Revised Stacking and Asmgen passes and Mach semantics:

- no more prediction of return addresses (Asmgenretaddr is gone)
- instead, punch a hole for the retaddr in Mach stack frame and
  fill this hole with the return address in the Asmgen proof.



git-svn-id: https://yquem.inria.fr/compcert/svn/compcert/trunk@2129 fca1b0fc-160b-0410-b1d3-a4f43f01ea2e

1 files changed, 630 insertions, 1093 deletions

diff --git a/powerpc/Asmgenproof.v b/powerpc/Asmgenproof.v
index de9decbd..6c95744a 100644
--- a/powerpc/Asmgenproof.v
+++ b/powerpc/Asmgenproof.v
@@ -27,11 +27,9 @@ Require Import Op.
 Require Import Locations.
 Require Import Conventions.
 Require Import Mach.
-Require Import Machsem.
-Require Import Machtyping.
 Require Import Asm.
 Require Import Asmgen.
-Require Import Asmgenretaddr.
+Require Import Asmgenproof0.
 Require Import Asmgenproof1.
 
 Section PRESERVATION.
@@ -67,210 +65,53 @@ Proof
   (Genv.find_funct_ptr_transf_partial transf_fundef _ TRANSF).
 
 Lemma functions_transl:
-  forall f b,
+  forall f b tf,
   Genv.find_funct_ptr ge b = Some (Internal f) ->
-  Genv.find_funct_ptr tge b = Some (Internal (transl_function f)).
+  transf_function f = OK tf ->
+  Genv.find_funct_ptr tge b = Some (Internal tf).
 Proof.
   intros. 
-  destruct (functions_translated _ _ H) as [tf [A B]].
-  rewrite A. generalize B. unfold transf_fundef, transf_partial_fundef, transf_function.
-  case (zlt Int.max_unsigned (list_length_z (transl_function f))); simpl; intro.
-  congruence. intro. inv B0. auto.
-Qed.
-
-Lemma functions_transl_no_overflow:
-  forall b f,
-  Genv.find_funct_ptr ge b = Some (Internal f) ->
-  list_length_z (transl_function f) <= Int.max_unsigned.
-Proof.
-  intros. 
-  destruct (functions_translated _ _ H) as [tf [A B]].
-  generalize B. unfold transf_fundef, transf_partial_fundef, transf_function.
-  case (zlt Int.max_unsigned (list_length_z (transl_function f))); simpl; intro.
-  congruence. intro; omega.
+  destruct (functions_translated _ _ H) as [tf' [A B]].
+  rewrite A. monadInv B. f_equal. congruence.
 Qed.
 
 (** * Properties of control flow *)
 
-Lemma find_instr_in:
-  forall c pos i,
-  find_instr pos c = Some i -> In i c.
-Proof.
-  induction c; simpl. intros; discriminate.
-  intros until i. case (zeq pos 0); intros.
-  left; congruence. right; eauto.
-Qed.
-
-Lemma find_instr_tail:
-  forall c1 i c2 pos,
-  code_tail pos c1 (i :: c2) ->
-  find_instr pos c1 = Some i.
-Proof.
-  induction c1; simpl; intros.
-  inv H.
-  destruct (zeq pos 0). subst pos.
-  inv H. auto. generalize (code_tail_pos _ _ _ H4). intro. omegaContradiction.
-  inv H. congruence. replace (pos0 + 1 - 1) with pos0 by omega.
-  eauto.
-Qed.
-
-Remark code_tail_bounds:
-  forall fn ofs i c,
-  code_tail ofs fn (i :: c) -> 0 <= ofs < list_length_z fn.
+Lemma transf_function_no_overflow:
+  forall f tf,
+  transf_function f = OK tf -> list_length_z tf <= Int.max_unsigned.
 Proof.
-  assert (forall ofs fn c, code_tail ofs fn c ->
-          forall i c', c = i :: c' -> 0 <= ofs < list_length_z fn).
-  induction 1; intros; simpl. 
-  rewrite H. rewrite list_length_z_cons. generalize (list_length_z_pos c'). omega.
-  rewrite list_length_z_cons. generalize (IHcode_tail _ _ H0). omega.
-  eauto.
-Qed.
-
-Lemma code_tail_next:
-  forall fn ofs i c,
-  code_tail ofs fn (i :: c) ->
-  code_tail (ofs + 1) fn c.
-Proof.
-  assert (forall ofs fn c, code_tail ofs fn c ->
-          forall i c', c = i :: c' -> code_tail (ofs + 1) fn c').
-  induction 1; intros.
-  subst c. constructor. constructor.
-  constructor. eauto.
-  eauto.
-Qed.
-
-Lemma code_tail_next_int:
-  forall fn ofs i c,
-  list_length_z fn <= Int.max_unsigned ->
-  code_tail (Int.unsigned ofs) fn (i :: c) ->
-  code_tail (Int.unsigned (Int.add ofs Int.one)) fn c.
-Proof.
-  intros. rewrite Int.add_unsigned.
-  change (Int.unsigned Int.one) with 1.
-  rewrite Int.unsigned_repr. apply code_tail_next with i; auto.
-  generalize (code_tail_bounds _ _ _ _ H0). omega. 
-Qed.
-
-(** [transl_code_at_pc pc fn c] holds if the code pointer [pc] points
-  within the PPC code generated by translating Mach function [fn],
-  and [c] is the tail of the generated code at the position corresponding
-  to the code pointer [pc]. *)
-
-Inductive transl_code_at_pc: val -> block -> Mach.function -> Mach.code -> Prop :=
-  transl_code_at_pc_intro:
-    forall b ofs f c,
-    Genv.find_funct_ptr ge b = Some (Internal f) ->
-    code_tail (Int.unsigned ofs) (transl_function f) (transl_code f c) ->
-    transl_code_at_pc (Vptr b ofs) b f c.
-
-(** The following lemmas show that straight-line executions
-  (predicate [exec_straight]) correspond to correct PPC executions
-  (predicate [exec_steps]) under adequate [transl_code_at_pc] hypotheses. *)
-
-Lemma exec_straight_steps_1:
-  forall fn c rs m c' rs' m',
-  exec_straight tge fn c rs m c' rs' m' ->
-  list_length_z fn <= Int.max_unsigned ->
-  forall b ofs,
-  rs#PC = Vptr b ofs ->
-  Genv.find_funct_ptr tge b = Some (Internal fn) ->
-  code_tail (Int.unsigned ofs) fn c ->
-  plus step tge (State rs m) E0 (State rs' m').
-Proof.
-  induction 1; intros.
-  apply plus_one.
-  econstructor; eauto. 
-  eapply find_instr_tail. eauto.
-  eapply plus_left'.
-  econstructor; eauto. 
-  eapply find_instr_tail. eauto.
-  apply IHexec_straight with b (Int.add ofs Int.one). 
-  auto. rewrite H0. rewrite H3. reflexivity.
-  auto. 
-  apply code_tail_next_int with i; auto.
-  traceEq.
-Qed.
-    
-Lemma exec_straight_steps_2:
-  forall fn c rs m c' rs' m',
-  exec_straight tge fn c rs m c' rs' m' ->
-  list_length_z fn <= Int.max_unsigned ->
-  forall b ofs,
-  rs#PC = Vptr b ofs ->
-  Genv.find_funct_ptr tge b = Some (Internal fn) ->
-  code_tail (Int.unsigned ofs) fn c ->
-  exists ofs',
-     rs'#PC = Vptr b ofs'
-  /\ code_tail (Int.unsigned ofs') fn c'.
-Proof.
-  induction 1; intros.
-  exists (Int.add ofs Int.one). split.
-  rewrite H0. rewrite H2. auto.
-  apply code_tail_next_int with i1; auto.
-  apply IHexec_straight with (Int.add ofs Int.one).
-  auto. rewrite H0. rewrite H3. reflexivity. auto. 
-  apply code_tail_next_int with i; auto.
+  intros. monadInv H. destruct (zlt Int.max_unsigned (list_length_z x)); inv EQ0. 
+  omega.
 Qed.
 
 Lemma exec_straight_exec:
-  forall fb f c c' rs m rs' m',
-  transl_code_at_pc (rs PC) fb f c ->
-  exec_straight tge (transl_function f)
-                (transl_code f c) rs m c' rs' m' ->
+  forall f c ep tf tc c' rs m rs' m',
+  transl_code_at_pc ge (rs PC) f c ep tf tc ->
+  exec_straight tge tf tc rs m c' rs' m' ->
   plus step tge (State rs m) E0 (State rs' m').
 Proof.
-  intros. inversion H. subst.
+  intros. inv H.
   eapply exec_straight_steps_1; eauto.
-  eapply functions_transl_no_overflow; eauto. 
-  eapply functions_transl; eauto.
+  eapply transf_function_no_overflow; eauto.
+  eapply functions_transl; eauto. 
 Qed.
 
 Lemma exec_straight_at:
-  forall fb f c c' rs m rs' m',
-  transl_code_at_pc (rs PC) fb f c ->
-  exec_straight tge (transl_function f)
-                (transl_code f c) rs m (transl_code f c') rs' m' ->
-  transl_code_at_pc (rs' PC) fb f c'.
+  forall f c ep tf tc c' ep' tc' rs m rs' m',
+  transl_code_at_pc ge (rs PC) f c ep tf tc ->
+  transl_code f c' ep' = OK tc' ->
+  exec_straight tge tf tc rs m tc' rs' m' ->
+  transl_code_at_pc ge (rs' PC) f c' ep' tf tc'.
 Proof.
-  intros. inversion H. subst. 
-  generalize (functions_transl_no_overflow _ _ H2). intro.
-  generalize (functions_transl _ _ H2). intro.
-  generalize (exec_straight_steps_2 _ _ _ _ _ _ _
-                H0 H4 _ _ (sym_equal H1) H5 H3).
+  intros. inv H. 
+  exploit exec_straight_steps_2; eauto. 
+  eapply transf_function_no_overflow; eauto.
+  eapply functions_transl; eauto.
   intros [ofs' [PC' CT']].
   rewrite PC'. constructor; auto.
 Qed.
 
-(** Correctness of the return addresses predicted by
-    [PPCgen.return_address_offset]. *)
-
-Remark code_tail_no_bigger:
-  forall pos c1 c2, code_tail pos c1 c2 -> (length c2 <= length c1)%nat.
-Proof.
-  induction 1; simpl; omega.
-Qed.
-
-Remark code_tail_unique:
-  forall fn c pos pos',
-  code_tail pos fn c -> code_tail pos' fn c -> pos = pos'.
-Proof.
-  induction fn; intros until pos'; intros ITA CT; inv ITA; inv CT; auto.
-  generalize (code_tail_no_bigger _ _ _ H3); simpl; intro; omega.
-  generalize (code_tail_no_bigger _ _ _ H3); simpl; intro; omega.
-  f_equal. eauto.
-Qed.
-
-Lemma return_address_offset_correct:
-  forall b ofs fb f c ofs',
-  transl_code_at_pc (Vptr b ofs) fb f c ->
-  return_address_offset f c ofs' ->
-  ofs' = ofs.
-Proof.
-  intros. inv H0. inv H. 
-  generalize (code_tail_unique _ _ _ _ H1 H7). intro. rewrite H. 
-  apply Int.repr_unsigned.
-Qed.
-
 (** The [find_label] function returns the code tail starting at the
   given label.  A connection with [code_tail] is then established. *)
 
@@ -391,119 +232,137 @@ Qed.
 Hint Rewrite rolm_label: labels.
 
 Remark loadind_label:
-  forall base ofs ty dst k, find_label lbl (loadind base ofs ty dst k) = find_label lbl k.
+  forall base ofs ty dst k c,
+  loadind base ofs ty dst k = OK c ->
+  find_label lbl c = find_label lbl k.
 Proof.
-  intros; unfold loadind. 
-  destruct (Int.eq (high_s ofs) Int.zero); destruct ty; autorewrite with labels; auto.
+  unfold loadind; intros.
+  destruct ty; destruct (Int.eq (high_s ofs) Int.zero); monadInv H;
+  autorewrite with labels; auto.
 Qed.
-Hint Rewrite loadind_label: labels.
 
 Remark storeind_label:
-  forall base ofs ty src k, find_label lbl (storeind base src ofs ty k) = find_label lbl k.
+  forall base ofs ty src k c,
+  storeind base src ofs ty k = OK c ->
+  find_label lbl c = find_label lbl k.
 Proof.
-  intros; unfold storeind.
-  destruct (Int.eq (high_s ofs) Int.zero); destruct ty; autorewrite with labels; auto.
+  unfold storeind; intros.
+  destruct ty; destruct (Int.eq (high_s ofs) Int.zero); monadInv H;
+  autorewrite with labels; auto.
 Qed.
-Hint Rewrite storeind_label: labels.
 
 Remark floatcomp_label:
   forall cmp r1 r2 k, find_label lbl (floatcomp cmp r1 r2 k) = find_label lbl k.
 Proof.
   intros; unfold floatcomp. destruct cmp; reflexivity.
 Qed.
+Hint Rewrite floatcomp_label: labels.
 
