+  intros. unfold ATree_Properties.of_list. fold prog_map. unfold ATree.elt. fold add_def.
   destruct (IS.mem id u) eqn:MEM.
 - erewrite filter_globdefs_map_2. rewrite List.rev_involutive. reflexivity.
   auto. auto.
-- apply filter_globdefs_map_1. auto. apply PTree.gempty.
+- apply filter_globdefs_map_1. auto. apply ATree.gempty.
 Qed.
 
 Lemma filter_globdefs_domain:
@@ -457,7 +457,7 @@ Definition kept (id: ident) : Prop := IS.In id used.
 
 Lemma kept_closed:
   forall id gd id',
-  kept id -> pm!id = Some gd -> ref_def gd id' -> kept id'.
+  kept id -> pm$id = Some gd -> ref_def gd id' -> kept id'.
 Proof.
   intros. eapply used_closed; eauto.
 Qed.
@@ -481,7 +481,7 @@ Lemma transform_find_symbol_1:
   Genv.find_symbol ge id = Some b -> kept id -> exists b', Genv.find_symbol tge id = Some b'.
 Proof.
   intros.
-  assert (A: exists g, (prog_defmap p)!id = Some g).
+  assert (A: exists g, (prog_defmap p)$id = Some g).
   { apply prog_defmap_dom. eapply Genv.find_symbol_inversion; eauto. }
   destruct A as (g & P).
   apply Genv.find_symbol_exists with g.
@@ -494,7 +494,7 @@ Lemma transform_find_symbol_2:
   Genv.find_symbol tge id = Some b -> kept id /\ exists b', Genv.find_symbol ge id = Some b'.
 Proof.
   intros.
-  assert (A: exists g, (prog_defmap tp)!id = Some g).
+  assert (A: exists g, (prog_defmap tp)$id = Some g).
   { apply prog_defmap_dom. eapply Genv.find_symbol_inversion; eauto. }
   destruct A as (g & P).
   erewrite match_prog_def in P by eauto.
@@ -568,15 +568,15 @@ Proof.
   exists b; split; auto. eapply init_meminj_eq; eauto.
 - exploit init_meminj_invert; eauto. intros (A & id & B & C).
   assert (kept id) by (eapply transform_find_symbol_2; eauto).
-  assert (pm!id = Some gd).
+  assert (pm$id = Some gd).
   { unfold pm; rewrite Genv.find_def_symbol. exists b; auto. }
-  assert ((prog_defmap tp)!id = Some gd).
+  assert ((prog_defmap tp)$id = Some gd).
   { erewrite match_prog_def by eauto. rewrite IS.mem_1 by auto. auto. }
   rewrite Genv.find_def_symbol in H3. destruct H3 as (b1 & P & Q).
   fold tge in P. replace b' with b1 by congruence. split; auto. split; auto.
   intros. eapply kept_closed; eauto.
 - exploit init_meminj_invert; eauto. intros (A & id & B & C).
-  assert ((prog_defmap tp)!id = Some gd).
+  assert ((prog_defmap tp)$id = Some gd).
   { rewrite Genv.find_def_symbol. exists b'; auto. }
   erewrite match_prog_def in H1 by eauto.
   destruct (IS.mem id used); try discriminate.
@@ -1079,7 +1079,7 @@ Lemma init_meminj_invert_strong:
   /\ (forall i, ref_def gd i -> kept i).
 Proof.
   intros. exploit init_meminj_invert; eauto. intros (A & id & B & C).
-  assert (exists gd, (prog_defmap p)!id = Some gd).
+  assert (exists gd, (prog_defmap p)$id = Some gd).
   { apply prog_defmap_dom. eapply Genv.find_symbol_inversion; eauto. }
   destruct H0 as [gd DM]. rewrite Genv.find_def_symbol in DM.
   destruct DM as (b'' & P & Q). fold ge in P. rewrite P in B; inv B.
@@ -1203,7 +1203,7 @@ Lemma init_mem_exists:
 Proof.
   intros. apply Genv.init_mem_exists.
   intros.
-  assert (P: (prog_defmap tp)!id = Some (Gvar v)).
+  assert (P: (prog_defmap tp)$id = Some (Gvar v)).
   { eapply prog_defmap_norepet; eauto. eapply match_prog_unique; eauto. }
   rewrite (match_prog_def _ _ _ TRANSF) in P. destruct (IS.mem id used) eqn:U; try discriminate.
   exploit Genv.init_mem_inversion; eauto. apply in_prog_defmap; eauto. intros [AL FV].
@@ -1305,7 +1305,7 @@ Qed.
 Remark used_not_defined:
   forall p used id,
   valid_used_set p used ->
-  (prog_defmap p)!id = None ->
+  (prog_defmap p)$id = None ->
   IS.mem id used = false \/ id = prog_main p.
 Proof.
   intros. destruct (IS.mem id used) eqn:M; auto.
@@ -1317,7 +1317,7 @@ Remark used_not_defined_2:
   forall p used id,
   valid_used_set p used ->
   id <> prog_main p ->
-  (prog_defmap p)!id = None ->
+  (prog_defmap p)$id = None ->
   ~IS.In id used.
 Proof.
   intros. exploit used_not_defined; eauto. intros [A|A].
@@ -1336,9 +1336,9 @@ Proof.
   destruct (link_prog_inv _ _ _ L) as (X & Y & Z).
   rewrite Z; clear Z; constructor.
 - intros. rewrite ISF.union_iff in H. rewrite ISF.union_iff.
-  rewrite prog_defmap_elements, PTree.gcombine in H0.
-  destruct (prog_defmap p1)!id as [gd1|] eqn:GD1;
-  destruct (prog_defmap p2)!id as [gd2|] eqn:GD2;
+  rewrite prog_defmap_elements, ATree.gcombine in H0.
+  destruct (prog_defmap p1)$id as [gd1|] eqn:GD1;
+  destruct (prog_defmap p2)$id as [gd2|] eqn:GD2;
   simpl in H0; try discriminate.
 + (* common definition *)
   exploit Y; eauto. intros (PUB1 & PUB2 & _).
@@ -1367,20 +1367,19 @@ Proof.
 - intros. rewrite ISF.union_iff in H.
   destruct (ident_eq id (prog_main p1)).
 + right; assumption.
-+ assert (E: exists g, link_prog_merge (prog_defmap p1)!id (prog_defmap p2)!id = Some g).
-  { destruct (prog_defmap p1)!id as [gd1|] eqn:GD1;
-    destruct (prog_defmap p2)!id as [gd2|] eqn:GD2; simpl.
++ assert (E: exists g, link_prog_merge (prog_defmap p1)$id (prog_defmap p2)$id = Some g).
+  { destruct (prog_defmap p1)$id as [gd1|] eqn:GD1;
+    destruct (prog_defmap p2)$id as [gd2|] eqn:GD2; simpl.
   * apply Y with id; auto.
   * exists gd1; auto.
   * exists gd2; auto.
   * eapply used_not_defined_2 in GD1; eauto. eapply used_not_defined_2 in GD2; eauto.
     tauto.
-    congruence.
   }
   destruct E as [g LD].
   left. unfold prog_defs_names; simpl.
-  change id with (fst (id, g)). apply in_map. apply PTree.elements_correct.
-  rewrite PTree.gcombine; auto.
+  change id with (fst (id, g)). apply in_map. apply ATree.elements_correct.
+  rewrite ATree.gcombine; auto.
 Qed.
 
 Theorem link_match_program:
@@ -1408,12 +1407,12 @@ Proof.
 + rewrite W. constructor; simpl; intros.
 * eapply match_prog_main; eauto.
 * rewrite (match_prog_public _ _ _ B1), (match_prog_public _ _ _ B2). auto.
-* rewrite ! prog_defmap_elements, !PTree.gcombine by auto.
+* rewrite ! prog_defmap_elements, !ATree.gcombine by auto.
   rewrite (match_prog_def _ _ _ B1 id), (match_prog_def _ _ _ B2 id).
   rewrite ISF.union_b.
 {
-  destruct (prog_defmap p1)!id as [gd1|] eqn:GD1;
-  destruct (prog_defmap p2)!id as [gd2|] eqn:GD2.
+  destruct (prog_defmap p1)$id as [gd1|] eqn:GD1;
+  destruct (prog_defmap p2)$id as [gd2|] eqn:GD2.
 - (* both defined *)
   exploit V; eauto. intros (PUB1 & PUB2 & _).
   assert (EQ1: IS.mem id used1 = true) by (apply IS.mem_1; eapply used_public; eauto).
@@ -1432,7 +1431,7 @@ Proof.
 - (* none defined *)
   destruct (IS.mem id used1), (IS.mem id used2); auto.
 }
-* intros. apply PTree.elements_keys_norepet.
+* intros. apply ATree.elements_keys_norepet.
 Qed.
 
 Instance TransfSelectionLink : TransfLink match_prog := link_match_program.
diff --git a/backend/ValueAnalysis.v b/backend/ValueAnalysis.v
index 1f80c293b1..2ca154c0cc 100644
--- a/backend/ValueAnalysis.v
+++ b/backend/ValueAnalysis.v
@@ -32,7 +32,7 @@ Definition mafter_public_call : amem := mtop.
 
 Definition mafter_private_call (am_before: amem) : amem :=
   {| am_stack := am_before.(am_stack);
-     am_glob := PTree.empty _;
+     am_glob := ATree.empty _;
      am_nonstack := Nonstack;
      am_top := plub (ab_summary (am_stack am_before)) Nonstack |}.
 
@@ -167,7 +167,7 @@ Module DS := Dataflow_Solver(VA)(NodeSetForward).
 
 Definition mfunction_entry :=
   {| am_stack := ablock_init Pbot;
-     am_glob := PTree.empty _;
+     am_glob := ATree.empty _;
      am_nonstack := Nonstack;
      am_top := Nonstack |}.
 
@@ -224,15 +224,15 @@ Definition definitive_initializer (init: list init_data) : bool :=
 Definition alloc_global (rm: romem) (idg: ident * globdef fundef unit): romem :=
   match idg with
   | (id, Gfun f) =>
-      PTree.remove id rm
+      ATree.remove id rm
   | (id, Gvar v) =>
       if v.(gvar_readonly) && negb v.(gvar_volatile) && definitive_initializer v.(gvar_init)
-      then PTree.set id (store_init_data_list (ablock_init Pbot) 0 v.(gvar_init)) rm
-      else PTree.remove id rm
+      then ATree.set id (store_init_data_list (ablock_init Pbot) 0 v.(gvar_init)) rm
+      else ATree.remove id rm
   end.
 
 Definition romem_for (p: program) : romem :=
-  List.fold_left alloc_global p.(prog_defs) (PTree.empty _).
+  List.fold_left alloc_global p.(prog_defs) (ATree.empty _).
 
 (** * Soundness proof *)
 
@@ -400,11 +400,11 @@ Proof.
 Qed.
 
 Lemma mmatch_no_stack: forall m am astk,
-  mmatch bc m am -> mmatch bc m {| am_stack := astk; am_glob := PTree.empty _; am_nonstack := Nonstack; am_top := Nonstack |}.
+  mmatch bc m am -> mmatch bc m {| am_stack := astk; am_glob := ATree.empty _; am_nonstack := Nonstack; am_top := Nonstack |}.
 Proof.
   intros. destruct H. constructor; simpl; intros.
 - elim (NOSTACK b); auto.
-- rewrite PTree.gempty in H0; discriminate.
+- rewrite ATree.gempty in H0; discriminate.
 - eapply smatch_no_stack; eauto.
 - eapply smatch_no_stack; eauto.
 - auto.
@@ -492,7 +492,7 @@ Proof.
     subst b. apply SMSTACK.
     elim (NOSTACK b); auto.
   + (* globals *)
-    rewrite PTree.gempty in H0; discriminate.
+    rewrite ATree.gempty in H0; discriminate.
   + (* nonstack *)
     destruct (eq_block b sp). congruence. eapply SM; auto. eapply mmatch_nonstack; eauto.
   + (* top *)
@@ -582,7 +582,7 @@ Proof.
 - (* mmatch top *)
   constructor; simpl; intros.
   + destruct (eq_block b sp). congruence. elim n. eapply bc_stack; eauto.
-  + rewrite PTree.gempty in H0; discriminate.
+  + rewrite ATree.gempty in H0; discriminate.
   + destruct (eq_block b sp).
     subst b. eapply SM. eapply mmatch_stack; eauto.
     eapply SM. eapply mmatch_nonstack; eauto.
@@ -669,7 +669,7 @@ Proof.
 - (* mmatch top *)
   constructor; simpl; intros.
   + destruct (eq_block b sp). congruence. elim n. eapply bc_stack; eauto.
-  + rewrite PTree.gempty in H0; discriminate.
+  + rewrite ATree.gempty in H0; discriminate.
   + destruct (eq_block b sp). congruence.
     eapply SM. eauto. eapply mmatch_nonstack; eauto.
   + destruct (eq_block b sp). congruence.
@@ -756,7 +756,7 @@ Proof.
     subst b. eapply SM. eapply mmatch_nonstack; eauto. congruence.
     elim (NOSTACK b); auto.
   + (* globals *)
-    rewrite PTree.gempty in H0; discriminate.
+    rewrite ATree.gempty in H0; discriminate.
   + (* nonstack *)
     destruct (eq_block b sp). congruence. eapply SM; auto. eapply mmatch_nonstack; eauto.
   + (* top *)
@@ -867,7 +867,7 @@ Proof.
     subst b. exact BSTK.
     elim (NOSTACK b); auto.
   + (* globals *)
-    rewrite PTree.gempty in H0; discriminate.
+    rewrite ATree.gempty in H0; discriminate.
   + (* nonstack *)
     destruct (eq_block b sp). congruence. eapply SM; auto. eapply mmatch_nonstack; eauto.
   + (* top *)
@@ -1005,7 +1005,7 @@ Proof.
 - (* mmatch top *)
   constructor; simpl; intros.
   + apply ablock_init_sound. apply SMTOP. simpl; congruence.
-  + rewrite PTree.gempty in H0; discriminate.
+  + rewrite ATree.gempty in H0; discriminate.
   + apply SMTOP; auto.
   + apply SMTOP; auto.
   + red; simpl; intros. destruct (plt b (Mem.nextblock m)).
@@ -1692,7 +1692,7 @@ Proof.
 - destruct (Mem.alloc m 0 1) as [m1 b1] eqn:ALLOC.
   unfold Genv.find_symbol in H2; simpl in H2.
   unfold Genv.find_var_info, Genv.find_def in H3; simpl in H3.
-  rewrite PTree.gsspec in H2. destruct (peq id id1).
+  rewrite ATree.gsspec in H2. destruct (ATree.elt_eq id id1).
   inv H2. rewrite PTree.gss in H3. discriminate.
   assert (Plt b (Genv.genv_next g)) by (eapply Genv.genv_symb_range; eauto).
   rewrite PTree.gso in H3 by (apply Plt_ne; auto).
@@ -1709,7 +1709,7 @@ Proof.
   destruct (Genv.store_init_data_list ge m2 b1 0 (gvar_init gv)) as [m3 | ] eqn:SIDL; try discriminate.
   unfold Genv.find_symbol in H2; simpl in H2.
   unfold Genv.find_var_info, Genv.find_def in H3; simpl in H3.
-  rewrite PTree.gsspec in H2. destruct (peq id id1).
+  rewrite ATree.gsspec in H2. destruct (ATree.elt_eq id id1).
 + injection H2; clear H2; intro EQ.
   rewrite EQ, PTree.gss in H3. injection H3; clear H3; intros EQ'; subst v.
   assert (b = b1). { erewrite Mem.alloc_result by eauto. congruence. }
@@ -1751,11 +1751,11 @@ Proof.
   eapply alloc_global_match; eauto.
 Qed.
 
-Definition romem_consistent (defmap: PTree.t (globdef fundef unit)) (rm: romem) :=
+Definition romem_consistent (defmap: ATree.t (globdef fundef unit)) (rm: romem) :=
   forall id ab,
-  rm!id = Some ab ->
+  rm$id = Some ab ->
   exists v,
-     defmap!id = Some (Gvar v)
+     defmap$id = Some (Gvar v)
   /\ v.(gvar_readonly) = true
   /\ v.(gvar_volatile) = false
   /\ definitive_initializer v.(gvar_init) = true
@@ -1764,18 +1764,18 @@ Definition romem_consistent (defmap: PTree.t (globdef fundef unit)) (rm: romem)
 Lemma alloc_global_consistent:
   forall dm rm idg,
   romem_consistent dm rm ->
-  romem_consistent (PTree.set (fst idg) (snd idg) dm) (alloc_global rm idg).
+  romem_consistent (ATree.set (fst idg) (snd idg) dm) (alloc_global rm idg).
 Proof.
   intros; red; intros. destruct idg as [id1 [f1 | v1]]; simpl in *.
-- rewrite PTree.grspec in H0. destruct (PTree.elt_eq id id1); try discriminate.
-  rewrite PTree.gso by auto. apply H; auto.
+- rewrite ATree.grspec in H0. destruct (ATree.elt_eq id id1); try discriminate.
+  rewrite ATree.gso by auto. apply H; auto.
 - destruct (gvar_readonly v1 && negb (gvar_volatile v1) && definitive_initializer (gvar_init v1)) eqn:RO.
 + InvBooleans. rewrite negb_true_iff in H4.
-  rewrite PTree.gsspec in *. destruct (peq id id1).
+  rewrite ATree.gsspec in *. destruct (ATree.elt_eq id id1).
 * inv H0. exists v1; auto.
 * apply H; auto.
-+ rewrite PTree.grspec in H0. destruct (PTree.elt_eq id id1); try discriminate.
-  rewrite PTree.gso by auto. apply H; auto.
++ rewrite ATree.grspec in H0. destruct (ATree.elt_eq id id1); try discriminate.
+  rewrite ATree.gso by auto. apply H; auto.
 Qed.
 
 Lemma romem_for_consistent:
@@ -1783,11 +1783,11 @@ Lemma romem_for_consistent:
 Proof.
   assert (REC: forall l dm rm,
             romem_consistent dm rm ->
-            romem_consistent (fold_left (fun m idg => PTree.set (fst idg) (snd idg) m) l dm)
+            romem_consistent (fold_left (fun m idg => ATree.set (fst idg) (snd idg) m) l dm)
                              (fold_left alloc_global l rm)).
   { induction l; intros; simpl; auto. apply IHl. apply alloc_global_consistent; auto. }
   intros. apply REC.
-  red; intros. rewrite PTree.gempty in H; discriminate.
+  red; intros. rewrite ATree.gempty in H; discriminate.
 Qed.
 
 Lemma romem_for_consistent_2:
@@ -1822,7 +1822,7 @@ Proof.
   assert (A: initial_mem_match bc m ge).
   {
     apply alloc_globals_match with (m := Mem.empty); auto.
-    red. unfold Genv.find_symbol; simpl; intros. rewrite PTree.gempty in H1; discriminate.
+    red. unfold Genv.find_symbol; simpl; intros. rewrite ATree.gempty in H1; discriminate.
   }
   assert (B: romem_consistent (prog_defmap prog) (romem_for cunit)) by (apply romem_for_consistent_2; auto).
   red; intros.
diff --git a/backend/ValueDomain.v b/backend/ValueDomain.v
index e7e44e29eb..f18d436ceb 100644
--- a/backend/ValueDomain.v
+++ b/backend/ValueDomain.v
@@ -25,7 +25,7 @@ Inductive block_class : Type :=
   | BCother.
 
 Definition block_class_eq: forall (x y: block_class), {x=y} + {x<>y}.
-Proof. decide equality. apply peq. Defined.
+Proof. decide equality. apply ident_eq. Defined.
 
 Record block_classification : Type := BC {
   bc_img :> block -> block_class;
@@ -290,9 +290,9 @@ Qed.
 Definition pincl (p q: aptr) : bool :=
   match p, q with
   | Pbot, _ => true
-  | Gl id1 ofs1, Gl id2 ofs2 => peq id1 id2 && Ptrofs.eq_dec ofs1 ofs2
-  | Gl id1 ofs1, Glo id2 => peq id1 id2
-  | Glo id1, Glo id2 => peq id1 id2
+  | Gl id1 ofs1, Gl id2 ofs2 => ident_eq id1 id2 && Ptrofs.eq_dec ofs1 ofs2
+  | Gl id1 ofs1, Glo id2 => ident_eq id1 id2
+  | Glo id1, Glo id2 => ident_eq id1 id2
   | (Gl _ _ | Glo _ | Glob), Glob => true
   | (Gl _ _ | Glo _ | Glob | Nonstack), Nonstack => true
   | Stk ofs1, Stk ofs2 => Ptrofs.eq_dec ofs1 ofs2
@@ -391,14 +391,14 @@ Definition pcmp (c: comparison) (p1 p2: aptr) : abool :=
   match p1, p2 with
   | Pbot, _ | _, Pbot => Bnone
   | Gl id1 ofs1, Gl id2 ofs2 =>
-      if peq id1 id2 then Maybe (Ptrofs.cmpu c ofs1 ofs2)
+      if ident_eq id1 id2 then Maybe (Ptrofs.cmpu c ofs1 ofs2)
       else cmp_different_blocks c
   | Gl id1 ofs1, Glo id2 =>
-      if peq id1 id2 then Btop else cmp_different_blocks c
+      if ident_eq id1 id2 then Btop else cmp_different_blocks c
   | Glo id1, Gl id2 ofs2 =>
-      if peq id1 id2 then Btop else cmp_different_blocks c
+      if ident_eq id1 id2 then Btop else cmp_different_blocks c
   | Glo id1, Glo id2 =>
-      if peq id1 id2 then Btop else cmp_different_blocks c
+      if ident_eq id1 id2 then Btop else cmp_different_blocks c
   | Stk ofs1, Stk ofs2 => Maybe (Ptrofs.cmpu c ofs1 ofs2)
   | (Gl _ _ | Glo _ | Glob | Nonstack), (Stk _ | Stack) => cmp_different_blocks c
   | (Stk _ | Stack), (Gl _ _ | Glo _ | Glob | Nonstack) => cmp_different_blocks c
@@ -435,11 +435,11 @@ Proof.
     constructor.
   }
   unfold pcmp; inv H; inv H0; (apply cmatch_top || (apply DIFF; congruence) || idtac).
-  - destruct (peq id id0). subst id0. apply SAME. eapply bc_glob; eauto.
+  - destruct (ident_eq id id0). subst id0. apply SAME. eapply bc_glob; eauto.
     auto with va.
-  - destruct (peq id id0); auto with va.
-  - destruct (peq id id0); auto with va.
-  - destruct (peq id id0); auto with va.
+  - destruct (ident_eq id id0); auto with va.
+  - destruct (ident_eq id id0); auto with va.
+  - destruct (ident_eq id id0); auto with va.
   - apply SAME. eapply bc_stack; eauto.
 Qed.
 
@@ -473,11 +473,11 @@ Proof.
     constructor.
   }
   unfold pcmp; inv H; inv H0; (apply cmatch_top || (apply DIFF; congruence) || idtac).
-  - destruct (peq id id0). subst id0. apply SAME. eapply bc_glob; eauto.
+  - destruct (ident_eq id id0). subst id0. apply SAME. eapply bc_glob; eauto.
     auto with va.
-  - destruct (peq id id0); auto with va.
-  - destruct (peq id id0); auto with va.
-  - destruct (peq id id0); auto with va.
+  - destruct (ident_eq id id0); auto with va.
+  - destruct (ident_eq id id0); auto with va.
+  - destruct (ident_eq id id0); auto with va.
   - apply SAME. eapply bc_stack; eauto.
 Qed.
 
@@ -486,7 +486,7 @@ Lemma pcmp_none:
 Proof.
   intros.
   unfold pcmp; destruct p1; try constructor; destruct p2;
-  try (destruct (peq id id0));  try constructor; try (apply cmp_different_blocks_none).
+  try (destruct (ident_eq id id0));  try constructor; try (apply cmp_different_blocks_none).
 Qed.
 
 Definition pdisjoint (p1: aptr) (sz1: Z) (p2: aptr) (sz2: Z) : bool :=
@@ -494,13 +494,13 @@ Definition pdisjoint (p1: aptr) (sz1: Z) (p2: aptr) (sz2: Z) : bool :=
   | Pbot, _ => true
   | _, Pbot => true
   | Gl id1 ofs1, Gl id2 ofs2 =>
-      if peq id1 id2
+      if ident_eq id1 id2
       then zle (Ptrofs.unsigned ofs1 + sz1) (Ptrofs.unsigned ofs2)
            || zle (Ptrofs.unsigned ofs2 + sz2) (Ptrofs.unsigned ofs1)
       else true
-  | Gl id1 ofs1, Glo id2 => negb(peq id1 id2)
-  | Glo id1, Gl id2 ofs2 => negb(peq id1 id2)
-  | Glo id1, Glo id2 => negb(peq id1 id2)
+  | Gl id1 ofs1, Glo id2 => negb(ident_eq id1 id2)
+  | Glo id1, Gl id2 ofs2 => negb(ident_eq id1 id2)
+  | Glo id1, Glo id2 => negb(ident_eq id1 id2)
   | Stk ofs1, Stk ofs2 =>
       zle (Ptrofs.unsigned ofs1 + sz1) (Ptrofs.unsigned ofs2)
       || zle (Ptrofs.unsigned ofs2 + sz2) (Ptrofs.unsigned ofs1)
@@ -516,11 +516,11 @@ Lemma pdisjoint_sound:
   b1 <> b2 \/ Ptrofs.unsigned ofs1 + sz1 <= Ptrofs.unsigned ofs2 \/ Ptrofs.unsigned ofs2 + sz2 <= Ptrofs.unsigned ofs1.
 Proof.
   intros. inv H0; inv H1; simpl in H; try discriminate; try (left; congruence).
-- destruct (peq id id0). subst id0. destruct (orb_true_elim _ _ H); InvBooleans; auto.
+- destruct (ident_eq id id0). subst id0. destruct (orb_true_elim _ _ H); InvBooleans; auto.
   left; congruence.
-- destruct (peq id id0); try discriminate. left; congruence.
-- destruct (peq id id0); try discriminate. left; congruence.
-- destruct (peq id id0); try discriminate. left; congruence.
+- destruct (ident_eq id id0); try discriminate. left; congruence.
+- destruct (ident_eq id id0); try discriminate. left; congruence.
+- destruct (ident_eq id id0); try discriminate. left; congruence.
 - destruct (orb_true_elim _ _ H); InvBooleans; auto.
 Qed.
 
@@ -3616,12 +3616,12 @@ Qed.
 
 (** * Abstracting read-only global variables *)
 
-Definition romem := PTree.t ablock.
+Definition romem := ATree.t ablock.
 
 Definition romatch  (m: mem) (rm: romem) : Prop :=
   forall b id ab,
   bc b = BCglob id ->
-  rm!id = Some ab ->
+  rm$id = Some ab ->
   pge Glob ab.(ab_summary)
   /\ bmatch m b ab
   /\ forall ofs, ~Mem.perm m b ofs Max Writable.
@@ -3697,7 +3697,7 @@ Qed.
 
 Record amem : Type := AMem {
   am_stack: ablock;
-  am_glob: PTree.t ablock;
+  am_glob: ATree.t ablock;
   am_nonstack: aptr;
   am_top: aptr
 }.
@@ -3708,7 +3708,7 @@ Record mmatch (m: mem) (am: amem) : Prop := mk_mem_match {
     bmatch m b am.(am_stack);
   mmatch_glob: forall id ab b,
     bc b = BCglob id ->
-    am.(am_glob)!id = Some ab ->
+    am.(am_glob)$id = Some ab ->
     bmatch m b ab;
   mmatch_nonstack: forall b,
     bc b <> BCstack -> bc b <> BCinvalid ->
@@ -3722,7 +3722,7 @@ Record mmatch (m: mem) (am: amem) : Prop := mk_mem_match {
 
 Definition minit (p: aptr) :=
   {| am_stack := ablock_init p;
-     am_glob := PTree.empty _;
+     am_glob := ATree.empty _;
      am_nonstack := p;
      am_top := p |}.
 
@@ -3733,19 +3733,19 @@ Definition load (chunk: memory_chunk) (rm: romem) (m: amem) (p: aptr) : aval :=
   match p with
   | Pbot => if va_strict tt then Vbot else Vtop
   | Gl id ofs =>
-      match rm!id with
+      match rm$id with
       | Some ab => ablock_load chunk ab (Ptrofs.unsigned ofs)
       | None =>
-          match m.(am_glob)!id with
+          match m.(am_glob)$id with
           | Some ab => ablock_load chunk ab (Ptrofs.unsigned ofs)
           | None => vnormalize chunk (Ifptr m.(am_nonstack))
           end
       end
   | Glo id =>
-      match rm!id with
+      match rm$id with
       | Some ab => ablock_load_anywhere chunk ab
       | None =>
-          match m.(am_glob)!id with
+          match m.(am_glob)$id with
           | Some ab => ablock_load_anywhere chunk ab
           | None => vnormalize chunk (Ifptr m.(am_nonstack))
           end
@@ -3769,12 +3769,12 @@ Definition store (chunk: memory_chunk) (m: amem) (p: aptr) (av: aval) : amem :=
      am_glob :=
        match p with
        | Gl id ofs =>
-           let ab := match m.(am_glob)!id with Some ab => ab | None => ablock_init m.(am_nonstack) end in
-           PTree.set id (ablock_store chunk ab (Ptrofs.unsigned ofs) av) m.(am_glob)
+           let ab := match m.(am_glob)$id with Some ab => ab | None => ablock_init m.(am_nonstack) end in
+           ATree.set id (ablock_store chunk ab (Ptrofs.unsigned ofs) av) m.(am_glob)
        | Glo id =>
-           let ab := match m.(am_glob)!id with Some ab => ab | None => ablock_init m.(am_nonstack) end in
-           PTree.set id (ablock_store_anywhere chunk ab av) m.(am_glob)
-       | Glob | Nonstack | Ptop => PTree.empty _
+           let ab := match m.(am_glob)$id with Some ab => ab | None => ablock_init m.(am_nonstack) end in
+           ATree.set id (ablock_store_anywhere chunk ab av) m.(am_glob)
+       | Glob | Nonstack | Ptop => ATree.empty _
        | _ => m.(am_glob)
        end;
      am_nonstack :=
@@ -3792,10 +3792,10 @@ Definition loadbytes (m: amem) (rm: romem) (p: aptr) : aptr :=
   match p with
   | Pbot => if va_strict tt then Pbot else Ptop
   | Gl id _ | Glo id =>
-      match rm!id with
+      match rm$id with
       | Some ab => ablock_loadbytes ab
       | None =>
-          match m.(am_glob)!id with
+          match m.(am_glob)$id with
           | Some ab => ablock_loadbytes ab
           | None => m.(am_nonstack)
           end
@@ -3815,12 +3815,12 @@ Definition storebytes (m: amem) (dst: aptr) (sz: Z) (p: aptr) : amem :=
      am_glob :=
        match dst with
        | Gl id ofs =>
-           let ab := match m.(am_glob)!id with Some ab => ab | None => ablock_init m.(am_nonstack) end in
-           PTree.set id (ablock_storebytes ab p (Ptrofs.unsigned ofs) sz) m.(am_glob)
+           let ab := match m.(am_glob)$id with Some ab => ab | None => ablock_init m.(am_nonstack) end in
+           ATree.set id (ablock_storebytes ab p (Ptrofs.unsigned ofs) sz) m.(am_glob)
        | Glo id =>
-           let ab := match m.(am_glob)!id with Some ab => ab | None => ablock_init m.(am_nonstack) end in
-           PTree.set id (ablock_storebytes_anywhere ab p) m.(am_glob)
-       | Glob | Nonstack | Ptop => PTree.empty _
+           let ab := match m.(am_glob)$id with Some ab => ab | None => ablock_init m.(am_nonstack) end in
+           ATree.set id (ablock_storebytes_anywhere ab p) m.(am_glob)
+       | Glob | Nonstack | Ptop => ATree.empty _
        | _ => m.(am_glob)
        end;
      am_nonstack :=
@@ -3841,15 +3841,15 @@ Theorem load_sound:
 Proof.
   intros. unfold load. inv H2.
 - (* Gl id ofs *)
-  destruct (rm!id) as [ab|] eqn:RM.
+  destruct (rm$id) as [ab|] eqn:RM.
   eapply ablock_load_sound; eauto. eapply H0; eauto.
-  destruct (am_glob am)!id as [ab|] eqn:AM.
+  destruct (am_glob am)$id as [ab|] eqn:AM.
   eapply ablock_load_sound; eauto. eapply mmatch_glob; eauto.
   eapply vnormalize_cast; eauto. eapply mmatch_nonstack; eauto; congruence.
 - (* Glo id *)
-  destruct (rm!id) as [ab|] eqn:RM.
+  destruct (rm$id) as [ab|] eqn:RM.
   eapply ablock_load_anywhere_sound; eauto. eapply H0; eauto.
-  destruct (am_glob am)!id as [ab|] eqn:AM.
+  destruct (am_glob am)$id as [ab|] eqn:AM.
   eapply ablock_load_anywhere_sound; eauto. eapply mmatch_glob; eauto.
   eapply vnormalize_cast; eauto. eapply mmatch_nonstack; eauto; congruence.
 - (* Glob *)
@@ -3899,32 +3899,32 @@ Proof.
 
