[Broken version] Some TODO eliminated

scheduling/RTLpathLivegen.v

@@ -152,29 +152,6 @@ Qed.
 
 Local Hint Resolve exit_list_checker_correct: core.
 
-(* TODO REMOVE (REPLACED) Definition final_inst_checker (pm: path_map) (alive: Regset.t) (i: instruction): option unit :=
-   match i with
-   | Icall sig ros args res pc' =>
-      ASSERT list_mem args alive IN
-      ASSERT reg_sum_mem ros alive IN
-      exit_checker pm (Regset.add res alive) pc' tt
-   | Itailcall sig ros args =>
-      ASSERT list_mem args alive IN
-      ASSERT reg_sum_mem ros alive IN
-      Some tt
-   | Ibuiltin ef args res pc' =>
-      ASSERT list_mem (params_of_builtin_args args) alive IN 
-      exit_checker pm (reg_builtin_res res alive) pc' tt
-   | Ijumptable arg tbl =>
-      ASSERT Regset.mem arg alive IN
-      ASSERT exit_list_checker pm alive tbl IN
-      Some tt
-   | Ireturn optarg =>
-      ASSERT (reg_option_mem optarg) alive IN
-      Some tt
-   | _ => None
-   end.*)
-
 Definition final_inst_checker (pm: path_map) (alive por: Regset.t) (i: instruction): option unit :=
    match i with
    | Icall sig ros args res pc' =>
@@ -208,14 +185,6 @@ Proof.
   try (generalize CHECK; clear CHECK; try (inversion_SOME path); repeat inversion_ASSERT; try_simplify_someHyps).
 Qed.
 
-(* TODO (REPLACED) Definition inst_checker (pm: path_map) (alive: Regset.t) (i: instruction): option unit :=
-   match iinst_checker pm alive i with
-   | Some res =>
-      exit_checker pm (fst res) (snd res) tt
-   | _ => 
-      final_inst_checker pm alive i
-   end.*)
-
 Definition inst_checker (pm: path_map) (alive por: Regset.t) (i: instruction): option unit :=
    match iinst_checker pm alive i with
    | Some res =>
@@ -242,11 +211,6 @@ Proof.
     generalize CHECK2. clear CHECK2. inversion_ASSERT. try_simplify_someHyps.
 Qed.
 
-(* TODO (REPLACED) Definition path_checker (f: RTL.function) pm (pc: node) (path:path_info): option unit :=
-   SOME res <- ipath_checker (path.(psize)) f pm (path.(input_regs)) pc  IN
-   SOME i <- f.(fn_code)!(snd res) IN
-   inst_checker pm (fst res) i. *)
-
 Definition path_checker (f: RTL.function) pm (pc: node) (path:path_info): option unit :=
    SOME res <- ipath_checker (path.(psize)) f pm (path.(input_regs)) pc  IN
    SOME i <- f.(fn_code)!(snd res) IN

scheduling/RTLpathLivegenproof.v

@@ -280,34 +280,22 @@ Proof.
     intuition.
   - (* Iload *)
     inversion_ASSERT; try_simplify_someHyps.
-    destruct t. (* TODO - simplify that proof ? *)
-    + inversion_SOME a0. intros EVAL.
-      erewrite <- eqlive_reg_listmem; eauto.
-      try_simplify_someHyps.
-      inversion_SOME v; try_simplify_someHyps.
-      repeat (econstructor; simpl; eauto).
-      eapply eqlive_reg_update.
-      eapply eqlive_reg_monotonic; eauto.
-      intros r0; rewrite regset_add_spec.
+    destruct t.
+    inversion_SOME a0. intros EVAL.
+    erewrite <- eqlive_reg_listmem; eauto.
+    try_simplify_someHyps.
+    inversion_SOME v; try_simplify_someHyps.
+    repeat (econstructor; simpl; eauto).
+    2:
+      erewrite <- (eqlive_reg_listmem _ _ rs1 rs2); eauto;
+      destruct (eval_addressing _ _ _ _);
+      try destruct (Memory.Mem.loadv _ _ _);
+      try (intros; inv H1; repeat (econstructor; simpl; eauto)).
+    all:
+      eapply eqlive_reg_update;
+      eapply eqlive_reg_monotonic; eauto;
+      intros r0; rewrite regset_add_spec;
       intuition.
-    + erewrite <- (eqlive_reg_listmem _ _ rs1 rs2); eauto.
-      destruct (eval_addressing _ _ _ _).
-      * destruct (Memory.Mem.loadv _ _ _).
-        ** intros. inv H1. repeat (econstructor; simpl; eauto).
-           eapply eqlive_reg_update.
-           eapply eqlive_reg_monotonic; eauto.
-           intros r0; rewrite regset_add_spec.
-           intuition.
-        ** intros. inv H1. repeat (econstructor; simpl; eauto).
-           eapply eqlive_reg_update.
-           eapply eqlive_reg_monotonic; eauto.
-           intros r0; rewrite regset_add_spec.
-           intuition.
-      * intros. inv H1. repeat (econstructor; simpl; eauto).
-        eapply eqlive_reg_update.
-        eapply eqlive_reg_monotonic; eauto.
-        intros r0; rewrite regset_add_spec.
-        intuition.
   - (* Istore *)
     (repeat inversion_ASSERT); try_simplify_someHyps.
     inversion_SOME a0. intros EVAL.
@@ -667,81 +655,6 @@ Proof.
       * eapply eqlive_states_return; eauto.
 Qed.
 