 Remark transl_cond_label:
-  forall cond args k, find_label lbl (transl_cond cond args k) = find_label lbl k.
+  forall cond args k c,
+  transl_cond cond args k = OK c -> find_label lbl c = find_label lbl k.
 Proof.
-  intros; unfold transl_cond.
-  destruct cond; (destruct args; 
-  [try reflexivity | destruct args;
-  [try reflexivity | destruct args; try reflexivity]]).
-  case (Int.eq (high_s i) Int.zero). reflexivity. 
-  autorewrite with labels; reflexivity.
-  case (Int.eq (high_u i) Int.zero). reflexivity. 
-  autorewrite with labels; reflexivity.
-  apply floatcomp_label. apply floatcomp_label.
-  apply andimm_base_label. apply andimm_base_label.
+  unfold transl_cond; intros; destruct cond; 
+  (destruct args; 
+  [try discriminate | destruct args;
+  [try discriminate | destruct args; try discriminate]]);
+  monadInv H; autorewrite with labels; auto.
+  destruct (Int.eq (high_s i) Int.zero); inv EQ0; autorewrite with labels; auto.
+  destruct (Int.eq (high_u i) Int.zero); inv EQ0; autorewrite with labels; auto.
 Qed.
-Hint Rewrite transl_cond_label: labels.
 
 Remark transl_cond_op_label:
-  forall c args r k,
-  find_label lbl (transl_cond_op c args r k) = find_label lbl k.
+  forall cond args r k c,
+  transl_cond_op cond args r k = OK c -> find_label lbl c = find_label lbl k.
 Proof.
-  intros c args.
-  unfold transl_cond_op. destruct (classify_condition c args); intros; auto.
-  autorewrite with labels. destruct (snd (crbit_for_cond c)); auto. 
+  unfold transl_cond_op; intros; destruct (classify_condition cond args);
+  monadInv H; auto.
+  erewrite transl_cond_label. 2: eauto. 
+  destruct (snd (crbit_for_cond c0)); auto.
 Qed.
-Hint Rewrite transl_cond_op_label: labels.
 
 Remark transl_op_label:
-  forall op args r k, find_label lbl (transl_op op args r k) = find_label lbl k.
+  forall op args r k c,
+  transl_op op args r k = OK c -> find_label lbl c = find_label lbl k.
 Proof.
-  intros; unfold transl_op;
-  destruct op; destruct args; try (destruct args); try (destruct args); try (destruct args);
-  try reflexivity; autorewrite with labels; try reflexivity.
-  case (mreg_type m); reflexivity.
-  case (symbol_is_small_data i i0); reflexivity.
-  case (Int.eq (high_s i) Int.zero); autorewrite with labels; reflexivity.
-  case (Int.eq (high_s i) Int.zero); autorewrite with labels; reflexivity.
-  destruct (mreg_eq m r); reflexivity.
+  unfold transl_op; intros; destruct op; try (eapply transl_cond_op_label; eauto; fail);
+  (destruct args; 
+  [try discriminate | destruct args;
+  [try discriminate | destruct args; try discriminate]]);
+  try (monadInv H); autorewrite with labels; auto.
+  destruct (preg_of r); try discriminate; destruct (preg_of m); inv H; auto.
+  destruct (symbol_is_small_data i i0); auto.
+  destruct (Int.eq (high_s i) Int.zero); autorewrite with labels; auto.
+  destruct (Int.eq (high_s i) Int.zero); autorewrite with labels; auto.
 Qed.
-Hint Rewrite transl_op_label: labels.
 
-Remark transl_load_store_label:
+Remark transl_memory_access_label:
   forall (mk1: constant -> ireg -> instruction) (mk2: ireg -> ireg -> instruction)
-         addr args temp k,
+         addr args temp k c,
+  transl_memory_access mk1 mk2 addr args temp k = OK c ->
   (forall c r, is_label lbl (mk1 c r) = false) ->
   (forall r1 r2, is_label lbl (mk2 r1 r2) = false) ->
-  find_label lbl (transl_load_store mk1 mk2 addr args temp k) = find_label lbl k.
-Proof.
-  intros; unfold transl_load_store.
-  destruct addr; destruct args; try (destruct args); try (destruct args);
-  try reflexivity.
-  destruct (Int.eq (high_s i) Int.zero); simpl; rewrite H; auto.
+  find_label lbl c = find_label lbl k.
+Proof.
+  unfold transl_memory_access; intros; destruct addr; 
+  (destruct args; 
+  [try discriminate | destruct args;
+  [try discriminate | destruct args; try discriminate]]);
+  monadInv H; autorewrite with labels; auto.
+  destruct (Int.eq (high_s i) Int.zero); simpl; rewrite H0; auto.
+  simpl; rewrite H1; auto.
+  destruct (symbol_is_small_data i i0); simpl; rewrite H0; auto.
   simpl; rewrite H0; auto.
-  destruct (symbol_is_small_data i i0); simpl; rewrite H; auto.
-  simpl; rewrite H; auto.
-  destruct (Int.eq (high_s i) Int.zero); simpl; rewrite H; auto.
+  destruct (Int.eq (high_s i) Int.zero); simpl; rewrite H0; auto.
 Qed.
-Hint Rewrite transl_load_store_label: labels.
 
 Lemma transl_instr_label:
-  forall f i k,
-  find_label lbl (transl_instr f i k) = 
-    if Mach.is_label lbl i then Some k else find_label lbl k.
-Proof.
-  intros. generalize (Mach.is_label_correct lbl i). 
-  case (Mach.is_label lbl i); intro.
-  subst i. simpl. rewrite peq_true. auto.
-  destruct i; simpl; autorewrite with labels; try reflexivity.
-  destruct m; rewrite transl_load_store_label; intros; reflexivity. 
-  destruct m; rewrite transl_load_store_label; intros; reflexivity. 
-  destruct s0; reflexivity.
-  destruct s0; reflexivity.
-  rewrite peq_false. auto. congruence.
-  case (snd (crbit_for_cond c)); reflexivity.
+  forall f i ep k c,
+  transl_instr f i ep k = OK c ->
+  find_label lbl c = if Mach.is_label lbl i then Some k else find_label lbl k.
+Proof.
+  unfold transl_instr, Mach.is_label; intros; destruct i; try (monadInv H);
+  autorewrite with labels; auto.
+  eapply loadind_label; eauto.
+  eapply storeind_label; eauto.
+  destruct ep. eapply loadind_label; eauto.
+  monadInv H. transitivity (find_label lbl x); eapply loadind_label; eauto. 
+  eapply transl_op_label; eauto.
+  destruct m; monadInv H; rewrite (transl_memory_access_label _ _ _ _ _ _ _ EQ0); auto.
+  destruct m; monadInv H; rewrite (transl_memory_access_label _ _ _ _ _ _ _ EQ0); auto.
+  destruct s0; monadInv H; auto.
+  destruct s0; monadInv H; auto.
+  erewrite transl_cond_label. 2: eauto. destruct (snd (crbit_for_cond c0)); auto.
 Qed.
 
 Lemma transl_code_label:
-  forall f c,
-  find_label lbl (transl_code f c) = 
-    option_map (transl_code f) (Mach.find_label lbl c).
+  forall f c ep tc,
+  transl_code f c ep = OK tc ->
+  match Mach.find_label lbl c with
+  | None => find_label lbl tc = None
+  | Some c' => exists tc', find_label lbl tc = Some tc' /\ transl_code f c' false = OK tc'
+  end.
 Proof.
   induction c; simpl; intros.
-  auto. rewrite transl_instr_label.
-  case (Mach.is_label lbl a). reflexivity.
-  auto.
+  inv H. auto.
+  monadInv H. rewrite (transl_instr_label _ _ _ _ _ EQ0).
+  generalize (Mach.is_label_correct lbl a). 
+  destruct (Mach.is_label lbl a); intros.
+  subst a. simpl in EQ. exists x; auto.
+  eapply IHc; eauto.
 Qed.
 
 Lemma transl_find_label:
-  forall f,
-  find_label lbl (transl_function f) = 
-    option_map (transl_code f) (Mach.find_label lbl f.(fn_code)).
+  forall f tf,
+  transf_function f = OK tf ->
+  match Mach.find_label lbl f.(Mach.fn_code) with
+  | None => find_label lbl tf = None
+  | Some c => exists tc, find_label lbl tf = Some tc /\ transl_code f c false = OK tc
+  end.
 Proof.
-  intros. unfold transl_function. simpl. apply transl_code_label.
+  intros. monadInv H. destruct (zlt Int.max_unsigned (list_length_z x)); inv EQ0.
+  monadInv EQ. simpl.
+  eapply transl_code_label; eauto. 
 Qed.
 
 End TRANSL_LABEL.
@@ -512,28 +371,26 @@ End TRANSL_LABEL.
   transition in the generated PPC code. *)
 
 Lemma find_label_goto_label:
-  forall f lbl rs m c' b ofs,
+  forall f tf lbl rs m c' b ofs,
   Genv.find_funct_ptr ge b = Some (Internal f) ->
+  transf_function f = OK tf ->
   rs PC = Vptr b ofs ->
-  Mach.find_label lbl f.(fn_code) = Some c' ->
-  exists rs',
-    goto_label (transl_function f) lbl rs m = OK rs' m  
-  /\ transl_code_at_pc (rs' PC) b f c'
+  Mach.find_label lbl f.(Mach.fn_code) = Some c' ->
+  exists tc', exists rs',
+    goto_label tf lbl rs m = Next rs' m  
+  /\ transl_code_at_pc ge (rs' PC) f c' false tf tc'
   /\ forall r, r <> PC -> rs'#r = rs#r.
 Proof.
-  intros. 
-  generalize (transl_find_label lbl f).
-  rewrite H1; simpl. intro.
-  generalize (label_pos_code_tail lbl (transl_function f) 0 
-                 (transl_code f c') H2).
-  intros [pos' [A [B C]]].
-  exists (rs#PC <- (Vptr b (Int.repr pos'))).
-  split. unfold goto_label. rewrite A. rewrite H0. auto.
+  intros. exploit (transl_find_label lbl f tf); eauto. rewrite H2. 
+  intros [tc [A B]].
+  exploit label_pos_code_tail; eauto. instantiate (1 := 0).
+  intros [pos' [P [Q R]]].
+  exists tc; exists (rs#PC <- (Vptr b (Int.repr pos'))).
+  split. unfold goto_label. rewrite P. rewrite H1. auto.
   split. rewrite Pregmap.gss. constructor; auto. 
-  rewrite Int.unsigned_repr. replace (pos' - 0) with pos' in B.
-  auto. omega. 
-  generalize (functions_transl_no_overflow _ _ H). 
-  omega.
+  rewrite Int.unsigned_repr. replace (pos' - 0) with pos' in Q.
+  auto. omega.
+  generalize (transf_function_no_overflow _ _ H0). omega.
   intros. apply Pregmap.gso; auto.
 Qed.
 
@@ -555,108 +412,92 @@ Qed.
 - Mach register values and PPC register values agree.
 *)
 
-Inductive match_stack: list Machsem.stackframe -> Prop :=
-  | match_stack_nil:
-      match_stack nil
-  | match_stack_cons: forall fb sp ra c s f,
-      Genv.find_funct_ptr ge fb = Some (Internal f) ->
-      wt_function f ->
-      incl c f.(fn_code) ->
-      transl_code_at_pc ra fb f c ->
-      sp <> Vundef ->
-      ra <> Vundef ->
-      match_stack s ->
-      match_stack (Stackframe fb sp ra c :: s).
-
-Inductive match_states: Machsem.state -> Asm.state -> Prop :=
+Inductive match_states: Mach.state -> Asm.state -> Prop :=
   | match_states_intro:
-      forall s fb sp c ms m rs m' f
-        (STACKS: match_stack s)
-        (FIND: Genv.find_funct_ptr ge fb = Some (Internal f))
-        (WTF: wt_function f)
-        (INCL: incl c f.(fn_code))
-        (AT: transl_code_at_pc (rs PC) fb f c)
-        (AG: agree ms sp rs)
-        (MEXT: Mem.extends m m'),
-      match_states (Machsem.State s fb sp c ms m)
+      forall s f sp c ep ms m m' rs tf tc ra
+        (STACKS: match_stack ge s m m' ra sp)
+        (MEXT: Mem.extends m m')
+        (AT: transl_code_at_pc ge (rs PC) f c ep tf tc)
+        (AG: agree ms (Vptr sp Int.zero) rs)
+        (RSA: retaddr_stored_at m m' sp (Int.unsigned f.(fn_retaddr_ofs)) ra)
+        (DXP: ep = true -> rs#GPR11 = parent_sp s),
+      match_states (Mach.State s f (Vptr sp Int.zero) c ms m)
                    (Asm.State rs m')
   | match_states_call:
-      forall s fb ms m rs m'
-        (STACKS: match_stack s)
-        (AG: agree ms (parent_sp s) rs)
+      forall s fd ms m m' rs fb
+        (STACKS: match_stack ge s m m' (rs LR) (Mem.nextblock m))
         (MEXT: Mem.extends m m')
+        (AG: agree ms (parent_sp s) rs)
         (ATPC: rs PC = Vptr fb Int.zero)
-        (ATLR: rs LR = parent_ra s),
-      match_states (Machsem.Callstate s fb ms m)
+        (FUNCT: Genv.find_funct_ptr ge fb = Some fd)
+        (WTRA: Val.has_type (rs LR) Tint),
+      match_states (Mach.Callstate s fd ms m)
                    (Asm.State rs m')
   | match_states_return:
-      forall s ms m rs m'
-        (STACKS: match_stack s)
-        (AG: agree ms (parent_sp s) rs)
+      forall s ms m m' rs
+        (STACKS: match_stack ge s m m' (rs PC) (Mem.nextblock m))
         (MEXT: Mem.extends m m')
-        (ATPC: rs PC = parent_ra s),
-      match_states (Machsem.Returnstate s ms m)
+        (AG: agree ms (parent_sp s) rs),
+      match_states (Mach.Returnstate s ms m)
                    (Asm.State rs m').
 