 - (* Globals *)
   rename b0 into b'.
-  assert (DFL: bc b <> BCglob id -> (am_glob am)!id = Some ab ->
+  assert (DFL: bc b <> BCglob id -> (am_glob am)$id = Some ab ->
                bmatch m' b' ab).
   { intros. apply bmatch_inv with m. eapply mmatch_glob; eauto.
     intros. eapply Mem.loadbytes_store_other; eauto. left; congruence. }
   inv PM.
-  + rewrite PTree.gsspec in H0. destruct (peq id id0).
+  + rewrite ATree.gsspec in H0. destruct (ATree.elt_eq id id0).
     subst id0; inv H0.
     assert (b' = b) by (eapply bc_glob; eauto). subst b'.
     eapply ablock_store_sound; eauto.
-    destruct (am_glob am)!id as [ab0|] eqn:GL.
+    destruct (am_glob am)$id as [ab0|] eqn:GL.
     eapply mmatch_glob; eauto.
     apply ablock_init_sound. eapply mmatch_nonstack; eauto; congruence.
     eapply DFL; eauto. congruence.
-  + rewrite PTree.gsspec in H0. destruct (peq id id0).
+  + rewrite ATree.gsspec in H0. destruct (ATree.elt_eq id id0).
     subst id0; inv H0.
     assert (b' = b) by (eapply bc_glob; eauto). subst b'.
     eapply ablock_store_anywhere_sound; eauto.
-    destruct (am_glob am)!id as [ab0|] eqn:GL.
+    destruct (am_glob am)$id as [ab0|] eqn:GL.
     eapply mmatch_glob; eauto.
     apply ablock_init_sound. eapply mmatch_nonstack; eauto; congruence.
     eapply DFL; eauto. congruence.
-  + rewrite PTree.gempty in H0; congruence.
+  + rewrite ATree.gempty in H0; congruence.
   + eapply DFL; eauto. congruence.
   + eapply DFL; eauto. congruence.
-  + rewrite PTree.gempty in H0; congruence.
-  + rewrite PTree.gempty in H0; congruence.
+  + rewrite ATree.gempty in H0; congruence.
+  + rewrite ATree.gempty in H0; congruence.
 
 - (* Nonstack *)
   assert (DFL: smatch m' b0 (vplub av (am_nonstack am))).
@@ -3964,15 +3964,15 @@ Theorem loadbytes_sound:
 Proof.
   intros. unfold loadbytes; inv H2.
 - (* Gl id ofs *)
-  destruct (rm!id) as [ab|] eqn:RM.
+  destruct (rm$id) as [ab|] eqn:RM.
   exploit H0; eauto. intros (A & B & C). eapply ablock_loadbytes_sound; eauto.
-  destruct (am_glob am)!id as [ab|] eqn:GL.
+  destruct (am_glob am)$id as [ab|] eqn:GL.
   eapply ablock_loadbytes_sound; eauto. eapply mmatch_glob; eauto.
   eapply smatch_loadbytes; eauto. eapply mmatch_nonstack; eauto with va.
 - (* Glo id *)
-  destruct (rm!id) as [ab|] eqn:RM.
+  destruct (rm$id) as [ab|] eqn:RM.
   exploit H0; eauto. intros (A & B & C). eapply ablock_loadbytes_sound; eauto.
-  destruct (am_glob am)!id as [ab|] eqn:GL.
+  destruct (am_glob am)$id as [ab|] eqn:GL.
   eapply ablock_loadbytes_sound; eauto. eapply mmatch_glob; eauto.
   eapply smatch_loadbytes; eauto. eapply mmatch_nonstack; eauto with va.
 - (* Glob *)
@@ -4011,32 +4011,32 @@ Proof.
 
 - (* Globals *)
   rename b0 into b'.
-  assert (DFL: bc b <> BCglob id -> (am_glob am)!id = Some ab ->
+  assert (DFL: bc b <> BCglob id -> (am_glob am)$id = Some ab ->
                bmatch m' b' ab).
   { intros. apply bmatch_inv with m. eapply mmatch_glob; eauto.
     intros. eapply Mem.loadbytes_storebytes_other; eauto. left; congruence. }
   inv PM.
-  + rewrite PTree.gsspec in H0. destruct (peq id id0).
+  + rewrite ATree.gsspec in H0. destruct (ATree.elt_eq id id0).
     subst id0; inv H0.
     assert (b' = b) by (eapply bc_glob; eauto). subst b'.
     eapply ablock_storebytes_sound; eauto.
-    destruct (am_glob am)!id as [ab0|] eqn:GL.
+    destruct (am_glob am)$id as [ab0|] eqn:GL.
     eapply mmatch_glob; eauto.
     apply ablock_init_sound. eapply mmatch_nonstack; eauto; congruence.
     eapply DFL; eauto. congruence.
-  + rewrite PTree.gsspec in H0. destruct (peq id id0).
+  + rewrite ATree.gsspec in H0. destruct (ATree.elt_eq id id0).
     subst id0; inv H0.
     assert (b' = b) by (eapply bc_glob; eauto). subst b'.
     eapply ablock_storebytes_anywhere_sound; eauto.
-    destruct (am_glob am)!id as [ab0|] eqn:GL.
+    destruct (am_glob am)$id as [ab0|] eqn:GL.
     eapply mmatch_glob; eauto.
     apply ablock_init_sound. eapply mmatch_nonstack; eauto; congruence.
     eapply DFL; eauto. congruence.
-  + rewrite PTree.gempty in H0; congruence.
+  + rewrite ATree.gempty in H0; congruence.
   + eapply DFL; eauto. congruence.
   + eapply DFL; eauto. congruence.
-  + rewrite PTree.gempty in H0; congruence.
-  + rewrite PTree.gempty in H0; congruence.
+  + rewrite ATree.gempty in H0; congruence.
+  + rewrite ATree.gempty in H0; congruence.
 
 - (* Nonstack *)
   assert (DFL: smatch m' b0 (plub q (am_nonstack am))).
@@ -4086,7 +4086,7 @@ Proof.
   intros. constructor; simpl; intros.
 - apply ablock_init_sound. apply smatch_ge with (ab_summary (am_stack am)).
   eapply mmatch_stack; eauto. constructor.
-- rewrite PTree.gempty in H1; discriminate.
+- rewrite ATree.gempty in H1; discriminate.
 - eapply smatch_ge. eapply mmatch_nonstack; eauto. constructor.
 - eapply smatch_ge. eapply mmatch_top; eauto. constructor.
 - eapply mmatch_below; eauto.
@@ -4098,21 +4098,21 @@ Definition mbeq (m1 m2: amem) : bool :=
   eq_aptr m1.(am_top) m2.(am_top)
   && eq_aptr m1.(am_nonstack) m2.(am_nonstack)
   && bbeq m1.(am_stack) m2.(am_stack)
-  && PTree.beq bbeq m1.(am_glob) m2.(am_glob).
+  && ATree.beq bbeq m1.(am_glob) m2.(am_glob).
 
 Lemma mbeq_sound:
   forall m1 m2, mbeq m1 m2 = true -> forall m, mmatch m m1 <-> mmatch m m2.
 Proof.
-  unfold mbeq; intros. InvBooleans. rewrite PTree.beq_correct in H1.
+  unfold mbeq; intros. InvBooleans. rewrite ATree.beq_correct in H1.
   split; intros M; inv M; constructor; intros.
 - erewrite <- bbeq_sound; eauto.
-- specialize (H1 id). rewrite H4 in H1. destruct (am_glob m1)!id eqn:G; try contradiction.
+- specialize (H1 id). rewrite H4 in H1. destruct (am_glob m1)$id eqn:G; try contradiction.
   erewrite <- bbeq_sound; eauto.
 - rewrite <- H; eauto.
 - rewrite <- H0; eauto.
 - auto.
 - erewrite bbeq_sound; eauto.
-- specialize (H1 id). rewrite H4 in H1. destruct (am_glob m2)!id eqn:G; try contradiction.
+- specialize (H1 id). rewrite H4 in H1. destruct (am_glob m2)$id eqn:G; try contradiction.
   erewrite bbeq_sound; eauto.
 - rewrite H; eauto.
 - rewrite H0; eauto.
@@ -4129,7 +4129,7 @@ Definition combine_ablock (ob1 ob2: option ablock) : option ablock :=
 
 Definition mlub (m1 m2: amem) : amem :=
 {| am_stack := blub m1.(am_stack) m2.(am_stack);
-   am_glob  := PTree.combine combine_ablock m1.(am_glob) m2.(am_glob);
+   am_glob  := ATree.combine combine_ablock m1.(am_glob) m2.(am_glob);
    am_nonstack := plub m1.(am_nonstack) m2.(am_nonstack);
    am_top := plub m1.(am_top) m2.(am_top) |}.
 
@@ -4138,9 +4138,9 @@ Lemma mmatch_lub_l:
 Proof.
   intros. inv H. constructor; simpl; intros.
 - apply bmatch_lub_l; auto.
-- rewrite PTree.gcombine in H0 by auto. unfold combine_ablock in H0.
-  destruct (am_glob x)!id as [b1|] eqn:G1;
-  destruct (am_glob y)!id as [b2|] eqn:G2;
+- rewrite ATree.gcombine in H0 by auto. unfold combine_ablock in H0.
+  destruct (am_glob x)$id as [b1|] eqn:G1;
+  destruct (am_glob y)$id as [b2|] eqn:G2;
   inv H0.
   apply bmatch_lub_l; eauto.
 - apply smatch_lub_l; auto.
@@ -4153,9 +4153,9 @@ Lemma mmatch_lub_r:
 Proof.
   intros. inv H. constructor; simpl; intros.
 - apply bmatch_lub_r; auto.
-- rewrite PTree.gcombine in H0 by auto. unfold combine_ablock in H0.
-  destruct (am_glob x)!id as [b1|] eqn:G1;
-  destruct (am_glob y)!id as [b2|] eqn:G2;
+- rewrite ATree.gcombine in H0 by auto. unfold combine_ablock in H0.
+  destruct (am_glob x)$id as [b1|] eqn:G1;
+  destruct (am_glob y)$id as [b2|] eqn:G2;
   inv H0.
   apply bmatch_lub_r; eauto.
 - apply smatch_lub_r; auto.
@@ -4364,7 +4364,7 @@ Proof.
   }
   constructor; simpl; intros.
   - apply ablock_init_sound. apply SM. congruence.
-  - rewrite PTree.gempty in H1; discriminate.
+  - rewrite ATree.gempty in H1; discriminate.
   - apply SM; auto.
   - apply SM; auto.
   - red; intros. eapply Mem.valid_block_inject_1. eapply inj_of_bc_valid; eauto. eauto.
diff --git a/cfrontend/C2C.ml b/cfrontend/C2C.ml
index b81345991b..6480a337e8 100644
--- a/cfrontend/C2C.ml
+++ b/cfrontend/C2C.ml
@@ -107,7 +107,7 @@ let atom_location a =
 
 (** The current environment of composite definitions *)
 
-let comp_env : composite_env ref = ref Maps.PTree.empty
+let comp_env : composite_env ref = ref Symbols.ATree.empty
 
 (** Hooks -- overriden in machine-dependent CPragmas module *)
 
@@ -1410,7 +1410,7 @@ let convertProgram p =
         comp_env := ce;
         let gl1 = convertGlobdecls env [] p in
         let gl2 = globals_for_strings gl1 in
-        comp_env := Maps.PTree.empty;
+        comp_env := Symbols.ATree.empty;
         let p' =
           { prog_defs = gl2;
             prog_public = public_globals gl2;
diff --git a/cfrontend/Cexec.v b/cfrontend/Cexec.v
index 823d2542d9..9f7e5205e3 100644
--- a/cfrontend/Cexec.v
+++ b/cfrontend/Cexec.v
@@ -154,7 +154,7 @@ Proof.
 - auto.
 - auto.
 - auto.
-- rewrite (Genv.find_invert_symbol _ _ H0). simpl in H; rewrite H.
+- rewrite (Genv.find_invert_symbol H0). simpl in H; rewrite H.
   rewrite dec_eq_true. auto. 
 Qed.
 
@@ -238,7 +238,7 @@ Lemma do_volatile_load_complete:
   do_volatile_load w chunk m b ofs = Some(w', t, v).
 Proof.
   unfold do_volatile_load; intros. inv H; simpl in *.
-  rewrite H1. rewrite (Genv.find_invert_symbol _ _ H2). inv H0. inv H8. inv H6. rewrite H9.
+  rewrite H1. rewrite (Genv.find_invert_symbol H2). inv H0. inv H8. inv H6. rewrite H9.
   rewrite (val_of_eventval_complete _ _ _ H3). auto.
   rewrite H1. rewrite H2. inv H0. auto.
 Qed.
@@ -261,7 +261,7 @@ Lemma do_volatile_store_complete:
   do_volatile_store w chunk m b ofs v = Some(w', t, m').
 Proof.
   unfold do_volatile_store; intros. inv H; simpl in *.
-  rewrite H1. rewrite (Genv.find_invert_symbol _ _ H2).
+  rewrite H1. rewrite (Genv.find_invert_symbol H2).
   rewrite (eventval_of_val_complete _ _ _ H3).
   inv H0. inv H8. inv H6. rewrite H9. auto.
   rewrite H1. rewrite H2. inv H0. auto.
@@ -682,7 +682,7 @@ Fixpoint step_expr (k: kind) (a: expr) (m: mem): reducts expr :=
   | LV, Eloc b ofs ty =>
       nil
   | LV, Evar x ty =>
-      match e!x with
+      match e$x with
       | Some(b, ty') =>
           check type_eq ty ty';
           topred (Lred "red_var_local" (Eloc b Ptrofs.zero ty) m)
@@ -704,13 +704,13 @@ Fixpoint step_expr (k: kind) (a: expr) (m: mem): reducts expr :=
       | Some(Vptr b ofs, ty') =>
           match ty' with
           | Tstruct id _ =>
-              do co <- ge.(genv_cenv)!id;
+              do co <- ge.(genv_cenv)$id;
               match field_offset ge f (co_members co) with
               | Error _ => stuck
               | OK delta => topred (Lred "red_field_struct" (Eloc b (Ptrofs.add ofs (Ptrofs.repr delta)) ty) m)
               end
           | Tunion id _ =>
-              do co <- ge.(genv_cenv)!id;
+              do co <- ge.(genv_cenv)$id;
               topred (Lred "red_field_union" (Eloc b ofs ty) m)
           | _ => stuck
           end
@@ -925,15 +925,15 @@ Definition invert_expr_prop (a: expr) (m: mem) : Prop :=
   | Eloc b ofs ty => False
   | Evar x ty =>
       exists b,
-      e!x = Some(b, ty)
-      \/ (e!x = None /\ Genv.find_symbol ge x = Some b)
+      e$x = Some(b, ty)
+      \/ (e$x = None /\ Genv.find_symbol ge x = Some b)
   | Ederef (Eval v ty1) ty =>
       exists b, exists ofs, v = Vptr b ofs
   | Efield (Eval v ty1) f ty =>
       exists b, exists ofs, v = Vptr b ofs /\
       match ty1 with
-      | Tstruct id _ => exists co delta, ge.(genv_cenv)!id = Some co /\ field_offset ge f (co_members co) = OK delta
-      | Tunion  id _ => exists co, ge.(genv_cenv)!id = Some co
+      | Tstruct id _ => exists co delta, ge.(genv_cenv)$id = Some co /\ field_offset ge f (co_members co) = OK delta
+      | Tunion  id _ => exists co, ge.(genv_cenv)$id = Some co
       | _ => False
       end
   | Eval v ty => False
@@ -1318,7 +1318,7 @@ Proof with (try (apply not_invert_ok; simpl; intro; myinv; intuition congruence;
 (* Eval *)
   split; intros. tauto. simpl; congruence.
 (* Evar *)
-  destruct (e!x) as [[b ty']|] eqn:?.
+  destruct (e$x) as [[b ty']|] eqn:?.
   destruct (type_eq ty ty')...
   subst. apply topred_ok; auto. apply red_var_local; auto.
   destruct (Genv.find_symbol ge x) as [b|] eqn:?...
@@ -1329,11 +1329,11 @@ Proof with (try (apply not_invert_ok; simpl; intro; myinv; intuition congruence;
   destruct v...
   destruct ty'...
   (* top struct *)
-  destruct (ge.(genv_cenv)!i0) as [co|] eqn:?...
+  destruct (ge.(genv_cenv)$i0) as [co|] eqn:?...
   destruct (field_offset ge f (co_members co)) as [delta|] eqn:?...
   apply topred_ok; auto. eapply red_field_struct; eauto.
   (* top union *)
-  destruct (ge.(genv_cenv)!i0) as [co|] eqn:?...
+  destruct (ge.(genv_cenv)$i0) as [co|] eqn:?...
   apply topred_ok; auto. eapply red_field_union; eauto.
   (* in depth *)
   eapply incontext_ok; eauto.
@@ -1846,7 +1846,7 @@ Fixpoint do_alloc_variables (e: env) (m: mem) (l: list (ident * type)) {struct l
   | nil => (e,m)
   | (id, ty) :: l' =>
       let (m1,b1) := Mem.alloc m 0 (sizeof ge ty) in
-      do_alloc_variables (PTree.set id (b1, ty) e) m1 l'
+      do_alloc_variables (ATree.set id (b1, ty) e) m1 l'
 end.
 
 Lemma do_alloc_variables_sound:
@@ -1872,7 +1872,7 @@ Function sem_bind_parameters (w: world) (e: env) (m: mem) (l: list (ident * type
   match l, lv  with
   | nil, nil => Some m
   | (id, ty) :: params, v1::lv =>
-      match PTree.get id e with
+      match ATree.get id e with
          | Some (b, ty') =>
              check (type_eq ty ty');
              do w', t, m1 <- do_assign_loc w ty m b Ptrofs.zero v1;
diff --git a/cfrontend/Clight.v b/cfrontend/Clight.v
index 7a4c49a2f3..55f1877075 100644
--- a/cfrontend/Clight.v
+++ b/cfrontend/Clight.v
@@ -188,13 +188,13 @@ Definition globalenv (p: program) :=
   types.  The current value of the variable is stored in the
   associated memory block. *)
 
-Definition env := PTree.t (block * type). (* map variable -> location & type *)
+Definition env := ATree.t (block * type). (* map variable -> location & type *)
 
-Definition empty_env: env := (PTree.empty (block * type)).
+Definition empty_env: env := (ATree.empty (block * type)).
 
 (** The temporary environment maps local temporaries to values. *)
 
-Definition temp_env := PTree.t val.
+Definition temp_env := ATree.t val.
 
 (** [deref_loc ty m b ofs v] computes the value of a datum
   of type [ty] residing in memory [m] at block [b], offset [ofs].
@@ -257,7 +257,7 @@ Inductive alloc_variables: env -> mem ->
   | alloc_variables_cons:
       forall e m id ty vars m1 b1 m2 e2,
       Mem.alloc m 0 (sizeof ge ty) = (m1, b1) ->
-      alloc_variables (PTree.set id (b1, ty) e) m1 vars e2 m2 ->
+      alloc_variables (ATree.set id (b1, ty) e) m1 vars e2 m2 ->
       alloc_variables e m ((id, ty) :: vars) e2 m2.
 
 (** Initialization of local variables that are parameters to a function.
@@ -273,7 +273,7 @@ Inductive bind_parameters (e: env):
       bind_parameters e m nil nil m
   | bind_parameters_cons:
       forall m id ty params v1 vl b m1 m2,
-      PTree.get id e = Some(b, ty) ->
+      ATree.get id e = Some(b, ty) ->
       assign_loc ge ty m b Ptrofs.zero v1 m1 ->
       bind_parameters e m1 params vl m2 ->
       bind_parameters e m ((id, ty) :: params) (v1 :: vl) m2.
@@ -282,8 +282,8 @@ Inductive bind_parameters (e: env):
 
 Fixpoint create_undef_temps (temps: list (ident * type)) : temp_env :=
   match temps with
-  | nil => PTree.empty val
-  | (id, t) :: temps' => PTree.set id Vundef (create_undef_temps temps')
+  | nil => ATree.empty val
+  | (id, t) :: temps' => ATree.set id Vundef (create_undef_temps temps')
  end.
 
 (** Initialization of temporary variables that are parameters to a function. *)
@@ -292,7 +292,7 @@ Fixpoint bind_parameter_temps (formals: list (ident * type)) (args: list val)
                               (le: temp_env) : option temp_env :=
  match formals, args with
  | nil, nil => Some le
- | (id, t) :: xl, v :: vl => bind_parameter_temps xl vl (PTree.set id v le)
+ | (id, t) :: xl, v :: vl => bind_parameter_temps xl vl (ATree.set id v le)
  | _, _ => None
  end.
 
@@ -302,14 +302,14 @@ Definition block_of_binding (id_b_ty: ident * (block * type)) :=
   match id_b_ty with (id, (b, ty)) => (b, 0, sizeof ge ty) end.
 
 Definition blocks_of_env (e: env) : list (block * Z * Z) :=
-  List.map block_of_binding (PTree.elements e).
+  List.map block_of_binding (ATree.elements e).
 
 (** Optional assignment to a temporary *)
 
 Definition set_opttemp (optid: option ident) (v: val) (le: temp_env) :=
   match optid with
   | None => le
-  | Some id => PTree.set id v le
+  | Some id => ATree.set id v le
   end.
 
 (** Selection of the appropriate case of a [switch], given the value [n]
@@ -365,7 +365,7 @@ Inductive eval_expr: expr -> val -> Prop :=
   | eval_Econst_long:   forall i ty,
       eval_expr (Econst_long i ty) (Vlong i)
   | eval_Etempvar:  forall id ty v,
-      le!id = Some v ->
+      le$id = Some v ->
       eval_expr (Etempvar id ty) v
   | eval_Eaddrof: forall a ty loc ofs,
       eval_lvalue a loc ofs ->
@@ -398,10 +398,10 @@ Inductive eval_expr: expr -> val -> Prop :=
 
 with eval_lvalue: expr -> block -> ptrofs -> Prop :=
   | eval_Evar_local:   forall id l ty,
-      e!id = Some(l, ty) ->
+      e$id = Some(l, ty) ->
       eval_lvalue (Evar id ty) l Ptrofs.zero
   | eval_Evar_global: forall id l ty,
-      e!id = None ->
+      e$id = None ->
       Genv.find_symbol ge id = Some l ->
       eval_lvalue (Evar id ty) l Ptrofs.zero
   | eval_Ederef: forall a ty l ofs,
@@ -410,13 +410,13 @@ with eval_lvalue: expr -> block -> ptrofs -> Prop :=
  | eval_Efield_struct:   forall a i ty l ofs id co att delta,
       eval_expr a (Vptr l ofs) ->
       typeof a = Tstruct id att ->
-      ge.(genv_cenv)!id = Some co ->
+      ge.(genv_cenv)$id = Some co ->
       field_offset ge i (co_members co) = OK delta ->
       eval_lvalue (Efield a i ty) l (Ptrofs.add ofs (Ptrofs.repr delta))
  | eval_Efield_union:   forall a i ty l ofs id co att,
       eval_expr a (Vptr l ofs) ->
       typeof a = Tunion id att ->
-      ge.(genv_cenv)!id = Some co ->
+      ge.(genv_cenv)$id = Some co ->
       eval_lvalue (Efield a i ty) l ofs.
 
 Scheme eval_expr_ind2 := Minimality for eval_expr Sort Prop
@@ -557,7 +557,7 @@ Inductive step: state -> trace -> state -> Prop :=
   | step_set:   forall f id a k e le m v,
       eval_expr e le m a v ->
       step (State f (Sset id a) k e le m)
-        E0 (State f Sskip k e (PTree.set id v le) m)
+        E0 (State f Sskip k e (ATree.set id v le) m)
 
   | step_call:   forall f optid a al k e le m tyargs tyres cconv vf vargs fd,
       classify_fun (typeof a) = fun_case_f tyargs tyres cconv ->
diff --git a/cfrontend/ClightBigstep.v b/cfrontend/ClightBigstep.v
index 92457586eb..2d8869c646 100644
--- a/cfrontend/ClightBigstep.v
+++ b/cfrontend/ClightBigstep.v
@@ -88,7 +88,7 @@ Inductive exec_stmt: env -> temp_env -> mem -> statement -> trace -> temp_env ->
   | exec_Sset:     forall e le m id a v,
       eval_expr ge e le m a v ->
       exec_stmt e le m (Sset id a)
-               E0 (PTree.set id v le) m Out_normal
+               E0 (ATree.set id v le) m Out_normal
   | exec_Scall:   forall e le m optid a al tyargs tyres cconv vf vargs f t m' vres,
       classify_fun (typeof a) = fun_case_f tyargs tyres cconv ->
       eval_expr ge e le m a vf ->
diff --git a/cfrontend/Cminorgen.v b/cfrontend/Cminorgen.v
index 45c21f9677..29bf470c3f 100644
--- a/cfrontend/Cminorgen.v
+++ b/cfrontend/Cminorgen.v
@@ -40,13 +40,13 @@ Local Open Scope error_monad_scope.
 (** To every Csharpminor variable, the compiler associates its offset
   in the Cminor stack data block. *)
 
-Definition compilenv := PTree.t Z.
+Definition compilenv := ATree.t Z.
 
 (** Generation of a Cminor expression for taking the address of
   a Csharpminor variable. *)
 
 Definition var_addr (cenv: compilenv) (id: ident): expr :=
-  match PTree.get id cenv with
+  match ATree.get id cenv with
   | Some ofs => Econst (Oaddrstack (Ptrofs.repr ofs))
   | None     => Econst (Oaddrsymbol id Ptrofs.zero)
   end.
@@ -226,7 +226,7 @@ Definition assign_variable
   let (id, sz) := id_sz in
   let (cenv, stacksize) := cenv_stacksize in
   let ofs := align stacksize (block_alignment sz) in
-  (PTree.set id ofs cenv, ofs + Z.max 0 sz).
+  (ATree.set id ofs cenv, ofs + Z.max 0 sz).
 
 Definition assign_variables (cenv_stacksize: compilenv * Z) (vars: list (ident * Z)) : compilenv * Z :=
   List.fold_left assign_variable vars cenv_stacksize.
@@ -248,7 +248,7 @@ End VarOrder.
 Module VarSort := Mergesort.Sort(VarOrder).
 
 Definition build_compilenv (f: Csharpminor.function) : compilenv * Z :=
-  assign_variables (PTree.empty Z, 0) (VarSort.sort (Csharpminor.fn_vars f)).
+  assign_variables (ATree.empty Z, 0) (VarSort.sort (Csharpminor.fn_vars f)).
 
 (** * Translation of functions *)
 
diff --git a/cfrontend/Cminorgenproof.v b/cfrontend/Cminorgenproof.v
index ffafc5d242..520bafa6f0 100644
--- a/cfrontend/Cminorgenproof.v
+++ b/cfrontend/Cminorgenproof.v
@@ -164,7 +164,7 @@ Qed.
 (** ** Matching between Cshaprminor's temporaries and Cminor's variables *)
 
 Definition match_temps (f: meminj) (le: Csharpminor.temp_env) (te: env) : Prop :=
-  forall id v, le!id = Some v -> exists v', te!(id) = Some v' /\ Val.inject f v v'.
+  forall id v, le$id = Some v -> exists v', te$(id) = Some v' /\ Val.inject f v v'.
 
 Lemma match_temps_invariant:
   forall f f' le te,
@@ -179,9 +179,9 @@ Lemma match_temps_assign:
   forall f le te id v tv,
   match_temps f le te ->
   Val.inject f v tv ->
-  match_temps f (PTree.set id v le) (PTree.set id tv te).
+  match_temps f (ATree.set id v le) (ATree.set id tv te).
 Proof.
-  intros; red; intros. rewrite PTree.gsspec in *. destruct (peq id0 id).
+  intros; red; intros. rewrite ATree.gsspec in *. destruct (ATree.elt_eq id0 id).
   inv H1. exists tv; auto.
   eauto.
 Qed.
@@ -206,7 +206,7 @@ Record match_env (f: meminj) (cenv: compilenv)
 
 (** C#minor local variables match sub-blocks of the Cminor stack data block. *)
     me_vars:
-      forall id, match_var f sp (e!id) (cenv!id);
+      forall id, match_var f sp (e$id) (cenv$id);
 
 (** [lo, hi] is a proper interval. *)
     me_low_high:
@@ -215,14 +215,14 @@ Record match_env (f: meminj) (cenv: compilenv)
 (** Every block appearing in the C#minor environment [e] must be
   in the range [lo, hi]. *)
     me_bounded:
-      forall id b sz, PTree.get id e = Some(b, sz) -> Ple lo b /\ Plt b hi;
+      forall id b sz, ATree.get id e = Some(b, sz) -> Ple lo b /\ Plt b hi;
 
 (** All blocks mapped to sub-blocks of the Cminor stack data must be
     images of variables from the C#minor environment [e] *)
     me_inv:
       forall b delta,
       f b = Some(sp, delta) ->
-      exists id, exists sz, PTree.get id e = Some(b, sz);
+      exists id, exists sz, ATree.get id e = Some(b, sz);
 
 (** All C#minor blocks below [lo] (i.e. allocated before the blocks
   referenced from [e]) must map to blocks that are below [sp]
@@ -294,39 +294,39 @@ Qed.
 
 Lemma match_env_alloc:
   forall f1 id cenv e sp lo m1 sz m2 b ofs f2,
-  match_env f1 (PTree.remove id cenv) e sp lo (Mem.nextblock m1) ->
+  match_env f1 (ATree.remove id cenv) e sp lo (Mem.nextblock m1) ->
   Mem.alloc m1 0 sz = (m2, b) ->
-  cenv!id = Some ofs ->
+  cenv$id = Some ofs ->
   inject_incr f1 f2 ->
   f2 b = Some(sp, ofs) ->
   (forall b', b' <> b -> f2 b' = f1 b') ->
-  e!id = None ->
-  match_env f2 cenv (PTree.set id (b, sz) e) sp lo (Mem.nextblock m2).
+  e$id = None ->
+  match_env f2 cenv (ATree.set id (b, sz) e) sp lo (Mem.nextblock m2).
 Proof.
   intros until f2; intros ME ALLOC CENV INCR SAME OTHER ENV.
   exploit Mem.nextblock_alloc; eauto. intros NEXTBLOCK.
   exploit Mem.alloc_result; eauto. intros RES.
   inv ME; constructor.
 (* vars *)
-  intros. rewrite PTree.gsspec. destruct (peq id0 id).
+  intros. rewrite ATree.gsspec. destruct (ATree.elt_eq id0 id).
   (* the new var *)
   subst id0. rewrite CENV. constructor. econstructor. eauto.
   rewrite Ptrofs.add_commut; rewrite Ptrofs.add_zero; auto.
   (* old vars *)
-  generalize (me_vars0 id0). rewrite PTree.gro; auto. intros M; inv M.
+  generalize (me_vars0 id0). rewrite ATree.gro; auto. intros M; inv M.
   constructor; eauto.
   constructor.
 (* low-high *)
   rewrite NEXTBLOCK; xomega.
 (* bounded *)
-  intros. rewrite PTree.gsspec in H. destruct (peq id0 id).
+  intros. rewrite ATree.gsspec in H. destruct (ATree.elt_eq id0 id).
   inv H. rewrite NEXTBLOCK; xomega.
   exploit me_bounded0; eauto. rewrite NEXTBLOCK; xomega.
 (* inv *)
   intros. destruct (eq_block b (Mem.nextblock m1)).
-  subst b. rewrite SAME in H; inv H. exists id; exists sz. apply PTree.gss.
+  subst b. rewrite SAME in H; inv H. exists id; exists sz. apply ATree.gss.
   rewrite OTHER in H; auto. exploit me_inv0; eauto.
-  intros [id1 [sz1 EQ]]. exists id1; exists sz1. rewrite PTree.gso; auto. congruence.
+  intros [id1 [sz1 EQ]]. exists id1; exists sz1. rewrite ATree.gso; auto. congruence.
 (* incr *)
   intros. rewrite OTHER in H. eauto. unfold block in *; xomega.
 Qed.
@@ -335,13 +335,13 @@ Qed.
 
 Definition match_bounds (e: Csharpminor.env) (m: mem) : Prop :=
   forall id b sz ofs p,
-  PTree.get id e = Some(b, sz) -> Mem.perm m b ofs Max p -> 0 <= ofs < sz.
+  ATree.get id e = Some(b, sz) -> Mem.perm m b ofs Max p -> 0 <= ofs < sz.
 