-(* TODO useless?
-Lemma subset_contra: forall por alive inputs,
-  Regset.Subset por alive ->
-  Regset.subset inputs alive = false ->
-  Regset.subset inputs por = true ->
-  False.
-Proof.
-  intros por alive inputs SUB CONTRA H.
-  assert (INV: Regset.Subset inputs alive).
-  { 
-    apply Regset.subset_2 in H.
-    unfold Regset.Subset in *; intros.
-    auto. }
-  apply Regset.subset_1 in INV. congruence.
-Qed.
-
-Lemma add_subset_contra: forall r por alive inputs,
-  Regset.Subset por alive ->
-  Regset.subset inputs (Regset.add r alive) = false ->
-  Regset.subset inputs (Regset.add r por) = true ->
-  False.
-Proof.
-  intros r por alive inputs SUB CONTRA H.
-  assert (INV: Regset.Subset inputs (Regset.add r alive)).
-  { 
-    apply Regset.subset_2 in H.
-    unfold Regset.Subset in *; intros.
-    destruct (Pos.eq_dec r a); subst.
-    * apply Regset.add_1; auto.
-    * specialize H with a.
-      apply Regset.add_2. 
-      apply SUB. apply Regset.add_3 in H; auto. }
-  apply Regset.subset_1 in INV. congruence.
-Qed.
-
-Lemma exit_list_checker_subset_contra: forall por alive f l,
-  Regset.Subset por alive ->
-  exit_list_checker (fn_path f) alive l = false ->
-  exit_list_checker (fn_path f) por l = true ->
-  False.
-Proof.
-  induction l.
-  - simpl in *; intuition.
-  - simpl in *. unfold exit_checker.
-    simplify_SOME path. generalize H2, H3. 
-    repeat inversion_ASSERT.
-    + intuition.
-    + intuition.
-      exploit (subset_contra por alive (input_regs path0)); eauto;
-      intros CONTRA; inv CONTRA.
-Qed.
-
-Lemma final_inst_checker_trans: forall alive por i f,
-  Regset.subset por alive = true ->
-  final_inst_checker (fn_path f) alive por i = Some () ->
-  final_inst_checker (fn_path f) alive alive i = Some ().
-Proof.
-  intros.
-  destruct i; simpl in *; try congruence;
-  generalize H0; clear H0; unfold exit_checker;
-  repeat inversion_ASSERT; simplify_SOME path;
-  repeat inversion_ASSERT; intuition.
-  - exploit (add_subset_contra r por alive (input_regs path0)); eauto;
-    intros CONTRA; inv CONTRA.
-  - destruct b; simpl in *.
-    + exploit (add_subset_contra x por alive (input_regs path0)); eauto;
-      intros CONTRA; inv CONTRA.
-    + exploit (subset_contra por alive (input_regs path0)); eauto;
-      intros CONTRA; inv CONTRA.
-    + exploit (subset_contra por alive (input_regs path0)); eauto;
-      intros CONTRA; inv CONTRA.
-  - exploit (exit_list_checker_subset_contra por alive f l); eauto;
-    intros CONTRA; inv CONTRA.
-Qed.*)
-
 Lemma inst_checker_eqlive (f: function) sp alive por pc i rs1 rs2 m stk1 stk2 t s1:
   list_forall2 eqlive_stackframes stk1 stk2 ->
   eqlive_reg (ext alive) rs1 rs2 -> 

scheduling/RTLpathSchedulerproof.v

@@ -260,21 +260,6 @@ Proof.
     + rewrite <- H. erewrite <- seval_preserved; eauto.
 Qed.
 
-(* TODO: deux lemmes à deplacer dans RTLpathLivegen ou RTLpathLivegenproof ? *)
-Lemma iinst_checker_default_succ f alive i res:
-  iinst_checker (fn_path f) alive i = Some res -> default_succ i = Some (snd res).
-Proof.
-  destruct i; simpl; try_simplify_someHyps.
-  + destruct (list_mem _ _); try_simplify_someHyps.
-  + destruct (list_mem _ _); try_simplify_someHyps.
-  + destruct (Regset.mem _ _); try_simplify_someHyps.
-    destruct (list_mem _ _); try_simplify_someHyps.
-  + destruct (list_mem _ _); try_simplify_someHyps.
-    unfold exit_checker.
-    inversion_SOME path.
-    destruct (Regset.subset _ _); try_simplify_someHyps.
-Qed.
-
 Lemma ipath_checker_default_succ (f: RTLpath.function) path: forall alive pc res,
   ipath_checker path f (fn_path f) alive pc = Some res
   -> nth_default_succ (fn_code f) path pc = Some (snd res).