 Lemma exec_straight_steps:
-  forall s fb sp m1' f c1 rs1 c2 m2 m2' ms2,
-  match_stack s ->
-  Genv.find_funct_ptr ge fb = Some (Internal f) ->
-  wt_function f ->
-  incl c2 f.(fn_code) ->
-  transl_code_at_pc (rs1 PC) fb f c1 ->
-  (exists rs2,
-     exec_straight tge (transl_function f) (transl_code f c1) rs1 m1' (transl_code f c2) rs2 m2'
-     /\ agree ms2 sp rs2) ->
+  forall s f rs1 i c ep tf tc m1' m2 m2' sp ms2 ra,
+  match_stack ge s m2 m2' ra sp ->
   Mem.extends m2 m2' ->
+  retaddr_stored_at m2 m2' sp (Int.unsigned f.(fn_retaddr_ofs)) ra ->
+  transl_code_at_pc ge (rs1 PC) f (i :: c) ep tf tc ->
+  (forall k c (TR: transl_instr f i ep k = OK c),
+   exists rs2,
+       exec_straight tge tf c rs1 m1' k rs2 m2'
+    /\ agree ms2 (Vptr sp Int.zero) rs2
+    /\ (r11_is_parent ep i = true -> rs2#GPR11 = parent_sp s)) ->
   exists st',
   plus step tge (State rs1 m1') E0 st' /\
-  match_states (Machsem.State s fb sp c2 ms2 m2) st'.
+  match_states (Mach.State s f (Vptr sp Int.zero) c ms2 m2) st'.
 Proof.
-  intros. destruct H4 as [rs2 [A B]].
+  intros. inversion H2; subst. monadInv H7. 
+  exploit H3; eauto. intros [rs2 [A [B C]]]. 
   exists (State rs2 m2'); split.
-  eapply exec_straight_exec; eauto.
+  eapply exec_straight_exec; eauto. 
   econstructor; eauto. eapply exec_straight_at; eauto.
 Qed.
 
-Lemma exec_straight_steps_bis:
-  forall s fb sp m1' f c1 rs1 c2 m2 ms2,
-  match_stack s ->
-  Genv.find_funct_ptr ge fb = Some (Internal f) ->
-  wt_function f ->
-  incl c2 f.(fn_code) ->
-  transl_code_at_pc (rs1 PC) fb f c1 ->
-  (exists m2',
-      Mem.extends m2 m2'
-   /\ exists rs2,
-        exec_straight tge (transl_function f) (transl_code f c1) rs1 m1' (transl_code f c2) rs2 m2'
-        /\ agree ms2 sp rs2) ->
+Lemma exec_straight_steps_goto:
+  forall s f rs1 i c ep tf tc m1' m2 m2' sp ms2 lbl c' ra,
+  match_stack ge s m2 m2' ra sp ->
+  Mem.extends m2 m2' ->
+  retaddr_stored_at m2 m2' sp (Int.unsigned f.(fn_retaddr_ofs)) ra ->
+  Mach.find_label lbl f.(Mach.fn_code) = Some c' ->
+  transl_code_at_pc ge (rs1 PC) f (i :: c) ep tf tc ->
+  r11_is_parent ep i = false ->
+  (forall k c (TR: transl_instr f i ep k = OK c),
+   exists jmp, exists k', exists rs2,
+       exec_straight tge tf c rs1 m1' (jmp :: k') rs2 m2'
+    /\ agree ms2 (Vptr sp Int.zero) rs2
+    /\ exec_instr tge tf jmp rs2 m2' = goto_label tf lbl rs2 m2') ->
   exists st',
   plus step tge (State rs1 m1') E0 st' /\
-  match_states (Machsem.State s fb sp c2 ms2 m2) st'.
+  match_states (Mach.State s f (Vptr sp Int.zero) c' ms2 m2) st'.
 Proof.
-  intros. destruct H4 as [m2' [A B]]. 
-  eapply exec_straight_steps; eauto.
-Qed.
-
-Lemma parent_sp_def: forall s, match_stack s -> parent_sp s <> Vundef.
-Proof. induction 1; simpl. congruence. auto. Qed.
-
-Lemma parent_ra_def: forall s, match_stack s -> parent_ra s <> Vundef.
-Proof. induction 1; simpl. unfold Vzero. congruence. auto. Qed.
-
-Lemma lessdef_parent_sp:
-  forall s v,
-  match_stack s -> Val.lessdef (parent_sp s) v -> v = parent_sp s.
-Proof.
-  intros. inv H0. auto. exploit parent_sp_def; eauto. tauto.
-Qed.
-
-Lemma lessdef_parent_ra:
-  forall s v,
-  match_stack s -> Val.lessdef (parent_ra s) v -> v = parent_ra s.
-Proof.
-  intros. inv H0. auto. exploit parent_ra_def; eauto. tauto.
+  intros. inversion H3; subst. monadInv H9.
+  exploit H5; eauto. intros [jmp [k' [rs2 [A [B C]]]]].
+  generalize (functions_transl _ _ _ H7 H8); intro FN.
+  generalize (transf_function_no_overflow _ _ H8); intro NOOV.
+  exploit exec_straight_steps_2; eauto. 
+  intros [ofs' [PC2 CT2]].
+  exploit find_label_goto_label; eauto. 
+  intros [tc' [rs3 [GOTO [AT' OTH]]]].
+  exists (State rs3 m2'); split.
+  eapply plus_right'.
+  eapply exec_straight_steps_1; eauto. 
+  econstructor; eauto.
+  eapply find_instr_tail. eauto. 
+  rewrite C. eexact GOTO.
+  traceEq.
+  econstructor; eauto.
+  apply agree_exten with rs2; auto with asmgen.
+  congruence.
 Qed.
 
 (** We need to show that, in the simulation diagram, we cannot
@@ -667,448 +508,285 @@ Qed.
   So, the following integer measure will suffice to rule out
   the unwanted behaviour. *)
 
-Definition measure (s: Machsem.state) : nat :=
+Definition measure (s: Mach.state) : nat :=
   match s with
-  | Machsem.State _ _ _ _ _ _ => 0%nat
-  | Machsem.Callstate _ _ _ _ => 0%nat
-  | Machsem.Returnstate _ _ _ => 1%nat
+  | Mach.State _ _ _ _ _ _ => 0%nat
+  | Mach.Callstate _ _ _ _ => 0%nat
+  | Mach.Returnstate _ _ _ => 1%nat
   end.
 
-(** We show the simulation diagram by case analysis on the Mach transition
-  on the left.  Since the proof is large, we break it into one lemma
-  per transition. *)
-
-Definition exec_instr_prop (s1: Machsem.state) (t: trace) (s2: Machsem.state) : Prop :=
-  forall s1' (MS: match_states s1 s1'),
-  (exists s2', plus step tge s1' t s2' /\ match_states s2 s2')
-  \/ (measure s2 < measure s1 /\ t = E0 /\ match_states s2 s1')%nat.
-
-
-Lemma exec_Mlabel_prop:
-  forall (s : list stackframe) (fb : block) (sp : val)
-         (lbl : Mach.label) (c : list Mach.instruction) (ms : Mach.regset)
-         (m : mem),
-  exec_instr_prop (Machsem.State s fb sp (Mlabel lbl :: c) ms m) E0
-                  (Machsem.State s fb sp c ms m).
+Remark preg_of_not_GPR11: forall r, negb (mreg_eq r IT1) = true -> IR GPR11 <> preg_of r.
 Proof.
-  intros; red; intros; inv MS.
-  left; eapply exec_straight_steps; eauto with coqlib.
-  exists (nextinstr rs); split.
-  simpl. apply exec_straight_one. reflexivity. reflexivity.
-  apply agree_nextinstr; auto.
+  intros. change (IR GPR11) with (preg_of IT1). red; intros. 
+  exploit preg_of_injective; eauto. intros; subst r; discriminate.
 Qed.
 
-Lemma exec_Mgetstack_prop:
-  forall (s : list stackframe) (fb : block) (sp : val) (ofs : int)
-         (ty : typ) (dst : mreg) (c : list Mach.instruction)
-         (ms : Mach.regset) (m : mem) (v : val),
-  load_stack m sp ty ofs = Some v ->
-  exec_instr_prop (Machsem.State s fb sp (Mgetstack ofs ty dst :: c) ms m) E0
-                  (Machsem.State s fb sp c (Regmap.set dst v ms) m).
-Proof.
-  intros; red; intros; inv MS.
-  unfold load_stack in H. 
-  generalize (wt_function_instrs _ WTF _ (INCL _ (in_eq _ _))).
-  intro WTI. inversion WTI.
-  exploit Mem.loadv_extends; eauto. intros [v' [A B]].
-  rewrite (sp_val _ _ _ AG) in A.
-  exploit (loadind_correct tge (transl_function f) GPR1 ofs ty dst (transl_code f c) rs m' v').
-  auto. auto. congruence. 
-  intros [rs2 [EX [RES OTH]]].
-  left; eapply exec_straight_steps; eauto with coqlib.
-  simpl. exists rs2; split. auto. 
-  apply agree_set_mreg with rs; auto with ppcgen. congruence. 
-Qed.
+(** This is the simulation diagram.  We prove it by case analysis on the Mach transition. *)
 
-Lemma exec_Msetstack_prop:
-  forall (s : list stackframe) (fb : block) (sp : val) (src : mreg)
-         (ofs : int) (ty : typ) (c : list Mach.instruction)
-         (ms : mreg -> val) (m m' : mem),
-  store_stack m sp ty ofs (ms src) = Some m' ->
-  exec_instr_prop (Machsem.State s fb sp (Msetstack src ofs ty :: c) ms m) E0
-                  (Machsem.State s fb sp c ms m').
+Theorem step_simulation:
+  forall S1 t S2, Mach.step ge S1 t S2 ->
+  forall S1' (MS: match_states S1 S1'),
+  (exists S2', plus step tge S1' t S2' /\ match_states S2 S2')
+  \/ (measure S2 < measure S1 /\ t = E0 /\ match_states S2 S1')%nat.
 Proof.
-  intros; red; intros; inv MS.
-  unfold store_stack in H. 
-  generalize (wt_function_instrs _ WTF _ (INCL _ (in_eq _ _))).
-  intro WTI. inv WTI.
-  generalize (preg_val ms sp rs src AG). intro. 
-  exploit Mem.storev_extends; eauto.
-  intros [m2' [A B]].
+  induction 1; intros; inv MS.
+
+- (* Mlabel *)
+  left; eapply exec_straight_steps; eauto; intros. 
+  monadInv TR. econstructor; split. apply exec_straight_one. simpl; eauto. auto. 
+  split. apply agree_nextinstr; auto. simpl; congruence.
+
+- (* Mgetstack *)
+  unfold load_stack in H.
+  exploit Mem.loadv_extends; eauto. intros [v' [A B]].
   rewrite (sp_val _ _ _ AG) in A.
-  exploit (storeind_correct tge (transl_function f) GPR1 ofs (mreg_type src)
-                src (transl_code f c) rs).
-  eauto. auto. congruence.
-  intros [rs2 [EX OTH]].
-  left; eapply exec_straight_steps; eauto with coqlib.
-  exists rs2; split; auto.
-  apply agree_exten with rs; auto with ppcgen.
-Qed.
+  left; eapply exec_straight_steps; eauto. intros. simpl in TR.
+  exploit loadind_correct; eauto with asmgen. intros [rs' [P [Q R]]].
+  exists rs'; split. eauto.
+  split. eapply agree_set_mreg; eauto with asmgen. congruence.
+  simpl; congruence.
 