 Lemma match_bounds_invariant:
   forall e m1 m2,
   match_bounds e m1 ->
   (forall id b sz ofs p,
-   PTree.get id e = Some(b, sz) -> Mem.perm m2 b ofs Max p -> Mem.perm m1 b ofs Max p) ->
+   ATree.get id e = Some(b, sz) -> Mem.perm m2 b ofs Max p -> Mem.perm m1 b ofs Max p) ->
   match_bounds e m2.
 Proof.
   intros; red; intros. eapply H; eauto.
@@ -354,7 +354,7 @@ Qed.
 
 Inductive is_reachable_from_env (f: meminj) (e: Csharpminor.env) (sp: block) (ofs: Z) : Prop :=
   | is_reachable_intro: forall id b sz delta,
-      e!id = Some(b, sz) ->
+      e$id = Some(b, sz) ->
       f b = Some(sp, delta) ->
       delta <= ofs < delta + sz ->
       is_reachable_from_env f e sp ofs.
@@ -395,7 +395,7 @@ Proof.
                                else false
                       end
                  end).
-  destruct (List.existsb pred (PTree.elements e)) eqn:?.
+  destruct (List.existsb pred (ATree.elements e)) eqn:?.
   (* yes *)
   rewrite List.existsb_exists in Heqb.
   destruct Heqb as [[id [b sz]] [A B]].
@@ -403,14 +403,14 @@ Proof.
   destruct (eq_block sp sp'); try discriminate.
   destruct (andb_prop _ _ B).
   left. apply is_reachable_intro with id b sz delta.
-  apply PTree.elements_complete; auto.
+  apply ATree.elements_complete; auto.
   congruence.
   split; eapply proj_sumbool_true; eauto.
   (* no *)
   right; red; intro NE; inv NE.
-  assert (existsb pred (PTree.elements e) = true).
+  assert (existsb pred (ATree.elements e) = true).
   rewrite List.existsb_exists. exists (id, (b, sz)); split.
-  apply PTree.elements_correct; auto.
+  apply ATree.elements_correct; auto.
   simpl. rewrite H0. rewrite dec_eq_true.
   unfold proj_sumbool. destruct H1. rewrite zle_true; auto. rewrite zlt_true; auto.
   congruence.
@@ -548,7 +548,7 @@ Lemma match_callstack_set_temp:
   forall f cenv e le te sp lo hi cs bound tbound m tm tf id v tv,
   Val.inject f v tv ->
   match_callstack f m tm (Frame cenv tf e le te sp lo hi :: cs) bound tbound ->
-  match_callstack f m tm (Frame cenv tf e (PTree.set id v le) (PTree.set id tv te) sp lo hi :: cs) bound tbound.
+  match_callstack f m tm (Frame cenv tf e (ATree.set id v le) (ATree.set id tv te) sp lo hi :: cs) bound tbound.
 Proof.
   intros. inv H0. constructor; auto.
   eapply match_temps_assign; eauto.
@@ -560,22 +560,22 @@ Qed.
 
 Lemma in_blocks_of_env:
   forall e id b sz,
-  e!id = Some(b, sz) -> In (b, 0, sz) (blocks_of_env e).
+  e$id = Some(b, sz) -> In (b, 0, sz) (blocks_of_env e).
 Proof.
   unfold blocks_of_env; intros.
   change (b, 0, sz) with (block_of_binding (id, (b, sz))).
-  apply List.in_map. apply PTree.elements_correct. auto.
+  apply List.in_map. apply ATree.elements_correct. auto.
 Qed.
 
 Lemma in_blocks_of_env_inv:
   forall b lo hi e,
   In (b, lo, hi) (blocks_of_env e) ->
-  exists id, e!id = Some(b, hi) /\ lo = 0.
+  exists id, e$id = Some(b, hi) /\ lo = 0.
 Proof.
   unfold blocks_of_env; intros.
   exploit list_in_map_inv; eauto. intros [[id [b' sz]] [A B]].
   unfold block_of_binding in A. inv A.
-  exists id; intuition. apply PTree.elements_complete. auto.
+  exists id; intuition. apply ATree.elements_complete. auto.
 Qed.
 
 Lemma match_callstack_freelist:
@@ -674,7 +674,7 @@ Lemma match_callstack_alloc_right:
   Mem.alloc tm 0 tf.(fn_stackspace) = (tm', sp) ->
   Mem.inject f m tm ->
   match_temps f le te ->
-  (forall id, cenv!id = None) ->
+  (forall id, cenv$id = None) ->
   match_callstack f m tm'
       (Frame cenv tf empty_env le te sp (Mem.nextblock m) (Mem.nextblock m) :: cs)
       (Mem.nextblock m) (Mem.nextblock tm').
@@ -687,12 +687,12 @@ Proof.
   unfold block in *; xomega.
   auto.
   constructor; intros.
-    rewrite H3. rewrite PTree.gempty. constructor.
+    rewrite H3. rewrite ATree.gempty. constructor.
     xomega.
-    rewrite PTree.gempty in H4; discriminate.
+    rewrite ATree.gempty in H4; discriminate.
     eelim Mem.fresh_block_alloc; eauto. eapply Mem.valid_block_inject_2; eauto.
     rewrite RES. change (Mem.valid_block tm tb). eapply Mem.valid_block_inject_2; eauto.
-  red; intros. rewrite PTree.gempty in H4. discriminate.
+  red; intros. rewrite ATree.gempty in H4. discriminate.
   red; intros. left. eapply Mem.perm_alloc_2; eauto.
   eapply match_callstack_invariant with (tm1 := tm); eauto.
   rewrite RES; auto.
@@ -702,16 +702,16 @@ Qed.
 Lemma match_callstack_alloc_left:
   forall f1 m1 tm id cenv tf e le te sp lo cs sz m2 b f2 ofs,
   match_callstack f1 m1 tm
-    (Frame (PTree.remove id cenv) tf e le te sp lo (Mem.nextblock m1) :: cs)
+    (Frame (ATree.remove id cenv) tf e le te sp lo (Mem.nextblock m1) :: cs)
     (Mem.nextblock m1) (Mem.nextblock tm) ->
   Mem.alloc m1 0 sz = (m2, b) ->
-  cenv!id = Some ofs ->
+  cenv$id = Some ofs ->
   inject_incr f1 f2 ->
   f2 b = Some(sp, ofs) ->
   (forall b', b' <> b -> f2 b' = f1 b') ->
-  e!id = None ->
+  e$id = None ->
   match_callstack f2 m2 tm
-    (Frame cenv tf (PTree.set id (b, sz) e) le te sp lo (Mem.nextblock m2) :: cs)
+    (Frame cenv tf (ATree.set id (b, sz) e) le te sp lo (Mem.nextblock m2) :: cs)
     (Mem.nextblock m2) (Mem.nextblock tm).
 Proof.
   intros. inv H.
@@ -723,13 +723,13 @@ Proof.
   auto.
   eapply match_temps_invariant; eauto.
   eapply match_env_alloc; eauto.
-  red; intros. rewrite PTree.gsspec in H. destruct (peq id0 id).
+  red; intros. rewrite ATree.gsspec in H. destruct (ATree.elt_eq id0 id).
   inversion H. subst b0 sz0 id0. eapply Mem.perm_alloc_3; eauto.
   eapply BOUND0; eauto. eapply Mem.perm_alloc_4; eauto.
   exploit me_bounded; eauto. unfold block in *; xomega.
   red; intros. exploit PERM; eauto. intros [A|A]. auto. right.
   inv A. apply is_reachable_intro with id0 b0 sz0 delta; auto.
-  rewrite PTree.gso. auto. congruence.
+  rewrite ATree.gso. auto. congruence.
   eapply match_callstack_invariant with (m1 := m1); eauto.
   intros. eapply Mem.perm_alloc_4; eauto.
   unfold block in *; xomega.
@@ -745,26 +745,26 @@ Qed.
   local variables as sub-blocks of the Cminor stack data.  This is the most difficult part of the proof. *)
 
 Definition cenv_remove (cenv: compilenv) (vars: list (ident * Z)) : compilenv :=
-  fold_right (fun id_lv ce => PTree.remove (fst id_lv) ce) cenv vars.
+  fold_right (fun id_lv ce => ATree.remove (fst id_lv) ce) cenv vars.
 
 Remark cenv_remove_gso:
   forall id vars cenv,
   ~In id (map fst vars) ->
-  PTree.get id (cenv_remove cenv vars) = PTree.get id cenv.
+  ATree.get id (cenv_remove cenv vars) = ATree.get id cenv.
 Proof.
   induction vars; simpl; intros.
   auto.
-  rewrite PTree.gro. apply IHvars. intuition. intuition.
+  rewrite ATree.gro. apply IHvars. intuition. intuition.
 Qed.
 
 Remark cenv_remove_gss:
   forall id vars cenv,
   In id (map fst vars) ->
-  PTree.get id (cenv_remove cenv vars) = None.
+  ATree.get id (cenv_remove cenv vars) = None.
 Proof.
   induction vars; simpl; intros.
   contradiction.
-  rewrite PTree.grspec. destruct (PTree.elt_eq id (fst a)). auto.
+  rewrite ATree.grspec. destruct (ATree.elt_eq id (fst a)). auto.
   destruct H. intuition. eauto.
 Qed.
 
@@ -772,7 +772,7 @@ Definition cenv_compat (cenv: compilenv) (vars: list (ident * Z)) (tsz: Z) : Pro
   forall id sz,
   In (id, sz) vars ->
   exists ofs,
-      PTree.get id cenv = Some ofs
+      ATree.get id cenv = Some ofs
    /\ Mem.inj_offset_aligned ofs sz
    /\ 0 <= ofs
    /\ ofs + Z.max 0 sz <= tsz.
@@ -780,13 +780,13 @@ Definition cenv_compat (cenv: compilenv) (vars: list (ident * Z)) (tsz: Z) : Pro
 Definition cenv_separated (cenv: compilenv) (vars: list (ident * Z)) : Prop :=
   forall id1 sz1 ofs1 id2 sz2 ofs2,
   In (id1, sz1) vars -> In (id2, sz2) vars ->
-  PTree.get id1 cenv = Some ofs1 -> PTree.get id2 cenv = Some ofs2 ->
+  ATree.get id1 cenv = Some ofs1 -> ATree.get id2 cenv = Some ofs2 ->
   id1 <> id2 ->
   ofs1 + sz1 <= ofs2 \/ ofs2 + sz2 <= ofs1.
 
 Definition cenv_mem_separated (cenv: compilenv) (vars: list (ident * Z)) (f: meminj) (sp: block) (m: mem) : Prop :=
   forall id sz ofs b delta ofs' k p,
-  In (id, sz) vars -> PTree.get id cenv = Some ofs ->
+  In (id, sz) vars -> ATree.get id cenv = Some ofs ->
   f b = Some (sp, delta) ->
   Mem.perm m b ofs' k p ->
   ofs <= ofs' + delta < sz + ofs -> False.
@@ -804,7 +804,7 @@ Lemma match_callstack_alloc_variables_rec:
   cenv_compat cenv vars (fn_stackspace tf) ->
   cenv_separated cenv vars ->
   cenv_mem_separated cenv vars f1 sp m1 ->
-  (forall id sz, In (id, sz) vars -> e1!id = None) ->
+  (forall id sz, In (id, sz) vars -> e1$id = None) ->
   match_callstack f1 m1 tm
     (Frame (cenv_remove cenv vars) tf e1 le te sp lo (Mem.nextblock m1) :: cs)
     (Mem.nextblock m1) (Mem.nextblock tm) ->
@@ -844,7 +844,7 @@ Proof.
     omega.
     eapply SEP2. apply in_cons; eauto. eauto.
     rewrite D in H5; eauto. eauto. auto.
-    intros. rewrite PTree.gso. eapply UNBOUND; eauto with coqlib.
+    intros. rewrite ATree.gso. eapply UNBOUND; eauto with coqlib.
     red; intros; subst id0. elim H3. change id with (fst (id, sz0)). apply in_map; auto.
     eapply match_callstack_alloc_left; eauto.
     rewrite cenv_remove_gso; auto.
@@ -859,7 +859,7 @@ Lemma match_callstack_alloc_variables:
   list_norepet (map fst vars) ->
   cenv_compat cenv vars (fn_stackspace fn) ->
   cenv_separated cenv vars ->
-  (forall id ofs, cenv!id = Some ofs -> In id (map fst vars)) ->
+  (forall id ofs, cenv$id = Some ofs -> In id (map fst vars)) ->
   Mem.inject f1 m1 tm1 ->
   match_callstack f1 m1 tm1 cs (Mem.nextblock m1) (Mem.nextblock tm1) ->
   match_temps f1 le te ->
@@ -875,12 +875,12 @@ Proof.
   intros. apply Mem.perm_implies with Freeable; auto with mem. eapply Mem.perm_alloc_2; eauto.
   instantiate (1 := f1). red; intros. eelim Mem.fresh_block_alloc; eauto.
   eapply Mem.valid_block_inject_2; eauto.
-  intros. apply PTree.gempty.
+  intros. apply ATree.gempty.
   eapply match_callstack_alloc_right; eauto.
-  intros. destruct (In_dec peq id (map fst vars)).
+  intros. destruct (In_dec ident_eq id (map fst vars)).
   apply cenv_remove_gss; auto.
   rewrite cenv_remove_gso; auto.
-  destruct (cenv!id) as [ofs|] eqn:?; auto. elim n; eauto.
+  destruct (cenv$id) as [ofs|] eqn:?; auto. elim n; eauto.
   eapply Mem.alloc_right_inject; eauto.
 Qed.
 
@@ -975,21 +975,21 @@ Proof.
   apply EITHER in H. destruct H as [[P Q] | P].
   exploit COMPAT; eauto. intros [ofs [A [B [C D]]]].
   exists ofs.
-  split. rewrite PTree.gso; auto.
+  split. rewrite ATree.gso; auto.
   split. auto. split. auto. zify; omega.
   inv P. exists (align sz1 (block_alignment sz)).
-  split. apply PTree.gss.
+  split. apply ATree.gss.
   split. apply inj_offset_aligned_block.
   split. omega.
   omega.
   apply EITHER in H; apply EITHER in H0.
   destruct H as [[P Q] | P]; destruct H0 as [[R S] | R].
-  rewrite PTree.gso in *; auto. eapply SEP; eauto.
-  inv R. rewrite PTree.gso in H1; auto. rewrite PTree.gss in H2; inv H2.
+  rewrite ATree.gso in *; auto. eapply SEP; eauto.
+  inv R. rewrite ATree.gso in H1; auto. rewrite ATree.gss in H2; inv H2.
   exploit COMPAT; eauto. intros [ofs [A [B [C D]]]].
   assert (ofs = ofs1) by congruence. subst ofs.
   left. zify; omega.
-  inv P. rewrite PTree.gso in H2; auto. rewrite PTree.gss in H1; inv H1.
+  inv P. rewrite ATree.gso in H2; auto. rewrite ATree.gss in H1; inv H1.
   exploit COMPAT; eauto. intros [ofs [A [B [C D]]]].
   assert (ofs = ofs2) by congruence. subst ofs.
   right. zify; omega.
@@ -1064,28 +1064,28 @@ Qed.
 
 Lemma assign_variables_domain:
   forall id vars cesz,
-  (fst (assign_variables cesz vars))!id <> None ->
-  (fst cesz)!id <> None \/ In id (map fst vars).
+  (fst (assign_variables cesz vars))$id <> None ->
+  (fst cesz)$id <> None \/ In id (map fst vars).
 Proof.
   induction vars; simpl; intros.
   auto.
   exploit IHvars; eauto. unfold assign_variable. destruct a as [id1 sz1].
   destruct cesz as [cenv stksz]. simpl.
-  rewrite PTree.gsspec. destruct (peq id id1). auto. tauto.
+  rewrite ATree.gsspec. destruct (ATree.elt_eq id id1). auto. tauto.
 Qed.
 
 Lemma build_compilenv_domain:
   forall f cenv sz id ofs,
   build_compilenv f = (cenv, sz) ->
-  cenv!id = Some ofs -> In id (map fst (Csharpminor.fn_vars f)).
+  cenv$id = Some ofs -> In id (map fst (Csharpminor.fn_vars f)).
 Proof.
   unfold build_compilenv; intros.
   set (vars1 := Csharpminor.fn_vars f) in *.
   generalize (VarSort.Permuted_sort vars1). intros P.
   set (vars2 := VarSort.sort vars1) in *.
-  generalize (assign_variables_domain id vars2 (PTree.empty Z, 0)).
+  generalize (assign_variables_domain id vars2 (ATree.empty Z, 0)).
   rewrite H. simpl. intros. destruct H1. congruence.
-  rewrite PTree.gempty in H1. congruence.
+  rewrite ATree.gempty in H1. congruence.
   apply Permutation_in with (map fst vars2); auto.
   apply Permutation_map. apply Permutation_sym; auto.
 Qed.
@@ -1093,19 +1093,19 @@ Qed.
 (** Initialization of C#minor temporaries and Cminor local variables. *)
 
 Lemma create_undef_temps_val:
-  forall id v temps, (create_undef_temps temps)!id = Some v -> In id temps /\ v = Vundef.
+  forall id v temps, (create_undef_temps temps)$id = Some v -> In id temps /\ v = Vundef.
 Proof.
   induction temps; simpl; intros.
-  rewrite PTree.gempty in H. congruence.
-  rewrite PTree.gsspec in H. destruct (peq id a).
+  rewrite ATree.gempty in H. congruence.
+  rewrite ATree.gsspec in H. destruct (ATree.elt_eq id a).
   split. auto. congruence.
   exploit IHtemps; eauto. tauto.
 Qed.
 
 Fixpoint set_params' (vl: list val) (il: list ident) (te: Cminor.env) : Cminor.env :=
   match il, vl with
-  | i1 :: is, v1 :: vs => set_params' vs is (PTree.set i1 v1 te)
-  | i1 :: is, nil => set_params' nil is (PTree.set i1 Vundef te)
+  | i1 :: is, v1 :: vs => set_params' vs is (ATree.set i1 v1 te)
+  | i1 :: is, nil => set_params' nil is (ATree.set i1 Vundef te)
   | _, _ => te
   end.
 
@@ -1116,88 +1116,88 @@ Lemma bind_parameters_agree_rec:
   match_temps f le1 te ->
   match_temps f le2 (set_params' tvals vars te).
 Proof.
-Opaque PTree.set.
+Opaque ATree.set.
   induction vars; simpl; intros.
   destruct vals; try discriminate. inv H. auto.
   destruct vals; try discriminate. inv H0.
   simpl. eapply IHvars; eauto.
-  red; intros. rewrite PTree.gsspec in *. destruct (peq id a).
+  red; intros. rewrite ATree.gsspec in *. destruct (ATree.elt_eq id a).
   inv H0. exists v'; auto.
   apply H1; auto.
 Qed.
 
 Lemma set_params'_outside:
-  forall id il vl te, ~In id il -> (set_params' vl il te)!id = te!id.
+  forall id il vl te, ~In id il -> (set_params' vl il te)$id = te$id.
 Proof.
   induction il; simpl; intros. auto.
   destruct vl; rewrite IHil.
-  apply PTree.gso. intuition. intuition.
-  apply PTree.gso. intuition. intuition.
+  apply ATree.gso. intuition. intuition.
+  apply ATree.gso. intuition. intuition.
 Qed.
 
 Lemma set_params'_inside:
   forall id il vl te1 te2,
   In id il ->
-  (set_params' vl il te1)!id = (set_params' vl il te2)!id.
+  (set_params' vl il te1)$id = (set_params' vl il te2)$id.
 Proof.
   induction il; simpl; intros.
   contradiction.
-  destruct vl; destruct (List.in_dec peq id il); auto;
+  destruct vl; destruct (List.in_dec ident_eq id il); auto;
   repeat rewrite set_params'_outside; auto;
-  assert (a = id) by intuition; subst a; repeat rewrite PTree.gss; auto.
+  assert (a = id) by intuition; subst a; repeat rewrite ATree.gss; auto.
 Qed.
 
 Lemma set_params_set_params':
   forall il vl id,
   list_norepet il ->
-  (set_params vl il)!id = (set_params' vl il (PTree.empty val))!id.
+  (set_params vl il)$id = (set_params' vl il (ATree.empty val))$id.
 Proof.
   induction il; simpl; intros.
   auto.
   inv H. destruct vl.
-  rewrite PTree.gsspec. destruct (peq id a).
-  subst a. rewrite set_params'_outside; auto. rewrite PTree.gss; auto.
+  rewrite ATree.gsspec. destruct (ATree.elt_eq id a).
+  subst a. rewrite set_params'_outside; auto. rewrite ATree.gss; auto.
   rewrite IHil; auto.
-  destruct (List.in_dec peq id il). apply set_params'_inside; auto.
-  repeat rewrite set_params'_outside; auto. rewrite PTree.gso; auto.
-  rewrite PTree.gsspec. destruct (peq id a).
-  subst a. rewrite set_params'_outside; auto. rewrite PTree.gss; auto.
+  destruct (List.in_dec ident_eq id il). apply set_params'_inside; auto.
+  repeat rewrite set_params'_outside; auto. rewrite ATree.gso; auto.
+  rewrite ATree.gsspec. destruct (ATree.elt_eq id a).
+  subst a. rewrite set_params'_outside; auto. rewrite ATree.gss; auto.
   rewrite IHil; auto.
-  destruct (List.in_dec peq id il). apply set_params'_inside; auto.
-  repeat rewrite set_params'_outside; auto. rewrite PTree.gso; auto.
+  destruct (List.in_dec ident_eq id il). apply set_params'_inside; auto.
+  repeat rewrite set_params'_outside; auto. rewrite ATree.gso; auto.
 Qed.
 
 Lemma set_locals_outside:
   forall e id il,
-  ~In id il -> (set_locals il e)!id = e!id.
+  ~In id il -> (set_locals il e)$id = e$id.
 Proof.
   induction il; simpl; intros.
   auto.
-  rewrite PTree.gso. apply IHil. tauto. intuition.
+  rewrite ATree.gso. apply IHil. tauto. intuition.
 Qed.
 
 Lemma set_locals_inside:
   forall e id il,
-  In id il -> (set_locals il e)!id = Some Vundef.
+  In id il -> (set_locals il e)$id = Some Vundef.
 Proof.
   induction il; simpl; intros.
   contradiction.
-  destruct H. subst a. apply PTree.gss.
-  rewrite PTree.gsspec. destruct (peq id a). auto. auto.
+  destruct H. subst a. apply ATree.gss.
+  rewrite ATree.gsspec. destruct (ATree.elt_eq id a). auto. auto.
 Qed.
 
 Lemma set_locals_set_params':
   forall vars vals params id,
   list_norepet params ->
   list_disjoint params vars ->
-  (set_locals vars (set_params vals params)) ! id =
-  (set_params' vals params (set_locals vars (PTree.empty val))) ! id.
+  (set_locals vars (set_params vals params)) $ id =
+  (set_params' vals params (set_locals vars (ATree.empty val))) $ id.
 Proof.
-  intros. destruct (in_dec peq id vars).
+  intros. destruct (in_dec ident_eq id vars).
   assert (~In id params). apply list_disjoint_notin with vars; auto. apply list_disjoint_sym; auto.
   rewrite set_locals_inside; auto. rewrite set_params'_outside; auto. rewrite set_locals_inside; auto.
   rewrite set_locals_outside; auto. rewrite set_params_set_params'; auto.
-  destruct (in_dec peq id params).
+  destruct (in_dec ident_eq id params).
   apply set_params'_inside; auto.
   repeat rewrite set_params'_outside; auto.
   rewrite set_locals_outside; auto.
@@ -1213,7 +1213,7 @@ Lemma bind_parameters_agree:
 Proof.
   intros; red; intros.
   exploit bind_parameters_agree_rec; eauto.
-  instantiate (1 := set_locals temps (PTree.empty val)).
+  instantiate (1 := set_locals temps (ATree.empty val)).
   red; intros. exploit create_undef_temps_val; eauto. intros [A B]. subst v0.
   exists Vundef; split. apply set_locals_inside; auto. auto.
   intros [v' [A B]]. exists v'; split; auto.
@@ -1434,7 +1434,7 @@ Lemma var_addr_correct:
   /\ Val.inject f (Vptr b Ptrofs.zero) tv.
 Proof.
   unfold var_addr; intros.
-  assert (match_var f sp e!id cenv!id).
+  assert (match_var f sp e$id cenv$id).
     inv H. inv MENV. auto.
   inv H1; inv H0; try congruence.
   (* local *)
@@ -2043,7 +2043,7 @@ Proof.
     eapply external_call_nextblock; eauto.
     eapply external_call_nextblock; eauto.
   econstructor; eauto.
-Opaque PTree.set.
+Opaque ATree.set.
   unfold set_optvar. destruct optid; simpl.
   eapply match_callstack_set_temp; eauto.
   auto.
@@ -2232,7 +2232,7 @@ Proof.
   eapply match_program_main; eauto. 
   eexact FIND.
   rewrite <- H2. apply sig_preserved; auto.
-  eapply match_callstate with (f := Mem.flat_inj (Mem.nextblock m0)) (cs := @nil frame) (cenv := PTree.empty Z).
+  eapply match_callstate with (f := Mem.flat_inj (Mem.nextblock m0)) (cs := @nil frame) (cenv := ATree.empty Z).
   auto.
   eapply Genv.initmem_inject; eauto.
   apply mcs_nil with (Mem.nextblock m0). apply match_globalenvs_init; auto. xomega. xomega.
diff --git a/cfrontend/Csem.v b/cfrontend/Csem.v
index 0c3e00de73..66606e953a 100644
--- a/cfrontend/Csem.v
+++ b/cfrontend/Csem.v
@@ -46,9 +46,9 @@ Definition globalenv (p: program) :=
   The current value of the variable is stored in the associated memory
   block. *)
 
-Definition env := PTree.t (block * type). (* map variable -> location & type *)
+Definition env := ATree.t (block * type). (* map variable -> location & type *)
 
-Definition empty_env: env := (PTree.empty (block * type)).
+Definition empty_env: env := (ATree.empty (block * type)).
 
 
 Section SEMANTICS.
@@ -125,7 +125,7 @@ Inductive alloc_variables: env -> mem ->
   | alloc_variables_cons:
       forall e m id ty vars m1 b1 m2 e2,
       Mem.alloc m 0 (sizeof ge ty) = (m1, b1) ->
-      alloc_variables (PTree.set id (b1, ty) e) m1 vars e2 m2 ->
+      alloc_variables (ATree.set id (b1, ty) e) m1 vars e2 m2 ->
       alloc_variables e m ((id, ty) :: vars) e2 m2.
 
 (** Initialization of local variables that are parameters to a function.
@@ -141,7 +141,7 @@ Inductive bind_parameters (e: env):
       bind_parameters e m nil nil m
   | bind_parameters_cons:
       forall m id ty params v1 vl b m1 m2,
-      PTree.get id e = Some(b, ty) ->
+      ATree.get id e = Some(b, ty) ->
       assign_loc ty m b Ptrofs.zero v1 E0 m1 ->
       bind_parameters e m1 params vl m2 ->
       bind_parameters e m ((id, ty) :: params) (v1 :: vl) m2.
@@ -152,7 +152,7 @@ Definition block_of_binding (id_b_ty: ident * (block * type)) :=
   match id_b_ty with (id, (b, ty)) => (b, 0, sizeof ge ty) end.
 
 Definition blocks_of_env (e: env) : list (block * Z * Z) :=
-  List.map block_of_binding (PTree.elements e).
+  List.map block_of_binding (ATree.elements e).
 
 (** Selection of the appropriate case of a [switch], given the value [n]
   of the selector expression. *)
@@ -209,11 +209,11 @@ Variable e: env.
 
 Inductive lred: expr -> mem -> expr -> mem -> Prop :=
   | red_var_local: forall x ty m b,
-      e!x = Some(b, ty) ->
+      e$x = Some(b, ty) ->
       lred (Evar x ty) m
            (Eloc b Ptrofs.zero ty) m
   | red_var_global: forall x ty m b,
-      e!x = None ->
+      e$x = None ->
       Genv.find_symbol ge x = Some b ->
       lred (Evar x ty) m
            (Eloc b Ptrofs.zero ty) m
@@ -221,12 +221,12 @@ Inductive lred: expr -> mem -> expr -> mem -> Prop :=
       lred (Ederef (Eval (Vptr b ofs) ty1) ty) m
            (Eloc b ofs ty) m
   | red_field_struct: forall b ofs id co a f ty m delta,
-      ge.(genv_cenv)!id = Some co ->
+      ge.(genv_cenv)$id = Some co ->
       field_offset ge f (co_members co) = OK delta ->
       lred (Efield (Eval (Vptr b ofs) (Tstruct id a)) f ty) m
            (Eloc b (Ptrofs.add ofs (Ptrofs.repr delta)) ty) m
   | red_field_union: forall b ofs id co a f ty m,
-      ge.(genv_cenv)!id = Some co ->
+      ge.(genv_cenv)$id = Some co ->
       lred (Efield (Eval (Vptr b ofs) (Tunion id a)) f ty) m
            (Eloc b ofs ty) m.
 
diff --git a/cfrontend/Csharpminor.v b/cfrontend/Csharpminor.v
index 4393640ced..1c924820b2 100644
--- a/cfrontend/Csharpminor.v
+++ b/cfrontend/Csharpminor.v
@@ -111,18 +111,18 @@ Definition funsig (fd: fundef) :=
 *)
 
 Definition genv := Genv.t fundef unit.
-Definition env := PTree.t (block * Z).
-Definition temp_env := PTree.t val.
+Definition env := ATree.t (block * Z).
+Definition temp_env := ATree.t val.
 
-Definition empty_env : env := PTree.empty (block * Z).
-Definition empty_temp_env : temp_env := PTree.empty val.
+Definition empty_env : env := ATree.empty (block * Z).
+Definition empty_temp_env : temp_env := ATree.empty val.
 
 (** Initialization of temporary variables *)
 
 Fixpoint create_undef_temps (temps: list ident) : temp_env :=
   match temps with
-  | nil => PTree.empty val
-  | id :: temps' => PTree.set id Vundef (create_undef_temps temps')
+  | nil => ATree.empty val
+  | id :: temps' => ATree.set id Vundef (create_undef_temps temps')
  end.
 
 (** Initialization of temporaries that are parameters. *)
@@ -131,7 +131,7 @@ Fixpoint bind_parameters (formals: list ident) (args: list val)
                          (le: temp_env) : option temp_env :=
  match formals, args with
  | nil, nil => Some le
- | id :: xl, v :: vl => bind_parameters xl vl (PTree.set id v le)
+ | id :: xl, v :: vl => bind_parameters xl vl (ATree.set id v le)
  | _, _ => None
  end.
 
@@ -275,7 +275,7 @@ Inductive alloc_variables: env -> mem ->
   | alloc_variables_cons:
       forall e m id sz vars m1 b1 m2 e2,
       Mem.alloc m 0 sz = (m1, b1) ->
-      alloc_variables (PTree.set id (b1, sz) e) m1 vars e2 m2 ->
+      alloc_variables (ATree.set id (b1, sz) e) m1 vars e2 m2 ->
       alloc_variables e m ((id, sz) :: vars) e2 m2.
 
 (** List of blocks mentioned in an environment, with low and high bounds *)
@@ -284,7 +284,7 @@ Definition block_of_binding (id_b_sz: ident * (block * Z)) :=
   match id_b_sz with (id, (b, sz)) => (b, 0, sz) end.
 
 Definition blocks_of_env (e: env) : list (block * Z * Z) :=
-  List.map block_of_binding (PTree.elements e).
+  List.map block_of_binding (ATree.elements e).
 
 Section RELSEM.
 
@@ -297,11 +297,11 @@ Variable ge: genv.
 Inductive eval_var_addr: env -> ident -> block -> Prop :=
   | eval_var_addr_local:
       forall e id b sz,
-      PTree.get id e = Some (b, sz) ->
+      ATree.get id e = Some (b, sz) ->
       eval_var_addr e id b
   | eval_var_addr_global:
       forall e id b,
-      PTree.get id e = None ->
+      ATree.get id e = None ->
       Genv.find_symbol ge id = Some b ->
       eval_var_addr e id b.
 
@@ -317,7 +317,7 @@ Variable m: mem.
 
