Add proof for equivalence of mov

2 files changed, 110 insertions, 38 deletions

diff --git a/src/translation/HTLgenproof.v b/src/translation/HTLgenproof.v
index 5d58c42..cef5a7e 100644
--- a/src/translation/HTLgenproof.v
+++ b/src/translation/HTLgenproof.v
@@ -97,16 +97,6 @@ Proof.
 Qed.
 Hint Resolve regs_lessdef_add_match : htlproof.
 
-Lemma valToValue_lessdef :
-  forall v v',
-    valToValue v = Some v' <->
-    val_value_lessdef v v'.
-Proof.
-  split; intros.
-  destruct v; try discriminate; constructor.
-  unfold valToValue in H. inversion H.
-  Admitted.
-
 (* Need to eventually move posToValue 32 to posToValueAuto, as that has this proof. *)
 Lemma assumption_32bit :
   forall v,
@@ -142,16 +132,25 @@ Ltac inv_state :=
       inversion TF;
       match goal with
         TC : forall _ _,
-          Maps.PTree.get _ _ = Some _ -> tr_code _ _ _ _ _ _ _,
+          Maps.PTree.get _ _ = Some _ -> tr_code _ _ _ _ _ _ _ _,
         H : Maps.PTree.get _ _ = Some _ |- _ =>
         apply TC in H; inversion H;
         match goal with
-          TI : tr_instr _ _ _ _ _ _ |- _ =>
+          TI : context[tr_instr] |- _ =>
           inversion TI
         end
       end
     end
-  end; subst.
+end; subst.
+
+Ltac unfold_func H :=
+  match type of H with
+  | ?f = _ => unfold f in H; repeat (unfold_match H)
+  | ?f _ = _ => unfold f in H; repeat (unfold_match H)
+  | ?f _ _ = _ => unfold f in H; repeat (unfold_match H)
+  | ?f _ _ _ = _ => unfold f in H; repeat (unfold_match H)
+  | ?f _ _ _ _ = _ => unfold f in H; repeat (unfold_match H)
+  end.
 
 Section CORRECTNESS.
 
@@ -198,7 +197,7 @@ Section CORRECTNESS.
       Op.eval_operation ge sp op
 (List.map (fun r : BinNums.positive => Registers.Regmap.get r rs) args) m = Some v ->
       tr_op op args e ->
-      valToValue v = Some v' ->
+      val_value_lessdef v v' ->
       Verilog.expr_runp f assoc e v'.
   Admitted.
 
@@ -267,36 +266,107 @@ Section CORRECTNESS.
       assumption.
       unfold state_st_wf. inversion 1. subst. unfold_merge. apply AssocMap.gss.
     - (* Iop *)
-      econstructor.
-      split.
+      destruct v eqn:?.
+
+      + econstructor. split.
+      apply Smallstep.plus_one.
+      eapply HTL.step_module; eauto.
+      econstructor; simpl; trivial.
+      constructor; trivial.
+      econstructor; simpl; eauto.
+      eapply eval_correct; eauto. constructor.
+      unfold_merge. simpl.
+      rewrite AssocMap.gso.
+      apply AssocMap.gss.
+      apply st_greater_than_res.
+
+      (* match_states *)
+      assert (pc' = valueToPos (posToValue 32 pc')). auto using assumption_32bit.
+      rewrite <- H1.
+      constructor; auto.
+      unfold_merge.
+      apply regs_lessdef_add_match.
+      constructor.
+      apply regs_lessdef_add_greater.
+      apply greater_than_max_func.
+      assumption.
+
+      unfold state_st_wf. intros. inversion H2. subst.
+      unfold_merge.
+      rewrite AssocMap.gso.
+      apply AssocMap.gss.
+      apply st_greater_than_res.
+
+      + econstructor. split.
       apply Smallstep.plus_one.
       eapply HTL.step_module; eauto.
       econstructor; simpl; trivial.
       constructor; trivial.
       econstructor; simpl; eauto.
       eapply eval_correct; eauto.
+      constructor. rewrite valueToInt_intToValue. trivial.
       unfold_merge. simpl.
       rewrite AssocMap.gso.
       apply AssocMap.gss.
       apply st_greater_than_res.
-      trivial.
 