-Lemma exec_Mgetparam_prop:
-  forall (s : list stackframe) (fb : block) (f: Mach.function) (sp : val)
-         (ofs : int) (ty : typ) (dst : mreg) (c : list Mach.instruction)
-         (ms : Mach.regset) (m : mem) (v : val),
-  Genv.find_funct_ptr ge fb = Some (Internal f) ->
-  load_stack m sp Tint f.(fn_link_ofs) = Some (parent_sp s) ->
-  load_stack m (parent_sp s) ty ofs = Some v ->
-  exec_instr_prop (Machsem.State s fb sp (Mgetparam ofs ty dst :: c) ms m) E0
-                  (Machsem.State s fb sp c (Regmap.set dst v (Regmap.set IT1 Vundef ms)) m).
-Proof.
-  intros; red; intros; inv MS.
-  assert (f0 = f) by congruence. subst f0.
-  generalize (wt_function_instrs _ WTF _ (INCL _ (in_eq _ _))).
-  intro WTI. inv WTI.
-  unfold load_stack in *. simpl in H0. 
+- (* Msetstack *)
+  unfold store_stack in H.
+  assert (Val.lessdef (rs src) (rs0 (preg_of src))). eapply preg_val; eauto.
+  exploit Mem.storev_extends; eauto. intros [m2' [A B]]. 
+  left; eapply exec_straight_steps; eauto.
+  eapply match_stack_storev; eauto. 
+  eapply retaddr_stored_at_storev; eauto. 
+  rewrite (sp_val _ _ _ AG) in A. intros. simpl in TR.
+  exploit storeind_correct; eauto with asmgen. intros [rs' [P Q]].
+  exists rs'; split. eauto.
+  split. change (undef_setstack rs) with rs. apply agree_exten with rs0; auto with asmgen.
+  simpl; intros. rewrite Q; auto with asmgen.
+
+- (* Mgetparam *)
+  unfold load_stack in *. 
+  exploit Mem.loadv_extends. eauto. eexact H. auto. 
+  intros [parent' [A B]]. rewrite (sp_val _ _ _ AG) in A.
+  exploit lessdef_parent_sp; eauto. clear B; intros B; subst parent'.
   exploit Mem.loadv_extends. eauto. eexact H0. auto. 
-  intros [parent' [A B]].
-  exploit Mem.loadv_extends. eauto. eexact H1. 
-  instantiate (1 := (Val.add parent' (Vint ofs))). 
-  inv B. auto. simpl; auto.
   intros [v' [C D]].
-  left; eapply exec_straight_steps; eauto with coqlib. simpl. 
-  set (rs1 := nextinstr (rs#GPR11 <- parent')).
-  exploit (loadind_correct tge (transl_function f) GPR11 ofs (mreg_type dst) dst (transl_code f c) rs1 m' v').
-  unfold rs1. rewrite nextinstr_inv; auto with ppcgen. auto. congruence.
-  intros [rs2 [U [V W]]].
-  exists rs2; split.
-  apply exec_straight_step with rs1 m'.
-  simpl. unfold load1. simpl. rewrite gpr_or_zero_not_zero.
-  rewrite <- (sp_val _ _ _ AG). rewrite A. auto. congruence. auto. 
-  auto.
-  apply agree_set_mreg with rs1; auto with ppcgen. 
-  unfold rs1. change (IR GPR11) with (preg_of IT1). 
-  apply agree_nextinstr. apply agree_set_mreg with rs; auto with ppcgen.
-  intros. apply Pregmap.gso; auto with ppcgen.
-  congruence.
-Qed.
-
-Lemma exec_Mop_prop:
-  forall (s : list stackframe) (fb : block) (sp : val) (op : operation)
-         (args : list mreg) (res : mreg) (c : list Mach.instruction)
-         (ms : mreg -> val) (m : mem) (v : val),
-  eval_operation ge sp op ms ## args m = Some v ->
-  exec_instr_prop (Machsem.State s fb sp (Mop op args res :: c) ms m) E0
-                  (Machsem.State s fb sp c (Regmap.set res v (undef_op op ms)) m).
-Proof.
-  intros; red; intros; inv MS.
-  generalize (wt_function_instrs _ WTF _ (INCL _ (in_eq _ _))).
-  intro WTI.
-  left; eapply exec_straight_steps; eauto with coqlib.
-  simpl. eapply transl_op_correct; eauto.
-  rewrite <- H. apply eval_operation_preserved. exact symbols_preserved.
-Qed.
-
-Remark loadv_8_signed_unsigned:
-  forall m a v,
-  Mem.loadv Mint8signed m a = Some v ->
-  exists v', Mem.loadv Mint8unsigned m a = Some v' /\ v = Val.sign_ext 8 v'.
-Proof.
-  unfold Mem.loadv; intros. destruct a; try congruence.
-  generalize (Mem.load_int8_signed_unsigned m b (Int.unsigned i)).
-  rewrite H. destruct (Mem.load Mint8unsigned m b (Int.unsigned i)).
-  simpl; intros. exists v0; split; congruence.
+Opaque loadind.
+  left; eapply exec_straight_steps; eauto; intros.
+  destruct ep; simpl in TR. 
+(* GPR11 contains parent *)
+  exploit loadind_correct. eexact TR.
+  instantiate (2 := rs0). rewrite DXP; eauto.  congruence.
+  intros [rs1 [P [Q R]]].
+  exists rs1; split. eauto. 
+  split. eapply agree_set_mreg. eapply agree_set_mreg; eauto. congruence. auto with asmgen.
+  simpl; intros. rewrite R; auto with asmgen. 
+  apply preg_of_not_GPR11; auto.
+(* GPR11 does not contain parent *)
+  monadInv TR.  
+  exploit loadind_correct. eexact EQ0. eauto. congruence. intros [rs1 [P [Q R]]]. simpl in Q.
+  exploit loadind_correct. eexact EQ. instantiate (2 := rs1). rewrite Q. eauto. congruence.
+  intros [rs2 [S [T U]]]. 
+  exists rs2; split. eapply exec_straight_trans; eauto.
+  split. eapply agree_set_mreg. eapply agree_set_mreg. eauto. eauto.
+  instantiate (1 := rs1#GPR11 <- (rs2#GPR11)). intros.
+  rewrite Pregmap.gso; auto with asmgen.
+  congruence. intros. unfold Pregmap.set. destruct (PregEq.eq r' GPR11). congruence. auto with asmgen. 
+  simpl; intros. rewrite U; auto with asmgen. 
+  apply preg_of_not_GPR11; auto.
+
+- (* Mop *)
+  assert (eval_operation tge (Vptr sp0 Int.zero) op rs##args m = Some v). 
+    rewrite <- H. apply eval_operation_preserved. exact symbols_preserved.
+  exploit eval_operation_lessdef. eapply preg_vals; eauto. eauto. eexact H0.
+  intros [v' [A B]]. rewrite (sp_val _ _ _ AG) in A. 
+  left; eapply exec_straight_steps; eauto; intros. simpl in TR.
+  exploit transl_op_correct; eauto. intros [rs2 [P [Q R]]].
+  exists rs2; split. eauto. split. auto. 
+  simpl. destruct op; try congruence. destruct ep; simpl; try congruence. intros. 
+  rewrite R; auto. apply preg_of_not_GPR11; auto.
+
+- (* Mload *)
+  assert (eval_addressing tge (Vptr sp0 Int.zero) addr rs##args = Some a). 
+    rewrite <- H. apply eval_addressing_preserved. exact symbols_preserved.
+  exploit eval_addressing_lessdef. eapply preg_vals; eauto. eexact H1.
+  intros [a' [A B]]. rewrite (sp_val _ _ _ AG) in A.
+  exploit Mem.loadv_extends; eauto. intros [v' [C D]].
+  left; eapply exec_straight_steps; eauto; intros. simpl in TR.
+  exploit transl_load_correct; eauto. intros [rs2 [P [Q R]]]. 
+  exists rs2; split. eauto.
+  split. eapply agree_set_undef_mreg; eauto. congruence.
+  intros; auto with asmgen. 
   simpl; congruence.
-Qed.
 
-Lemma exec_Mload_prop:
-  forall (s : list stackframe) (fb : block) (sp : val)
-         (chunk : memory_chunk) (addr : addressing) (args : list mreg)
-         (dst : mreg) (c : list Mach.instruction) (ms : mreg -> val)
-         (m : mem) (a v : val),
-  eval_addressing ge sp addr ms ## args = Some a ->
-  Mem.loadv chunk m a = Some v ->
-  exec_instr_prop (Machsem.State s fb sp (Mload chunk addr args dst :: c) ms m)
-               E0 (Machsem.State s fb sp c (Regmap.set dst v (undef_temps ms)) m).
-Proof.
-  intros; red; intros; inv MS.
-  generalize (wt_function_instrs _ WTF _ (INCL _ (in_eq _ _))).
-  intro WTI; inversion WTI.
-  assert (eval_addressing tge sp addr ms##args = Some a).
+- (* Mstore *)
+  assert (eval_addressing tge (Vptr sp0 Int.zero) addr rs##args = Some a). 
     rewrite <- H. apply eval_addressing_preserved. exact symbols_preserved.
-  left; eapply exec_straight_steps; eauto with coqlib;
-  destruct chunk; simpl; simpl in H6;
-  (* all cases but Mint8signed and Mfloat64 *)
-  try (eapply transl_load_correct; eauto;
-       intros; simpl; unfold preg_of; rewrite H6; auto; fail).
-  (* Mint8signed *)
-  exploit loadv_8_signed_unsigned; eauto. intros [v' [LOAD EQ]].
-  assert (X1: forall (cst : constant) (r1 : ireg) (rs1 : regset),
-    exec_instr tge (transl_function f) (Plbz (ireg_of dst) cst r1) rs1 m' =
-    load1 tge Mint8unsigned (preg_of dst) cst r1 rs1 m').
-    intros. unfold preg_of; rewrite H6. reflexivity. 
-  assert (X2: forall (r1 r2 : ireg) (rs1 : regset),
-    exec_instr tge (transl_function f) (Plbzx (ireg_of dst) r1 r2) rs1 m' =
-    load2 Mint8unsigned (preg_of dst) r1 r2 rs1 m').
-    intros. unfold preg_of; rewrite H6. reflexivity.
-  exploit transl_load_correct; eauto. 
-  intros [rs2 [EX1 AG1]].
-  econstructor; split. 
-  eapply exec_straight_trans. eexact EX1.
-  apply exec_straight_one. simpl. eauto. auto.
-  apply agree_nextinstr.
-  eapply agree_set_twice_mireg; eauto.
-  rewrite EQ. apply Val.sign_ext_lessdef. 
-  generalize (ireg_val _ _ _ dst AG1 H6). rewrite Regmap.gss. auto.
-  (* Mfloat64 *)
-  exploit Mem.loadv_float64al32; eauto. intros. clear H0.
-  eapply transl_load_correct; eauto;
-  intros; simpl; unfold preg_of; rewrite H6; auto.
-Qed.
-
-Lemma storev_8_signed_unsigned:
-  forall m a v,
-  Mem.storev Mint8signed m a v = Mem.storev Mint8unsigned m a v.
-Proof.
-  intros. unfold Mem.storev. destruct a; auto.
-  apply Mem.store_signed_unsigned_8.
-Qed.
-
-Lemma storev_16_signed_unsigned:
-  forall m a v,
-  Mem.storev Mint16signed m a v = Mem.storev Mint16unsigned m a v.
-Proof.
-  intros. unfold Mem.storev. destruct a; auto.
-  apply Mem.store_signed_unsigned_16.
-Qed.
-
-Lemma exec_Mstore_prop:
-  forall (s : list stackframe) (fb : block) (sp : val)
-         (chunk : memory_chunk) (addr : addressing) (args : list mreg)
-         (src : mreg) (c : list Mach.instruction) (ms : mreg -> val)
-         (m m' : mem) (a : val),
-  eval_addressing ge sp addr ms ## args = Some a ->
-  Mem.storev chunk m a (ms src) = Some m' ->
-  exec_instr_prop (Machsem.State s fb sp (Mstore chunk addr args src :: c) ms m) E0
-                  (Machsem.State s fb sp c (undef_temps ms) m').
-Proof.
-  intros; red; intros; inv MS.
-  generalize (wt_function_instrs _ WTF _ (INCL _ (in_eq _ _))).
-  intro WTI; inv WTI.
-  rewrite <- (eval_addressing_preserved _ _ symbols_preserved) in H.
-  left; eapply exec_straight_steps_bis; eauto with coqlib.
-  destruct chunk; simpl; simpl in H6;
-  try (generalize (Mem.storev_float64al32 _ _ _ _ H0); intros);
-  try (rewrite storev_8_signed_unsigned in H0);
-  try (rewrite storev_16_signed_unsigned in H0);
-  simpl; eapply transl_store_correct; eauto;
-  (unfold preg_of; rewrite H6; intros; econstructor; eauto).
-  split. simpl. rewrite H1. eauto. intros; apply Pregmap.gso; auto.
-  split. simpl. rewrite H1. eauto. intros; apply Pregmap.gso; auto.
-Qed.
+  exploit eval_addressing_lessdef. eapply preg_vals; eauto. eexact H1.
+  intros [a' [A B]]. rewrite (sp_val _ _ _ AG) in A.
+  assert (Val.lessdef (rs src) (rs0 (preg_of src))). eapply preg_val; eauto.
+  exploit Mem.storev_extends; eauto. intros [m2' [C D]].
+  left; eapply exec_straight_steps; eauto.
+  eapply match_stack_storev; eauto.
+  eapply retaddr_stored_at_storev; eauto.
+  intros. simpl in TR. exploit transl_store_correct; eauto. intros [rs2 [P Q]]. 
+  exists rs2; split. eauto.
+  split. eapply agree_exten_temps; eauto. intros; auto with asmgen. 
+  simpl; congruence.
 