 Inductive eval_expr: expr -> val -> Prop :=
   | eval_Evar: forall id v,
-      le!id = Some v ->
+      le$id = Some v ->
       eval_expr (Evar id) v
   | eval_Eaddrof: forall id b,
       eval_var_addr e id b ->
@@ -373,7 +373,7 @@ Inductive step: state -> trace -> state -> Prop :=
   | step_set: forall f id a k e le m v,
       eval_expr e le m a v ->
       step (State f (Sset id a) k e le m)
-        E0 (State f Sskip k e (PTree.set id v le) m)
+        E0 (State f Sskip k e (ATree.set id v le) m)
 
   | step_store: forall f chunk addr a k e le m vaddr v m',
       eval_expr e le m addr vaddr ->
diff --git a/cfrontend/Cshmgen.v b/cfrontend/Cshmgen.v
index 792a73f98d..6c46a6c823 100644
--- a/cfrontend/Cshmgen.v
+++ b/cfrontend/Cshmgen.v
@@ -443,7 +443,7 @@ Definition transl_binop (ce: composite_env)
 Definition make_field_access (ce: composite_env) (ty: type) (f: ident) (a: expr) : res expr :=
   match ty with
   | Tstruct id _ =>
-      match ce!id with
+      match ce$id with
       | None =>
           Error (MSG "Undefined struct " :: CTX id :: nil)
       | Some co =>
diff --git a/cfrontend/Cshmgenproof.v b/cfrontend/Cshmgenproof.v
index 09e31cb2b5..c1a3fdceac 100644
--- a/cfrontend/Cshmgenproof.v
+++ b/cfrontend/Cshmgenproof.v
@@ -112,14 +112,14 @@ Proof.
   split.
 - symmetry. apply Ctypes.sizeof_stable; auto.
 - revert C. induction t; simpl; auto;
-  destruct (prog_comp_env cunit)!i as [co|] eqn:X; try discriminate; erewrite H1 by eauto; auto.
+  destruct (prog_comp_env cunit)$i as [co|] eqn:X; try discriminate; erewrite H1 by eauto; auto.
 Qed.
 
 Lemma field_offset_stable:
   forall (cunit prog: Clight.program) id co f,
   linkorder cunit prog ->
-  cunit.(prog_comp_env)!id = Some co ->
-  prog.(prog_comp_env)!id = Some co /\
+  cunit.(prog_comp_env)$id = Some co ->
+  prog.(prog_comp_env)$id = Some co /\
   field_offset prog.(prog_comp_env) f (co_members co) = field_offset cunit.(prog_comp_env) f (co_members co).
 Proof.
   intros.
@@ -1038,19 +1038,19 @@ Record match_env (e: Clight.env) (te: Csharpminor.env) : Prop :=
   mk_match_env {
     me_local:
       forall id b ty,
-      e!id = Some (b, ty) -> te!id = Some(b, Ctypes.sizeof ge ty);
+      e$id = Some (b, ty) -> te$id = Some(b, Ctypes.sizeof ge ty);
     me_local_inv:
       forall id b sz,
-      te!id = Some (b, sz) -> exists ty, e!id = Some(b, ty)
+      te$id = Some (b, sz) -> exists ty, e$id = Some(b, ty)
   }.
 
 Lemma match_env_globals:
   forall e te id,
   match_env e te ->
-  e!id = None ->
-  te!id = None.
+  e$id = None ->
+  te$id = None.
 Proof.
-  intros. destruct (te!id) as [[b sz] | ] eqn:?; auto.
+  intros. destruct (te$id) as [[b sz] | ] eqn:?; auto.
   exploit me_local_inv; eauto. intros [ty EQ]. congruence.
 Qed.
 
@@ -1066,8 +1066,8 @@ Proof.
          end).
   assert (list_forall2
             (fun i_x i_y => fst i_x = fst i_y /\ R (snd i_x) (snd i_y))
-            (PTree.elements e) (PTree.elements te)).
-  apply PTree.elements_canonical_order.
+            (ATree.elements e) (ATree.elements te)).
+  apply ATree.elements_canonical_order.
   intros id [b ty] GET. exists (b, Ctypes.sizeof ge ty); split. eapply me_local; eauto. red; auto.
   intros id [b sz] GET. exploit me_local_inv; eauto. intros [ty EQ].
   exploit me_local; eauto. intros EQ1.
@@ -1095,8 +1095,8 @@ Lemma match_env_empty:
 Proof.
   unfold Clight.empty_env, Csharpminor.empty_env.
   constructor.
-  intros until ty. repeat rewrite PTree.gempty. congruence.
-  intros until sz. rewrite PTree.gempty. congruence.
+  intros until ty. repeat rewrite ATree.gempty. congruence.
+  intros until sz. rewrite ATree.gempty. congruence.
 Qed.
 
 (** The following lemmas establish the [match_env] invariant at
@@ -1117,15 +1117,15 @@ Proof.
 - inv H0. exists te1; split. constructor. auto.
 - monadInv H2. monadInv EQ. simpl in *.
   exploit transl_sizeof. eexact H. eauto. intros SZ; rewrite SZ.
-  exploit (IHalloc_variables x0 (PTree.set id (b1, Ctypes.sizeof ge ty) te1)).
+  exploit (IHalloc_variables x0 (ATree.set id (b1, Ctypes.sizeof ge ty) te1)).
   auto.
   constructor.
     (* me_local *)
-    intros until ty0. repeat rewrite PTree.gsspec.
-    destruct (peq id0 id); intros. congruence. eapply me_local; eauto.
+    intros until ty0. repeat rewrite ATree.gsspec.
+    destruct (ATree.elt_eq id0 id); intros. congruence. eapply me_local; eauto.
     (* me_local_inv *)
-    intros until sz. repeat rewrite PTree.gsspec.
-    destruct (peq id0 id); intros. exists ty; congruence. eapply me_local_inv; eauto.
+    intros until sz. repeat rewrite ATree.gsspec.
+    destruct (ATree.elt_eq id0 id); intros. exists ty; congruence. eapply me_local_inv; eauto.
   intros [te2 [ALLOC MENV]].
   exists te2; split. econstructor; eauto. auto.
 Qed.
@@ -1239,7 +1239,7 @@ Proof.
   simpl in TR. eauto.
 - (* field struct *)
   unfold make_field_access in EQ0. rewrite H1 in EQ0.
-  destruct (prog_comp_env cunit)!id as [co'|] eqn:CO; monadInv EQ0.
+  destruct (prog_comp_env cunit)$id as [co'|] eqn:CO; monadInv EQ0.
   exploit field_offset_stable. eexact LINK. eauto. instantiate (1 := i). intros [A B].
   rewrite <- B in EQ1.
   assert (x0 = delta) by (unfold ge in *; simpl in *; congruence).
diff --git a/cfrontend/Cstrategy.v b/cfrontend/Cstrategy.v
index 2f73106833..ecb88bf905 100644
--- a/cfrontend/Cstrategy.v
+++ b/cfrontend/Cstrategy.v
@@ -88,10 +88,10 @@ Inductive eval_simple_lvalue: expr -> block -> ptrofs -> Prop :=
   | esl_loc: forall b ofs ty,
       eval_simple_lvalue (Eloc b ofs ty) b ofs
   | esl_var_local: forall x ty b,
-      e!x = Some(b, ty) ->
+      e$x = Some(b, ty) ->
       eval_simple_lvalue (Evar x ty) b Ptrofs.zero
   | esl_var_global: forall x ty b,
-      e!x = None ->
+      e$x = None ->
       Genv.find_symbol ge x = Some b ->
       eval_simple_lvalue (Evar x ty) b Ptrofs.zero
   | esl_deref: forall r ty b ofs,
@@ -100,13 +100,13 @@ Inductive eval_simple_lvalue: expr -> block -> ptrofs -> Prop :=
   | esl_field_struct: forall r f ty b ofs id co a delta,
       eval_simple_rvalue r (Vptr b ofs) ->
       typeof r = Tstruct id a ->
-      ge.(genv_cenv)!id = Some co ->
+      ge.(genv_cenv)$id = Some co ->
       field_offset ge f (co_members co) = OK delta ->
       eval_simple_lvalue (Efield r f ty) b (Ptrofs.add ofs (Ptrofs.repr delta))
   | esl_field_union: forall r f ty b ofs id co a,
       eval_simple_rvalue r (Vptr b ofs) ->
       typeof r = Tunion id a ->
-      ge.(genv_cenv)!id = Some co ->
+      ge.(genv_cenv)$id = Some co ->
       eval_simple_lvalue (Efield r f ty) b ofs
 
 with eval_simple_rvalue: expr -> val -> Prop :=
@@ -521,15 +521,15 @@ Definition invert_expr_prop (a: expr) (m: mem) : Prop :=
   | Eloc b ofs ty => False
   | Evar x ty =>
       exists b,
-      e!x = Some(b, ty)
-      \/ (e!x = None /\ Genv.find_symbol ge x = Some b)
+      e$x = Some(b, ty)
+      \/ (e$x = None /\ Genv.find_symbol ge x = Some b)
   | Ederef (Eval v ty1) ty =>
       exists b, exists ofs, v = Vptr b ofs
   | Efield (Eval v ty1) f ty =>
       exists b, exists ofs, v = Vptr b ofs /\
       match ty1 with
-      | Tstruct id _ => exists co delta, ge.(genv_cenv)!id = Some co /\ field_offset ge f (co_members co) = Errors.OK delta
-      | Tunion id _ => exists co, ge.(genv_cenv)!id = Some co
+      | Tstruct id _ => exists co delta, ge.(genv_cenv)$id = Some co /\ field_offset ge f (co_members co) = Errors.OK delta
+      | Tunion id _ => exists co, ge.(genv_cenv)$id = Some co
       | _ => False
       end
   | Eval v ty => False
diff --git a/cfrontend/Ctypes.v b/cfrontend/Ctypes.v
index 036b768bca..8805955c63 100644
--- a/cfrontend/Ctypes.v
+++ b/cfrontend/Ctypes.v
@@ -190,7 +190,7 @@ Record composite : Type := {
   co_sizeof_alignof: (co_alignof | co_sizeof)
 }.
 
-Definition composite_env : Type := PTree.t composite.
+Definition composite_env : Type := ATree.t composite.
 
 (** * Operations over types *)
 
@@ -240,7 +240,7 @@ Fixpoint complete_type (env: composite_env) (t: type) : bool :=
   | Tarray t' _ _ => complete_type env t'
   | Tfunction _ _ _ => false
   | Tstruct id _ | Tunion id _ =>
-      match env!id with Some co => true | None => false end
+      match env$id with Some co => true | None => false end
   end.
 
 Definition complete_or_function_type (env: composite_env) (t: type) : bool :=
@@ -280,7 +280,7 @@ Fixpoint alignof (env: composite_env) (t: type) : Z :=
       | Tarray t' _ _ => alignof env t'
       | Tfunction _ _ _ => 1
       | Tstruct id _ | Tunion id _ =>
-          match env!id with Some co => co_alignof co | None => 1 end
+          match env$id with Some co => co_alignof co | None => 1 end
     end).
 
 Remark align_attr_two_p:
@@ -310,8 +310,8 @@ Proof.
   exists (if Archi.ptr64 then 3%nat else 2%nat); destruct Archi.ptr64; auto.
   apply IHt.
   exists 0%nat; auto.
-  destruct (env!i). apply co_alignof_two_p. exists 0%nat; auto.
-  destruct (env!i). apply co_alignof_two_p. exists 0%nat; auto.
+  destruct (env$i). apply co_alignof_two_p. exists 0%nat; auto.
+  destruct (env$i). apply co_alignof_two_p. exists 0%nat; auto.
 Qed.
 
 Lemma alignof_pos:
@@ -343,7 +343,7 @@ Fixpoint sizeof (env: composite_env) (t: type) : Z :=
   | Tarray t' n _ => sizeof env t' * Z.max 0 n
   | Tfunction _ _ _ => 1
   | Tstruct id _ | Tunion id _ =>
-      match env!id with Some co => co_sizeof co | None => 0 end
+      match env$id with Some co => co_sizeof co | None => 0 end
   end.
 
 Lemma sizeof_pos:
@@ -354,8 +354,8 @@ Proof.
   destruct f; omega.
   destruct Archi.ptr64; omega.
   change 0 with (0 * Z.max 0 z) at 2. apply Zmult_ge_compat_r. auto. xomega.
-  destruct (env!i). apply co_sizeof_pos. omega.
-  destruct (env!i). apply co_sizeof_pos. omega.
+  destruct (env$i). apply co_sizeof_pos. omega.
+  destruct (env$i). apply co_sizeof_pos. omega.
 Qed.
 
 (** The size of a type is an integral multiple of its alignment,
@@ -380,8 +380,8 @@ Proof.
 - apply Z.divide_refl.
 - apply Z.divide_mul_l; auto.
 - apply Z.divide_refl.
-- destruct (env!i). apply co_sizeof_alignof. apply Z.divide_0_r.
-- destruct (env!i). apply co_sizeof_alignof. apply Z.divide_0_r.
+- destruct (env$i). apply co_sizeof_alignof. apply Z.divide_0_r.
+- destruct (env$i). apply co_sizeof_alignof. apply Z.divide_0_r.
 Qed.
 
 (** ** Size and alignment for composite definitions *)
@@ -618,7 +618,7 @@ Fixpoint alignof_blockcopy (env: composite_env) (t: type) : Z :=
   | Tarray t' _ _ => alignof_blockcopy env t'
   | Tfunction _ _ _ => 1
   | Tstruct id _ | Tunion id _ =>
-      match env!id with
+      match env$id with
       | Some co => Z.min 8 (co_alignof co)
       | None => 1
       end
@@ -646,8 +646,8 @@ Proof.
   destruct Archi.ptr64; auto.
   apply IHty.
   auto.
-  destruct (env!i); auto.
-  destruct (env!i); auto.
+  destruct (env$i); auto.
+  destruct (env$i); auto.
 Qed.
 
 Lemma alignof_blockcopy_pos:
@@ -681,8 +681,8 @@ Proof.
   apply Z.divide_refl.
   apply Z.divide_mul_l. auto.
   apply Z.divide_refl.
-  destruct (env!i). apply X. apply Z.divide_0_r.
-  destruct (env!i). apply X. apply Z.divide_0_r.
+  destruct (env$i). apply X. apply Z.divide_0_r.
+  destruct (env$i). apply X. apply Z.divide_0_r.
 Qed.
 
 (** Type ranks *)
@@ -697,7 +697,7 @@ Fixpoint rank_type (ce: composite_env) (t: type) : nat :=
   match t with
   | Tarray t' _ _ => S (rank_type ce t')
   | Tstruct id _ | Tunion id _ =>
-      match ce!id with
+      match ce$id with
       | None => O
       | Some co => S (co_rank co)
       end
@@ -800,7 +800,7 @@ Qed.
 Program Definition composite_of_def
      (env: composite_env) (id: ident) (su: struct_or_union) (m: members) (a: attr)
      : res composite :=
-  match env!id, complete_members env m return _ with
+  match env$id, complete_members env m return _ with
   | Some _, _ =>
       Error (MSG "Multiple definitions of struct or union " :: CTX id :: nil)
   | None, false =>
@@ -841,11 +841,11 @@ Fixpoint add_composite_definitions (env: composite_env) (defs: list composite_de
   | nil => OK env
   | Composite id su m a :: defs =>
       do co <- composite_of_def env id su m a;
-      add_composite_definitions (PTree.set id co env) defs
+      add_composite_definitions (ATree.set id co env) defs
   end.
 
 Definition build_composite_env (defs: list composite_definition) :=
-  add_composite_definitions (PTree.empty _) defs.
+  add_composite_definitions (ATree.empty _) defs.
 
 (** Stability properties for alignments, sizes, and ranks.  If the type is
   complete in a composite environment [env], its size, alignment, and rank
@@ -854,15 +854,15 @@ Definition build_composite_env (defs: list composite_definition) :=
 Section STABILITY.
 
 Variables env env': composite_env.
-Hypothesis extends: forall id co, env!id = Some co -> env'!id = Some co.
+Hypothesis extends: forall id co, env$id = Some co -> env'$id = Some co.
 
 Lemma alignof_stable:
   forall t, complete_type env t = true -> alignof env' t = alignof env t.
 Proof.
   induction t; simpl; intros; f_equal; auto.
-  destruct (env!i) as [co|] eqn:E; try discriminate.
+  destruct (env$i) as [co|] eqn:E; try discriminate.
   erewrite extends by eauto. auto.
-  destruct (env!i) as [co|] eqn:E; try discriminate.
+  destruct (env$i) as [co|] eqn:E; try discriminate.
   erewrite extends by eauto. auto.
 Qed.
 
@@ -871,9 +871,9 @@ Lemma sizeof_stable:
 Proof.
   induction t; simpl; intros; auto.
   rewrite IHt by auto. auto.
-  destruct (env!i) as [co|] eqn:E; try discriminate.
+  destruct (env$i) as [co|] eqn:E; try discriminate.
   erewrite extends by eauto. auto.
-  destruct (env!i) as [co|] eqn:E; try discriminate.
+  destruct (env$i) as [co|] eqn:E; try discriminate.
   erewrite extends by eauto. auto.
 Qed.
 
@@ -881,9 +881,9 @@ Lemma complete_type_stable:
   forall t, complete_type env t = true -> complete_type env' t = true.
 Proof.
   induction t; simpl; intros; auto.
-  destruct (env!i) as [co|] eqn:E; try discriminate.
+  destruct (env$i) as [co|] eqn:E; try discriminate.
   erewrite extends by eauto. auto.
-  destruct (env!i) as [co|] eqn:E; try discriminate.
+  destruct (env$i) as [co|] eqn:E; try discriminate.
   erewrite extends by eauto. auto.
 Qed.
 
@@ -891,9 +891,9 @@ Lemma rank_type_stable:
   forall t, complete_type env t = true -> rank_type env' t = rank_type env t.
 Proof.
   induction t; simpl; intros; auto.
-  destruct (env!i) as [co|] eqn:E; try discriminate.
+  destruct (env$i) as [co|] eqn:E; try discriminate.
   erewrite extends by eauto. auto.
-  destruct (env!i) as [co|] eqn:E; try discriminate.
+  destruct (env$i) as [co|] eqn:E; try discriminate.
   erewrite extends by eauto. auto.
 Qed.
 
@@ -951,12 +951,12 @@ End STABILITY.
 Lemma add_composite_definitions_incr:
   forall id co defs env1 env2,
   add_composite_definitions env1 defs = OK env2 ->
-  env1!id = Some co -> env2!id = Some co.
+  env1$id = Some co -> env2$id = Some co.
 Proof.
   induction defs; simpl; intros.
 - inv H; auto.
 - destruct a; monadInv H.
-  eapply IHdefs; eauto. rewrite PTree.gso; auto.
+  eapply IHdefs; eauto. rewrite ATree.gso; auto.
   red; intros; subst id0. unfold composite_of_def in EQ. rewrite H0 in EQ; discriminate.
 Qed.
 
@@ -976,11 +976,11 @@ Record composite_consistent (env: composite_env) (co: composite) : Prop := {
 }.
 
 Definition composite_env_consistent (env: composite_env) : Prop :=
-  forall id co, env!id = Some co -> composite_consistent env co.
+  forall id co, env$id = Some co -> composite_consistent env co.
 
 Lemma composite_consistent_stable:
   forall (env env': composite_env)
-         (EXTENDS: forall id co, env!id = Some co -> env'!id = Some co)
+         (EXTENDS: forall id co, env$id = Some co -> env'$id = Some co)
          co,
   composite_consistent env co -> composite_consistent env' co.
 Proof.
@@ -997,7 +997,7 @@ Lemma composite_of_def_consistent:
   composite_consistent env co.
 Proof.
   unfold composite_of_def; intros. 
-  destruct (env!id); try discriminate. destruct (complete_members env m) eqn:C; inv H.
+  destruct (env$id); try discriminate. destruct (complete_members env m) eqn:C; inv H.
   constructor; auto.
 Qed. 
 
@@ -1008,18 +1008,18 @@ Proof.
        add_composite_definitions env0 defs = OK env ->
        composite_env_consistent env0 ->
        composite_env_consistent env).
-  intros. eapply H; eauto. red; intros. rewrite PTree.gempty in H1; discriminate.
+  intros. eapply H; eauto. red; intros. rewrite ATree.gempty in H1; discriminate.
   induction defs as [|d1 defs]; simpl; intros.
 - inv H; auto.
 - destruct d1; monadInv H.
   eapply IHdefs; eauto.
-  set (env1 := PTree.set id x env0) in *.
-  assert (env0!id = None). 
-  { unfold composite_of_def in EQ. destruct (env0!id). discriminate. auto. }
-  assert (forall id1 co1, env0!id1 = Some co1 -> env1!id1 = Some co1).
-  { intros. unfold env1. rewrite PTree.gso; auto. congruence. }
+  set (env1 := ATree.set id x env0) in *.
+  assert (env0$id = None).
+  { unfold composite_of_def in EQ. destruct (env0$id). discriminate. auto. }
+  assert (forall id1 co1, env0$id1 = Some co1 -> env1$id1 = Some co1).
+  { intros. unfold env1. rewrite ATree.gso; auto. congruence. }
   red; intros. apply composite_consistent_stable with env0; auto.
-  unfold env1 in H2; rewrite PTree.gsspec in H2; destruct (peq id0 id).
+  unfold env1 in H2; rewrite ATree.gsspec in H2; destruct (ATree.elt_eq id0 id).
 + subst id0. inversion H2; clear H2. subst co.
   eapply composite_of_def_consistent; eauto.
 + eapply H0; eauto. 
@@ -1031,42 +1031,42 @@ Theorem build_composite_env_charact:
   forall id su m a defs env,
   build_composite_env defs = OK env ->
   In (Composite id su m a) defs ->
-  exists co, env!id = Some co /\ co_members co = m /\ co_attr co = a /\ co_su co = su.
+  exists co, env$id = Some co /\ co_members co = m /\ co_attr co = a /\ co_su co = su.
 Proof.
-  intros until defs. unfold build_composite_env. generalize (PTree.empty composite) as env0.
+  intros until defs. unfold build_composite_env. generalize (ATree.empty composite) as env0.
   revert defs. induction defs as [|d1 defs]; simpl; intros.
 - contradiction.
 - destruct d1; monadInv H.
   destruct H0; [idtac|eapply IHdefs;eauto]. inv H.
   unfold composite_of_def in EQ.
-  destruct (env0!id) eqn:E; try discriminate.
+  destruct (env0$id) eqn:E; try discriminate.
   destruct (complete_members env0 m) eqn:C; simplify_eq EQ. clear EQ; intros EQ.
   exists x.
-  split. eapply add_composite_definitions_incr; eauto. apply PTree.gss.
+  split. eapply add_composite_definitions_incr; eauto. apply ATree.gss.
   subst x; auto.
 Qed.
 
 Theorem build_composite_env_domain:
   forall env defs id co,
   build_composite_env defs = OK env ->
-  env!id = Some co ->
+  env$id = Some co ->
   In (Composite id (co_su co) (co_members co) (co_attr co)) defs.
 Proof.
   intros env0 defs0 id co.
   assert (REC: forall l env env',
     add_composite_definitions env l = OK env' ->
-    env'!id = Some co ->
-    env!id = Some co \/ In (Composite id (co_su co) (co_members co) (co_attr co)) l).
+    env'$id = Some co ->
+    env$id = Some co \/ In (Composite id (co_su co) (co_members co) (co_attr co)) l).
   { induction l; simpl; intros. 
   - inv H; auto.
   - destruct a; monadInv H. exploit IHl; eauto.
-    unfold composite_of_def in EQ. destruct (env!id0) eqn:E; try discriminate.
+    unfold composite_of_def in EQ. destruct (env$id0) eqn:E; try discriminate.
     destruct (complete_members env m) eqn:C; simplify_eq EQ. clear EQ; intros EQ.
-    rewrite PTree.gsspec. intros [A|A]; auto.
-    destruct (peq id id0); auto.
+    rewrite ATree.gsspec. intros [A|A]; auto.
+    destruct (_ id id0); auto.
     inv A. rewrite <- H0; auto.
   }
-  intros. exploit REC; eauto. rewrite PTree.gempty. intuition congruence.
+  intros. exploit REC; eauto. rewrite ATree.gempty. intuition congruence.
 Qed.
 
 (** As a corollay, in a consistent environment, the rank of a composite type
@@ -1083,7 +1083,7 @@ Qed.
 Lemma rank_struct_member:
   forall ce id a co id1 t1,
   composite_env_consistent ce ->
-  ce!id = Some co ->
+  ce$id = Some co ->
   In (id1, t1) (co_members co) ->
   (rank_type ce t1 < rank_type ce (Tstruct id a))%nat.
 Proof.
@@ -1096,7 +1096,7 @@ Qed.
 Lemma rank_union_member:
   forall ce id a co id1 t1,
   composite_env_consistent ce ->
-  ce!id = Some co ->
+  ce$id = Some co ->
   In (id1, t1) (co_members co) ->
   (rank_type ce t1 < rank_type ce (Tunion id a))%nat.
 Proof.
@@ -1265,7 +1265,7 @@ Qed.
 Lemma composite_of_def_eq:
   forall env id co,
   composite_consistent env co ->
-  env!id = None ->
+  env$id = None ->
   composite_of_def env id (co_su co) (co_members co) (co_attr co) = OK co.
 Proof.
   intros. destruct H as [A B C D]. unfold composite_of_def. rewrite H0, A.
@@ -1286,15 +1286,15 @@ Qed.
 
 Lemma composite_of_def_stable:
   forall (env env': composite_env)
-         (EXTENDS: forall id co, env!id = Some co -> env'!id = Some co)
+         (EXTENDS: forall id co, env$id = Some co -> env'$id = Some co)
          id su m a co,
-  env'!id = None ->
+  env'$id = None ->
   composite_of_def env id su m a = OK co ->
   composite_of_def env' id su m a = OK co.
 Proof.
   intros. 
   unfold composite_of_def in H0. 
-  destruct (env!id) eqn:E; try discriminate.
+  destruct (env$id) eqn:E; try discriminate.
   destruct (complete_members env m) eqn:CM; try discriminate.
   transitivity (composite_of_def env' id (co_su co) (co_members co) (co_attr co)).
   inv H0; auto. 
@@ -1308,26 +1308,26 @@ Lemma link_add_composite_definitions:
   build_composite_env l0 = OK env0 ->
   forall l env1 env1' env2,
   add_composite_definitions env1 l = OK env1' ->
-  (forall id co, env1!id = Some co -> env2!id = Some co) ->
-  (forall id co, env0!id = Some co -> env2!id = Some co) ->
-  (forall id, env2!id = if In_dec ident_eq id (map name_composite_def l0) then env0!id else env1!id) ->
+  (forall id co, env1$id = Some co -> env2$id = Some co) ->
+  (forall id co, env0$id = Some co -> env2$id = Some co) ->
+  (forall id, env2$id = if In_dec ident_eq id (map name_composite_def l0) then env0$id else env1$id) ->
   ((forall cd1 cd2, In cd1 l0 -> In cd2 l -> name_composite_def cd2 = name_composite_def cd1 -> cd2 = cd1)) ->
   { env2' |
       add_composite_definitions env2 (filter_redefs l0 l) = OK env2'
-  /\ (forall id co, env1'!id = Some co -> env2'!id = Some co)
-  /\ (forall id co, env0!id = Some co -> env2'!id = Some co) }.
+  /\ (forall id co, env1'$id = Some co -> env2'$id = Some co)
+  /\ (forall id co, env0$id = Some co -> env2'$id = Some co) }.
 Proof.
   induction l; simpl; intros until env2; intros ACD AGREE1 AGREE0 AGREE2 UNIQUE.
 - inv ACD. exists env2; auto.
 - destruct a. destruct (composite_of_def env1 id su m a) as [x|e] eqn:EQ; try discriminate.
   simpl in ACD.
   generalize EQ. unfold composite_of_def at 1. 
-  destruct (env1!id) eqn:E1; try congruence.
+  destruct (env1$id) eqn:E1; try congruence.
   destruct (complete_members env1 m) eqn:CM1; try congruence. 
   intros EQ1.
   simpl. destruct (in_dec ident_eq id (map name_composite_def l0)); simpl.
 + eapply IHl; eauto.
-* intros. rewrite PTree.gsspec in H0. destruct (peq id0 id); auto.
+* intros. rewrite ATree.gsspec in H0. destruct (ATree.elt_eq id0 id); auto.
   inv H0.
   exploit list_in_map_inv; eauto. intros ([id' su' m' a'] & P & Q).
   assert (X: Composite id su m a = Composite id' su' m' a').
@@ -1345,16 +1345,16 @@ Proof.
     inversion EQ1; auto. }
   subst co'. apply AGREE0; auto. 
 * intros. rewrite AGREE2. destruct (in_dec ident_eq id0 (map name_composite_def l0)); auto. 
-  rewrite PTree.gsspec. destruct (peq id0 id); auto. subst id0. contradiction.
-+ assert (E2: env2!id = None).
+  rewrite ATree.gsspec. destruct (ATree.elt_eq id0 id); auto. subst id0. contradiction.
++ assert (E2: env2$id = None).
   { rewrite AGREE2. rewrite pred_dec_false by auto. auto. }
   assert (E3: composite_of_def env2 id su m a = OK x).
   { eapply composite_of_def_stable. eexact AGREE1. eauto. eauto. }
   rewrite E3. simpl. eapply IHl; eauto. 
-* intros until co; rewrite ! PTree.gsspec. destruct (peq id0 id); auto.
-* intros until co; rewrite ! PTree.gsspec. intros. destruct (peq id0 id); auto.
+* intros until co; rewrite ! ATree.gsspec. destruct (ATree.elt_eq id0 id); auto.
+* intros until co; rewrite ! ATree.gsspec. intros. destruct (ATree.elt_eq id0 id); auto.
   subst id0. apply AGREE0 in H0. congruence.
-* intros. rewrite ! PTree.gsspec. destruct (peq id0 id); auto. subst id0. 
+* intros. rewrite ! ATree.gsspec. destruct (ATree.elt_eq id0 id); auto. subst id0.
   rewrite pred_dec_false by auto. auto.
 Qed.
 
@@ -1365,17 +1365,17 @@ Theorem link_build_composite_env:
   link l1 l2 = Some l ->
   { env |
      build_composite_env l = OK env
-  /\ (forall id co, env1!id = Some co -> env!id = Some co)
-  /\ (forall id co, env2!id = Some co -> env!id = Some co) }.
+  /\ (forall id co, env1$id = Some co -> env$id = Some co)
+  /\ (forall id co, env2$id = Some co -> env$id = Some co) }.
 Proof.
   intros. edestruct link_composite_def_inv as (A & B & C); eauto.
   edestruct link_add_composite_definitions as (env & P & Q & R).
   eexact H.
   eexact H0.
-  instantiate (1 := env1). intros. rewrite PTree.gempty in H2; discriminate.
+  instantiate (1 := env1). intros. rewrite ATree.gempty in H2; discriminate.
   auto.
   intros. destruct (in_dec ident_eq id (map name_composite_def l1)); auto.
-  rewrite PTree.gempty. destruct (env1!id) eqn:E1; auto. 
+  rewrite ATree.gempty. destruct (env1$id) eqn:E1; auto.
   exploit build_composite_env_domain. eexact H. eauto.
   intros. apply (in_map name_composite_def) in H2. elim n; auto. 
   auto.
@@ -1463,7 +1463,7 @@ Definition link_program {F:Type} (p1 p2: program F): option (program F) :=
 
 Definition linkorder_program {F: Type} (p1 p2: program F) : Prop :=
      linkorder (program_of_program p1) (program_of_program p2)
-  /\ (forall id co, p1.(prog_comp_env)!id = Some co -> p2.(prog_comp_env)!id = Some co).
+  /\ (forall id co, p1.(prog_comp_env)$id = Some co -> p2.(prog_comp_env)$id = Some co).
 
 Instance Linker_program (F: Type): Linker (program F) := {
   link := link_program;
diff --git a/cfrontend/Ctyping.v b/cfrontend/Ctyping.v
index ba1d34fbdd..6120269d9c 100644
--- a/cfrontend/Ctyping.v
+++ b/cfrontend/Ctyping.v
@@ -258,7 +258,7 @@ Definition type_conditional (ty1 ty2: type) : res type :=
 
 (** Type environments map identifiers to their types. *)
 
-Definition typenv := PTree.t type.
+Definition typenv := ATree.t type.
 
 Definition wt_cast (from to: type) : Prop :=
   classify_cast from to <> cast_case_default.
@@ -408,7 +408,7 @@ with wt_lvalue : expr -> Prop :=
   | wt_Eloc: forall b ofs ty,
       wt_lvalue (Eloc b ofs ty)
   | wt_Evar: forall x ty,
-      e!x = Some ty ->
+      e$x = Some ty ->
       wt_lvalue (Evar x ty)
   | wt_Ederef: forall r ty,
       wt_rvalue r ->
@@ -417,7 +417,7 @@ with wt_lvalue : expr -> Prop :=
   | wt_Efield: forall r f id a co ty,
       wt_rvalue r ->
       typeof r = Tstruct id a \/ typeof r = Tunion id a ->
-      ce!id = Some co ->
+      ce$id = Some co ->
       type_of_member a f co.(co_members) = OK ty ->
       wt_lvalue (Efield r f ty)
 
@@ -502,7 +502,7 @@ End WT_EXPR_STMT.
 Fixpoint bind_vars (e: typenv) (l: list (ident * type)) : typenv :=
   match l with
   | nil => e
-  | (id, ty) :: l => bind_vars (PTree.set id ty e) l
+  | (id, ty) :: l => bind_vars (ATree.set id ty e) l
   end.
 