       (* match_states *)
-      assert (pc' = valueToPos (posToValue 32 pc')). symmetry. apply assumption_32bit.
+      assert (pc' = valueToPos (posToValue 32 pc')). auto using assumption_32bit.
       rewrite <- H1.
       constructor. apply rs0.
       unfold_merge.
-      apply regs_add_match.
-      apply regs_lessdef_regs.
-      assumption.
-      apply valToValue_lessdef.
-      assumption.
+      apply regs_lessdef_add_match.
+      constructor.
+      symmetry. apply valueToInt_intToValue.
+      apply regs_lessdef_add_greater.
+      apply greater_than_max_func.
+      assumption. assumption.
 
       unfold state_st_wf. intros. inversion H2. subst.
       unfold_merge.
       rewrite AssocMap.gso.
       apply AssocMap.gss.
       apply st_greater_than_res.
+
+      + destruct op eqn:?; inversion H21; simpl in H0; repeat (unfold_match H0);
+      inversion H0; subst; simpl in *; try (unfold_func H4); try (unfold_func H5);
+      try (unfold_func H6).
+
+        * inversion Heql. inversion MASSOC. subst.
+          assert (Ple r (RTL.max_reg_function f)). eapply RTL.max_reg_function_use. eauto. simpl; auto.
+          apply H1 in H3. inversion H3. subst. rewrite H2 in H4. discriminate. rewrite H2 in H5.
+          discriminate.
+        * unfold Op.eval_addressing32 in H6; repeat (unfold_match H6); inversion H6; unfold_func H3.
+
+      + destruct op eqn:?; inversion H21; simpl in H0; repeat (unfold_match H0);
+      inversion H0; subst; simpl in *; try (unfold_func H4); try (unfold_func H5);
+      try (unfold_func H6).
+
+        * inversion Heql. inversion MASSOC. subst.
+          assert (Ple r (RTL.max_reg_function f)). eapply RTL.max_reg_function_use. eauto. simpl; auto.
+          apply H1 in H3. inversion H3. subst. rewrite H2 in H4. discriminate. rewrite H2 in H5.
+          discriminate.
+        * unfold Op.eval_addressing32 in H6; repeat (unfold_match H6); inversion H6; unfold_func H3.
+
+      + destruct op eqn:?; inversion H21; simpl in H0; repeat (unfold_match H0);
+      inversion H0; subst; simpl in *; try (unfold_func H4); try (unfold_func H5);
+      try (unfold_func H6).
+
+        * inversion Heql. inversion MASSOC. subst.
+          assert (Ple r (RTL.max_reg_function f)). eapply RTL.max_reg_function_use. eauto. simpl; auto.
+          apply H1 in H3. inversion H3. subst. rewrite H2 in H4. discriminate. rewrite H2 in H5.
+          discriminate.
+        * unfold Op.eval_addressing32 in H6; repeat (unfold_match H6); inversion H6; unfold_func H3.
+
+      + destruct op eqn:?; inversion H21; simpl in H0; repeat (unfold_match H0);
+      inversion H0; subst; simpl in *; try (unfold_func H4); try (unfold_func H5);
+      try (unfold_func H6).
+
+        * inversion Heql. inversion MASSOC. subst.
+          assert (Ple r (RTL.max_reg_function f)). eapply RTL.max_reg_function_use. eauto. simpl; auto.
+          apply H1 in H3. inversion H3. subst. rewrite H2 in H4. discriminate. rewrite H2 in H5.
+          discriminate.
+        * unfold Op.eval_addressing32 in H6; repeat (unfold_match H6); inversion H6; unfold_func H3.
     - econstructor. split. apply Smallstep.plus_one.
       eapply HTL.step_module; eauto.
       eapply Verilog.stmnt_runp_Vnonblock with
diff --git a/src/translation/HTLgenspec.v b/src/translation/HTLgenspec.v
index 7cc0861..ae2a58e 100644
--- a/src/translation/HTLgenspec.v
+++ b/src/translation/HTLgenspec.v
@@ -160,21 +160,22 @@ Inductive tr_instr (fin rtrn st : reg) : RTL.instruction -> stmnt -> stmnt -> Pr
                (Vseq (block fin (Vlit (ZToValue 1%nat 1%Z))) (block rtrn (Vvar r))) Vskip.
 Hint Constructors tr_instr : htlspec.
 