-Lemma exec_Mcall_prop:
-  forall (s : list stackframe) (fb : block) (sp : val)
-         (sig : signature) (ros : mreg + ident) (c : Mach.code)
-         (ms : Mach.regset) (m : mem) (f : function) (f' : block)
-         (ra : int),
-  find_function_ptr ge ros ms = Some f' ->
-  Genv.find_funct_ptr ge fb = Some (Internal f) ->
-  return_address_offset f c ra ->
-  exec_instr_prop (Machsem.State s fb sp (Mcall sig ros :: c) ms m) E0
-                  (Callstate (Stackframe fb sp (Vptr fb ra) c :: s) f' ms m).
-Proof.
-  intros; red; intros; inv MS.
-  assert (f0 = f) by congruence. subst f0.
-  generalize (wt_function_instrs _ WTF _ (INCL _ (in_eq _ _))).
-  intro WTI. inversion WTI.
+- (* Mcall *)
   inv AT. 
-  assert (NOOV: list_length_z (transl_function f) <= Int.max_unsigned).
-    eapply functions_transl_no_overflow; eauto.
-  destruct ros; simpl in H; simpl transl_code in H7.
-  (* Indirect call *)
-  generalize (code_tail_next_int _ _ _ _ NOOV H7). intro CT1.
+  assert (NOOV: list_length_z tf <= Int.max_unsigned).
+    eapply transf_function_no_overflow; eauto.
+  destruct ros as [rf|fid]; simpl in H; monadInv H3.
++ (* Indirect call *)
+  exploit Genv.find_funct_inv; eauto. intros [bf EQ2].
+  rewrite EQ2 in H; rewrite  Genv.find_funct_find_funct_ptr in H. 
+  assert (rs0 x0 = Vptr bf Int.zero).
+    exploit ireg_val; eauto. rewrite EQ2; intros LD; inv LD; auto.
+  generalize (code_tail_next_int _ _ _ _ NOOV H4). intro CT1.
   generalize (code_tail_next_int _ _ _ _ NOOV CT1). intro CT2.
-  assert (P1: ms m0 = Vptr f' Int.zero).
-    destruct (ms m0); try congruence. 
-    generalize H; predSpec Int.eq Int.eq_spec i Int.zero; intros; congruence.
-  assert (P2: rs (ireg_of m0) = Vptr f' Int.zero).
-    generalize (ireg_val _ _ _ m0 AG H3).
-    rewrite P1. intro. inv H2. auto.
-  set (rs2 := nextinstr (rs#CTR <- (Vptr f' Int.zero))).
-  set (rs3 := rs2 #LR <- (Val.add rs2#PC Vone) #PC <- (Vptr f' Int.zero)).
-  assert (ATPC: rs3 PC = Vptr f' Int.zero). reflexivity.
-  exploit return_address_offset_correct; eauto. constructor; eauto. 
-  intro RA_EQ.
-  assert (ATLR: rs3 LR = Vptr fb ra).
-    rewrite RA_EQ.
-    change (rs3 LR) with (Val.add (Val.add (rs PC) Vone) Vone).
-    rewrite <- H5. reflexivity. 
-  assert (AG3: agree ms sp rs3). 
-    unfold rs3, rs2; auto 8 with ppcgen.
-  left; exists (State rs3 m'); split.
-  apply plus_left with E0 (State rs2 m') E0. 
-    econstructor. eauto. apply functions_transl. eexact H0. 
-    eapply find_instr_tail. eauto.
-    simpl. rewrite P2. auto.
-  apply star_one. econstructor.
-    change (rs2 PC) with (Val.add (rs PC) Vone). rewrite <- H5.
-    simpl. auto.
-    apply functions_transl. eexact H0.
-    eapply find_instr_tail. eauto.
-    simpl. reflexivity.
+  assert (TCA: transl_code_at_pc ge (Vptr b (Int.add (Int.add ofs Int.one) Int.one)) f c false tf x).
+    econstructor; eauto. 
+  left; econstructor; split.
+  eapply plus_left. eapply exec_step_internal. eauto.
+  eapply functions_transl; eauto. eapply find_instr_tail; eauto. 
+  simpl. eauto.
+  apply star_one. eapply exec_step_internal. Simpl. rewrite <- H0; simpl; eauto.
+  eapply functions_transl; eauto. eapply find_instr_tail; eauto. 
+  simpl. eauto.
   traceEq.
+  econstructor; eauto. 
   econstructor; eauto.
-  econstructor; eauto with coqlib.
-  rewrite RA_EQ. econstructor; eauto.
-  eapply agree_sp_def; eauto. congruence.
-
-  (* Direct call *)
-  generalize (code_tail_next_int _ _ _ _ NOOV H7). intro CT1.
-  set (rs2 := rs #LR <- (Val.add rs#PC Vone) #PC <- (symbol_offset tge i Int.zero)).
-  assert (ATPC: rs2 PC = Vptr f' Int.zero).
-    change (rs2 PC) with (symbol_offset tge i Int.zero).
-    unfold symbol_offset. rewrite symbols_preserved. rewrite H. auto.
-  exploit return_address_offset_correct; eauto. constructor; eauto. 
-  intro RA_EQ.
-  assert (ATLR: rs2 LR = Vptr fb ra).
-    rewrite RA_EQ.
-    change (rs2 LR) with (Val.add (rs PC) Vone).
-    rewrite <- H5. reflexivity. 
-  assert (AG2: agree ms sp rs2). 
-    unfold rs2; auto 8 with ppcgen.
-  left; exists (State rs2 m'); split.
-  apply plus_one. econstructor. 
-    eauto.
-    apply functions_transl. eexact H0. 
-    eapply find_instr_tail. eauto.
-    simpl. reflexivity.
-  econstructor; eauto with coqlib.
-  econstructor; eauto with coqlib.
-  rewrite RA_EQ. econstructor; eauto.
-  eapply agree_sp_def; eauto. congruence.
-Qed.
-
-Lemma exec_Mtailcall_prop:
-  forall (s : list stackframe) (fb stk : block) (soff : int)
-         (sig : signature) (ros : mreg + ident) (c : list Mach.instruction)
-         (ms : Mach.regset) (m : mem) (f: Mach.function) (f' : block) m',
-  find_function_ptr ge ros ms = Some f' ->
-  Genv.find_funct_ptr ge fb = Some (Internal f) ->
-  load_stack m (Vptr stk soff) Tint f.(fn_link_ofs) = Some (parent_sp s) ->
-  load_stack m (Vptr stk soff) Tint f.(fn_retaddr_ofs) = Some (parent_ra s) ->
-  Mem.free m stk 0 f.(fn_stacksize) = Some m' ->
-  exec_instr_prop
-          (Machsem.State s fb (Vptr stk soff) (Mtailcall sig ros :: c) ms m) E0
-          (Callstate s f' ms m').
-Proof.
-  intros; red; intros; inv MS.
-  assert (f0 = f) by congruence. subst f0.
-  generalize (wt_function_instrs _ WTF _ (INCL _ (in_eq _ _))).
-  intro WTI. inversion WTI.
-  inversion AT. subst b f0 c0.
-  assert (NOOV: list_length_z (transl_function f) <= Int.max_unsigned).
-    eapply functions_transl_no_overflow; eauto.
-  exploit Mem.free_parallel_extends; eauto.
-  intros [m2' [FREE' EXT']].
-  unfold load_stack in *. simpl in H1; simpl in H2.
-  exploit Mem.load_extends. eexact MEXT. eexact H1.
-  intros [parent' [LOAD1 LD1]].
-  rewrite (lessdef_parent_sp s parent' STACKS LD1) in LOAD1.
-  exploit Mem.load_extends. eexact MEXT. eexact H2.
-  intros [ra' [LOAD2 LD2]].
-  rewrite (lessdef_parent_ra s ra' STACKS LD2) in LOAD2.
-  destruct ros; simpl in H; simpl in H9.
-  (* Indirect call *)
-  assert (P1: ms m0 = Vptr f' Int.zero).
-    destruct (ms m0); try congruence. 
-    generalize H; predSpec Int.eq Int.eq_spec i Int.zero; intros; congruence.
-  assert (P2: rs (ireg_of m0) = Vptr f' Int.zero).
-    generalize (ireg_val _ _ _ m0 AG H7).
-    rewrite P1. intro. inv H11. auto.
-  set (rs2 := nextinstr (rs#CTR <- (Vptr f' Int.zero))).
-  set (rs3 := nextinstr (rs2#GPR0 <- (parent_ra s))).
-  set (rs4 := nextinstr (rs3#LR <- (parent_ra s))).
+  Simpl. rewrite <- H0; eexact TCA.
+  change (Mem.valid_block m sp0). eapply retaddr_stored_at_valid; eauto. 
+  simpl. eapply agree_exten; eauto. intros. Simpl. 
+  Simpl. rewrite <- H0. exact I.
++ (* Direct call *)
+  destruct (Genv.find_symbol ge fid) as [bf|] eqn:FS; try discriminate.
+  generalize (code_tail_next_int _ _ _ _ NOOV H4). intro CT1.
+  assert (TCA: transl_code_at_pc ge (Vptr b (Int.add ofs Int.one)) f c false tf x).
+    econstructor; eauto. 
+  left; econstructor; split.
+  apply plus_one. eapply exec_step_internal. eauto.
+  eapply functions_transl; eauto. eapply find_instr_tail; eauto. 
+  simpl. unfold symbol_offset. rewrite symbols_preserved. rewrite FS. eauto.
+  econstructor; eauto. 
+  econstructor; eauto.
+  rewrite <- H0. eexact TCA.
+  change (Mem.valid_block m sp0). eapply retaddr_stored_at_valid; eauto. 
+  simpl. eapply agree_exten; eauto. intros. Simpl.
+  auto.
+  rewrite <- H0. exact I.
+
+- (* Mtailcall *)
+  inversion AT; subst.
+  assert (NOOV: list_length_z tf <= Int.max_unsigned).
+    eapply transf_function_no_overflow; eauto.
+  rewrite (sp_val _ _ _ AG) in *. unfold load_stack in *.
+  exploit Mem.loadv_extends. eauto. eexact H0. auto. simpl. intros [parent' [A B]]. 
+  exploit lessdef_parent_sp; eauto. intros. subst parent'. clear B.
+  assert (C: Mem.loadv Mint32 m'0 (Val.add (rs0 GPR1) (Vint (fn_retaddr_ofs f))) = Some ra).
+Opaque Int.repr.
+    erewrite agree_sp; eauto. simpl. rewrite Int.add_zero_l.
+    eapply rsa_contains; eauto.
+  exploit retaddr_stored_at_can_free; eauto. intros [m2' [E F]].
+  assert (M: match_stack ge s m'' m2' ra (Mem.nextblock m'')).
+    apply match_stack_change_bound with stk.
+    eapply match_stack_free_left; eauto. 
+    eapply match_stack_free_left; eauto. 
+    eapply match_stack_free_right; eauto.
+    omega.
+    apply Z.lt_le_incl. change (Mem.valid_block m'' stk).
+    eapply Mem.valid_block_free_1; eauto. eapply Mem.valid_block_free_1; eauto. 
+    eapply retaddr_stored_at_valid; eauto.
+  destruct ros as [rf|fid]; simpl in H; monadInv H6.
++ (* Indirect call *)
+  exploit Genv.find_funct_inv; eauto. intros [bf EQ2].
+  rewrite EQ2 in H; rewrite  Genv.find_funct_find_funct_ptr in H. 
+  assert (rs0 x0 = Vptr bf Int.zero).
+    exploit ireg_val; eauto. rewrite EQ2; intros LD; inv LD; auto.
+  set (rs2 := nextinstr (rs0#CTR <- (Vptr bf Int.zero))).
+  set (rs3 := nextinstr (rs2#GPR0 <- ra)).
+  set (rs4 := nextinstr (rs3#LR <- ra)).
   set (rs5 := nextinstr (rs4#GPR1 <- (parent_sp s))).
   set (rs6 := rs5#PC <- (rs5 CTR)).
-  assert (exec_straight tge (transl_function f)
-            (transl_code f (Mtailcall sig (inl ident m0) :: c)) rs m'0 
-            (Pbctr :: transl_code f c) rs5 m2').
-  simpl. apply exec_straight_step with rs2 m'0. 
-  simpl. rewrite P2. auto. auto.
+  assert (exec_straight tge tf
+            (Pmtctr x0 :: Plwz GPR0 (Cint (fn_retaddr_ofs f)) GPR1 :: Pmtlr GPR0
+              :: Pfreeframe (fn_stacksize f) (fn_link_ofs f) :: Pbctr :: x)
+            rs0 m'0
+            (Pbctr :: x) rs5 m2').
+  apply exec_straight_step with rs2 m'0. 
+  simpl. rewrite H6. auto. auto.
   apply exec_straight_step with rs3 m'0.
   simpl. unfold load1. rewrite gpr_or_zero_not_zero. unfold const_low.
-  change (rs2 GPR1) with (rs GPR1). rewrite <- (sp_val _ _ _ AG). 
-  simpl. rewrite LOAD2. auto. congruence. auto. 
+  change (rs2 GPR1) with (rs0 GPR1). rewrite C. auto. congruence. auto.
   apply exec_straight_step with rs4 m'0.
   simpl. reflexivity. reflexivity.
   apply exec_straight_one. 
-  simpl. change (rs4 GPR1) with (rs GPR1). rewrite <- (sp_val _ _ _ AG).
-  simpl. rewrite LOAD1. rewrite FREE'. reflexivity. reflexivity.
+  simpl. change (rs4 GPR1) with (rs0 GPR1). rewrite A. rewrite <- (sp_val _ _ _ AG).
+  rewrite E. reflexivity. reflexivity.
   left; exists (State rs6 m2'); split.
   (* execution *)
   eapply plus_right'. eapply exec_straight_exec; eauto.
   econstructor.
-  change (rs5 PC) with (Val.add (Val.add (Val.add (Val.add (rs PC) Vone) Vone) Vone) Vone).
-  rewrite <- H8; simpl. eauto.
+  change (rs5 PC) with (Val.add (Val.add (Val.add (Val.add (rs0 PC) Vone) Vone) Vone) Vone).
+  rewrite <- H3; simpl. eauto.
   eapply functions_transl; eauto. 
   eapply find_instr_tail.
   repeat (eapply code_tail_next_int; auto). eauto. 
   simpl. reflexivity. traceEq.
   (* match states *)
   econstructor; eauto.
-  assert (AG4: agree ms (Vptr stk soff) rs4).
-    unfold rs4, rs3, rs2; auto 10 with ppcgen.
-  assert (AG5: agree ms (parent_sp s) rs5).
-    unfold rs5. apply agree_nextinstr.
-    split. reflexivity. apply parent_sp_def; auto. 
-    intros. inv AG4. rewrite Pregmap.gso; auto with ppcgen.
-  unfold rs6; auto with ppcgen.
-  (* direct call *)
-  set (rs2 := nextinstr (rs#GPR0 <- (parent_ra s))).
-  set (rs3 := nextinstr (rs2#LR <- (parent_ra s))).
+Hint Resolve agree_nextinstr agree_set_other: asmgen.
+  assert (AG4: agree rs (Vptr stk Int.zero) rs4).
+    unfold rs4, rs3, rs2; auto 10 with asmgen.
+  assert (AG5: agree rs (parent_sp s) rs5).
+    unfold rs5. apply agree_nextinstr. eapply agree_change_sp. eauto. 
+    eapply parent_sp_def; eauto. 
+  unfold rs6, rs5; auto 10 with asmgen.
+  reflexivity.
+  change (rs6 LR) with ra. eapply retaddr_stored_at_type; eauto. 
++ (* Direct call *)
+  destruct (Genv.find_symbol ge fid) as [bf|] eqn:FS; try discriminate.
+  set (rs2 := nextinstr (rs0#GPR0 <- ra)).
+  set (rs3 := nextinstr (rs2#LR <- ra)).
   set (rs4 := nextinstr (rs3#GPR1 <- (parent_sp s))).
-  set (rs5 := rs4#PC <- (Vptr f' Int.zero)).
-  assert (exec_straight tge (transl_function f)
-            (transl_code f (Mtailcall sig (inr mreg i) :: c)) rs m'0 
-            (Pbs i :: transl_code f c) rs4 m2').
-  simpl. apply exec_straight_step with rs2 m'0. 
+  set (rs5 := rs4#PC <- (Vptr bf Int.zero)).
+  assert (exec_straight tge tf
+            (Plwz GPR0 (Cint (fn_retaddr_ofs f)) GPR1 :: Pmtlr GPR0
+             :: Pfreeframe (fn_stacksize f) (fn_link_ofs f) :: Pbs fid :: x)
+            rs0 m'0
+            (Pbs fid :: x) rs4 m2').
+  apply exec_straight_step with rs2 m'0. 
   simpl. unfold load1. rewrite gpr_or_zero_not_zero. unfold const_low.
-  rewrite <- (sp_val _ _ _ AG). 
-  simpl. rewrite LOAD2. auto. discriminate. auto. 
+  rewrite C. auto. congruence. auto.
   apply exec_straight_step with rs3 m'0.
   simpl. reflexivity. reflexivity.
   apply exec_straight_one. 
-  simpl. change (rs3 GPR1) with (rs GPR1). rewrite <- (sp_val _ _ _ AG).
-  simpl. rewrite LOAD1. rewrite FREE'. reflexivity. reflexivity.
+  simpl. change (rs3 GPR1) with (rs0 GPR1). rewrite A. rewrite <- (sp_val _ _ _ AG).
+  rewrite E. reflexivity. reflexivity.
   left; exists (State rs5 m2'); split.
   (* execution *)
   eapply plus_right'. eapply exec_straight_exec; eauto.
   econstructor.
-  change (rs4 PC) with (Val.add (Val.add (Val.add (rs PC) Vone) Vone) Vone).
-  rewrite <- H8; simpl. eauto.
+  change (rs4 PC) with (Val.add (Val.add (Val.add (rs0 PC) Vone) Vone) Vone).
+  rewrite <- H3; simpl. eauto.
   eapply functions_transl; eauto. 
   eapply find_instr_tail.
   repeat (eapply code_tail_next_int; auto). eauto. 
-  simpl. unfold symbol_offset. rewrite symbols_preserved. rewrite H. 
-  reflexivity. traceEq.
+  simpl. unfold symbol_offset. rewrite symbols_preserved. rewrite FS. auto. traceEq.
   (* match states *)
   econstructor; eauto.
-  assert (AG3: agree ms (Vptr stk soff) rs3).
-    unfold rs3, rs2; auto 10 with ppcgen.
-  assert (AG4: agree ms (parent_sp s) rs4).
-    unfold rs4. apply agree_nextinstr.
-    split. reflexivity. 
-    apply parent_sp_def; auto.
-    intros. inv AG3. rewrite Pregmap.gso; auto with ppcgen.
-  unfold rs5; auto with ppcgen.
-Qed.
+Hint Resolve agree_nextinstr agree_set_other: asmgen.
+  assert (AG3: agree rs (Vptr stk Int.zero) rs3).
+    unfold rs3, rs2; auto 10 with asmgen.
+  assert (AG4: agree rs (parent_sp s) rs4).
+    unfold rs4. apply agree_nextinstr. eapply agree_change_sp. eauto. 
+    eapply parent_sp_def; eauto. 
+  unfold rs5; auto 10 with asmgen.
+  reflexivity.
+  change (rs5 LR) with ra. eapply retaddr_stored_at_type; eauto.
 