 Inductive wt_function (ce: composite_env) (e: typenv) : function -> Prop :=
@@ -513,13 +513,13 @@ Inductive wt_function (ce: composite_env) (e: typenv) : function -> Prop :=
 Fixpoint bind_globdef (e: typenv) (l: list (ident * globdef fundef type)) : typenv :=
   match l with
   | nil => e
-  | (id, Gfun fd) :: l => bind_globdef (PTree.set id (type_of_fundef fd) e) l
-  | (id, Gvar v) :: l => bind_globdef (PTree.set id v.(gvar_info) e) l
+  | (id, Gfun fd) :: l => bind_globdef (ATree.set id (type_of_fundef fd) e) l
+  | (id, Gvar v) :: l => bind_globdef (ATree.set id v.(gvar_info) e) l
   end.
 
 Inductive wt_program : program -> Prop :=
   | wt_program_intro: forall p,
-      let e := bind_globdef (PTree.empty _) p.(prog_defs) in
+      let e := bind_globdef (ATree.empty _) p.(prog_defs) in
       (forall id f, In (id, Gfun (Internal f)) p.(prog_defs) ->
          wt_function p.(prog_comp_env) e f) ->
       wt_program p.
@@ -607,7 +607,7 @@ Fixpoint check_rvals (el: exprlist) : res unit :=
   type annotation. *)
 
 Definition evar (e: typenv) (x: ident) : res expr :=
-  match e!x with
+  match e$x with
   | Some ty => OK (Evar x ty)
   | None => Error (MSG "unbound variable " :: CTX x :: nil)
   end.
@@ -621,7 +621,7 @@ Definition efield (ce: composite_env) (r: expr) (f: ident) : res expr :=
   do x1 <- check_rval r;
   match typeof r with
   | Tstruct id a | Tunion id a =>
-      match ce!id with
+      match ce$id with
       | None => Error (MSG "unbound composite " :: CTX id :: nil)
       | Some co =>
           do ty <- type_of_member a f co.(co_members);
@@ -909,7 +909,7 @@ Definition retype_fundef (ce: composite_env) (e: typenv) (fd: fundef) : res fund
   end.
 
 Definition typecheck_program (p: program) : res program :=
-  let e := bind_globdef (PTree.empty _) p.(prog_defs) in
+  let e := bind_globdef (ATree.empty _) p.(prog_defs) in
   let ce := p.(prog_comp_env) in
   do tp <- transform_partial_program (retype_fundef ce e) p;
   OK {| prog_defs := tp.(AST.prog_defs);
@@ -1062,7 +1062,7 @@ Hint Extern 1 (wt_expr _ _ _) => (unfold wt_expr; simpl): ty.
 Lemma evar_sound:
   forall x a, evar e x = OK a -> wt_expr ce e a.
 Proof.
-  unfold evar; intros. destruct (e!x) as [ty|] eqn:E; inv H. eauto with ty.
+  unfold evar; intros. destruct (e$x) as [ty|] eqn:E; inv H. eauto with ty.
 Qed.
 
 Lemma ederef_sound:
@@ -1076,7 +1076,7 @@ Lemma efield_sound:
 Proof.
   intros. monadInv H.
   destruct (typeof r) eqn:TR; try discriminate;
-  destruct (ce!i) as [co|] eqn:CE; monadInv EQ0; eauto with ty.
+  destruct (ce$i) as [co|] eqn:CE; monadInv EQ0; eauto with ty.
 Qed.
 
 Lemma econst_int_sound:
@@ -1349,13 +1349,13 @@ Proof.
   rename x into tp.
   constructor; simpl.
   set (ce := prog_comp_env p) in *.
-  set (e := bind_globdef (PTree.empty type) (prog_defs p)) in *.
-  set (e' := bind_globdef (PTree.empty type) (AST.prog_defs tp)) in *.
+  set (e := bind_globdef (ATree.empty type) (prog_defs p)) in *.
+  set (e' := bind_globdef (ATree.empty type) (AST.prog_defs tp)) in *.
   assert (M: match_program (fun ctx f tf => retype_fundef ce e f = OK tf) eq p tp)
   by (eapply match_transform_partial_program; eauto).
   destruct M as (MATCH & _). simpl in MATCH.
   assert (ENVS: e' = e).
-  { unfold e, e'. revert MATCH; generalize (prog_defs p) (AST.prog_defs tp) (PTree.empty type).
+  { unfold e, e'. revert MATCH; generalize (prog_defs p) (AST.prog_defs tp) (ATree.empty type).
     induction l as [ | [id gd] l ]; intros l' t M; inv M.
     auto.
     destruct b1 as [id' gd']; destruct H1; simpl in *. inv H0; simpl.
@@ -1852,7 +1852,7 @@ Section PRESERVATION.
 Variable prog: program.
 Hypothesis WTPROG: wt_program prog.
 Let ge := globalenv prog.
-Let gtenv := bind_globdef (PTree.empty _) prog.(prog_defs).
+Let gtenv := bind_globdef (ATree.empty _) prog.(prog_defs).
 
 Hypothesis WT_EXTERNAL:
   forall id ef args res cc vargs m t vres m',
diff --git a/cfrontend/Initializers.v b/cfrontend/Initializers.v
index 77d6cfea85..27b384d44d 100644
--- a/cfrontend/Initializers.v
+++ b/cfrontend/Initializers.v
@@ -44,7 +44,7 @@ Definition do_cast (v: val) (t1 t2: type) : res val :=
   end.
 
 Definition lookup_composite (ce: composite_env) (id: ident) : res composite :=
-  match ce!id with
+  match ce$id with
   | Some co => OK co
   | None => Error (MSG "Undefined struct or union " :: CTX id :: nil)
   end.
@@ -110,7 +110,7 @@ Fixpoint constval (ce: composite_env) (a: expr) : res val :=
   | Ecomma r1 r2 ty =>
       do v1 <- constval ce r1; constval ce r2
   | Evar x ty =>
-      OK(Vptr x Ptrofs.zero)
+      OK(Vptr (Ident.to_positive x) Ptrofs.zero)
   | Ederef r ty =>
       constval ce r
   | Efield l f ty =>
@@ -163,9 +163,9 @@ Definition transl_init_single (ce: composite_env) (ty: type) (a: expr) : res ini
   | Vlong n, Tpointer _ _ => assertion (Archi.ptr64); OK(Init_int64 n)
   | Vsingle f, Tfloat F32 _ => OK(Init_float32 f)
   | Vfloat f, Tfloat F64 _ => OK(Init_float64 f)
-  | Vptr id ofs, Tint I32 sg _ => assertion (negb Archi.ptr64); OK(Init_addrof id ofs)
-  | Vptr id ofs, Tlong _ _ => assertion (Archi.ptr64); OK(Init_addrof id ofs)
-  | Vptr id ofs, Tpointer _ _ => OK(Init_addrof id ofs)
+  | Vptr id ofs, Tint I32 sg _ => assertion (negb Archi.ptr64); OK(Init_addrof (Ident.of_positive id) ofs)
+  | Vptr id ofs, Tlong _ _ => assertion (Archi.ptr64); OK(Init_addrof (Ident.of_positive id) ofs)
+  | Vptr id ofs, Tpointer _ _ => OK(Init_addrof (Ident.of_positive id) ofs)
   | Vundef, _ => Error(msg "undefined operation in initializer")
   | _, _ => Error (msg "type mismatch in initializer")
   end.
diff --git a/cfrontend/Initializersproof.v b/cfrontend/Initializersproof.v
index 272b929f1a..f2089226dc 100644
--- a/cfrontend/Initializersproof.v
+++ b/cfrontend/Initializersproof.v
@@ -69,10 +69,10 @@ Inductive eval_simple_lvalue: expr -> block -> ptrofs -> Prop :=
   | esl_loc: forall b ofs ty,
       eval_simple_lvalue (Eloc b ofs ty) b ofs
   | esl_var_local: forall x ty b,
-      e!x = Some(b, ty) ->
+      e$x = Some(b, ty) ->
       eval_simple_lvalue (Evar x ty) b Ptrofs.zero
   | esl_var_global: forall x ty b,
-      e!x = None ->
+      e$x = None ->
       Genv.find_symbol ge x = Some b ->
       eval_simple_lvalue (Evar x ty) b Ptrofs.zero
   | esl_deref: forall r ty b ofs,
@@ -80,7 +80,7 @@ Inductive eval_simple_lvalue: expr -> block -> ptrofs -> Prop :=
       eval_simple_lvalue (Ederef r ty) b ofs
   | esl_field_struct: forall r f ty b ofs id co a delta,
       eval_simple_rvalue r (Vptr b ofs) ->
-      typeof r = Tstruct id a -> ge.(genv_cenv)!id = Some co -> field_offset ge f (co_members co) = OK delta ->
+      typeof r = Tstruct id a -> ge.(genv_cenv)$id = Some co -> field_offset ge f (co_members co) = OK delta ->
       eval_simple_lvalue (Efield r f ty) b (Ptrofs.add ofs (Ptrofs.repr delta))
   | esl_field_union: forall r f ty b ofs id a,
       eval_simple_rvalue r (Vptr b ofs) ->
@@ -323,7 +323,7 @@ Qed.
   [Vptr b ofs] where [Genv.find_symbol ge id = Some b]. *)
 
 Definition inj (b: block) :=
-  match Genv.find_symbol ge b with
+  match Genv.find_symbol ge (Ident.of_positive b) with
   | Some b' => Some (b', 0)
   | None => None
   end.
@@ -438,9 +438,9 @@ Proof.
   (* lvalue *)
   induction 1; intros v' CV; simpl in CV; try (monadInv CV).
   (* var local *)
-  unfold empty_env in H. rewrite PTree.gempty in H. congruence.
+  unfold empty_env in H. rewrite ATree.gempty in H. congruence.
   (* var_global *)
-  econstructor. unfold inj. rewrite H0. eauto. auto.
+  econstructor. unfold inj. rewrite Ident.of_to_positive, H0. eauto. auto.
   (* deref *)
   eauto.
   (* field struct *)
@@ -627,13 +627,13 @@ Proof.
   destruct f1; inv EQ0; simpl in H2; inv H2; assumption.
 - (* pointer *)
   unfold inj in H.
-  assert (data = Init_addrof b1 ofs1 /\ chunk = Mptr).
+  assert (data = Init_addrof (Ident.of_positive b1) ofs1 /\ chunk = Mptr).
   { remember Archi.ptr64 as ptr64.
     destruct ty; inversion EQ0.
     destruct i; inv H5. unfold Mptr. destruct Archi.ptr64; inv H6; inv H2; auto.
     subst ptr64. unfold Mptr. destruct Archi.ptr64; inv H5; inv H2; auto.
     inv H2. auto. }
-  destruct H4; subst. destruct (Genv.find_symbol ge b1); inv H.
+  destruct H4; subst. destruct Genv.find_symbol; inv H.
   rewrite Ptrofs.add_zero in H3. auto.
 - (* undef *)
   discriminate.
@@ -716,13 +716,13 @@ Local Opaque sizeof.
 + Local Transparent sizeof. simpl. eapply tr_init_array_size; eauto. 
 + replace (idlsize d) with (idlsize d + 0) by omega.
   eapply tr_init_struct_size; eauto. simpl.
-  unfold lookup_composite in H. destruct (ge.(genv_cenv)!id) as [co'|] eqn:?; inv H.
+  unfold lookup_composite in H. destruct (ge.(genv_cenv)$id) as [co'|] eqn:?; inv H.
   erewrite co_consistent_sizeof by (eapply ce_consistent; eauto).
   unfold sizeof_composite. rewrite H0. apply align_le.
   destruct (co_alignof_two_p co) as [n EQ]. rewrite EQ. apply two_power_nat_pos.
 + rewrite idlsize_app, padding_size. 
   exploit tr_init_size; eauto. intros EQ; rewrite EQ. omega.
-  simpl. unfold lookup_composite in H. destruct (ge.(genv_cenv)!id) as [co'|] eqn:?; inv H.
+  simpl. unfold lookup_composite in H. destruct (ge.(genv_cenv)$id) as [co'|] eqn:?; inv H.
   apply Z.le_trans with (sizeof_union ge (co_members co)).
   eapply union_field_size; eauto.
   erewrite co_consistent_sizeof by (eapply ce_consistent; eauto).
@@ -771,11 +771,11 @@ Inductive exec_init: mem -> block -> Z -> type -> initializer -> mem -> Prop :=
       exec_init_array m b ofs ty sz il m' ->
       exec_init m b ofs (Tarray ty sz a) (Init_array il) m'
   | exec_init_struct: forall m b ofs id a il co m',
-      ge.(genv_cenv)!id = Some co -> co_su co = Struct ->
+      ge.(genv_cenv)$id = Some co -> co_su co = Struct ->
       exec_init_list m b ofs (fields_of_struct (co_members co) 0) il m' ->
       exec_init m b ofs (Tstruct id a) (Init_struct il) m'
   | exec_init_union: forall m b ofs id a f i ty co m',
-      ge.(genv_cenv)!id = Some co -> co_su co = Union ->
+      ge.(genv_cenv)$id = Some co -> co_su co = Union ->
       field_type f (co_members co) = OK ty ->
       exec_init m b ofs ty i m' ->
       exec_init m b ofs (Tunion id a) (Init_union f i) m'
diff --git a/cfrontend/PrintClight.ml b/cfrontend/PrintClight.ml
index ca378c1126..d2f19db236 100644
--- a/cfrontend/PrintClight.ml
+++ b/cfrontend/PrintClight.ml
@@ -23,10 +23,6 @@ open Cop
 open PrintCsyntax
 open Clight
 
-(* Naming temporaries *)
-
-let temp_name (id: AST.ident) = "$" ^ Z.to_string (Z.Zpos id)
-
 (* Declarator (identifier + type) -- reuse from PrintCsyntax *)
 
 (* Precedences and associativity (H&S section 7.2) *)
@@ -69,7 +65,7 @@ let rec expr p (prec, e) =
   | Evar(id, _) ->
       fprintf p "%s" (extern_atom id)
   | Etempvar(id, _) ->
-      fprintf p "%s" (temp_name id)
+      fprintf p "%s" (extern_atom id)
   | Ederef(a1, _) ->
       fprintf p "*%a" expr (prec', a1)
   | Efield(a1, f, _) ->
@@ -123,14 +119,14 @@ let rec print_stmt p s =
   | Sassign(e1, e2) ->
       fprintf p "@[<hv 2>%a =@ %a;@]" print_expr e1 print_expr e2
   | Sset(id, e2) ->
-      fprintf p "@[<hv 2>%s =@ %a;@]" (temp_name id) print_expr e2
+      fprintf p "@[<hv 2>%s =@ %a;@]" (extern_atom id) print_expr e2
   | Scall(None, e1, el) ->
       fprintf p "@[<hv 2>%a@,(@[<hov 0>%a@]);@]"
                 expr (15, e1)
                 print_expr_list (true, el)
   | Scall(Some id, e1, el) ->
       fprintf p "@[<hv 2>%s =@ %a@,(@[<hov 0>%a@]);@]"
-                (temp_name id)
+                (extern_atom id)
                 expr (15, e1)
                 print_expr_list (true, el)
   | Sbuiltin(None, ef, tyargs, el) ->
@@ -139,7 +135,7 @@ let rec print_stmt p s =
                 print_expr_list (true, el)
   | Sbuiltin(Some id, ef, tyargs, el) ->
       fprintf p "@[<hv 2>%s =@ builtin %s@,(@[<hov 0>%a@]);@]"
-                (temp_name id)
+                (extern_atom id)
                 (name_of_external ef)
                 print_expr_list (true, el)
   | Ssequence(Sskip, s2) ->
@@ -210,7 +206,7 @@ and print_stmt_for p s =
   | Sassign(e1, e2) ->
       fprintf p "%a = %a" print_expr e1 print_expr e2
   | Sset(id, e2) ->
-      fprintf p "%s = %a" (temp_name id) print_expr e2
+      fprintf p "%s = %a" (extern_atom id) print_expr e2
   | Ssequence(Sskip, s2) ->
       print_stmt_for p s2
   | Ssequence(s1, s2) ->
@@ -221,7 +217,7 @@ and print_stmt_for p s =
                 print_expr_list (true, el)
   | Scall(Some id, e1, el) ->
       fprintf p "@[<hv 2>%s =@ %a@,(@[<hov 0>%a@])@]"
-                (temp_name id)
+                (extern_atom id)
                 expr (15, e1)
                 print_expr_list (true, el)
   | Sbuiltin(None, ef, tyargs, el) ->
@@ -230,7 +226,7 @@ and print_stmt_for p s =
                 print_expr_list (true, el)
   | Sbuiltin(Some id, ef, tyargs, el) ->
       fprintf p "@[<hv 2>%s =@ builtin %s@,(@[<hov 0>%a@]);@]"
-                (temp_name id)
+                (extern_atom id)
                 (name_of_external ef)
                 print_expr_list (true, el)
   | _ ->
@@ -248,7 +244,7 @@ let print_function p id f =
     f.fn_vars;
   List.iter
     (fun (id, ty) ->
-      fprintf p "register %s;@ " (name_cdecl (temp_name id) ty))
+      fprintf p "register %s;@ " (name_cdecl (extern_atom id) ty))
     f.fn_temps;
   print_stmt p f.fn_body;
   fprintf p "@;<0 -2>}@]@ @ "
diff --git a/cfrontend/SimplExpr.v b/cfrontend/SimplExpr.v
index 45b686f3d3..f3a36f8672 100644
--- a/cfrontend/SimplExpr.v
+++ b/cfrontend/SimplExpr.v
@@ -13,6 +13,7 @@
 (** Translation from Compcert C to Clight.
     Side effects are pulled out of Compcert C expressions. *)
 
+Require Import String.
 Require Import Coqlib.
 Require Import Errors.
 Require Import Integers.
@@ -25,12 +26,10 @@ Require Import Cop.
 Require Import Csyntax.
 Require Import Clight.
 
-Local Open Scope string_scope.
-
 (** State and error monad for generating fresh identifiers. *)
 
 Record generator : Type := mkgenerator {
-  gen_next: ident;
+  gen_next: positive;
   gen_trail: list (ident * type)
 }.
 
@@ -72,15 +71,58 @@ Notation "'do' ( X , Y ) <- A ; B" := (bind2 A (fun X Y => B))
 
 Local Open Scope gensym_monad_scope.
 
-Parameter first_unused_ident: unit -> ident.
-
 Definition initial_generator (x: unit) : generator :=
-  mkgenerator (first_unused_ident x) nil.
+  mkgenerator 1%positive nil.
+
+(** We need to generate symbols of the form "$n", where n is a decimal
+  representation for the current value of genv_next. Because such
+  symbols are not legal C identifiers, they will not conflict with the
+  ones we got from the parser. *)
+
+Lemma N_size_nat_le m n:
+  N.le m n -> le (N.size_nat m) (N.size_nat n).
+Proof.
+  intros H.
+  apply N.right_induction with (z := m) (n := n); eauto.
+  - intros x y []. tauto.
+  - intros.
+    transitivity (N.size_nat n0); eauto.
+    clear.
+    destruct n0; simpl. { apply Nat.le_0_1. }
+    induction p; simpl; eauto using le_n_S.
+Qed.
+
+Definition digit_of (n: N) :=
+  String (Ascii.ascii_of_N (48 + n)) EmptyString.
+
+Function digits_of (n: N) {measure N.size_nat} :=
+  if N.eqb n 0%N then
+    EmptyString
+  else
+    let (q, r) := N.div_eucl n 10%N in
+    String.append (digits_of q) (digit_of r).
+Proof.
+  intros n Hnz q r Hqr.
+  apply N.eqb_neq in Hnz. destruct n as [|n]; try congruence. simpl in Hqr.
+  destruct q as [|q]. { destruct n; apply Nat.lt_0_succ. }
+  pose proof (N.pos_div_eucl_spec n 10) as Hspec.
+  rewrite Hqr in Hspec. rewrite Hspec.
+  apply lt_le_trans with (N.size_nat (N.pos q * 2)).
+  {
+    rewrite N.mul_comm. simpl.
+    apply Nat.lt_succ_diag_r.
+  }
+  apply N_size_nat_le.
+  xomega.
+Defined.
+
+Definition string_of_resid n :=
+  String "$" (digits_of (Npos n)).
 
 Definition gensym (ty: type): mon ident :=
   fun (g: generator) =>
-    Res (gen_next g)
-        (mkgenerator (Pos.succ (gen_next g)) ((gen_next g, ty) :: gen_trail g))
+    Res #(string_of_resid (gen_next g))
+        (mkgenerator (Pos.succ (gen_next g)) ((#(string_of_resid (gen_next g)), ty) :: gen_trail g))
         (Ple_succ (gen_next g)).
 
 (** Construct a sequence from a list of statements.  To facilitate the
diff --git a/cfrontend/SimplExprproof.v b/cfrontend/SimplExprproof.v
index ee1df409d5..062e379770 100644
--- a/cfrontend/SimplExprproof.v
+++ b/cfrontend/SimplExprproof.v
@@ -367,7 +367,7 @@ Lemma tr_expr_leftcontext_rec:
   /\ incl tmp' tmps
   /\ (forall le' e' sl3,
         tr_expr le' dst' e' sl3 a' tmp' ->
-        (forall id, ~In id tmp' -> le'!id = le!id) ->
+        (forall id, ~In id tmp' -> le'$id = le$id) ->
         Csyntax.typeof e' = Csyntax.typeof e ->
         tr_expr le' dst (C e') (sl3 ++ sl2) a tmps)
  ) /\ (
@@ -380,7 +380,7 @@ Lemma tr_expr_leftcontext_rec:
   /\ incl tmp' tmps
   /\ (forall le' e' sl3,
         tr_expr le' dst' e' sl3 a' tmp' ->
-        (forall id, ~In id tmp' -> le'!id = le!id) ->
+        (forall id, ~In id tmp' -> le'$id = le$id) ->
         Csyntax.typeof e' = Csyntax.typeof e ->
         tr_exprlist le' (C e') (sl3 ++ sl2) a tmps)
 ).
@@ -400,8 +400,8 @@ Ltac NOTIN :=
 
 Ltac UNCHANGED :=
   match goal with
-  | [ H: (forall (id: ident), ~In id _ -> ?le' ! id = ?le ! id) |-
-         (forall (id: ident), In id _ -> ?le' ! id = ?le ! id) ] =>
+  | [ H: (forall (id: ident), ~In id _ -> ?le' $ id = ?le $ id) |-
+         (forall (id: ident), In id _ -> ?le' $ id = ?le $ id) ] =>
       intros; apply H; NOTIN
   end.
 
@@ -725,7 +725,7 @@ Theorem tr_expr_leftcontext:
   /\ incl tmp' tmps
   /\ (forall le' r' sl3,
         tr_expr le' dst' r' sl3 a' tmp' ->
-        (forall id, ~In id tmp' -> le'!id = le!id) ->
+        (forall id, ~In id tmp' -> le'$id = le$id) ->
         Csyntax.typeof r' = Csyntax.typeof r ->
         tr_expr le' dst (C r') (sl3 ++ sl2) a tmps).
 Proof.
@@ -744,7 +744,7 @@ Theorem tr_top_leftcontext:
   /\ incl tmp' tmps
   /\ (forall le' m' r' sl3,
         tr_expr le' dst' r' sl3 a' tmp' ->
-        (forall id, ~In id tmp' -> le'!id = le!id) ->
+        (forall id, ~In id tmp' -> le'$id = le$id) ->
         Csyntax.typeof r' = Csyntax.typeof r ->
         tr_top tge e le' m' dst (C r') (sl3 ++ sl2) a tmps).
 Proof.
@@ -833,12 +833,12 @@ Lemma step_make_set:
   eval_lvalue tge e le m a b ofs ->
   typeof a = ty ->
   step1 tge (State f (make_set id a) k e le m)
-          t (State f Sskip k e (PTree.set id v le) m).
+          t (State f Sskip k e (ATree.set id v le) m).
 Proof.
   intros. exploit deref_loc_translated; eauto. rewrite <- H1.
   unfold make_set. destruct (chunk_for_volatile_type (typeof a)) as [chunk|].
 (* volatile case *)
-  intros. change (PTree.set id v le) with (set_opttemp (Some id) v le). econstructor.
+  intros. change (ATree.set id v le) with (set_opttemp (Some id) v le). econstructor.
   econstructor. constructor. eauto.
   simpl. unfold sem_cast. simpl. eauto. constructor.
   simpl. econstructor; eauto.
@@ -903,7 +903,7 @@ Lemma step_tr_rvalof:
                  t (State f Sskip k e le' m)
   /\ eval_expr tge e le' m a' v
   /\ typeof a' = typeof a
-  /\ forall x, ~In x tmp -> le'!x = le!x.
+  /\ forall x, ~In x tmp -> le'$x = le$x.
 Proof.
   intros. inv H1.
   (* not volatile *)
@@ -913,11 +913,11 @@ Proof.
   split. eapply eval_Elvalue; eauto.
   auto.
   (* volatile *)
-  intros. exists (PTree.set t0 v le); split.
+  intros. exists (ATree.set t0 v le); split.
   simpl. eapply star_two. econstructor. eapply step_make_set; eauto. traceEq.
-  split. constructor. apply PTree.gss.
+  split. constructor. apply ATree.gss.
   split. auto.
-  intros. apply PTree.gso. congruence.
+  intros. apply ATree.gso. congruence.
 Qed.
 
 (** Matching between continuations *)
@@ -1204,7 +1204,7 @@ Lemma tr_find_label_expression:
 Proof.
   intros. inv H.
   assert (nolabel (makeseq sl)). apply makeseq_nolabel.
-  eapply tr_find_label_top with (e := empty_env) (le := PTree.empty val) (m := Mem.empty).
+  eapply tr_find_label_top with (e := empty_env) (le := ATree.empty val) (m := Mem.empty).
   eauto. apply H.
 Qed.
 
@@ -1213,7 +1213,7 @@ Lemma tr_find_label_expr_stmt:
 Proof.
   intros. inv H.
   assert (nolabel (makeseq sl)). apply makeseq_nolabel.
-  eapply tr_find_label_top with (e := empty_env) (le := PTree.empty val) (m := Mem.empty).
+  eapply tr_find_label_top with (e := empty_env) (le := ATree.empty val) (m := Mem.empty).
   eauto. apply H.
 Qed.
 
@@ -1226,7 +1226,7 @@ Proof.
   assert (nolabel (makeseq (sl ++ makeif a Sskip Sbreak :: nil))).
   apply makeseq_nolabel.
   apply nolabel_list_app.
-  eapply tr_find_label_top with (e := empty_env) (le := PTree.empty val) (m := Mem.empty).
+  eapply tr_find_label_top with (e := empty_env) (le := ATree.empty val) (m := Mem.empty).
   eauto.
   simpl; split; auto. apply makeif_nolabel. red; simpl; auto. red; simpl; auto.
   apply H.
@@ -1419,7 +1419,7 @@ Lemma tr_val_gen:
   forall le dst v ty a tmp,
   typeof a = ty ->
   (forall tge e le' m,
-      (forall id, In id tmp -> le'!id = le!id) ->
+      (forall id, In id tmp -> le'$id = le$id) ->
       eval_expr tge e le' m a v) ->
   tr_expr le dst (Csyntax.Eval v ty) (final dst a) a tmp.
 Proof.
@@ -1463,8 +1463,8 @@ Proof.
   econstructor; eauto.
   change (final dst' (Etempvar t0 (Csyntax.typeof l)) ++ sl2) with (nil ++ (final dst' (Etempvar t0 (Csyntax.typeof l)) ++ sl2)).
   apply S. apply tr_val_gen. auto.
-  intros. constructor. rewrite H5; auto. apply PTree.gss.
-  intros. apply PTree.gso. red; intros; subst; elim H5; auto.
+  intros. constructor. rewrite H5; auto. apply ATree.gss.
+  intros. apply ATree.gso. red; intros; subst; elim H5; auto.
   auto.
 (* seqand true *)
   exploit tr_top_leftcontext; eauto. clear H9.
@@ -1516,8 +1516,8 @@ Proof.
   apply star_one. constructor. constructor. reflexivity. reflexivity.
   eapply match_exprstates; eauto.
   change sl2 with (nil ++ sl2). apply S. econstructor; eauto.
-  intros. constructor. rewrite H2. apply PTree.gss. auto.
-  intros. apply PTree.gso. congruence.
+  intros. constructor. rewrite H2. apply ATree.gss. auto.
+  intros. apply ATree.gso. congruence.
   auto.
   (* for effects *)
   exploit tr_simple_rvalue; eauto. intros [SL [TY EV]].
@@ -1552,8 +1552,8 @@ Proof.
   apply star_one. constructor. constructor. reflexivity. reflexivity.
   eapply match_exprstates; eauto.
   change sl2 with (nil ++ sl2). apply S. econstructor; eauto.
-  intros. constructor. rewrite H2. apply PTree.gss. auto.
-  intros. apply PTree.gso. congruence.
+  intros. constructor. rewrite H2. apply ATree.gss. auto.
+  intros. apply ATree.gso. congruence.
   auto.
   (* for effects *)
   exploit tr_simple_rvalue; eauto. intros [SL [TY EV]].
@@ -1696,8 +1696,8 @@ Proof.
   (* for value *)
   exploit tr_simple_rvalue; eauto. intros [SL2 [TY2 EV2]].
   exploit tr_simple_lvalue. eauto.
-    eapply tr_expr_invariant with (le' := PTree.set t0 v' le). eauto.
-    intros. apply PTree.gso. intuition congruence.
+    eapply tr_expr_invariant with (le' := ATree.set t0 v' le). eauto.
+    intros. apply ATree.gso. intuition congruence.
   intros [SL1 [TY1 EV1]].
   subst; simpl Kseqlist.
   econstructor; split.
@@ -1705,12 +1705,12 @@ Proof.
   eapply star_left. constructor. econstructor. eauto. rewrite <- TY2; eauto. 
   eapply star_left. constructor.
   apply star_one. eapply step_make_assign; eauto.
-  constructor. apply PTree.gss. simpl. eapply cast_idempotent; eauto. 
+  constructor. apply ATree.gss. simpl. eapply cast_idempotent; eauto.
   reflexivity. reflexivity. traceEq.
   econstructor. auto. apply S.
   apply tr_val_gen. auto. intros. constructor.
-  rewrite H4; auto. apply PTree.gss.
-  intros. apply PTree.gso. intuition congruence.
+  rewrite H4; auto. apply ATree.gss.
+  intros. apply ATree.gso. intuition congruence.
   auto. auto.
 (* assignop *)
   exploit tr_top_leftcontext; eauto. clear H15.
@@ -1740,8 +1740,8 @@ Proof.
   exploit tr_simple_rvalue. eauto. eapply tr_expr_invariant with (le := le) (le' := le'). eauto.
   intros. apply INV. NOTIN. simpl. intros [SL2 [TY2 EV2]].
   exploit tr_simple_lvalue. eauto.
-    eapply tr_expr_invariant with (le := le) (le' := PTree.set t v4 le'). eauto.
-    intros. rewrite PTree.gso. apply INV. NOTIN. intuition congruence.
+    eapply tr_expr_invariant with (le := le) (le' := ATree.set t v4 le'). eauto.
+    intros. rewrite ATree.gso. apply INV. NOTIN. intuition congruence.
   intros [? [? EV1'']].
   subst; simpl Kseqlist.
   econstructor; split.
@@ -1752,12 +1752,12 @@ Proof.
     rewrite TY3; rewrite <- TY1; rewrite <- TY2; rewrite comp_env_preserved; eauto.
     eassumption.
   econstructor. eapply step_make_assign; eauto.
-    constructor. apply PTree.gss. simpl. eapply cast_idempotent; eauto.
+    constructor. apply ATree.gss. simpl. eapply cast_idempotent; eauto.
     reflexivity. traceEq.
   econstructor. auto. apply S.
   apply tr_val_gen. auto. intros. constructor.
-  rewrite H10; auto. apply PTree.gss.
-  intros. rewrite PTree.gso. apply INV.
+  rewrite H10; auto. apply ATree.gss.
+  intros. rewrite ATree.gso. apply INV.
   red; intros; elim H10; auto.
   intuition congruence.
   auto. auto.
@@ -1808,8 +1808,8 @@ Proof.
   (* for value *)
   exploit tr_simple_lvalue; eauto. intros [SL1 [TY1 EV1]].
   exploit tr_simple_lvalue. eauto.
-    eapply tr_expr_invariant with (le' := PTree.set t v1 le). eauto.
-    intros. apply PTree.gso. intuition congruence.
+    eapply tr_expr_invariant with (le' := ATree.set t v1 le). eauto.
+    intros. apply ATree.gso. intuition congruence.
   intros [SL2 [TY2 EV2]].
   subst; simpl Kseqlist.
   econstructor; split.
@@ -1818,16 +1818,16 @@ Proof.
   constructor.
   eapply step_make_assign; eauto.
   unfold transl_incrdecr. destruct id; simpl in H2.
-  econstructor. constructor. apply PTree.gss. constructor.
+  econstructor. constructor. apply ATree.gss. constructor.
   rewrite comp_env_preserved; simpl; eauto.
-  econstructor. constructor. apply PTree.gss. constructor.
+  econstructor. constructor. apply ATree.gss. constructor.
   rewrite comp_env_preserved; simpl; eauto.
   destruct id; auto.
   traceEq.
   econstructor. auto. apply S.
   apply tr_val_gen. auto. intros. econstructor; eauto.
-  rewrite H5; auto. apply PTree.gss.
-  intros. apply PTree.gso. intuition congruence.
+  rewrite H5; auto. apply ATree.gss.
+  intros. apply ATree.gso. intuition congruence.
   auto. auto.
 (* postincr stuck *)
   exploit tr_top_leftcontext; eauto. clear H11.
@@ -1872,8 +1872,8 @@ Proof.
   econstructor. econstructor; eauto. rewrite <- TY1; eauto. traceEq.
   econstructor; eauto.
   change sl2 with (final For_val (Etempvar t (Csyntax.typeof r)) ++ sl2). apply S.
-  constructor. auto. intros. constructor. rewrite H2; auto. apply PTree.gss.
-  intros. apply PTree.gso. intuition congruence.
+  constructor. auto. intros. constructor. rewrite H2; auto. apply ATree.gss.
+  intros. apply ATree.gso. intuition congruence.
   auto.
   (* for effects *)
   econstructor; split.
@@ -1890,8 +1890,8 @@ Proof.
   rewrite <- TY1; eauto. traceEq.
   econstructor; eauto.
   apply S. constructor; auto.
-  intros. constructor. rewrite H2. apply PTree.gss. auto.
-  intros. apply PTree.gso. congruence.
+  intros. constructor. rewrite H2. apply ATree.gss. auto.
+  intros. apply ATree.gso. congruence.
   auto.
 