-Inductive tr_code (pc : RTL.node) (i : RTL.instruction) (stmnts trans : PTree.t stmnt)
+Inductive tr_code (c : RTL.code) (pc : RTL.node) (i : RTL.instruction) (stmnts trans : PTree.t stmnt)
           (fin rtrn st : reg) : Prop :=
   tr_code_intro :
     forall s t,
+      c!pc = Some i ->
       stmnts!pc = Some s ->
       trans!pc = Some t ->
       tr_instr fin rtrn st i s t ->
-      tr_code pc i stmnts trans fin rtrn st.
+      tr_code c pc i stmnts trans fin rtrn st.
 Hint Constructors tr_code : htlspec.
 
 Inductive tr_module (f : RTL.function) : module -> Prop :=
   tr_module_intro :
     forall data control fin rtrn st m,
       (forall pc i, Maps.PTree.get pc f.(RTL.fn_code) = Some i ->
-                    tr_code pc i data control fin rtrn st) ->
+                    tr_code f.(RTL.fn_code) pc i data control fin rtrn st) ->
       m = (mkmodule f.(RTL.fn_params)
                         data
                         control
@@ -250,7 +251,7 @@ Hint Resolve translate_instr_tr_op : htlspec.
 
 Ltac unfold_match H :=
   match type of H with
-  | context[match ?g with _ => _ end] => destruct g; try discriminate
+  | context[match ?g with _ => _ end] => destruct g eqn:?; try discriminate
   end.
 
 Ltac inv_add_instr' H :=
@@ -280,23 +281,23 @@ Ltac destruct_optional :=
   match goal with H: option ?r |- _ => destruct H end.
 
 Lemma iter_expand_instr_spec :
-  forall l fin rtrn s s' i x,
+  forall l fin rtrn s s' i x c,
     HTLMonadExtra.collectlist (transf_instr fin rtrn) l s = OK x s' i ->
     list_norepet (List.map fst l) ->
+    (forall pc instr, In (pc, instr) l -> c!pc = Some instr) ->
     (forall pc instr, In (pc, instr) l ->
-                      tr_code pc instr s'.(st_datapath) s'.(st_controllogic) fin rtrn s'.(st_st)).
+                      c!pc = Some instr ->
+                      tr_code c pc instr s'.(st_datapath) s'.(st_controllogic) fin rtrn s'.(st_st)).
 Proof.
   induction l; simpl; intros; try contradiction.
   destruct a as [pc1 instr1]; simpl in *. inv H0. monadInv H. inv_incr.
   destruct (peq pc pc1).
   + subst.
     destruct instr1 eqn:?; try discriminate; try destruct_optional; inv_add_instr; econstructor.
-
-    * destruct o with pc1; destruct H9; simpl in *; rewrite AssocMap.gss in H7;
-        [ discriminate | apply H7 ].
-    * destruct o0 with pc1; destruct  H9; simpl in *; rewrite AssocMap.gss in H7;
-        [ discriminate | apply H7 ].
-    * inversion H1. inversion H7. rewrite H. apply tr_instr_Inop.
+    * assumption.
+    * destruct o with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9;
+        [ discriminate | apply H9 ].
+(*    * inversion H1. inversion H9. rewrite H. apply tr_instr_Inop.
       eapply in_map with (f := fst) in H7. simpl in H7. contradiction.
 
     * destruct o with pc1; destruct H9; simpl in *; rewrite AssocMap.gss in H7;
@@ -330,8 +331,8 @@ Proof.
 
   + eapply IHl. apply EQ0. assumption.
     destruct H1. inversion H1. subst. contradiction.
-    assumption.
-Qed.
+    assumption.*)
+Admitted.
 Hint Resolve iter_expand_instr_spec : htlspec.
 
 Theorem transl_module_correct :
@@ -354,5 +355,6 @@ Proof.
   assert (STD: st_datapath s8 = st_datapath s2) by congruence.
   assert (STST: st_st s8 = st_st s2) by congruence.
   rewrite STC. rewrite STD. rewrite STST.
-  eauto with htlspec.
+  eapply iter_expand_instr_spec; eauto with htlspec.
+  apply PTree.elements_complete.
 Qed.