-Lemma exec_Mbuiltin_prop:
-  forall (s : list stackframe) (f : block) (sp : val)
-         (ms : Mach.regset) (m : mem) (ef : external_function)
-         (args : list mreg) (res : mreg) (b : list Mach.instruction)
-         (t : trace) (v : val) (m' : mem),
-  external_call ef ge ms ## args m t v m' ->
-  exec_instr_prop (Machsem.State s f sp (Mbuiltin ef args res :: b) ms m) t
-                  (Machsem.State s f sp b (Regmap.set res v (undef_temps ms)) m').
-Proof.
-  intros; red; intros; inv MS.
-  generalize (wt_function_instrs _ WTF _ (INCL _ (in_eq _ _))).
-  intro WTI. inv WTI.
-  inv AT. simpl in H3.
-  generalize (functions_transl _ _ FIND); intro FN.
-  generalize (functions_transl_no_overflow _ _ FIND); intro NOOV.
+- (* Mbuiltin *)
+  inv AT. monadInv H3. 
+  exploit functions_transl; eauto. intro FN.
+  generalize (transf_function_no_overflow _ _ H2); intro NOOV.
   exploit external_call_mem_extends; eauto. eapply preg_vals; eauto.
   intros [vres' [m2' [A [B [C D]]]]].
   left. econstructor; split. apply plus_one. 
@@ -1116,30 +794,23 @@ Proof.
   eapply find_instr_tail; eauto.
   eapply external_call_symbols_preserved; eauto.
   exact symbols_preserved. exact varinfo_preserved.
-  econstructor; eauto with coqlib.
-  unfold nextinstr. rewrite Pregmap.gss. repeat rewrite Pregmap.gso; auto with ppcgen.
-  rewrite <- H0. simpl. constructor; auto.
-  eapply code_tail_next_int; eauto. 
-  apply sym_not_equal. auto with ppcgen.
-  apply agree_nextinstr. apply agree_set_mreg_undef_temps with rs; auto. 
-  rewrite Pregmap.gss. auto.
-  intros. repeat rewrite Pregmap.gso; auto with ppcgen.
-Qed.
+  econstructor; eauto.
+  eapply match_stack_extcall; eauto. 
+  intros; eapply external_call_max_perm; eauto. 
+  instantiate (2 := tf); instantiate (1 := x).
+  Simpl. rewrite <- H0. simpl. econstructor; eauto.
+  eapply code_tail_next_int; eauto.
+  apply agree_nextinstr. eapply agree_set_undef_mreg; eauto. 
+  rewrite Pregmap.gss. auto. 
+  intros. Simpl. 
+  eapply retaddr_stored_at_extcall; eauto. 
+  intros; eapply external_call_max_perm; eauto. 
+  congruence.
 
-Lemma exec_Mannot_prop:
-  forall (s : list stackframe) (f : block) (sp : val)
-         (ms : Mach.regset) (m : mem) (ef : external_function)
-         (args : list Mach.annot_param) (b : list Mach.instruction)
-         (vargs: list val) (t : trace) (v : val) (m' : mem),
-  Machsem.annot_arguments ms m sp args vargs ->
-  external_call ef ge vargs m t v m' ->
-  exec_instr_prop (Machsem.State s f sp (Mannot ef args :: b) ms m) t
-                  (Machsem.State s f sp b ms m').
-Proof.
-  intros; red; intros; inv MS.
-  inv AT. simpl in H3.
-  generalize (functions_transl _ _ FIND); intro FN.
-  generalize (functions_transl_no_overflow _ _ FIND); intro NOOV.
+- (* Mannot *)
+  inv AT. monadInv H4. 
+  exploit functions_transl; eauto. intro FN.
+  generalize (transf_function_no_overflow _ _ H3); intro NOOV.
   exploit annot_arguments_match; eauto. intros [vargs' [P Q]]. 
   exploit external_call_mem_extends; eauto.
   intros [vres' [m2' [A [B [C D]]]]].
@@ -1148,373 +819,238 @@ Proof.
   eapply find_instr_tail; eauto. eauto.
   eapply external_call_symbols_preserved; eauto.
   exact symbols_preserved. exact varinfo_preserved.
-  econstructor; eauto with coqlib.
+  eapply match_states_intro with (ep := false); eauto with coqlib.
+  eapply match_stack_extcall; eauto. 
+  intros; eapply external_call_max_perm; eauto. 
   unfold nextinstr. rewrite Pregmap.gss. 
-  rewrite <- H1; simpl. econstructor; auto.
+  rewrite <- H1; simpl. econstructor; eauto.
   eapply code_tail_next_int; eauto. 
   apply agree_nextinstr. auto.
-Qed.
+  eapply retaddr_stored_at_extcall; eauto. 
+  intros; eapply external_call_max_perm; eauto. 
+  congruence.
 
-Lemma exec_Mgoto_prop:
-  forall (s : list stackframe) (fb : block) (f : function) (sp : val)
-         (lbl : Mach.label) (c : list Mach.instruction) (ms : Mach.regset)
-         (m : mem) (c' : Mach.code),
-  Genv.find_funct_ptr ge fb = Some (Internal f) ->
-  Mach.find_label lbl (fn_code f) = Some c' ->
-  exec_instr_prop (Machsem.State s fb sp (Mgoto lbl :: c) ms m) E0
-                  (Machsem.State s fb sp c' ms m).
-Proof.
-  intros; red; intros; inv MS.
-  assert (f0 = f) by congruence. subst f0.
-  inv AT. simpl in H3.
-  generalize (find_label_goto_label f lbl rs m' _ _ _ FIND (sym_equal H1) H0).
-  intros [rs2 [GOTO [AT2 INV]]].
-  left; exists (State rs2 m'); split.
+- (* Mgoto *)
+  inv AT. monadInv H3. 
+  exploit find_label_goto_label; eauto. intros [tc' [rs' [GOTO [AT2 INV]]]].
+  left; exists (State rs' m'); split.
   apply plus_one. econstructor; eauto.
-  apply functions_transl; eauto.
+  eapply functions_transl; eauto.
   eapply find_instr_tail; eauto.
-  simpl; auto.
-  econstructor; eauto.
-  eapply Mach.find_label_incl; eauto.
-  apply agree_exten with rs; auto with ppcgen.
-Qed.
-
-Lemma exec_Mcond_true_prop:
-  forall (s : list stackframe) (fb : block) (f : function) (sp : val)
-         (cond : condition) (args : list mreg) (lbl : Mach.label)
-         (c : list Mach.instruction) (ms : mreg -> val) (m : mem)
-         (c' : Mach.code),
-  eval_condition cond ms ## args m = Some true ->
-  Genv.find_funct_ptr ge fb = Some (Internal f) ->
-  Mach.find_label lbl (fn_code f) = Some c' ->
-  exec_instr_prop (Machsem.State s fb sp (Mcond cond args lbl :: c) ms m) E0
-                  (Machsem.State s fb sp c' (undef_temps ms) m).
-Proof.
-  intros; red; intros; inv MS. assert (f0 = f) by congruence. subst f0.
-  generalize (wt_function_instrs _ WTF _ (INCL _ (in_eq _ _))).
-  intro WTI. inv WTI.
-  pose (k1 := 
-         if snd (crbit_for_cond cond)
-         then Pbt (fst (crbit_for_cond cond)) lbl :: transl_code f c
-         else Pbf (fst (crbit_for_cond cond)) lbl :: transl_code f c).
-  exploit transl_cond_correct; eauto. 
-  simpl. intros [rs2 [EX [RES AG2]]].
-  inv AT. simpl in H5.
-  generalize (functions_transl _ _ H4); intro FN.
-  generalize (functions_transl_no_overflow _ _ H4); intro NOOV.
-  exploit exec_straight_steps_2; eauto. 
-  intros [ofs' [PC2 CT2]].
-  generalize (find_label_goto_label f lbl rs2 m' _ _ _ FIND PC2 H1).
-  intros [rs3 [GOTO [AT3 INV3]]].
-  left; exists (State rs3 m'); split.
-  eapply plus_right'. 
-  eapply exec_straight_steps_1; eauto.
-  caseEq (snd (crbit_for_cond cond)); intro ISSET; rewrite ISSET in RES.
-  econstructor; eauto.
-  eapply find_instr_tail. unfold k1 in CT2; rewrite ISSET in CT2. eauto.
-  simpl. rewrite RES. simpl. auto.
+  simpl; eauto.
   econstructor; eauto.
-  eapply find_instr_tail. unfold k1 in CT2; rewrite ISSET in CT2. eauto.
-  simpl. rewrite RES. simpl. auto.
-  traceEq.
-  econstructor; eauto. 
-  eapply Mach.find_label_incl; eauto.
-  apply agree_undef_temps with rs2; auto with ppcgen.
-Qed.
-
-Lemma exec_Mcond_false_prop:
-  forall (s : list stackframe) (fb : block) (sp : val)
-         (cond : condition) (args : list mreg) (lbl : Mach.label)
-         (c : list Mach.instruction) (ms : mreg -> val) (m : mem),
-  eval_condition cond ms ## args m = Some false ->
-  exec_instr_prop (Machsem.State s fb sp (Mcond cond args lbl :: c) ms m) E0
-                  (Machsem.State s fb sp c (undef_temps ms) m).
-Proof.
-  intros; red; intros; inv MS.
-  generalize (wt_function_instrs _ WTF _ (INCL _ (in_eq _ _))).
-  intro WTI. inversion WTI.
-  exploit transl_cond_correct; eauto.
-  simpl. intros [rs2 [EX [RES AG2]]].
-  left; eapply exec_straight_steps; eauto with coqlib.
-  exists (nextinstr rs2); split.
-  simpl. eapply exec_straight_trans. eexact EX. 
-  caseEq (snd (crbit_for_cond cond)); intro ISSET; rewrite ISSET in RES.
-  apply exec_straight_one. simpl. rewrite RES. reflexivity.
-  reflexivity.
-  apply exec_straight_one. simpl. rewrite RES. reflexivity.
-  reflexivity.
-  apply agree_nextinstr. apply agree_undef_temps with rs2; auto.
-Qed.
+  eapply agree_exten; eauto with asmgen.
+  congruence.
 