 (* call *)
@@ -1924,9 +1924,9 @@ Proof.
   constructor; auto. econstructor; eauto.
   intros. apply S.
   destruct dst'; constructor.
-  auto. intros. constructor. rewrite H5; auto. apply PTree.gss.
-  auto. intros. constructor. rewrite H5; auto. apply PTree.gss.
-  intros. apply PTree.gso. intuition congruence.
+  auto. intros. constructor. rewrite H5; auto. apply ATree.gss.
+  auto. intros. constructor. rewrite H5; auto. apply ATree.gss.
+  intros. apply ATree.gso. intuition congruence.
   auto.
 
 (* builtin *)
@@ -1953,8 +1953,8 @@ Proof.
   traceEq.
   econstructor; eauto.
   change sl2 with (nil ++ sl2). apply S.
-  apply tr_val_gen. auto. intros. constructor. rewrite H2; auto. simpl. apply PTree.gss.
-  intros; simpl. apply PTree.gso. intuition congruence.
+  apply tr_val_gen. auto. intros. constructor. rewrite H2; auto. simpl. apply ATree.gss.
+  intros; simpl. apply ATree.gso. intuition congruence.
   auto.
 Qed.
 
diff --git a/cfrontend/SimplExprspec.v b/cfrontend/SimplExprspec.v
index 37e2cd9603..819b84be39 100644
--- a/cfrontend/SimplExprspec.v
+++ b/cfrontend/SimplExprspec.v
@@ -12,6 +12,7 @@
 
 (** Relational specification of expression simplification. *)
 
+Require Import String.
 Require Import Coqlib Maps Errors Integers Floats.
 Require Import AST Linking Memory.
 Require Import Ctypes Cop Csyntax Clight SimplExpr.
@@ -65,14 +66,14 @@ Inductive tr_expr: temp_env -> destination -> Csyntax.expr -> list statement ->
   | tr_val_value: forall le v ty a tmp,
       typeof a = ty ->
       (forall tge e le' m,
-         (forall id, In id tmp -> le'!id = le!id) ->
+         (forall id, In id tmp -> le'$id = le$id) ->
          eval_expr tge e le' m a v) ->
       tr_expr le For_val (Csyntax.Eval v ty)
                            nil a tmp
   | tr_val_set: forall le sd v ty a any tmp,
       typeof a = ty ->
       (forall tge e le' m,
-         (forall id, In id tmp -> le'!id = le!id) ->
+         (forall id, In id tmp -> le'$id = le$id) ->
          eval_expr tge e le' m a v) ->
       tr_expr le (For_set sd) (Csyntax.Eval v ty)
                    (do_set sd a) any tmp
@@ -327,16 +328,16 @@ Combined Scheme tr_expr_exprlist from tr_expr_ind2, tr_exprlist_ind2.
 
 Lemma tr_expr_invariant:
   forall le dst r sl a tmps, tr_expr le dst r sl a tmps ->
-  forall le', (forall x, In x tmps -> le'!x = le!x) ->
+  forall le', (forall x, In x tmps -> le'$x = le$x) ->
   tr_expr le' dst r sl a tmps
 with tr_exprlist_invariant:
   forall le rl sl al tmps, tr_exprlist le rl sl al tmps ->
-  forall le', (forall x, In x tmps -> le'!x = le!x) ->
+  forall le', (forall x, In x tmps -> le'$x = le$x) ->
   tr_exprlist le' rl sl al tmps.
 Proof.
   induction 1; intros; econstructor; eauto.
-    intros. apply H0. intros. transitivity (le'!id); auto.
-    intros. apply H0. auto. intros. transitivity (le'!id); auto.
+    intros. apply H0. intros. transitivity (le'$id); auto.
+    intros. apply H0. auto. intros. transitivity (le'$id); auto.
   induction 1; intros; econstructor; eauto.
 Qed.
 
@@ -552,16 +553,70 @@ Ltac monadInv H :=
       ((progress simpl in H) || unfold F in H); monadInv1 H
   end.
 
+(** ** Injectivity of symbol generation *)
+
+Lemma app_one_inj s1 s2 c1 c2:
+  (s1 ++ String c1 "" = s2 ++ String c2 "")%string ->
+  s1 = s2 /\ c1 = c2.
+Proof.
+  revert s2 c1 c2.
+  induction s1; intros.
+  - destruct s2; inv H; eauto.
+    induction s2; discriminate.
+  - destruct s2; inv H.
+    + induction s1; discriminate.
+    + apply IHs1 in H2. intuition congruence.
+Qed.
+
+Lemma string_of_resid_inj:
+  forall x y, string_of_resid x = string_of_resid y -> x = y.
+Proof.
+  intros x y H.
+  inv H. cut (N.pos x = N.pos y). { congruence. }
+  revert H1. generalize (N.pos x), (N.pos y). clear.
+  intros p.
+  functional induction (digits_of p); intros m Hm.
+  - apply Neqb_ok in e; subst.
+    rewrite digits_of_equation in Hm.
+    destruct (N.eqb_spec m 0); eauto.
+    destruct N.div_eucl. induction digits_of; discriminate.
+  - apply N.eqb_neq in e.
+    rewrite (digits_of_equation m) in Hm.
+    destruct (N.eqb_spec m 0); eauto.
+    destruct N.div_eucl. induction digits_of; discriminate.
+    destruct n as [|n]; try congruence. simpl in *.
+    destruct m as [|m]; try congruence. simpl in *.
+    pose proof (N.pos_div_eucl_remainder n 10) as Hrem.
+    pose proof (N.pos_div_eucl_remainder m 10) as Hrem'.
+    pose proof (N.pos_div_eucl_spec n 10) as Hspec.
+    pose proof (N.pos_div_eucl_spec m 10) as Hspec'.
+    rewrite e0 in Hspec, Hrem; subst. simpl in Hrem.
+    destruct (N.pos_div_eucl m 10) as [q' r']; subst. simpl in Hrem'.
+    cut (q = q' /\ r = r'). { xomega. }
+    clear - IHs Hrem Hrem' Hm.
+    apply app_one_inj in Hm. destruct Hm as [Hq Hr].
+    split; eauto.
+    assert (10 <> 0)%N by congruence. specialize (Hrem H). specialize (Hrem' H).
+    cut (48 + r = 48 + r')%N. { xomega. }
+    rewrite <- (Ascii.N_ascii_embedding (48 + r)%N) by xomega.
+    rewrite <- (Ascii.N_ascii_embedding (48 + r')%N) by xomega.
+    congruence.
+Qed.
+
 (** ** Freshness and separation properties. *)
 
 Definition within (id: ident) (g1 g2: generator) : Prop :=
-  Ple (gen_next g1) id /\ Plt id (gen_next g2).
+  exists p,
+    id = #(string_of_resid p) /\
+    Ple (gen_next g1) p /\ Plt p (gen_next g2).
 
 Lemma gensym_within:
   forall ty g1 id g2 I,
   gensym ty g1 = Res id g2 I -> within id g1 g2.
 Proof.
-  intros. monadInv H. split. apply Ple_refl. apply Plt_succ.
+  intros. monadInv H.
+  exists (gen_next g1); intuition idtac.
+  apply Ple_refl. apply Plt_succ.
 Qed.
 
 Lemma within_widen:
@@ -571,7 +626,8 @@ Lemma within_widen:
   Ple (gen_next g2) (gen_next g2') ->
   within id g1' g2'.
 Proof.
-  intros. destruct H. split.
+  intros. destruct H as (? & ? & ?).
+  exists x; intuition idtac.
   eapply Ple_trans; eauto.
   eapply Plt_Ple_trans; eauto.
 Qed.
@@ -614,21 +670,26 @@ Lemma contained_disjoint:
   contained l1 g1 g2 -> contained l2 g2 g3 -> list_disjoint l1 l2.
 Proof.
   intros; red; intros. red; intro; subst y.
-  exploit H; eauto. intros [A B]. exploit H0; eauto. intros [Csyntax D].
-  elim (Plt_strict x). apply Plt_Ple_trans with (gen_next g2); auto.
+  exploit H; eauto. intros (p & Hp & A & B).
+  exploit H0; eauto. intros (q & Hq & Csyntax & D).
+  assert (p = q) by (apply string_of_resid_inj, ident_of_string_inj; congruence).
+  subst q. elim (Plt_strict p). apply Plt_Ple_trans with (gen_next g2); auto.
 Qed.
 
 Lemma contained_notin:
   forall g1 l g2 id g3,
   contained l g1 g2 -> within id g2 g3 -> ~In id l.
 Proof.
-  intros; red; intros. exploit H; eauto. intros [Csyntax D]. destruct H0 as [A B].
-  elim (Plt_strict id). apply Plt_Ple_trans with (gen_next g2); auto.
+  intros; red; intros.
+  exploit H; eauto. intros (p & Hp & Csyntax & D).
+  destruct H0 as (q & Hq & A & B).
+  assert (p = q) by (apply string_of_resid_inj, ident_of_string_inj; congruence).
+  subst q. elim (Plt_strict p). apply Plt_Ple_trans with (gen_next g2); auto.
 Qed.
 
 Definition dest_below (dst: destination) (g: generator) : Prop :=
   match dst with
-  | For_set sd => Plt (sd_temp sd) g.(gen_next)
+  | For_set sd => exists p, sd_temp sd = #(string_of_resid p) /\ Plt p g.(gen_next)
   | _ => True
   end.
 
@@ -642,7 +703,7 @@ Lemma dest_for_set_seqbool_val:
   forall tmp ty g1 g2,
   within tmp g1 g2 -> dest_below (For_set (sd_seqbool_val tmp ty)) g2.
 Proof.
-  intros. destruct H. simpl. auto.
+  intros. destruct H as (p & Hp & A & B). simpl. eauto.
 Qed.
 
 Lemma dest_for_set_seqbool_set:
@@ -654,27 +715,30 @@ Qed.
 Lemma dest_for_set_condition_val:
   forall tmp tycast ty g1 g2, within tmp g1 g2 -> dest_below (For_set (SDbase tycast ty tmp)) g2.
 Proof.
-  intros. destruct H. simpl. auto.
+  intros. destruct H as (p & Hp & A & B). simpl. eauto.
 Qed.
 
 Lemma dest_for_set_condition_set:
   forall sd tmp tycast ty g1 g2, dest_below (For_set sd) g2 -> within tmp g1 g2 -> dest_below (For_set (SDcons tycast ty tmp sd)) g2.
 Proof.
-  intros. destruct H0. simpl. auto.
+  intros. destruct H0 as (p & Hp & A & B). simpl. eauto.
 Qed.
 
 Lemma sd_temp_notin:
   forall sd g1 g2 l, dest_below (For_set sd) g1 -> contained l g1 g2 -> ~In (sd_temp sd) l.
 Proof.
-  intros. simpl in H. red; intros. exploit H0; eauto. intros [A B].
-  elim (Plt_strict (sd_temp sd)). apply Plt_Ple_trans with (gen_next g1); auto.
+  intros. destruct H as (p & Hp & H). red; intros.
+  exploit H0; eauto. intros (q & Hq & A & B).
+  assert (p = q) by (apply string_of_resid_inj, ident_of_string_inj; congruence).
+  subst q. elim (Plt_strict p). apply Plt_Ple_trans with (gen_next g1); auto.
 Qed.
 
 Lemma dest_below_le:
   forall dst g1 g2,
   dest_below dst g1 -> Ple g1.(gen_next) g2.(gen_next) -> dest_below dst g2.
 Proof.
-  intros. destruct dst; simpl in *; auto. eapply Plt_Ple_trans; eauto.
+  intros. destruct dst; simpl in *; auto.
+  destruct H as (p & Hp & H). eauto using Plt_Ple_trans.
 Qed.
 
 Hint Resolve gensym_within within_widen contained_widen
diff --git a/cfrontend/SimplLocals.v b/cfrontend/SimplLocals.v
index b142d3cc51..e7a47c08da 100644
--- a/cfrontend/SimplLocals.v
+++ b/cfrontend/SimplLocals.v
@@ -23,7 +23,7 @@ Require Compopts.
 Open Scope error_monad_scope.
 Open Scope string_scope.
 
-Module VSet := FSetAVL.Make(OrderedPositive).
+Module VSet := FSetAVL.Make(OrderedIdent).
 
 (** The set of local variables that can be lifted to temporaries,
   because they are scalar and their address is not taken. *)
diff --git a/cfrontend/SimplLocalsproof.v b/cfrontend/SimplLocalsproof.v
index 7af499f487..b627267c16 100644
--- a/cfrontend/SimplLocalsproof.v
+++ b/cfrontend/SimplLocalsproof.v
@@ -78,24 +78,24 @@ Qed.
 
 Inductive match_var (f: meminj) (cenv: compilenv) (e: env) (m: mem) (te: env) (tle: temp_env) (id: ident) : Prop :=
   | match_var_lifted: forall b ty chunk v tv
-      (ENV: e!id = Some(b, ty))
-      (TENV: te!id = None)
+      (ENV: e$id = Some(b, ty))
+      (TENV: te$id = None)
       (LIFTED: VSet.mem id cenv = true)
       (MAPPED: f b = None)
       (MODE: access_mode ty = By_value chunk)
       (LOAD: Mem.load chunk m b 0 = Some v)
-      (TLENV: tle!(id) = Some tv)
+      (TLENV: tle$(id) = Some tv)
       (VINJ: Val.inject f v tv),
       match_var f cenv e m te tle id
   | match_var_not_lifted: forall b ty b'
-      (ENV: e!id = Some(b, ty))
-      (TENV: te!id = Some(b', ty))
+      (ENV: e$id = Some(b, ty))
+      (TENV: te$id = Some(b', ty))
       (LIFTED: VSet.mem id cenv = false)
       (MAPPED: f b = Some(b', 0)),
       match_var f cenv e m te tle id
   | match_var_not_local: forall
-      (ENV: e!id = None)
-      (TENV: te!id = None)
+      (ENV: e$id = None)
+      (TENV: te$id = None)
       (LIFTED: VSet.mem id cenv = false),
       match_var f cenv e m te tle id.
 
@@ -107,21 +107,21 @@ Record match_envs (f: meminj) (cenv: compilenv)
       forall id, match_var f cenv e m te tle id;
     me_temps:
       forall id v,
-      le!id = Some v ->
-      (exists tv, tle!id = Some tv /\ Val.inject f v tv)
+      le$id = Some v ->
+      (exists tv, tle$id = Some tv /\ Val.inject f v tv)
       /\ (VSet.mem id cenv = true -> v = Vundef);
     me_inj:
-      forall id1 b1 ty1 id2 b2 ty2, e!id1 = Some(b1, ty1) -> e!id2 = Some(b2, ty2) -> id1 <> id2 -> b1 <> b2;
+      forall id1 b1 ty1 id2 b2 ty2, e$id1 = Some(b1, ty1) -> e$id2 = Some(b2, ty2) -> id1 <> id2 -> b1 <> b2;
     me_range:
-      forall id b ty, e!id = Some(b, ty) -> Ple lo b /\ Plt b hi;
+      forall id b ty, e$id = Some(b, ty) -> Ple lo b /\ Plt b hi;
     me_trange:
-      forall id b ty, te!id = Some(b, ty) -> Ple tlo b /\ Plt b thi;
+      forall id b ty, te$id = Some(b, ty) -> Ple tlo b /\ Plt b thi;
     me_mapped:
       forall id b' ty,
-      te!id = Some(b', ty) -> exists b, f b = Some(b', 0) /\ e!id = Some(b, ty);
+      te$id = Some(b', ty) -> exists b, f b = Some(b', 0) /\ e$id = Some(b, ty);
     me_flat:
       forall id b' ty b delta,
-      te!id = Some(b', ty) -> f b = Some(b', delta) -> e!id = Some(b, ty) /\ delta = 0;
+      te$id = Some(b', ty) -> f b = Some(b', delta) -> e$id = Some(b, ty) /\ delta = 0;
     me_incr:
       Ple lo hi;
     me_tincr:
@@ -288,7 +288,7 @@ Qed.
 
 Lemma step_Sdebug_temp:
   forall f id ty k e le m v,
-  le!id = Some v ->
+  le$id = Some v ->
   val_casted v ty ->
   step2 tge (State f (Sdebug_temp id ty) k e le m)
          E0 (State f Sskip k e le m).
@@ -300,7 +300,7 @@ Qed.
 
 Lemma step_Sdebug_var:
   forall f id ty k e le m b,
-  e!id = Some(b, ty) ->
+  e$id = Some(b, ty) ->
   step2 tge (State f (Sdebug_var id ty) k e le m)
          E0 (State f Sskip k e le m).
 Proof.
@@ -315,25 +315,25 @@ Lemma step_Sset_debug:
   eval_expr tge e le m a v ->
   sem_cast v (typeof a) ty m = Some v' ->
   plus step2 tge (State f (Sset_debug id ty a) k e le m)
-              E0 (State f Sskip k e (PTree.set id v' le) m).
+              E0 (State f Sskip k e (ATree.set id v' le) m).
 Proof.
   intros; unfold Sset_debug.
   assert (forall k, step2 tge (State f (Sset id (make_cast a ty)) k e le m)
-                           E0 (State f Sskip k e (PTree.set id v' le) m)).
+                           E0 (State f Sskip k e (ATree.set id v' le) m)).
   { intros. apply step_set. eapply make_cast_correct; eauto. }
   destruct (Compopts.debug tt).
 - eapply plus_left. constructor.
   eapply star_left. apply H1.
   eapply star_left. constructor.
   apply star_one. apply step_Sdebug_temp with (v := v').
-  apply PTree.gss. eapply cast_val_is_casted; eauto.
+  apply ATree.gss. eapply cast_val_is_casted; eauto.
   reflexivity. reflexivity. reflexivity.
 - apply plus_one. apply H1.
 Qed.
 
 Lemma step_add_debug_vars:
   forall f s e le m vars k,
-  (forall id ty, In (id, ty) vars -> exists b, e!id = Some (b, ty)) ->
+  (forall id ty, In (id, ty) vars -> exists b, e$id = Some (b, ty)) ->
   star step2 tge (State f (add_debug_vars vars s) k e le m)
               E0 (State f s k e le m).
 Proof.
@@ -354,13 +354,13 @@ Remark bind_parameter_temps_inv:
   forall id params args le le',
   bind_parameter_temps params args le = Some le' ->
   ~In id (var_names params) ->
-  le'!id = le!id.
+  le'$id = le$id.
 Proof.
   induction params; simpl; intros.
   destruct args; inv H. auto.
   destruct a as [id1 ty1]. destruct args; try discriminate.
-  transitivity ((PTree.set id1 v le)!id).
-  eapply IHparams; eauto. apply PTree.gso. intuition.
+  transitivity ((ATree.set id1 v le)$id).
+  eapply IHparams; eauto. apply ATree.gso. intuition.
 Qed.
 
 Lemma step_add_debug_params:
@@ -374,7 +374,7 @@ Proof.
   unfold add_debug_params. destruct (Compopts.debug tt).
 - induction params as [ | [id ty] params ]; simpl; intros until le1; intros NR CAST BIND; inv CAST; inv NR.
   + apply star_refl.
-  + assert (le!id = Some a1). { erewrite bind_parameter_temps_inv by eauto. apply PTree.gss. }
+  + assert (le$id = Some a1). { erewrite bind_parameter_temps_inv by eauto. apply ATree.gss. }
     eapply star_left. constructor.
     eapply star_left. eapply step_Sdebug_temp; eauto.
     eapply star_left. constructor.
@@ -388,31 +388,31 @@ Qed.
 Lemma match_envs_assign_lifted:
   forall f cenv e le m lo hi te tle tlo thi b ty v m' id tv,
   match_envs f cenv e le m lo hi te tle tlo thi ->
-  e!id = Some(b, ty) ->
+  e$id = Some(b, ty) ->
   val_casted v ty ->
   Val.inject f v tv ->
   assign_loc ge ty m b Ptrofs.zero v m' ->
   VSet.mem id cenv = true ->
-  match_envs f cenv e le m' lo hi te (PTree.set id tv tle) tlo thi.
+  match_envs f cenv e le m' lo hi te (ATree.set id tv tle) tlo thi.
 Proof.
   intros. destruct H. generalize (me_vars0 id); intros MV; inv MV; try congruence.
   rewrite ENV in H0; inv H0. inv H3; try congruence.
   unfold Mem.storev in H0. rewrite Ptrofs.unsigned_zero in H0.
   constructor; eauto; intros.
 (* vars *)
-  destruct (peq id0 id). subst id0.
+  destruct (ATree.elt_eq id0 id). subst id0.
   eapply match_var_lifted with (v := v); eauto.
   exploit Mem.load_store_same; eauto. erewrite val_casted_load_result; eauto.
-  apply PTree.gss.
+  apply ATree.gss.
   generalize (me_vars0 id0); intros MV; inv MV.
   eapply match_var_lifted; eauto.
   rewrite <- LOAD0. eapply Mem.load_store_other; eauto.
-  rewrite PTree.gso; auto.
+  rewrite ATree.gso; auto.
   eapply match_var_not_lifted; eauto.
   eapply match_var_not_local; eauto.
 (* temps *)
   exploit me_temps0; eauto. intros [[tv1 [A B]] C]. split; auto.
-  rewrite PTree.gsspec. destruct (peq id0 id).
+  rewrite ATree.gsspec. destruct (ATree.elt_eq id0 id).
   subst id0. exists tv; split; auto. rewrite C; auto.
   exists tv1; auto.
 Qed.
@@ -424,18 +424,18 @@ Lemma match_envs_set_temp:
   match_envs f cenv e le m lo hi te tle tlo thi ->
   Val.inject f v tv ->
   check_temp cenv id = OK x ->
-  match_envs f cenv e (PTree.set id v le) m lo hi te (PTree.set id tv tle) tlo thi.
+  match_envs f cenv e (ATree.set id v le) m lo hi te (ATree.set id tv tle) tlo thi.
 Proof.
   intros. unfold check_temp in H1.
   destruct (VSet.mem id cenv) eqn:?; monadInv H1.
   destruct H. constructor; eauto; intros.
 (* vars *)
   generalize (me_vars0 id0); intros MV; inv MV.
-  eapply match_var_lifted; eauto. rewrite PTree.gso. eauto. congruence.
+  eapply match_var_lifted; eauto. rewrite ATree.gso. eauto. congruence.
   eapply match_var_not_lifted; eauto.
   eapply match_var_not_local; eauto.
 (* temps *)
-  rewrite PTree.gsspec in *. destruct (peq id0 id).
+  rewrite ATree.gsspec in *. destruct (ATree.elt_eq id0 id).
   inv H. split. exists tv; auto. intros; congruence.
   eapply me_temps0; eauto.
 Qed.
@@ -457,7 +457,7 @@ Qed.
 Lemma match_envs_temps_exten:
   forall f cenv e le m lo hi te tle tlo thi tle',
   match_envs f cenv e le m lo hi te tle tlo thi ->
-  (forall id, tle'!id = tle!id) ->
+  (forall id, tle'$id = tle$id) ->
   match_envs f cenv e le m lo hi te tle' tlo thi.
 Proof.
   intros. destruct H. constructor; auto; intros.
@@ -475,17 +475,17 @@ Qed.
 Lemma match_envs_change_temp:
   forall f cenv e le m lo hi te tle tlo thi id v,
   match_envs f cenv e le m lo hi te tle tlo thi ->
-  le!id = None -> VSet.mem id cenv = false ->
-  match_envs f cenv e le m lo hi te (PTree.set id v tle) tlo thi.
+  le$id = None -> VSet.mem id cenv = false ->
+  match_envs f cenv e le m lo hi te (ATree.set id v tle) tlo thi.
 Proof.
   intros. destruct H. constructor; auto; intros.
   (* vars *)
   generalize (me_vars0 id0); intros MV; inv MV.
-  eapply match_var_lifted; eauto. rewrite PTree.gso; auto. congruence.
+  eapply match_var_lifted; eauto. rewrite ATree.gso; auto. congruence.
   eapply match_var_not_lifted; eauto.
   eapply match_var_not_local; eauto.
   (* temps *)
-  rewrite PTree.gso. eauto. congruence.
+  rewrite ATree.gso. eauto. congruence.
 Qed.
 
 (** Properties of [cenv_for]. *)
@@ -596,12 +596,12 @@ Qed.
 Lemma alloc_variables_range:
   forall ge id b ty e m vars e' m',
   alloc_variables ge e m vars e' m' ->
-  e'!id = Some(b, ty) -> e!id = Some(b, ty) \/ Ple (Mem.nextblock m) b /\ Plt b (Mem.nextblock m').
+  e'$id = Some(b, ty) -> e$id = Some(b, ty) \/ Ple (Mem.nextblock m) b /\ Plt b (Mem.nextblock m').
 Proof.
   induction 1; intros.
   auto.
-  exploit IHalloc_variables; eauto. rewrite PTree.gsspec. intros [A|A].
-  destruct (peq id id0). inv A.
+  exploit IHalloc_variables; eauto. rewrite ATree.gsspec. intros [A|A].
+  destruct (ATree.elt_eq id id0). inv A.
   right. exploit Mem.alloc_result; eauto. exploit Mem.nextblock_alloc; eauto.
   generalize (alloc_variables_nextblock _ _ _ _ _ _ H0). intros A B C.
   subst b. split. apply Ple_refl. eapply Pos.lt_le_trans; eauto. rewrite B. apply Plt_succ.
@@ -612,20 +612,20 @@ Qed.
 Lemma alloc_variables_injective:
   forall ge id1 b1 ty1 id2 b2 ty2 e m vars e' m',
   alloc_variables ge e m vars e' m' ->
-  (e!id1 = Some(b1, ty1) -> e!id2 = Some(b2, ty2) -> id1 <> id2 -> b1 <> b2) ->
-  (forall id b ty, e!id = Some(b, ty) -> Plt b (Mem.nextblock m)) ->
-  (e'!id1 = Some(b1, ty1) -> e'!id2 = Some(b2, ty2) -> id1 <> id2 -> b1 <> b2).
+  (e$id1 = Some(b1, ty1) -> e$id2 = Some(b2, ty2) -> id1 <> id2 -> b1 <> b2) ->
+  (forall id b ty, e$id = Some(b, ty) -> Plt b (Mem.nextblock m)) ->
+  (e'$id1 = Some(b1, ty1) -> e'$id2 = Some(b2, ty2) -> id1 <> id2 -> b1 <> b2).
 Proof.
   induction 1; intros.
   eauto.
   eapply IHalloc_variables; eauto.
-  repeat rewrite PTree.gsspec; intros.
-  destruct (peq id1 id); destruct (peq id2 id).
+  repeat rewrite ATree.gsspec; intros.
+  destruct (ATree.elt_eq id1 id); destruct (ATree.elt_eq id2 id).
   congruence.
   inv H6. exploit Mem.alloc_result; eauto. exploit H2; eauto. unfold block; xomega.
   inv H7. exploit Mem.alloc_result; eauto. exploit H2; eauto. unfold block; xomega.
   eauto.
-  intros. rewrite PTree.gsspec in H6. destruct (peq id0 id). inv H6.
+  intros. rewrite ATree.gsspec in H6. destruct (ATree.elt_eq id0 id). inv H6.
   exploit Mem.alloc_result; eauto. exploit Mem.nextblock_alloc; eauto. unfold block; xomega.
   exploit H2; eauto. exploit Mem.nextblock_alloc; eauto. unfold block; xomega.
 Qed.
@@ -643,14 +643,14 @@ Lemma match_alloc_variables:
   /\ (forall b, Mem.valid_block m b -> j' b = j b)
   /\ (forall b b' delta, j' b = Some(b', delta) -> Mem.valid_block tm b' -> j' b = j b)
   /\ (forall b b' delta, j' b = Some(b', delta) -> ~Mem.valid_block tm b' ->
-         exists id, exists ty, e'!id = Some(b, ty) /\ te'!id = Some(b', ty) /\ delta = 0)
+         exists id, exists ty, e'$id = Some(b, ty) /\ te'$id = Some(b', ty) /\ delta = 0)
   /\ (forall id ty, In (id, ty) vars ->
       exists b,
-          e'!id = Some(b, ty)
+          e'$id = Some(b, ty)
        /\ if VSet.mem id cenv
-          then te'!id = te!id /\ j' b = None
-          else exists tb, te'!id = Some(tb, ty) /\ j' b = Some(tb, 0))
-  /\ (forall id, ~In id (var_names vars) -> e'!id = e!id /\ te'!id = te!id).
+          then te'$id = te$id /\ j' b = None
+          else exists tb, te'$id = Some(tb, ty) /\ j' b = Some(tb, 0))
+  /\ (forall id, ~In id (var_names vars) -> e'$id = e$id /\ te'$id = te$id).
 Proof.
   induction 1; intros.
   (* base case *)
@@ -686,19 +686,19 @@ Proof.
       destruct H1. congruence. elim H5. unfold var_names. change id with (fst (id, ty0)). apply in_map; auto.
     subst ty0.
     exploit P; eauto. intros [X Y]. rewrite Heqb. rewrite X. rewrite Y.
-    exists b1. split. apply PTree.gss.
+    exists b1. split. apply ATree.gss.
     split. auto.
     rewrite M. auto. eapply Mem.valid_new_block; eauto.
     (* other vars *)
     eapply O; eauto. destruct H1. congruence. auto.
   intros. exploit (P id0). tauto. intros [X Y]. rewrite X; rewrite Y.
-    split; auto. apply PTree.gso. intuition.
+    split; auto. apply ATree.gso. intuition.
 