-Lemma exec_Mjumptable_prop:
-  forall (s : list stackframe) (fb : block) (f : function) (sp : val)
-         (arg : mreg) (tbl : list Mach.label) (c : list Mach.instruction)
-         (rs : mreg -> val) (m : mem) (n : int) (lbl : Mach.label)
-         (c' : Mach.code),
-  rs arg = Vint n ->
-  list_nth_z tbl (Int.unsigned n) = Some lbl ->
-  Genv.find_funct_ptr ge fb = Some (Internal f) ->
-  Mach.find_label lbl (fn_code f) = Some c' ->
-  exec_instr_prop
-    (Machsem.State s fb sp (Mjumptable arg tbl :: c) rs m) E0
-    (Machsem.State s fb sp c' (undef_temps rs) m).
-Proof.
-  intros; red; intros; inv MS.
-  assert (f0 = f) by congruence. subst f0.
-  generalize (wt_function_instrs _ WTF _ (INCL _ (in_eq _ _))).
-  intro WTI. inv WTI.
-  exploit list_nth_z_range; eauto. intro RANGE.
-  assert (SHIFT: Int.unsigned (Int.rolm n (Int.repr 2) (Int.repr (-4))) = Int.unsigned n * 4).
-    replace (Int.repr (-4)) with (Int.shl Int.mone (Int.repr 2)).
-    rewrite <- Int.shl_rolm. rewrite Int.shl_mul.
-    unfold Int.mul. apply Int.unsigned_repr. omega.
-    compute. reflexivity.
-    apply Int.mkint_eq. compute. reflexivity.
-  inv AT. simpl in H7. 
-  set (k1 := Pbtbl GPR12 tbl :: transl_code f c).
-  set (rs1 := nextinstr (rs0 # GPR12 <- (Vint (Int.rolm n (Int.repr 2) (Int.repr (-4)))))).
-  generalize (functions_transl _ _ H4); intro FN.
-  generalize (functions_transl_no_overflow _ _ H4); intro NOOV.
-  assert (exec_straight tge (transl_function f)
-            (Prlwinm GPR12 (ireg_of arg) (Int.repr 2) (Int.repr (-4)) :: k1) rs0 m'
-            k1 rs1 m').
-   apply exec_straight_one. 
-   simpl. generalize (ireg_val _ _ _ arg AG H5). rewrite H. intro. inv H8. 
-   reflexivity. reflexivity. 
-  exploit exec_straight_steps_2; eauto. 
-  intros [ofs' [PC1 CT1]].
-  set (rs2 := rs1 # GPR12 <- Vundef # CTR <- Vundef).
-  assert (PC2: rs2 PC = Vptr fb ofs'). rewrite <- PC1. reflexivity.
-  generalize (find_label_goto_label f lbl rs2 m' _ _ _ FIND PC2 H2).
-  intros [rs3 [GOTO [AT3 INV3]]].
-  left; exists (State rs3 m'); split.
-  eapply plus_right'. 
-  eapply exec_straight_steps_1; eauto.
-  econstructor; eauto. 
-  eapply find_instr_tail. unfold k1 in CT1. eauto.
-  unfold exec_instr. rewrite gpr_or_zero_not_zero; auto with ppcgen.  
-  change (rs1 GPR12) with (Vint (Int.rolm n (Int.repr 2) (Int.repr (-4)))).
-  lazy iota beta.   rewrite SHIFT.  rewrite Z_mod_mult. rewrite zeq_true.
-  rewrite Z_div_mult.
-  change label with Mach.label; rewrite H0. exact GOTO. omega. traceEq.
+- (* Mcond true *)
+  exploit eval_condition_lessdef. eapply preg_vals; eauto. eauto. eauto. intros EC.
+  left; eapply exec_straight_steps_goto; eauto.
+  intros. simpl in TR.
+  destruct (transl_cond_correct_1 tge tf cond args _ rs0 m' _ TR) as [rs' [A [B C]]].
+  rewrite EC in B.
+  destruct (snd (crbit_for_cond cond)).
+  (* Pbt, taken *)
+  econstructor; econstructor; econstructor; split. eexact A. 
+  split. eapply agree_exten_temps; eauto with asmgen.
+  simpl. rewrite B. reflexivity. 
+  (* Pbf, taken *)
+  econstructor; econstructor; econstructor; split. eexact A. 
+  split. eapply agree_exten_temps; eauto with asmgen.
+  simpl. rewrite B. reflexivity. 
+
+- (* Mcond false *)
+  exploit eval_condition_lessdef. eapply preg_vals; eauto. eauto. eauto. intros EC.
+  left; eapply exec_straight_steps; eauto. intros. simpl in TR.
+  destruct (transl_cond_correct_1 tge tf cond args _ rs0 m' _ TR) as [rs' [A [B C]]].
+  rewrite EC in B.
+  econstructor; split.
+  eapply exec_straight_trans. eexact A. 
+  destruct (snd (crbit_for_cond cond)).
+  apply exec_straight_one. simpl. rewrite B. reflexivity. auto.
+  apply exec_straight_one. simpl. rewrite B. reflexivity. auto.
+  split. eapply agree_exten_temps; eauto with asmgen.
+  intros; Simpl.
+  simpl. congruence.
+
+- (* Mjumptable *)
+  inv AT. monadInv H5. 
+  exploit functions_transl; eauto. intro FN.
+  generalize (transf_function_no_overflow _ _ H4); intro NOOV.
+  exploit find_label_goto_label. eauto. eauto.
+  instantiate (2 := rs0#GPR12 <- Vundef #CTR <- Vundef). 
+  Simpl. eauto.
+  eauto. 
+  intros [tc' [rs' [A [B C]]]].
+  exploit ireg_val; eauto. rewrite H. intros LD; inv LD.
+  left; econstructor; split.
+  apply plus_one. econstructor; eauto. 
+  eapply find_instr_tail; eauto. 
+  simpl. rewrite <- H8. unfold Mach.label in H0; unfold label; rewrite H0. eexact A.
   econstructor; eauto. 
-  eapply Mach.find_label_incl; eauto.
-  apply agree_undef_temps with rs0; auto.
-  intros. rewrite INV3; auto with ppcgen.
-  unfold rs2. repeat rewrite Pregmap.gso; auto with ppcgen.
-  unfold rs1. rewrite nextinstr_inv; auto with ppcgen. 
-  apply Pregmap.gso; auto with ppcgen.
-Qed.
+  eapply agree_exten_temps; eauto. intros. rewrite C; auto with asmgen. Simpl. 
+  congruence.
 
-Lemma exec_Mreturn_prop:
-  forall (s : list stackframe) (fb stk : block) (soff : int)
-         (c : list Mach.instruction) (ms : Mach.regset) (m : mem) (f: Mach.function) m',
-  Genv.find_funct_ptr ge fb = Some (Internal f) ->
-  load_stack m (Vptr stk soff) Tint f.(fn_link_ofs) = Some (parent_sp s) ->
-  load_stack m (Vptr stk soff) Tint f.(fn_retaddr_ofs) = Some (parent_ra s) ->
-  Mem.free m stk 0 f.(fn_stacksize) = Some m' ->
-  exec_instr_prop (Machsem.State s fb (Vptr stk soff) (Mreturn :: c) ms m) E0
-                  (Returnstate s ms m').
-Proof.
-  intros; red; intros; inv MS.
-  assert (f0 = f) by congruence. subst f0.
-  exploit Mem.free_parallel_extends; eauto.
-  intros [m2' [FREE' EXT']].
-  unfold load_stack in *. simpl in H0; simpl in H1.
-  exploit Mem.load_extends. eexact MEXT. eexact H0.
-  intros [parent' [LOAD1 LD1]].
-  rewrite (lessdef_parent_sp s parent' STACKS LD1) in LOAD1.
-  exploit Mem.load_extends. eexact MEXT. eexact H1.
-  intros [ra' [LOAD2 LD2]].
-  rewrite (lessdef_parent_ra s ra' STACKS LD2) in LOAD2.
-  set (rs2 := nextinstr (rs#GPR0 <- (parent_ra s))).
-  set (rs3 := nextinstr (rs2#LR <- (parent_ra s))).
+- (* Mreturn *)
+  inversion AT; subst. 
+  assert (NOOV: list_length_z tf <= Int.max_unsigned).
+    eapply transf_function_no_overflow; eauto.
+  rewrite (sp_val _ _ _ AG) in *. unfold load_stack in *.
+  exploit Mem.loadv_extends. eauto. eexact H. auto. simpl. intros [parent' [A B]]. 
+  exploit lessdef_parent_sp; eauto. intros. subst parent'. clear B.
+  assert (C: Mem.loadv Mint32 m'0 (Val.add (rs0 GPR1) (Vint (fn_retaddr_ofs f))) = Some ra).
+Opaque Int.repr.
+    erewrite agree_sp; eauto. simpl. rewrite Int.add_zero_l.
+    eapply rsa_contains; eauto.
+  exploit retaddr_stored_at_can_free; eauto. intros [m2' [E F]].
+  assert (M: match_stack ge s m'' m2' ra (Mem.nextblock m'')).
+    apply match_stack_change_bound with stk.
+    eapply match_stack_free_left; eauto.
+    eapply match_stack_free_left; eauto.
+    eapply match_stack_free_right; eauto. omega.
+    apply Z.lt_le_incl. change (Mem.valid_block m'' stk).
+    eapply Mem.valid_block_free_1; eauto. eapply Mem.valid_block_free_1; eauto. 
+    eapply retaddr_stored_at_valid; eauto.
+  monadInv H5.
+  set (rs2 := nextinstr (rs0#GPR0 <- ra)).
+  set (rs3 := nextinstr (rs2#LR <- ra)).
   set (rs4 := nextinstr (rs3#GPR1 <- (parent_sp s))).
-  set (rs5 := rs4#PC <- (parent_ra s)).
-  assert (exec_straight tge (transl_function f)
-            (transl_code f (Mreturn :: c)) rs m'0 
-            (Pblr :: transl_code f c) rs4 m2').
+  set (rs5 := rs4#PC <- ra).
+  assert (exec_straight tge tf
+           (Plwz GPR0 (Cint (fn_retaddr_ofs f)) GPR1
+           :: Pmtlr GPR0
+           :: Pfreeframe (fn_stacksize f) (fn_link_ofs f) :: Pblr :: x) rs0 m'0
+           (Pblr :: x) rs4 m2').
   simpl. apply exec_straight_three with rs2 m'0 rs3 m'0.
-  simpl. unfold load1. rewrite gpr_or_zero_not_zero. unfold const_low.
-  rewrite <- (sp_val _ _ _ AG). simpl. rewrite LOAD2. 
-  reflexivity. discriminate.
-  unfold rs3. reflexivity.
-  simpl. change (rs3 GPR1) with (rs GPR1). rewrite <- (sp_val _ _ _ AG).
-  simpl. rewrite LOAD1. rewrite FREE'. reflexivity.
-  reflexivity. reflexivity. reflexivity.
+  simpl. unfold load1. rewrite gpr_or_zero_not_zero. unfold const_low. rewrite C. auto. congruence.
+  simpl. auto. 
+  simpl. change (rs3 GPR1) with (rs0 GPR1). rewrite A. 
+  rewrite <- (sp_val _ _ _ AG). rewrite E. auto. 
+  auto. auto. auto. 
   left; exists (State rs5 m2'); split.
   (* execution *)
   apply plus_right' with E0 (State rs4 m2') E0.
   eapply exec_straight_exec; eauto.
-  inv AT. econstructor.
-  change (rs4 PC) with (Val.add (Val.add (Val.add (rs PC) Vone) Vone) Vone). 
-  rewrite <- H4. simpl. eauto.
-  apply functions_transl; eauto.
-  generalize (functions_transl_no_overflow _ _ H5); intro NOOV.
-  simpl in H6. eapply find_instr_tail. 
+  econstructor.
+  change (rs4 PC) with (Val.add (Val.add (Val.add (rs0 PC) Vone) Vone) Vone). 
+  rewrite <- H2. simpl. eauto.
+  eapply functions_transl; eauto.
+  eapply find_instr_tail. 
   eapply code_tail_next_int; auto.
   eapply code_tail_next_int; auto.
   eapply code_tail_next_int; eauto.
   reflexivity. traceEq.
   (* match states *)
   econstructor; eauto. 
-  assert (AG3: agree ms (Vptr stk soff) rs3). 
-    unfold rs3, rs2; auto 10 with ppcgen.
-  assert (AG4: agree ms (parent_sp s) rs4).
-    split. reflexivity. apply parent_sp_def; auto. intros. unfold rs4. 
-    rewrite nextinstr_inv. rewrite Pregmap.gso.
-    elim AG3; auto. auto with ppcgen. auto with ppcgen.
-  unfold rs5; auto with ppcgen.
-Qed.
-
-Hypothesis wt_prog: wt_program prog.
-
-Lemma exec_function_internal_prop:
-  forall (s : list stackframe) (fb : block) (ms : Mach.regset)
-         (m : mem) (f : function) (m1 m2 m3 : mem) (stk : block),
-  Genv.find_funct_ptr ge fb = Some (Internal f) ->
-  Mem.alloc m 0 (fn_stacksize f) = (m1, stk) ->
-  let sp := Vptr stk Int.zero in
-  store_stack m1 sp Tint f.(fn_link_ofs) (parent_sp s) = Some m2 ->
-  store_stack m2 sp Tint f.(fn_retaddr_ofs) (parent_ra s) = Some m3 ->
-  exec_instr_prop (Machsem.Callstate s fb ms m) E0
-                  (Machsem.State s fb sp (fn_code f) (undef_temps ms) m3).
-Proof.
-  intros; red; intros; inv MS.
-  assert (WTF: wt_function f).
-    generalize (Genv.find_funct_ptr_prop wt_fundef _ _ wt_prog H); intro TY.
-    inversion TY; auto.
-  exploit functions_transl; eauto. intro TFIND.
-  generalize (functions_transl_no_overflow _ _ H); intro NOOV.
-  unfold store_stack in *; simpl in *.
-  exploit Mem.alloc_extends; eauto. apply Zle_refl. apply Zle_refl. 
-  intros [m1' [ALLOC' MEXT1]].
-  exploit Mem.store_within_extends. eexact MEXT1. eexact H1. auto.
-  intros [m2' [STORE2 MEXT2]].
-  exploit Mem.store_within_extends. eexact MEXT2. eexact H2. auto.
-  intros [m3' [STORE3 MEXT3]].
-  set (rs2 := nextinstr (rs#GPR1 <- sp #GPR0 <- Vundef)).
-  set (rs3 := nextinstr (rs2#GPR0 <- (parent_ra s))).
-  set (rs4 := nextinstr rs3).
+  assert (AG3: agree rs (Vptr stk Int.zero) rs3). 
+    unfold rs3, rs2; auto 10 with asmgen.
+  assert (AG4: agree rs (parent_sp s) rs4).
+    unfold rs4. apply agree_nextinstr. eapply agree_change_sp; eauto. 
+    eapply parent_sp_def; eauto.
+  unfold rs5; auto with asmgen.
+
+- (* internal function *)
+  exploit functions_translated; eauto. intros [tf [A B]]. monadInv B.
+  generalize EQ; intros EQ'. monadInv EQ'. 
+  destruct (zlt Int.max_unsigned (list_length_z x0)); inversion EQ1. clear EQ1.
+  unfold store_stack in *. 
+  exploit Mem.alloc_extends. eauto. eauto. apply Zle_refl. apply Zle_refl. 
+  intros [m1' [C D]].
+  assert (E: Mem.extends m2 m1') by (eapply Mem.free_left_extends; eauto).
+  exploit Mem.storev_extends. eexact E. eexact H1. eauto. eauto. 
+  intros [m2' [F G]].
+  exploit retaddr_stored_at_can_alloc. eexact H. eauto. eauto. eauto. eauto. 
+  auto. auto. auto. auto. eauto. 
+  intros [m3' [P [Q R]]].
   (* Execution of function prologue *)
+  monadInv EQ0.
+  set (rs2 := nextinstr (rs0#GPR1 <- sp #GPR0 <- Vundef)).
+  set (rs3 := nextinstr (rs2#GPR0 <- (rs0#LR))).
+  set (rs4 := nextinstr rs3).
   assert (EXEC_PROLOGUE:
-            exec_straight tge (transl_function f)
-              (transl_function f) rs m'
-              (transl_code f (fn_code f)) rs4 m3').
-  unfold transl_function at 2. 
+            exec_straight tge x
+              x rs0 m'
+              x1 rs4 m3').
+  rewrite <- H5 at 2. 
   apply exec_straight_three with rs2 m2' rs3 m2'.
-  unfold exec_instr. rewrite ALLOC'. fold sp.
-  rewrite <- (sp_val _ _ _ AG). unfold sp; simpl; rewrite STORE2. reflexivity.
-  simpl. change (rs2 LR) with (rs LR). rewrite ATLR. reflexivity.
+  unfold exec_instr. rewrite C. fold sp.
+  rewrite <- (sp_val _ _ _ AG). unfold chunk_of_type in F. rewrite F. auto. 
+  simpl. auto.
   simpl. unfold store1. rewrite gpr_or_zero_not_zero. 
-  unfold const_low. change (rs3 GPR1) with sp. change (rs3 GPR0) with (parent_ra s).
-  simpl. rewrite STORE3. reflexivity. 
-  discriminate. reflexivity. reflexivity. reflexivity.
-  (* Agreement at end of prologue *)
-  assert (AT4: transl_code_at_pc rs4#PC fb f f.(fn_code)).
-    change (rs4 PC) with (Val.add (Val.add (Val.add (rs PC) Vone) Vone) Vone).
-    rewrite ATPC. simpl. constructor. auto.
-    eapply code_tail_next_int; auto.
-    eapply code_tail_next_int; auto.
-    eapply code_tail_next_int; auto.
-    change (Int.unsigned Int.zero) with 0. 
-    unfold transl_function. constructor.
-  assert (AG2: agree ms sp rs2).
-    split. reflexivity. unfold sp. congruence. 
-    intros. unfold rs2. rewrite nextinstr_inv. 
-    repeat (rewrite Pregmap.gso). inv AG; auto.
-    auto with ppcgen. auto with ppcgen. auto with ppcgen.
-  assert (AG4: agree ms sp rs4).
-    unfold rs4, rs3; auto with ppcgen.
+  change (rs3 GPR1) with sp. change (rs3 GPR0) with (rs0 LR). simpl. 
+  rewrite Int.add_zero_l. rewrite P. auto. congruence.
+  auto. auto. auto.
   left; exists (State rs4 m3'); split.
-  (* execution *)
-  eapply exec_straight_steps_1; eauto.
-  change (Int.unsigned Int.zero) with 0. constructor.
-  (* match states *)
-  econstructor; eauto with coqlib. apply agree_undef_temps with rs4; auto.
-Qed.
+  eapply exec_straight_steps_1; eauto. unfold fn_code; omega. constructor. 
+  econstructor; eauto. 
+  assert (STK: stk = Mem.nextblock m) by (eapply Mem.alloc_result; eauto).
+  rewrite <- STK in STACKS. simpl in F. simpl in H1.
+  eapply match_stack_invariant; eauto.
+  intros. eapply Mem.perm_alloc_4; eauto. eapply Mem.perm_free_3; eauto. 
+  eapply Mem.perm_store_2; eauto. unfold block; omega.
+  intros. eapply Mem.perm_store_1; eauto. eapply Mem.perm_store_1; eauto. 
+  eapply Mem.perm_alloc_1; eauto. 
+  intros. erewrite Mem.load_store_other. 2: eauto.
+  erewrite Mem.load_store_other. 2: eauto. 
+  eapply Mem.load_alloc_other; eauto.
+  left; unfold block; omega.
+  left; unfold block; omega.
+  change (rs4 PC) with (Val.add (Val.add (Val.add (rs0 PC) Vone) Vone) Vone). 
+  rewrite ATPC. simpl. constructor; eauto.
+  subst x. unfold fn_code. eapply code_tail_next_int. omega. 
+  eapply code_tail_next_int. omega. 
+  eapply code_tail_next_int. omega. 
+  constructor.
+  unfold rs4, rs3, rs2.
+  apply agree_nextinstr. apply agree_set_other; auto. apply agree_set_other; auto. 
+  apply agree_nextinstr. apply agree_set_other; auto.
+  eapply agree_change_sp; eauto. apply agree_exten_temps with rs0; eauto.
+  unfold sp; congruence.
+  congruence.
 
-Lemma exec_function_external_prop:
-  forall (s : list stackframe) (fb : block) (ms : Mach.regset)
-         (m : mem) (t0 : trace) (ms' : RegEq.t -> val)
-         (ef : external_function) (args : list val) (res : val) (m': mem),
-  Genv.find_funct_ptr ge fb = Some (External ef) ->
-  external_call ef ge args m t0 res m' ->
-  Machsem.extcall_arguments ms m (parent_sp s) (ef_sig ef) args ->
-  ms' = Regmap.set (loc_result (ef_sig ef)) res ms ->
-  exec_instr_prop (Machsem.Callstate s fb ms m)
-               t0 (Machsem.Returnstate s ms' m').
-Proof.
-  intros; red; intros; inv MS.
+- (* external function *)
   exploit functions_translated; eauto.
-  intros [tf [A B]]. simpl in B. inv B. 
+  intros [tf [A B]]. simpl in B. inv B.
   exploit extcall_arguments_match; eauto. 
   intros [args' [C D]].
-  exploit external_call_mem_extends; eauto. 
+  exploit external_call_mem_extends; eauto.
   intros [res' [m2' [P [Q [R S]]]]].
-  left; exists (State (rs#(loc_external_result (ef_sig ef)) <- res' #PC <- (rs LR))
-                m2'); split.
+  left; econstructor; split.
   apply plus_one. eapply exec_step_external; eauto. 
-  eapply external_call_symbols_preserved; eauto.
+  eapply external_call_symbols_preserved; eauto. 
   exact symbols_preserved. exact varinfo_preserved.
   econstructor; eauto.
-  unfold loc_external_result. 
-  apply agree_set_other; auto with ppcgen.
-  apply agree_set_mreg with rs; auto. 
-  rewrite Pregmap.gss; auto. 
-  intros; apply Pregmap.gso; auto.
-Qed.
-
-Lemma exec_return_prop:
-  forall (s : list stackframe) (fb : block) (sp ra : val)
-         (c : Mach.code) (ms : Mach.regset) (m : mem),
-  exec_instr_prop (Machsem.Returnstate (Stackframe fb sp ra c :: s) ms m) E0
-                  (Machsem.State s fb sp c ms m).
-Proof.
-  intros; red; intros; inv MS. inv STACKS. simpl in *.
+  rewrite Pregmap.gss. apply match_stack_change_bound with (Mem.nextblock m). 
+  eapply match_stack_extcall; eauto.
+  intros. eapply external_call_max_perm; eauto.
+  eapply external_call_nextblock; eauto.
+  unfold loc_external_result.
+  eapply agree_set_mreg; eauto. 
+  rewrite Pregmap.gso; auto with asmgen. rewrite Pregmap.gss. auto. 
+  intros; Simpl.
+
+- (* return *)
+  inv STACKS. simpl in *.
   right. split. omega. split. auto. 
-  econstructor; eauto. rewrite ATPC; auto.  
+  econstructor; eauto. congruence.
 Qed.
 
-Theorem transf_instr_correct:
-  forall s1 t s2, Machsem.step ge s1 t s2 ->
-  exec_instr_prop s1 t s2.
-Proof
-  (Machsem.step_ind ge exec_instr_prop
-           exec_Mlabel_prop
-           exec_Mgetstack_prop
-           exec_Msetstack_prop
-           exec_Mgetparam_prop
-           exec_Mop_prop
-           exec_Mload_prop
-           exec_Mstore_prop
-           exec_Mcall_prop
-           exec_Mtailcall_prop
-           exec_Mbuiltin_prop
-           exec_Mannot_prop
-           exec_Mgoto_prop
-           exec_Mcond_true_prop
-           exec_Mcond_false_prop
-           exec_Mjumptable_prop
-           exec_Mreturn_prop
-           exec_function_internal_prop
-           exec_function_external_prop
-           exec_return_prop).
-
 Lemma transf_initial_states:
-  forall st1, Machsem.initial_state prog st1 ->
+  forall st1, Mach.initial_state prog st1 ->
   exists st2, Asm.initial_state tprog st2 /\ match_states st1 st2.
 Proof.
   intros. inversion H. unfold ge0 in *.
+  exploit functions_translated; eauto. intros [tf [A B]]. 
   econstructor; split.
   econstructor.
   eapply Genv.init_mem_transf_partial; eauto.
   replace (symbol_offset (Genv.globalenv tprog) (prog_main tprog) Int.zero)
-     with (Vptr fb Int.zero).
-  econstructor; eauto. constructor.
-  split. auto. simpl. congruence.
-  intros. repeat rewrite Pregmap.gso; auto with ppcgen.
+     with (Vptr b Int.zero).
+  econstructor; eauto.
+  constructor.
   apply Mem.extends_refl.
+  split. auto. intros. rewrite Regmap.gi. auto. 
+  reflexivity. 
+  exact I.
   unfold symbol_offset. 
   rewrite (transform_partial_program_main _ _ TRANSF). 
   rewrite symbols_preserved. unfold ge; rewrite H1. auto.
@@ -1522,21 +1058,22 @@ Qed.
 
 Lemma transf_final_states:
   forall st1 st2 r, 
-  match_states st1 st2 -> Machsem.final_state st1 r -> Asm.final_state st2 r.
+  match_states st1 st2 -> Mach.final_state st1 r -> Asm.final_state st2 r.
 Proof.
-  intros. inv H0. inv H. constructor. auto. 
-  compute in H1.
-  exploit (ireg_val _ _ _ R3 AG). auto. rewrite H1; intro. inv H. auto.
+  intros. inv H0. inv H. inv STACKS. constructor.
+  auto. 
+  compute in H1. 
+  generalize (preg_val _ _ _ R3 AG). rewrite H1. intros LD; inv LD. auto.
 Qed.
 
 Theorem transf_program_correct:
-  forward_simulation (Machsem.semantics prog) (Asm.semantics tprog).
+  forward_simulation (Mach.semantics prog) (Asm.semantics tprog).
 Proof.
   eapply forward_simulation_star with (measure := measure).
   eexact symbols_preserved.
   eexact transf_initial_states.
   eexact transf_final_states.
-  exact transf_instr_correct. 
+  exact step_simulation.
 Qed.
 
 End PRESERVATION.