   (* variable is not lifted out of memory *)
   exploit Mem.alloc_parallel_inject.
     eauto. eauto. apply Z.le_refl. apply Z.le_refl.
   intros [j1 [tm1 [tb1 [A [B [C [D E]]]]]]].
-  exploit IHalloc_variables; eauto. instantiate (1 := PTree.set id (tb1, ty) te).
+  exploit IHalloc_variables; eauto. instantiate (1 := ATree.set id (tb1, ty) te).
   intros [j' [te' [tm' [J [K [L [M [N [Q [O P]]]]]]]]]].
   exists j'; exists te'; exists tm'.
   split. simpl. econstructor; eauto. rewrite comp_env_preserved; auto.
@@ -714,7 +714,7 @@ Proof.
     subst b'. rewrite (N _ _ _ H1) in H1.
     destruct (eq_block b b1). subst b. rewrite D in H1; inv H1.
     exploit (P id); auto. intros [X Y]. exists id; exists ty.
-    rewrite X; rewrite Y. repeat rewrite PTree.gss. auto.
+    rewrite X; rewrite Y. repeat rewrite ATree.gss. auto.
     rewrite E in H1; auto. elim H3. eapply Mem.mi_mappedblocks; eauto.
     eapply Mem.valid_new_block; eauto.
     eapply Q; eauto. unfold Mem.valid_block in *.
@@ -727,15 +727,15 @@ Proof.
       destruct H1. congruence. elim H5. unfold var_names. change id with (fst (id, ty0)). apply in_map; auto.
     subst ty0.
     exploit P; eauto. intros [X Y]. rewrite Heqb. rewrite X. rewrite Y.
-    exists b1. split. apply PTree.gss.
+    exists b1. split. apply ATree.gss.
     exists tb1; split.
-    apply PTree.gss.
+    apply ATree.gss.
     rewrite M. auto. eapply Mem.valid_new_block; eauto.
     (* other vars *)
     exploit (O id0 ty0). destruct H1. congruence. auto.
-    rewrite PTree.gso; auto.
+    rewrite ATree.gso; auto.
   intros. exploit (P id0). tauto. intros [X Y]. rewrite X; rewrite Y.
-    split; apply PTree.gso; intuition.
+    split; apply ATree.gso; intuition.
 Qed.
 
 Lemma alloc_variables_load:
@@ -765,7 +765,7 @@ Qed.
 
 Definition env_initial_value (e: env) (m: mem) :=
   forall id b ty chunk,
-  e!id = Some(b, ty) -> access_mode ty = By_value chunk -> Mem.load chunk m b 0 = Some Vundef.
+  e$id = Some(b, ty) -> access_mode ty = By_value chunk -> Mem.load chunk m b 0 = Some Vundef.
 
 Lemma alloc_variables_initial_value:
   forall e m vars e' m',
@@ -775,8 +775,8 @@ Lemma alloc_variables_initial_value:
 Proof.
   induction 1; intros.
   auto.
-  apply IHalloc_variables. red; intros. rewrite PTree.gsspec in H2.
-  destruct (peq id0 id). inv H2.
+  apply IHalloc_variables. red; intros. rewrite ATree.gsspec in H2.
+  destruct (ATree.elt_eq id0 id). inv H2.
   eapply Mem.load_alloc_same'; eauto.
   omega. rewrite Z.add_0_l. eapply sizeof_by_value; eauto.
   apply Z.divide_0_r.
@@ -784,20 +784,20 @@ Proof.
 Qed.
 
 Lemma create_undef_temps_charact:
-  forall id ty vars, In (id, ty) vars -> (create_undef_temps vars)!id = Some Vundef.
+  forall id ty vars, In (id, ty) vars -> (create_undef_temps vars)$id = Some Vundef.
 Proof.
   induction vars; simpl; intros.
   contradiction.
-  destruct H. subst a. apply PTree.gss.
-  destruct a as [id1 ty1]. rewrite PTree.gsspec. destruct (peq id id1); auto.
+  destruct H. subst a. apply ATree.gss.
+  destruct a as [id1 ty1]. rewrite ATree.gsspec. destruct (ATree.elt_eq id id1); auto.
 Qed.
 
 Lemma create_undef_temps_inv:
-  forall vars id v, (create_undef_temps vars)!id = Some v -> v = Vundef /\ In id (var_names vars).
+  forall vars id v, (create_undef_temps vars)$id = Some v -> v = Vundef /\ In id (var_names vars).
 Proof.
   induction vars; simpl; intros.
-  rewrite PTree.gempty in H; congruence.
-  destruct a as [id1 ty1]. rewrite PTree.gsspec in H. destruct (peq id id1).
+  rewrite ATree.gempty in H; congruence.
+  destruct a as [id1 ty1]. rewrite ATree.gsspec in H. destruct (ATree.elt_eq id id1).
   inv H. auto.
   exploit IHvars; eauto. tauto.
 Qed.
@@ -805,12 +805,12 @@ Qed.
 Lemma create_undef_temps_exten:
   forall id l1 l2,
   (In id (var_names l1) <-> In id (var_names l2)) ->
-  (create_undef_temps l1)!id = (create_undef_temps l2)!id.
+  (create_undef_temps l1)$id = (create_undef_temps l2)$id.
 Proof.
   assert (forall id l1 l2,
           (In id (var_names l1) -> In id (var_names l2)) ->
-          (create_undef_temps l1)!id = None \/ (create_undef_temps l1)!id = (create_undef_temps l2)!id).
-    intros. destruct ((create_undef_temps l1)!id) as [v1|] eqn:?; auto.
+          (create_undef_temps l1)$id = None \/ (create_undef_temps l1)$id = (create_undef_temps l2)$id).
+    intros. destruct ((create_undef_temps l1)$id) as [v1|] eqn:?; auto.
     exploit create_undef_temps_inv; eauto. intros [A B]. subst v1.
     exploit list_in_map_inv. unfold var_names in H. apply H. eexact B.
     intros [[id1 ty1] [P Q]]. simpl in P; subst id1.
@@ -867,8 +867,8 @@ Qed.
 Lemma create_undef_temps_lifted:
   forall id f,
   ~ In id (var_names (fn_params f)) ->
-  (create_undef_temps (add_lifted (cenv_for f) (fn_vars f) (fn_temps f))) ! id =
-  (create_undef_temps (add_lifted (cenv_for f) (fn_params f ++ fn_vars f) (fn_temps f))) ! id.
+  (create_undef_temps (add_lifted (cenv_for f) (fn_vars f) (fn_temps f))) $ id =
+  (create_undef_temps (add_lifted (cenv_for f) (fn_params f ++ fn_vars f) (fn_temps f))) $ id.
 Proof.
   intros. apply create_undef_temps_exten.
   unfold add_lifted. rewrite filter_app.
@@ -918,7 +918,7 @@ Theorem match_envs_alloc_variables:
   /\ inject_incr j j'
   /\ (forall b, Mem.valid_block m b -> j' b = j b)
   /\ (forall b b' delta, j' b = Some(b', delta) -> Mem.valid_block tm b' -> j' b = j b)
-  /\ (forall id ty, In (id, ty) vars -> VSet.mem id cenv = false -> exists b, te!id = Some(b, ty)).
+  /\ (forall id ty, In (id, ty) vars -> VSet.mem id cenv = false -> exists b, te$id = Some(b, ty)).
 Proof.
   intros.
   exploit (match_alloc_variables cenv); eauto. instantiate (1 := empty_env).
@@ -935,9 +935,9 @@ Proof.
   (* local var, lifted *)
   destruct R as [U V]. exploit H2; eauto. intros [chunk X].
   eapply match_var_lifted with (v := Vundef) (tv := Vundef); eauto.
-  rewrite U; apply PTree.gempty.
+  rewrite U; apply ATree.gempty.
   eapply alloc_variables_initial_value; eauto.
-  red. unfold empty_env; intros. rewrite PTree.gempty in H4; congruence.
+  red. unfold empty_env; intros. rewrite ATree.gempty in H4; congruence.
   apply create_undef_temps_charact with ty.
   unfold add_lifted. apply in_or_app. left.
   rewrite filter_In. auto.
@@ -945,7 +945,7 @@ Proof.
   destruct R as [tb [U V]].
   eapply match_var_not_lifted; eauto.
   (* non-local var *)
-  exploit G; eauto. unfold empty_env. rewrite PTree.gempty. intros [U V].
+  exploit G; eauto. unfold empty_env. rewrite ATree.gempty. intros [U V].
   eapply match_var_not_local; eauto.
   destruct (VSet.mem id cenv) eqn:?; auto.
   elim n; eauto.
@@ -960,17 +960,17 @@ Proof.
 
   (* injective *)
   eapply alloc_variables_injective. eexact H.
-  rewrite PTree.gempty. congruence.
-  intros. rewrite PTree.gempty in H7. congruence.
+  rewrite ATree.gempty. congruence.
+  intros. rewrite ATree.gempty in H7. congruence.
   eauto. eauto. auto.
 
   (* range *)
   exploit alloc_variables_range. eexact H. eauto.
-  rewrite PTree.gempty. intuition congruence.
+  rewrite ATree.gempty. intuition congruence.
 
   (* trange *)
   exploit alloc_variables_range. eexact A. eauto.
-  rewrite PTree.gempty. intuition congruence.
+  rewrite ATree.gempty. intuition congruence.
 
   (* mapped *)
   destruct (In_dec ident_eq id (var_names vars)).
@@ -978,20 +978,20 @@ Proof.
   intros [[id' ty'] [EQ IN]]; simpl in EQ; subst id'.
   exploit F; eauto. intros [b [P Q]].
   destruct (VSet.mem id cenv).
-  rewrite PTree.gempty in Q. destruct Q; congruence.
+  rewrite ATree.gempty in Q. destruct Q; congruence.
   destruct Q as [tb [U V]]. exists b; split; congruence.
-  exploit G; eauto. rewrite PTree.gempty. intuition congruence.
+  exploit G; eauto. rewrite ATree.gempty. intuition congruence.
 
   (* flat *)
   exploit alloc_variables_range. eexact A. eauto.
-  rewrite PTree.gempty. intros [P|P]. congruence.
+  rewrite ATree.gempty. intros [P|P]. congruence.
   exploit K; eauto. unfold Mem.valid_block. xomega.
   intros [id0 [ty0 [U [V W]]]]. split; auto.
   destruct (ident_eq id id0). congruence.
   assert (b' <> b').
   eapply alloc_variables_injective with (e' := te) (id1 := id) (id2 := id0); eauto.
-  rewrite PTree.gempty; congruence.
-  intros until ty1; rewrite PTree.gempty; congruence.
+  rewrite ATree.gempty; congruence.
+  intros until ty1; rewrite ATree.gempty; congruence.
   congruence.
 
   (* incr *)
@@ -1098,8 +1098,8 @@ Theorem store_params_correct:
   Val.inject_list j args targs ->
   match_envs j cenv e le m lo hi te tle1 tlo thi ->
   Mem.inject j m tm ->
-  (forall id, ~In id (var_names params) -> tle2!id = tle1!id) ->
-  (forall id, In id (var_names params) -> le!id = None) ->
+  (forall id, ~In id (var_names params) -> tle2$id = tle1$id) ->
+  (forall id, In id (var_names params) -> le$id = None) ->
   exists tle, exists tm',
   star step2 tge (State f (store_params cenv params s) k te tle tm)
               E0 (State f s k te tle tm')
@@ -1117,25 +1117,25 @@ Proof.
   exploit me_vars; eauto. instantiate (1 := id); intros MV.
   destruct (VSet.mem id cenv) eqn:?.
   (* lifted to temp *)
-  eapply IHbind_parameters with (tle1 := PTree.set id v' tle1); eauto.
+  eapply IHbind_parameters with (tle1 := ATree.set id v' tle1); eauto.
   eapply match_envs_assign_lifted; eauto.
   inv MV; try congruence. rewrite ENV in H; inv H.
   inv H0; try congruence.
   unfold Mem.storev in H2. eapply Mem.store_unmapped_inject; eauto.
-  intros. repeat rewrite PTree.gsspec. destruct (peq id0 id). auto.
+  intros. repeat rewrite ATree.gsspec. destruct (ATree.elt_eq id0 id). auto.
   apply TLE. intuition.
   (* still in memory *)
   inv MV; try congruence. rewrite ENV in H; inv H.
   exploit assign_loc_inject; eauto.
   intros [tm1 [A [B C]]].
   exploit IHbind_parameters. eauto. eauto. eauto.
-  instantiate (1 := PTree.set id v' tle1).
+  instantiate (1 := ATree.set id v' tle1).
   apply match_envs_change_temp.
   eapply match_envs_invariant; eauto.
   apply LE; auto. auto.
   eauto.
-  instantiate (1 := PTree.set id v' tle2).
-  intros. repeat rewrite PTree.gsspec. destruct (peq id0 id). auto.
+  instantiate (1 := ATree.set id v' tle2).
+  intros. repeat rewrite ATree.gsspec. destruct (ATree.elt_eq id0 id). auto.
   apply TLE. intuition.
   intros. apply LE. auto.
   instantiate (1 := s).
@@ -1146,7 +1146,7 @@ Proof.
   eapply star_left. econstructor.
     eapply eval_Evar_local. eauto.
     eapply eval_Etempvar. erewrite bind_parameter_temps_inv; eauto.
-    apply PTree.gss.
+    apply ATree.gss.
     simpl. instantiate (1 := v'). apply cast_val_casted.
     eapply val_casted_inject with (v := v1); eauto.
     simpl. eexact A.
@@ -1168,7 +1168,7 @@ Qed.
 
 Lemma bind_parameters_load:
   forall ge e chunk b ofs,
-  (forall id b' ty, e!id = Some(b', ty) -> b <> b') ->
+  (forall id b' ty, e$id = Some(b', ty) -> b <> b') ->
   forall m params args m',
   bind_parameters ge e m params args m' ->
   Mem.load chunk m' b ofs = Mem.load chunk m b ofs.
@@ -1187,7 +1187,7 @@ Qed.
 Lemma free_blocks_of_env_perm_1:
   forall ce m e m' id b ty ofs k p,
   Mem.free_list m (blocks_of_env ce e) = Some m' ->
-  e!id = Some(b, ty) ->
+  e$id = Some(b, ty) ->
   Mem.perm m' b ofs k p ->
   0 <= ofs < sizeof ce ty ->
   False.
@@ -1195,7 +1195,7 @@ Proof.
   intros. exploit Mem.perm_free_list; eauto. intros [A B].
   apply B with 0 (sizeof ce ty); auto.
   unfold blocks_of_env. change (b, 0, sizeof ce ty) with (block_of_binding ce (id, (b, ty))).
-  apply in_map. apply PTree.elements_correct. auto.
+  apply in_map. apply ATree.elements_correct. auto.
 Qed.
 
 Lemma free_list_perm':
@@ -1215,12 +1215,12 @@ Qed.
 Lemma free_blocks_of_env_perm_2:
   forall ce m e m' id b ty,
   Mem.free_list m (blocks_of_env ce e) = Some m' ->
-  e!id = Some(b, ty) ->
+  e$id = Some(b, ty) ->
   Mem.range_perm m b 0 (sizeof ce ty) Cur Freeable.
 Proof.
   intros. eapply free_list_perm'; eauto.
   unfold blocks_of_env. change (b, 0, sizeof ce ty) with (block_of_binding ce (id, (b, ty))).
-  apply in_map. apply PTree.elements_correct. auto.
+  apply in_map. apply ATree.elements_correct. auto.
 Qed.
 
 Fixpoint freelist_no_overlap (l: list (block * Z * Z)) : Prop :=
@@ -1253,10 +1253,10 @@ Lemma blocks_of_env_no_overlap:
   match_envs j cenv e le m lo hi te tle tlo thi ->
   Mem.inject j m tm ->
   (forall id b ty,
-   e!id = Some(b, ty) -> Mem.range_perm m b 0 (sizeof ge ty) Cur Freeable) ->
+   e$id = Some(b, ty) -> Mem.range_perm m b 0 (sizeof ge ty) Cur Freeable) ->
   forall l,
   list_norepet (List.map fst l) ->
-  (forall id bty, In (id, bty) l -> te!id = Some bty) ->
+  (forall id bty, In (id, bty) l -> te$id = Some bty) ->
   freelist_no_overlap (List.map (block_of_binding ge) l).
 Proof.
   intros until tm; intros ME MINJ PERMS. induction l; simpl; intros.
@@ -1265,8 +1265,8 @@ Proof.
   + apply IHl; auto.
   + intros. exploit list_in_map_inv; eauto. intros [[id' [b'' ty']] [A B]].
     simpl in A. inv A. rename b'' into b'.
-    assert (TE: te!id = Some(b, ty)) by eauto.
-    assert (TE': te!id' = Some(b', ty')) by eauto.
+    assert (TE: te$id = Some(b, ty)) by eauto.
+    assert (TE': te$id' = Some(b', ty')) by eauto.
     exploit me_mapped. eauto. eexact TE. intros [b0 [INJ E]].
     exploit me_mapped. eauto. eexact TE'. intros [b0' [INJ' E']].
     destruct (zle (sizeof ge0 ty) 0); auto.
@@ -1324,7 +1324,7 @@ Local Opaque ge tge.
     intros. unfold blocks_of_env in H2.
     exploit list_in_map_inv; eauto. intros [[id [b' ty]] [EQ IN]].
     unfold block_of_binding in EQ; inv EQ.
-    exploit me_mapped; eauto. eapply PTree.elements_complete; eauto.
+    exploit me_mapped; eauto. eapply ATree.elements_complete; eauto.
     intros [b [A B]].
     change 0 with (0 + 0). replace (sizeof ge ty) with (sizeof ge ty + 0) by omega.
     eapply Mem.range_perm_inject; eauto.
@@ -1332,8 +1332,8 @@ Local Opaque ge tge.
   - (* no overlap *)
     unfold blocks_of_env; eapply blocks_of_env_no_overlap; eauto.
     intros. eapply free_blocks_of_env_perm_2; eauto.
-    apply PTree.elements_keys_norepet.
-    intros. apply PTree.elements_complete; auto.
+    apply ATree.elements_keys_norepet.
+    intros. apply ATree.elements_complete; auto.
   }
   destruct X as [tm' FREE].
   exists tm'; split; auto.
@@ -1341,7 +1341,7 @@ Local Opaque ge tge.
   eapply Mem.free_list_left_inject; eauto.
   intros. unfold blocks_of_env in H3. exploit list_in_map_inv; eauto.
   intros [[id [b' ty]] [EQ IN]]. unfold block_of_binding in EQ. inv EQ.
-  exploit me_flat; eauto. apply PTree.elements_complete; eauto.
+  exploit me_flat; eauto. apply ATree.elements_complete; eauto.
   intros [P Q]. subst delta. eapply free_blocks_of_env_perm_1 with (m := m); eauto.
   rewrite <- comp_env_preserved. omega.
 Qed.
@@ -1708,7 +1708,7 @@ Proof.
   intros. rewrite <- H7. eapply free_list_load; eauto.
   unfold blocks_of_env; intros. exploit list_in_map_inv; eauto.
   intros [[id [b1 ty]] [P Q]]. simpl in P. inv P.
-  exploit me_range; eauto. eapply PTree.elements_complete; eauto. xomega.
+  exploit me_range; eauto. eapply ATree.elements_complete; eauto. xomega.
   rewrite (free_list_nextblock _ _ _ H3). inv H; xomega.
   rewrite (free_list_nextblock _ _ _ H4). inv H; xomega.
 Qed.
@@ -2191,7 +2191,7 @@ Proof.
     apply val_inject_list_incr with j'; eauto.
     eexact B. eexact C.
     intros. apply (create_undef_temps_lifted id f). auto.
-    intros. destruct (create_undef_temps (fn_temps f))!id as [v|] eqn:?; auto.
+    intros. destruct (create_undef_temps (fn_temps f))$id as [v|] eqn:?; auto.
     exploit create_undef_temps_inv; eauto. intros [P Q]. elim (l id id); auto.
   intros [tel [tm1 [P [Q [R [S T]]]]]].
   change (cenv_for_gen (addr_taken_stmt (fn_body f)) (fn_params f ++ fn_vars f))
@@ -2211,7 +2211,7 @@ Proof.
   intros. transitivity (Mem.load chunk m0 b 0).
   eapply bind_parameters_load; eauto. intros.
   exploit alloc_variables_range. eexact H1. eauto.
-  unfold empty_env. rewrite PTree.gempty. intros [?|?]. congruence.
+  unfold empty_env. rewrite ATree.gempty. intros [?|?]. congruence.
   red; intros; subst b'. xomega.
   eapply alloc_variables_load; eauto.
   apply compat_cenv_for.
diff --git a/common/AST.v b/common/AST.v
index 145f49190a..160837ec08 100644
--- a/common/AST.v
+++ b/common/AST.v
@@ -18,18 +18,21 @@
 
 Require Import String.
 Require Import Coqlib Maps Errors Integers Floats.
+Require Export Symbols.
 Require Archi.
 
 Set Implicit Arguments.
 
 (** * Syntactic elements *)
 
-(** Identifiers (names of local variables, of global symbols and functions,
-  etc) are represented by the type [positive] of positive integers. *)
+(** The type [ident] provides an efficient representation for the
+  names of local variables, of global symbols and functions, etc. *)
 
-Definition ident := positive.
+Definition ident := Ident.t.
 
-Definition ident_eq := peq.
+Definition ident_eq := Ident.eq.
+
+Notation "# s" := (Ident.of_string s) (at level 1, format "'#' s").
 
 (** The intermediate languages are weakly typed, using the following types: *)
 
@@ -275,8 +278,8 @@ Definition prog_defs_names (F V: Type) (p: program F V) : list ident :=
 (** The "definition map" of a program maps names of globals to their definitions.
   If several definitions have the same name, the one appearing last in [p.(prog_defs)] wins. *)
 
-Definition prog_defmap (F V: Type) (p: program F V) : PTree.t (globdef F V) :=
-  PTree_Properties.of_list p.(prog_defs).
+Definition prog_defmap (F V: Type) (p: program F V) : ATree.t (globdef F V) :=
+  ATree_Properties.of_list p.(prog_defs).
 
 Section DEFMAP.
 
@@ -284,33 +287,33 @@ Variables F V: Type.
 Variable p: program F V.
 
 Lemma in_prog_defmap:
-  forall id g, (prog_defmap p)!id = Some g -> In (id, g) (prog_defs p).
+  forall id g, (prog_defmap p)$id = Some g -> In (id, g) (prog_defs p).
 Proof.
-  apply PTree_Properties.in_of_list.
+  apply ATree_Properties.in_of_list.
 Qed.
 
 Lemma prog_defmap_dom:
-  forall id, In id (prog_defs_names p) -> exists g, (prog_defmap p)!id = Some g.
+  forall id, In id (prog_defs_names p) -> exists g, (prog_defmap p)$id = Some g.
 Proof.
-  apply PTree_Properties.of_list_dom.
+  apply ATree_Properties.of_list_dom.
 Qed.
 
 Lemma prog_defmap_unique:
   forall defs1 id g defs2,
   prog_defs p = defs1 ++ (id, g) :: defs2 ->
   ~In id (map fst defs2) ->
-  (prog_defmap p)!id = Some g.
+  (prog_defmap p)$id = Some g.
 Proof.
-  unfold prog_defmap; intros. rewrite H. apply PTree_Properties.of_list_unique; auto.
+  unfold prog_defmap; intros. rewrite H. apply ATree_Properties.of_list_unique; auto.
 Qed.
 
 Lemma prog_defmap_norepet:
   forall id g,
   list_norepet (prog_defs_names p) ->
   In (id, g) (prog_defs p) ->
-  (prog_defmap p)!id = Some g.
+  (prog_defmap p)$id = Some g.
 Proof.
-  apply PTree_Properties.of_list_norepet.
+  apply ATree_Properties.of_list_norepet.
 Qed.
 
 End DEFMAP.
@@ -519,7 +522,7 @@ Definition ef_reloads (ef: external_function) : bool :=
 
 Definition external_function_eq: forall (ef1 ef2: external_function), {ef1=ef2} + {ef1<>ef2}.
 Proof.
-  generalize ident_eq string_dec signature_eq chunk_eq typ_eq list_eq_dec zeq Int.eq_dec; intros.
+  generalize ident_eq string_dec signature_eq chunk_eq typ_eq list_eq_dec zeq Int.eq_dec peq; intros.
   decide equality.
 Defined.
 Global Opaque external_function_eq.
diff --git a/common/Errors.v b/common/Errors.v
index 28933313d5..ecb4940023 100644
--- a/common/Errors.v
+++ b/common/Errors.v
@@ -17,6 +17,7 @@
 
 Require Import String.
 Require Import Coqlib.
+Require Import Symbols.
 
 Close Scope string_scope.
 
@@ -30,7 +31,7 @@ Set Implicit Arguments.
 
 Inductive errcode: Type :=
   | MSG: string -> errcode
-  | CTX: positive -> errcode    (* a top-level identifier *)
+  | CTX: Ident.t -> errcode    (* a top-level identifier *)
   | POS: positive -> errcode.   (* a positive integer, e.g. a PC *)
 
 Definition errmsg: Type := list errcode.
diff --git a/common/Globalenvs.v b/common/Globalenvs.v
index d37fbd4637..adca12719e 100644
--- a/common/Globalenvs.v
+++ b/common/Globalenvs.v
@@ -146,13 +146,13 @@ Variable V: Type.  (**r The type of information attached to variables *)
 
 Record t: Type := mkgenv {
   genv_public: list ident;              (**r which symbol names are public *)
-  genv_symb: PTree.t block;             (**r mapping symbol -> block *)
+  genv_symb: ATree.t block;             (**r mapping symbol -> block *)
   genv_defs: PTree.t (globdef F V);     (**r mapping block -> definition *)
   genv_next: block;                     (**r next symbol pointer *)
-  genv_symb_range: forall id b, PTree.get id genv_symb = Some b -> Plt b genv_next;
+  genv_symb_range: forall id b, ATree.get id genv_symb = Some b -> Plt b genv_next;
   genv_defs_range: forall b g, PTree.get b genv_defs = Some g -> Plt b genv_next;
   genv_vars_inj: forall id1 id2 b,
-    PTree.get id1 genv_symb = Some b -> PTree.get id2 genv_symb = Some b -> id1 = id2
+    ATree.get id1 genv_symb = Some b -> ATree.get id2 genv_symb = Some b -> id1 = id2
 }.
 
 (** ** Lookup functions *)
@@ -160,7 +160,7 @@ Record t: Type := mkgenv {
 (** [find_symbol ge id] returns the block associated with the given name, if any *)
 
 Definition find_symbol (ge: t) (id: ident) : option block :=
-  PTree.get id ge.(genv_symb).
+  ATree.get id ge.(genv_symb).
 
 (** [symbol_address ge id ofs] returns a pointer into the block associated
   with [id], at byte offset [ofs].  [Vundef] is returned if no block is associated
@@ -203,7 +203,7 @@ Definition find_funct (ge: t) (v: val) : option F :=
 (** [invert_symbol ge b] returns the name associated with the given block, if any *)
 
 Definition invert_symbol (ge: t) (b: block) : option ident :=
-  PTree.fold
+  ATree.fold
     (fun res id b' => if eq_block b b' then Some id else res)
     ge.(genv_symb) None.
 
@@ -227,13 +227,13 @@ Definition block_is_volatile (ge: t) (b: block) : bool :=
 Program Definition add_global (ge: t) (idg: ident * globdef F V) : t :=
   @mkgenv
     ge.(genv_public)
-    (PTree.set idg#1 ge.(genv_next) ge.(genv_symb))
+    (ATree.set idg#1 ge.(genv_next) ge.(genv_symb))
     (PTree.set ge.(genv_next) idg#2 ge.(genv_defs))
     (Pos.succ ge.(genv_next))
     _ _ _.
 Next Obligation.
   destruct ge; simpl in *.
-  rewrite PTree.gsspec in H. destruct (peq id i). inv H. apply Plt_succ.
+  rewrite ATree.gsspec in H. destruct (ATree.elt_eq id i). inv H. apply Plt_succ.
   apply Plt_trans_succ; eauto.
 Qed.
 Next Obligation.
@@ -244,8 +244,8 @@ Next Obligation.
 Qed.
 Next Obligation.
   destruct ge; simpl in *.
-  rewrite PTree.gsspec in H. rewrite PTree.gsspec in H0.
-  destruct (peq id1 i); destruct (peq id2 i).
+  rewrite ATree.gsspec in H. rewrite ATree.gsspec in H0.
+  destruct (ATree.elt_eq id1 i); destruct (ATree.elt_eq id2 i).
   congruence.
   inv H. eelim Plt_strict. eapply genv_symb_range0; eauto.
   inv H0. eelim Plt_strict. eapply genv_symb_range0; eauto.
@@ -263,15 +263,15 @@ Proof.
 Qed.
 
 Program Definition empty_genv (pub: list ident): t :=
-  @mkgenv pub (PTree.empty _) (PTree.empty _) 1%positive _ _ _.
+  @mkgenv pub (ATree.empty _) (PTree.empty _) 1%positive _ _ _.
 Next Obligation.
-  rewrite PTree.gempty in H. discriminate.
+  rewrite ATree.gempty in H. discriminate.
 Qed.
 Next Obligation.
   rewrite PTree.gempty in H. discriminate.
 Qed.
 Next Obligation.
-  rewrite PTree.gempty in H. discriminate.
+  rewrite ATree.gempty in H. discriminate.
 Qed.
 
 Definition globalenv (p: program F V) :=
@@ -418,18 +418,18 @@ Qed.
 
 Theorem find_def_symbol:
   forall p id g,
-  (prog_defmap p)!id = Some g <-> exists b, find_symbol (globalenv p) id = Some b /\ find_def (globalenv p) b = Some g.
+  (prog_defmap p)$id = Some g <-> exists b, find_symbol (globalenv p) id = Some b /\ find_def (globalenv p) b = Some g.
 Proof.
   intros.
-  set (P := fun m ge => m!id = Some g <-> exists b, find_symbol ge id = Some b /\ find_def ge b = Some g).
+  set (P := fun m ge => m$id = Some g <-> exists b, find_symbol ge id = Some b /\ find_def ge b = Some g).
   assert (REC: forall l m ge,
             P m ge ->
-            P (fold_left (fun m idg => PTree.set idg#1 idg#2 m) l m)
+            P (fold_left (fun m idg => ATree.set idg#1 idg#2 m) l m)
               (add_globals ge l)).
   { induction l as [ | [id1 g1] l]; intros; simpl.
   - auto.
   - apply IHl. unfold P, add_global, find_symbol, find_def; simpl.
-    rewrite ! PTree.gsspec. destruct (peq id id1).
+    rewrite ! ATree.gsspec. destruct (ATree.elt_eq id id1).
     + subst id1. split; intros.
       inv H0. exists (genv_next ge); split; auto. apply PTree.gss.
       destruct H0 as (b & A & B). inv A. rewrite PTree.gss in B. auto.
@@ -440,7 +440,7 @@ Proof.
       apply Plt_ne. eapply genv_symb_range; eauto.
   }
   apply REC. unfold P, find_symbol, find_def; simpl.
-  rewrite ! PTree.gempty. split.
+  rewrite ! ATree.gempty. split.
   congruence.
   intros (b & A & B); congruence.
 Qed.
@@ -452,11 +452,11 @@ Theorem find_symbol_exists:
 Proof.
   intros. unfold globalenv. eapply add_globals_ensures; eauto.
 (* preserves *)
-  intros. unfold find_symbol; simpl. rewrite PTree.gsspec. destruct (peq id id0).
+  intros. unfold find_symbol; simpl. rewrite ATree.gsspec. destruct (ATree.elt_eq id id0).
   econstructor; eauto.
   auto.
 (* ensures *)
-  intros. unfold find_symbol; simpl. rewrite PTree.gss. econstructor; eauto.
+  intros. unfold find_symbol; simpl. rewrite ATree.gss. econstructor; eauto.
 Qed.
 
 Theorem find_symbol_inversion : forall p x b,
@@ -465,11 +465,11 @@ Theorem find_symbol_inversion : forall p x b,
 Proof.
   intros until b; unfold globalenv. eapply add_globals_preserves.
 (* preserves *)
-  unfold find_symbol; simpl; intros. rewrite PTree.gsspec in H1.
-  destruct (peq x id). subst x. change id with (fst (id, g)). apply List.in_map; auto.
+  unfold find_symbol; simpl; intros. rewrite ATree.gsspec in H1.
+  destruct (ATree.elt_eq x id). subst x. change id with (fst (id, g)). apply List.in_map; auto.
   auto.
 (* base *)
-  unfold find_symbol; simpl; intros. rewrite PTree.gempty in H. discriminate.
+  unfold find_symbol; simpl; intros. rewrite ATree.gempty in H. discriminate.
 Qed.
 
 Theorem find_def_inversion:
@@ -538,12 +538,12 @@ Theorem invert_find_symbol:
   invert_symbol ge b = Some id -> find_symbol ge id = Some b.
 Proof.
   intros until b; unfold find_symbol, invert_symbol.
-  apply PTree_Properties.fold_rec.
+  apply ATree_Properties.fold_rec.
   intros. rewrite H in H0; auto.
   congruence.
-  intros. destruct (eq_block b v). inv H2. apply PTree.gss.
-  rewrite PTree.gsspec. destruct (peq id k).
-  subst. assert (m!k = Some b) by auto. congruence.
+  intros. destruct (eq_block b v). inv H2. apply ATree.gss.
+  rewrite ATree.gsspec. destruct (ATree.elt_eq id k).
+  subst. assert (m$k = Some b) by auto. congruence.
   auto.
 Qed.
 
@@ -554,11 +554,11 @@ Proof.
   intros until b.
   assert (find_symbol ge id = Some b -> exists id', invert_symbol ge b = Some id').
   unfold find_symbol, invert_symbol.
-  apply PTree_Properties.fold_rec.
+  apply ATree_Properties.fold_rec.
   intros. rewrite H in H0; auto.
-  rewrite PTree.gempty; congruence.
+  rewrite ATree.gempty; congruence.
   intros. destruct (eq_block b v). exists k; auto.
-  rewrite PTree.gsspec in H2. destruct (peq id k).
+  rewrite ATree.gsspec in H2. destruct (ATree.elt_eq id k).
   inv H2. congruence. auto.
 
   intros; exploit H; eauto. intros [id' A].
@@ -611,8 +611,8 @@ Definition to_senv (ge: t) : Senv.t :=
     (block_is_volatile ge)
     ge.(genv_next)
     ge.(genv_vars_inj)
-    (invert_find_symbol ge)
-    (find_invert_symbol ge)
+    (@invert_find_symbol ge)
+    (@find_invert_symbol ge)
     (public_symbol_exists ge)
     ge.(genv_symb_range)
     (block_is_volatile_below ge).
@@ -1672,7 +1672,7 @@ Record match_genvs (ge1: t A V) (ge2: t B W): Prop := {
   mge_next:
     genv_next ge2 = genv_next ge1;
   mge_symb:
-    forall id, PTree.get id (genv_symb ge2) = PTree.get id (genv_symb ge1);
+    forall id, ATree.get id (genv_symb ge2) = ATree.get id (genv_symb ge1);
   mge_defs:
     forall b, option_rel R (PTree.get b (genv_defs ge1)) (PTree.get b (genv_defs ge2))
 }.
@@ -1685,7 +1685,7 @@ Lemma add_global_match:
 Proof.
   intros. destruct H. constructor; simpl; intros.
 - congruence.
-- rewrite mge_next0, ! PTree.gsspec. destruct (peq id0 id); auto.
+- rewrite mge_next0, ! ATree.gsspec. destruct (ATree.elt_eq id0 id); auto.
 - rewrite mge_next0, ! PTree.gsspec. destruct (peq b (genv_next ge1)).
   constructor; auto.
   auto.
diff --git a/common/Linking.v b/common/Linking.v
index eaa954621e..805ceb7422 100644
--- a/common/Linking.v
+++ b/common/Linking.v
@@ -246,11 +246,11 @@ Let dm1 := prog_defmap p1.
 Let dm2 := prog_defmap p2.
 
 Definition link_prog_check (x: ident) (gd1: globdef F V) :=
-  match dm2!x with
+  match dm2$x with
   | None => true
   | Some gd2 =>
-      In_dec peq x p1.(prog_public)
-      && In_dec peq x p2.(prog_public)
+      In_dec ident_eq x p1.(prog_public)
+      && In_dec ident_eq x p2.(prog_public)
       && match link gd1 gd2 with Some _ => true | None => false end
   end.
 
@@ -263,10 +263,10 @@ Definition link_prog_merge (o1 o2: option (globdef F V)) :=
 
 Definition link_prog :=
   if ident_eq p1.(prog_main) p2.(prog_main)
-  && PTree_Properties.for_all dm1 link_prog_check then
+  && ATree_Properties.for_all dm1 link_prog_check then
     Some {| prog_main := p1.(prog_main);
             prog_public := p1.(prog_public) ++ p2.(prog_public);
-            prog_defs := PTree.elements (PTree.combine link_prog_merge dm1 dm2) |}
+            prog_defs := ATree.elements (ATree.combine link_prog_merge dm1 dm2) |}
   else
     None.
 
@@ -275,20 +275,20 @@ Lemma link_prog_inv:
   link_prog = Some p ->
       p1.(prog_main) = p2.(prog_main)
    /\ (forall id gd1 gd2,
-         dm1!id = Some gd1 -> dm2!id = Some gd2 ->
+         dm1$id = Some gd1 -> dm2$id = Some gd2 ->
          In id p1.(prog_public) /\ In id p2.(prog_public) /\ exists gd, link gd1 gd2 = Some gd)
   /\ p = {| prog_main := p1.(prog_main);
             prog_public := p1.(prog_public) ++ p2.(prog_public);
-            prog_defs := PTree.elements (PTree.combine link_prog_merge dm1 dm2) |}.
+            prog_defs := ATree.elements (ATree.combine link_prog_merge dm1 dm2) |}.
 Proof.
   unfold link_prog; intros p E.
   destruct (ident_eq (prog_main p1) (prog_main p2)); try discriminate.
-  destruct (PTree_Properties.for_all dm1 link_prog_check) eqn:C; inv E.
-  rewrite PTree_Properties.for_all_correct in C.
+  destruct (ATree_Properties.for_all dm1 link_prog_check) eqn:C; inv E.
+  rewrite ATree_Properties.for_all_correct in C.
   split; auto. split; auto.
   intros. exploit C; eauto. unfold link_prog_check. rewrite H0. intros.
-  destruct (in_dec peq id (prog_public p1)); try discriminate.
-  destruct (in_dec peq id (prog_public p2)); try discriminate.
+  destruct (in_dec ident_eq id (prog_public p1)); try discriminate.
+  destruct (in_dec ident_eq id (prog_public p2)); try discriminate.
   destruct (link gd1 gd2) eqn:L; try discriminate.
   intuition auto. exists g; auto.
 Qed.
@@ -296,26 +296,26 @@ Qed.
 Lemma link_prog_succeeds:
   p1.(prog_main) = p2.(prog_main) ->
   (forall id gd1 gd2,
-      dm1!id = Some gd1 -> dm2!id = Some gd2 ->
+      dm1$id = Some gd1 -> dm2$id = Some gd2 ->
       In id p1.(prog_public) /\ In id p2.(prog_public) /\ link gd1 gd2 <> None) ->
   link_prog =
     Some {| prog_main := p1.(prog_main);
             prog_public := p1.(prog_public) ++ p2.(prog_public);
-            prog_defs := PTree.elements (PTree.combine link_prog_merge dm1 dm2) |}.
+            prog_defs := ATree.elements (ATree.combine link_prog_merge dm1 dm2) |}.
 Proof.
   intros. unfold link_prog. unfold proj_sumbool. rewrite H, dec_eq_true. simpl.
-  replace (PTree_Properties.for_all dm1 link_prog_check) with true; auto.
-  symmetry. apply PTree_Properties.for_all_correct; intros. rename a into gd1.
-  unfold link_prog_check. destruct dm2!x as [gd2|] eqn:G2; auto.
+  replace (ATree_Properties.for_all dm1 link_prog_check) with true; auto.
+  symmetry. apply ATree_Properties.for_all_correct; intros. rename a into gd1.
+  unfold link_prog_check. destruct dm2$x as [gd2|] eqn:G2; auto.
   exploit H0; eauto. intros (P & Q & R). unfold proj_sumbool; rewrite ! pred_dec_true by auto.
   destruct (link gd1 gd2); auto; discriminate.
 Qed.
 
 Lemma prog_defmap_elements:
-  forall (m: PTree.t (globdef F V)) pub mn x,
-  (prog_defmap {| prog_defs := PTree.elements m; prog_public := pub; prog_main := mn |})!x = m!x.
+  forall (m: ATree.t (globdef F V)) pub mn x,
+  (prog_defmap {| prog_defs := ATree.elements m; prog_public := pub; prog_main := mn |})$x = m$x.
 Proof.
-  intros. unfold prog_defmap; simpl. apply PTree_Properties.of_list_elements.
+  intros. unfold prog_defmap; simpl. apply ATree_Properties.of_list_elements.
 Qed.
 
 End LINKER_PROG.
@@ -326,9 +326,9 @@ Instance Linker_prog (F V: Type) {LF: Linker F} {LV: Linker V} : Linker (program
      p1.(prog_main) = p2.(prog_main)
   /\ incl p1.(prog_public) p2.(prog_public)
   /\ forall id gd1,
-     (prog_defmap p1)!id = Some gd1 ->
+     (prog_defmap p1)$id = Some gd1 ->
      exists gd2,
-        (prog_defmap p2)!id = Some gd2
+        (prog_defmap p2)$id = Some gd2
      /\ linkorder gd1 gd2
      /\ (~In id p2.(prog_public) -> gd2 = gd1)
 }.
@@ -346,15 +346,15 @@ Proof.
 - intros. apply link_prog_inv in H. destruct H as (L1 & L2 & L3).
   subst z; simpl. intuition auto.
 + red; intros; apply in_app_iff; auto.
-+ rewrite prog_defmap_elements, PTree.gcombine, H by auto.
-  destruct (prog_defmap y)!id as [gd2|] eqn:GD2; simpl.
++ rewrite prog_defmap_elements, ATree.gcombine, H by auto.
+  destruct (prog_defmap y)$id as [gd2|] eqn:GD2; simpl.
 * exploit L2; eauto. intros (P & Q & gd & R).
   exists gd; split. auto. split. apply link_linkorder in R; tauto.
   rewrite in_app_iff; tauto.
 * exists gd1; split; auto. split. apply linkorder_refl. auto.
 + red; intros; apply in_app_iff; auto.
-+ rewrite prog_defmap_elements, PTree.gcombine, H by auto.
-  destruct (prog_defmap x)!id as [gd2|] eqn:GD2; simpl.
++ rewrite prog_defmap_elements, ATree.gcombine, H by auto.
+  destruct (prog_defmap x)$id as [gd2|] eqn:GD2; simpl.
 * exploit L2; eauto. intros (P & Q & gd & R).
   exists gd; split. auto. split. apply link_linkorder in R; tauto.
   rewrite in_app_iff; tauto.
@@ -364,8 +364,8 @@ Defined.
 Lemma prog_defmap_linkorder:
   forall {F V: Type} {LF: Linker F} {LV: Linker V} (p1 p2: program F V) id gd1,
   linkorder p1 p2 ->
-  (prog_defmap p1)!id = Some gd1 ->
-  exists gd2, (prog_defmap p2)!id = Some gd2 /\ linkorder gd1 gd2.
+  (prog_defmap p1)$id = Some gd1 ->
+  exists gd2, (prog_defmap p2)$id = Some gd2 /\ linkorder gd1 gd2.
 Proof.
   intros. destruct H as (A & B & C).
   exploit C; eauto. intros (gd2 & P & Q & R). exists gd2; auto.
@@ -415,9 +415,9 @@ Definition match_program_gen (ctx: C) (p1: program F1 V1) (p2: program F2 V2) :
 
 Theorem match_program_defmap:
   forall ctx p1 p2, match_program_gen ctx p1 p2 ->
-  forall id, option_rel (match_globdef ctx) (prog_defmap p1)!id (prog_defmap p2)!id.
+  forall id, option_rel (match_globdef ctx) (prog_defmap p1)$id (prog_defmap p2)$id.
 Proof.
-  intros. apply PTree_Properties.of_list_related. apply H.
+  intros. apply ATree_Properties.of_list_related. apply H.
 Qed.
 
 Lemma match_program_gen_main:
@@ -644,8 +644,8 @@ Proof.
   exploit link_match_globdef. eexact H2. eexact H3. eauto. eauto. eauto.
   intros (tg & TL & _). intuition congruence.
 - split; [|split].
-+ rewrite R. apply PTree.elements_canonical_order'. intros id.
-  rewrite ! PTree.gcombine by auto.
++ rewrite R. apply ATree.elements_canonical_order'. intros id.
+  rewrite ! ATree.gcombine by auto.
   generalize (match_program_defmap _ _ _ _ _ H0 id) (match_program_defmap _ _ _ _ _ H1 id).
   clear R. intros R1 R2; inv R1; inv R2; unfold link_prog_merge.
 * constructor.
diff --git a/driver/Interp.ml b/driver/Interp.ml
index 6760e76c73..818a783f63 100644
--- a/driver/Interp.ml
+++ b/driver/Interp.ml
@@ -95,7 +95,7 @@ let name_of_function prog fn =
   in find_name prog.Ctypes.prog_defs
 
 let invert_local_variable e b =
-  Maps.PTree.fold
+  Symbols.ATree.fold
     (fun res id (b', _) -> if b = b' then Some id else res)
     e None
 
@@ -129,12 +129,12 @@ let print_state p (prog, ge, s) =
               (name_of_function prog f)
               PrintCsyntax.print_expr r
   | Callstate(fd, args, k, m) ->
-      PrintCsyntax.print_pointer_hook := print_pointer ge.genv_genv Maps.PTree.empty;
+      PrintCsyntax.print_pointer_hook := print_pointer ge.genv_genv Symbols.ATree.empty;
       fprintf p "calling@ @[<hov 2>%s(%a)@]"
               (name_of_fundef prog fd)
               print_val_list args
   | Returnstate(res, k, m) ->
-      PrintCsyntax.print_pointer_hook := print_pointer ge.genv_genv Maps.PTree.empty;
+      PrintCsyntax.print_pointer_hook := print_pointer ge.genv_genv Symbols.ATree.empty;
       fprintf p "returning@ %a"
               print_val res
   | Stuckstate ->
diff --git a/exportclight/Clightnorm.ml b/exportclight/Clightnorm.ml
index 4b01d77770..22e146ae1f 100644
--- a/exportclight/Clightnorm.ml
+++ b/exportclight/Clightnorm.ml
@@ -33,12 +33,12 @@ open Camlcoq
 open Ctypes
 open Clight
 
-let gen_next : AST.ident ref = ref P.one
+let gen_next : int ref = ref 1
 let gen_trail : (AST.ident * coq_type) list ref = ref []
 
 let gensym ty =
-  let id = !gen_next in
-  gen_next := P.succ id;
+  let id = intern_string (Printf.sprintf "@%d" !gen_next) in
+  gen_next := !gen_next + 1;
   gen_trail := (id, ty) :: !gen_trail;
   id
 
@@ -148,10 +148,7 @@ let next_var curr (v, _) = if P.lt v curr then curr else P.succ v
 let next_var_list vars start = List.fold_left next_var start vars
 
 let norm_function f =
-  gen_next := next_var_list f.fn_params
-                (next_var_list f.fn_vars
-                   (next_var_list f.fn_temps
-                     (Camlcoq.first_unused_ident ())));
+  gen_next := 1;
   gen_trail := [];
   let s' = norm_stmt f.fn_body in
   let new_temps = !gen_trail in
diff --git a/exportclight/ExportClight.ml b/exportclight/ExportClight.ml
index 1b1402c36e..011c045099 100644
--- a/exportclight/ExportClight.ml
+++ b/exportclight/ExportClight.ml
@@ -47,59 +47,8 @@ let print_list fn p l =
 
 exception Not_an_identifier
 
-let sanitize s =
-  let s' = Bytes.create (String.length s) in
-  for i = 0 to String.length s - 1 do
-    Bytes.set  s' i
-    (match String.get s i with
-      | 'A'..'Z' | 'a'..'z' | '0'..'9' | '_' as c -> c
-      | ' ' | '$' -> '_'
-      | _ -> raise Not_an_identifier)
-  done;
-  Bytes.to_string s'
-
-let temp_names : (ident, string) Hashtbl.t = Hashtbl.create 17
-
 let ident p id =
-  try
-    let s = Hashtbl.find string_of_atom id in
-    fprintf p "_%s" (sanitize s)
-  with Not_found | Not_an_identifier ->
-  try
-    let s = Hashtbl.find temp_names id in
-    fprintf p "%s" s
-  with Not_found ->
-    fprintf p "%ld%%positive" (P.to_int32 id)
-
-let iter_hashtbl_sorted (h: ('a, string) Hashtbl.t) (f: 'a * string -> unit) =
-  List.iter f
-    (List.fast_sort (fun (k1, d1) (k2, d2) -> String.compare d1 d2)
-      (Hashtbl.fold (fun k d accu -> (k, d) :: accu) h []))
-
-let define_idents p =
-  iter_hashtbl_sorted
-    string_of_atom
-    (fun (id, name) ->
-      try
-        fprintf p "Definition _%s : ident := %ld%%positive.@ "
-                  (sanitize name) (P.to_int32 id)
-      with Not_an_identifier ->
-        ());
-  iter_hashtbl_sorted
-    temp_names
-    (fun (id, name) ->
-      fprintf p "Definition %s : ident := %ld%%positive.@ "
-                name (P.to_int32 id));
-  fprintf p "@ "
-
-let name_temporary t =
-  let t1 = P.to_int t and t0 = P.to_int (first_unused_ident ()) in
-  if t1 >= t0 && not (Hashtbl.mem temp_names t)
-  then Hashtbl.add temp_names t (sprintf "_t'%d" (t1 - t0 + 1))
-
-let name_opt_temporary = function
-  | None -> ()
-  | Some id -> name_temporary id
+  fprintf p "#\"%s\"" (extern_atom id)
 
 (* Numbers *)
 
@@ -263,7 +212,7 @@ let external_function p = function
       assertions := (camlstring_of_coqstring text, [targ]) :: !assertions;
       fprintf p "(EF_annot_val %a %a)" coqstring text asttype targ
   | EF_debug(kind, text, targs) ->
-      fprintf p "(EF_debug %ld%%positive %ld%%positive %a)" (P.to_int32 kind) (P.to_int32 text) (print_list asttype) targs
+      fprintf p "(EF_debug %ld%%positive %a %a)" (P.to_int32 kind) ident text (print_list asttype) targs
   | EF_inline_asm(text, sg, clob) ->
       fprintf p "@[<hov 2>(EF_inline_asm %a@ %a@ %a)@]"
               coqstring text
@@ -490,67 +439,11 @@ From compcert Require Import Coqlib Integers Floats AST Ctypes Cop Clight Clight
 Local Open Scope Z_scope.\n\
 \n"
 
-(* Naming the compiler-generated temporaries occurring in the program *)
-
-let rec name_expr = function
-  | Evar(id, t) -> ()
-  | Etempvar(id, t) -> name_temporary id
-  | Ederef(a1, t) -> name_expr a1
-  | Efield(a1, f, t) -> name_expr a1
-  | Econst_int(n, t) -> ()
-  | Econst_float(n, t) -> ()
-  | Econst_long(n, t) -> ()
-  | Econst_single(n, t) -> ()
-  | Eunop(op, a1, t) -> name_expr a1
-  | Eaddrof(a1, t) -> name_expr a1
-  | Ebinop(op, a1, a2, t) -> name_expr a1; name_expr a2
-  | Ecast(a1, t) -> name_expr a1
-  | Esizeof(t1, t) -> ()
-  | Ealignof(t1, t) -> ()
-
-let rec name_stmt = function
-  | Sskip -> ()
-  | Sassign(e1, e2) -> name_expr e1; name_expr e2
-  | Sset(id, e2) -> name_temporary id; name_expr e2
-  | Scall(optid, e1, el) ->
-      name_opt_temporary optid; name_expr e1; List.iter name_expr el
-  | Sbuiltin(optid, ef, tyl, el) ->
-      name_opt_temporary optid; List.iter name_expr el
-  | Ssequence(s1, s2) -> name_stmt s1; name_stmt s2
-  | Sifthenelse(e, s1, s2) -> name_expr e; name_stmt s1; name_stmt s2
-  | Sloop(s1, s2) -> name_stmt s1; name_stmt s2
-  | Sbreak -> ()
-  | Scontinue -> ()
-  | Sswitch(e, cases) -> name_expr e; name_lblstmts cases
-  | Sreturn (Some e) -> name_expr e
-  | Sreturn None -> ()
-  | Slabel(lbl, s1) -> name_stmt s1
-  | Sgoto lbl -> ()
-
-and name_lblstmts = function
-  | LSnil -> ()
-  | LScons(lbl, s, ls) -> name_stmt s; name_lblstmts ls
-
-let name_function f =
-  List.iter (fun (id, ty) -> name_temporary id) f.fn_temps;
-  name_stmt f.fn_body
-
-let name_globdef (id, g) =
-  match g with
-  | Gfun(Ctypes.Internal f) -> name_function f
-  | _ -> ()
-
-let name_program p =
-  List.iter name_globdef p.Ctypes.prog_defs
-
 (* All together *)
 
 let print_program p prog =
-  Hashtbl.clear temp_names;
-  name_program prog;
   fprintf p "@[<v 0>";
   fprintf p "%s" prologue;
-  define_idents p;
   List.iter (print_globdef p) prog.Ctypes.prog_defs;
   fprintf p "Definition composites : list composite_definition :=@ ";
   print_list print_composite_definition p prog.prog_types;
diff --git a/extraction/extraction.v b/extraction/extraction.v
index a47a72373a..c283bedebd 100644
--- a/extraction/extraction.v
+++ b/extraction/extraction.v
@@ -47,6 +47,10 @@ Extract Inlined Constant Coqlib.proj_sumbool => "(fun x -> x)".
 Extract Inlined Constant Datatypes.fst => "fst".
 Extract Inlined Constant Datatypes.snd => "snd".
 
+(* Symbols *)
+Extract Constant Symbols.Ident.of_string => "FastIdent.of_coqstring".
+Extract Constant Symbols.Ident.to_string => "FastIdent.to_coqstring".
+
 (* Decidable *)
 
 Extraction Inline DecidableClass.Decidable_witness DecidableClass.decide
@@ -90,7 +94,6 @@ Extract Constant Allocation.regalloc => "Regalloc.regalloc".
 Extract Constant Linearize.enumerate_aux => "Linearizeaux.enumerate_aux".
 
 (* SimplExpr *)
-Extract Constant SimplExpr.first_unused_ident => "Camlcoq.first_unused_ident".
 Extraction Inline SimplExpr.ret SimplExpr.error SimplExpr.bind SimplExpr.bind2.
 
 (* Compopts *)
diff --git a/lib/Camlcoq.ml b/lib/Camlcoq.ml
index 5c25796ec7..d25dbbbe7a 100644
--- a/lib/Camlcoq.ml
+++ b/lib/Camlcoq.ml
@@ -275,31 +275,6 @@ let coqint_of_camlint64 : int64 -> Integers.Int64.int = Z.of_uint64
 let camlint64_of_ptrofs : Integers.Ptrofs.int -> int64 =
   fun x -> Z.to_int64 (Integers.Ptrofs.signed x)
 
-(* Atoms (positive integers representing strings) *)
-
-type atom = positive
-
-let atom_of_string = (Hashtbl.create 17 : (string, atom) Hashtbl.t)
-let string_of_atom = (Hashtbl.create 17 : (atom, string) Hashtbl.t)
-let next_atom = ref Coq_xH
-
-let intern_string s =
-  try
-    Hashtbl.find atom_of_string s
-  with Not_found ->
-    let a = !next_atom in
-    next_atom := Pos.succ !next_atom;
-    Hashtbl.add atom_of_string s a;
-    Hashtbl.add string_of_atom a s;
-    a
-let extern_atom a =
-  try
-    Hashtbl.find string_of_atom a
-  with Not_found ->
-    Printf.sprintf "$%d" (P.to_int a)
-
-let first_unused_ident () = !next_atom
-
 (* Strings *)
 
 let camlstring_of_coqstring (s: char list) =
@@ -324,6 +299,15 @@ let coqstring_uppercase_ascii_of_camlstring s =
     cstring (d :: accu) (pos - 1)
   in cstring [] (String.length s - 1)
 
+(* Atoms (positive integers representing strings) *)
+
+type atom = Symbols.Ident.t
+
+let intern_string s =
+  Symbols.Ident.of_string (coqstring_of_camlstring s)
+let extern_atom a =
+  camlstring_of_coqstring (Symbols.Ident.to_string a)
+
 (* Floats *)
 
 let coqfloat_of_camlfloat f =
diff --git a/lib/FastIdent.ml b/lib/FastIdent.ml
new file mode 100644
index 0000000000..2300588a88
--- /dev/null
+++ b/lib/FastIdent.ml
@@ -0,0 +1,31 @@
+(* The functions below are used in Symbols.v to implement a fast way to
+  refer to global identifiers, where they are axiomatized as a bijective
+  mapping. The bijection is built incrementally, and of_coqstring may
+  insert a new entry in the hashtable, but cruicially the statefulness
+  is not observable from the outside. As far as Coq knows, the mapping
+  existed all along and we simply observed it for the first time.
+
+  The functions below should not be used directly from ML code. Instead,
+  the Camlcoq module provides wrappers to access them through the Ident
+  module defined in Symbols.v. *)
+
+open BinNums
+open BinPos
+
+let atom_of_coqstring = (Hashtbl.create 17 : (char list, positive) Hashtbl.t)
+let coqstring_of_atom = (Hashtbl.create 17 : (positive, char list) Hashtbl.t)
+let next_atom = ref Coq_xH
+
+let of_coqstring s =
+  try
+    Hashtbl.find atom_of_coqstring s
+  with Not_found ->
+    let a = !next_atom in
+    next_atom := Pos.succ !next_atom;
+    Hashtbl.add atom_of_coqstring s a;
+    Hashtbl.add coqstring_of_atom a s;
+    a
+
+let to_coqstring a =
+  Hashtbl.find coqstring_of_atom a
+
diff --git a/lib/FastIdent.mli b/lib/FastIdent.mli
new file mode 100644
index 0000000000..207f381a46
--- /dev/null
+++ b/lib/FastIdent.mli
@@ -0,0 +1,4 @@
+open Camlcoq
+
+val of_coqstring : char list -> P.t
+val to_coqstring : P.t -> char list
diff --git a/lib/Maps.v b/lib/Maps.v
index cfb866baa8..ea12d5c11a 100644
--- a/lib/Maps.v
+++ b/lib/Maps.v
@@ -128,6 +128,19 @@ Module Type TREE.
   Axiom elements_keys_norepet:
     forall (A: Type) (m: t A),
     list_norepet (List.map (@fst elt A) (elements m)).
+  Axiom elements_canonical_order:
+    forall (A B: Type) (R: A -> B -> Prop) (m: t A) (n: t B),
+    (forall i x, get i m = Some x -> exists y, get i n = Some y /\ R x y) ->
+    (forall i y, get i n = Some y -> exists x, get i m = Some x /\ R x y) ->
+    list_forall2
+      (fun i_x i_y => fst i_x = fst i_y /\ R (snd i_x) (snd i_y))
+      (elements m) (elements n).
+  Axiom elements_canonical_order':
+    forall (A B: Type) (R: A -> B -> Prop) (m: t A) (n: t B),
+    (forall i, option_rel R (get i m) (get i n)) ->
+    list_forall2
+      (fun i_x i_y => fst i_x = fst i_y /\ R (snd i_x) (snd i_y))
+      (elements m) (elements n).
   Axiom elements_extensional:
     forall (A: Type) (m n: t A),
     (forall i, get i m = get i n) ->
diff --git a/lib/Symbols.v b/lib/Symbols.v
new file mode 100644
index 0000000000..a5a21217b5
--- /dev/null
+++ b/lib/Symbols.v
@@ -0,0 +1,110 @@
+Require Import String.
+Require Import FSets.
+Require Import Coqlib.
+Require Import Maps.
+Require Import Ordered.
+
+(** The mapping between the external representation of identifiers as
+  [string]s and their internal representation as [ident]s is axiomatized
+  as a bijection, and constructed incrementally by Camlcoq.ml.
+
+  In the future we may want to have an alternative implementation the
+  [IDENT] interface entirely in Coq, which the user could choose at
+  [./configure] time depending on their needs. Such an implementation
+  would have to forgo string interning and use less efficient
+  primitives, but would compute within Coq and avoid relying on
+  trusted ML code. *)
+
+Module Type IDENT.
+  Parameter t: Type.
+  Parameter eq: forall i j: t, {i = j} + {i <> j}.
+  Parameter of_string: string -> t.
+  Parameter to_string: t -> string.
+  Parameter lt: t -> t -> Prop.
+  Parameter compare: t -> t -> comparison.
+
+  Axiom of_to_string: forall i, of_string (to_string i) = i.
+  Axiom to_of_string: forall s, to_string (of_string s) = s.
+
+  Axiom lt_trans: forall i j k, lt i j -> lt j k -> lt i k.
+  Axiom lt_not_eq: forall i j, lt i j -> i <> j.
+
+  Axiom compare_spec:
+    forall i j, CompareSpec (i = j) (lt i j) (lt j i) (compare i j).
+
+  Declare Module Tree : TREE
+    with Definition elt := t
+    with Definition elt_eq := eq.
+
+  (** This is a temporary workaround to enable the hack in Initializers.v,
+    whereby identifiers are stored in the [block] components of pointers.
+    We can remove it if we merge PR #220 or something such. *)
+  Parameter to_positive: t -> positive.
+  Parameter of_positive: positive -> t.
+  Axiom of_to_positive: forall p, of_positive (to_positive p) = p.
+End IDENT.
+
+Module Ident : IDENT.
+  Definition t := positive.
+  Definition eq := peq.
+  Definition lt := Pos.lt.
+  Definition compare := Pos.compare.
+  Definition lt_trans := Pos.lt_trans.
+  Definition compare_spec := Pos.compare_spec.
+
+  Lemma lt_not_eq i j:
+    lt i j -> i <> j.
+  Proof.
+    intros H Hij. subst.
+    eapply Pos.lt_irrefl; eauto.
+  Qed.
+
+  Module Tree := PTree.
+
+  Parameter of_string: string -> t.
+  Parameter to_string: t -> string.
+
+  Axiom of_to_string: forall i, of_string (to_string i) = i.
+  Axiom to_of_string: forall s, to_string (of_string s) = s.
+
+  Definition to_positive i: t := i.
+  Definition of_positive i: t := i.
+  Definition of_to_positive i: to_positive (of_positive i) = i := eq_refl.
+End Ident.
+
+Module OrderedIdent <: OrderedType.
+  Definition t := Ident.t.
+  Definition eq := @eq Ident.t.
+  Definition lt := Ident.lt.
+  Definition eq_dec := Ident.eq.
+  Definition eq_refl := @eq_refl Ident.t.
+  Definition eq_trans := @eq_trans Ident.t.
+  Definition eq_sym := @eq_sym Ident.t.
+  Definition lt_trans := Ident.lt_trans.
+  Definition lt_not_eq := Ident.lt_not_eq.
+
+  Program Definition compare x y: Compare lt eq x y :=
+    match Ident.compare x y with Lt => LT _ | Eq => EQ _ | Gt => GT _ end.
+  Next Obligation.
+    destruct (Ident.compare_spec x y); try discriminate; eauto.
+  Qed.
+  Next Obligation.
+    destruct (Ident.compare_spec x y); try discriminate; eauto.
+  Qed.
+  Next Obligation.
+    destruct (Ident.compare_spec x y); try discriminate; eauto.
+  Qed.
+End OrderedIdent.
+
+Lemma ident_of_string_inj s t:
+  Ident.of_string s = Ident.of_string t -> s = t.
+Proof.
+  intros Hst.
+  rewrite <- (Ident.to_of_string s).
+  rewrite <- (Ident.to_of_string t).
+  congruence.
+Qed.
+
+Module ATree := Ident.Tree.
+Module ATree_Properties := Tree_Properties ATree.
+Notation "a $ b" := (ATree.get b a) (at level 1).
diff --git a/powerpc/AsmToJSON.ml b/powerpc/AsmToJSON.ml
index 7c4c8f8a14..78d22dd92e 100644
--- a/powerpc/AsmToJSON.ml
+++ b/powerpc/AsmToJSON.ml
@@ -70,7 +70,7 @@ type instruction_arg =
   | ALabel of positive
   | Float32 of Floats.float32
   | Float64 of Floats.float
-  | Atom of positive
+  | Atom of ident
   | String of string
 
 let pp_arg pp = function
diff --git a/x86/TargetPrinter.ml b/x86/TargetPrinter.ml
index 3171847cf6..14ce1cad5a 100644
--- a/x86/TargetPrinter.ml
+++ b/x86/TargetPrinter.ml
@@ -89,17 +89,17 @@ let rec log2 n =
 module type SYSTEM =
     sig
       val raw_symbol: out_channel -> string -> unit
-      val symbol: out_channel -> P.t -> unit
+      val symbol: out_channel -> ident -> unit
       val label: out_channel -> int -> unit
       val name_of_section: section_name -> string
       val stack_alignment: int
       val print_align: out_channel -> int -> unit
       val print_mov_rs: out_channel -> ireg -> ident -> unit
-      val print_fun_info:  out_channel -> P.t -> unit
-      val print_var_info: out_channel -> P.t -> unit
+      val print_fun_info:  out_channel -> ident -> unit
+      val print_var_info: out_channel -> ident -> unit
       val print_epilogue: out_channel -> unit
-      val print_comm_decl: out_channel -> P.t -> Z.t -> int -> unit
-      val print_lcomm_decl: out_channel -> P.t -> Z.t -> int -> unit
+      val print_comm_decl: out_channel -> ident -> Z.t -> int -> unit
+      val print_lcomm_decl: out_channel -> ident -> Z.t -> int -> unit
     end
 
 (* Printer functions for ELF *)