Finish most of Veriloggenproof

1 files changed, 180 insertions, 6 deletions

diff --git a/src/translation/Veriloggenproof.v b/src/translation/Veriloggenproof.v
index ca4ecab..3052d03 100644
--- a/src/translation/Veriloggenproof.v
+++ b/src/translation/Veriloggenproof.v
@@ -16,9 +16,12 @@
  * along with this program.  If not, see <https://www.gnu.org/licenses/>.
  *)
 
-From compcert Require Import Smallstep Linking.
+From compcert Require Import Smallstep Linking Integers.
 From coqup Require HTL.
-From coqup Require Import Coquplib Veriloggen Verilog.
+From coqup Require Import Coquplib Veriloggen Verilog ValueInt AssocMap.
+Require Import Lia.
+
+Local Open Scope assocmap.
 
 Definition match_prog (prog : HTL.program) (tprog : Verilog.program) :=
   match_program (fun cu f tf => tf = transl_fundef f) eq prog tprog.
@@ -52,6 +55,96 @@ Inductive match_states : HTL.state -> state -> Prop :=
     forall m,
       match_states (HTL.Callstate nil m nil) (Callstate nil (transl_module m) nil).
 
+Lemma Vlit_inj :
+  forall a b, Vlit a = Vlit b -> a = b.
+Proof. inversion 1. trivial. Qed.
+
+Lemma posToValue_inj :
+  forall a b,
+    0 <= Z.pos a <= Int.max_unsigned ->
+    0 <= Z.pos b <= Int.max_unsigned ->
+    posToValue a = posToValue b ->
+    a = b.
+Proof.
+  intros. rewrite <- Pos2Z.id at 1. rewrite <- Pos2Z.id.
+  rewrite <- Int.unsigned_repr at 1; try assumption.
+  symmetry.
+  rewrite <- Int.unsigned_repr at 1; try assumption.
+  unfold posToValue in *. rewrite H1; auto.
+Qed.
+
+Lemma valueToPos_inj :
+  forall a b,
+    0 < Int.unsigned a ->
+    0 < Int.unsigned b ->
+    valueToPos a = valueToPos b ->
+    a = b.
+Proof.
+  intros. unfold valueToPos in *.
+  rewrite <- Int.repr_unsigned at 1.
+  rewrite <- Int.repr_unsigned.
+  apply Pos2Z.inj_iff in H1.
+  rewrite Z2Pos.id in H1; auto.
+  rewrite Z2Pos.id in H1; auto.
+  rewrite H1. auto.
+Qed.
+
+Lemma transl_list_fun_fst :
+  forall p1 p2 a b,
+    0 <= Z.pos p1 <= Int.max_unsigned ->
+    0 <= Z.pos p2 <= Int.max_unsigned ->
+    transl_list_fun (p1, a) = transl_list_fun (p2, b) ->
+    (p1, a) = (p2, b).
+Proof.
+  intros. unfold transl_list_fun in H1. apply pair_equal_spec in H1.
+  destruct H1. rewrite H2. apply Vlit_inj in H1.
+  apply posToValue_inj in H1; try assumption.
+  rewrite H1; auto.
+Qed.
+
+Lemma transl_in :
+  forall l p,
+  0 <= Z.pos p <= Int.max_unsigned ->
+  (forall p0, In p0 (List.map fst l) -> 0 <= Z.pos p0 <= Int.max_unsigned) ->
+  In (Vlit (posToValue p)) (map fst (map transl_list_fun l)) ->
+  In p (map fst l).
+Proof.
+  induction l.
+  - simplify. auto.
+  - intros. destruct a. simplify. destruct (peq p0 p); auto.
+    right. inv H1. apply Vlit_inj in H. apply posToValue_inj in H; auto. contradiction.
+    apply IHl; auto.
+Qed.
+
+Lemma transl_notin :
+  forall l p,
+    0 <= Z.pos p <= Int.max_unsigned ->
+    (forall p0, In p0 (List.map fst l) -> 0 <= Z.pos p0 <= Int.max_unsigned) ->
+    ~ In p (List.map fst l) -> ~ In (Vlit (posToValue p)) (List.map fst (transl_list l)).
+Proof.
+  induction l; auto. intros. destruct a. unfold not in *. intros.
+  simplify.
+  destruct (peq p0 p). apply H1. auto. apply H1.
+  unfold transl_list in *. inv H2. apply Vlit_inj in H. apply posToValue_inj in H.
+  contradiction.
+  apply H0; auto. auto.
+  right. apply transl_in; auto.
+Qed.
+
+Lemma transl_norepet :
+  forall l,
+    (forall p0, In p0 (List.map fst l) -> 0 <= Z.pos p0 <= Int.max_unsigned) ->
+    list_norepet (List.map fst l) -> list_norepet (List.map fst (transl_list l)).
+Proof.
+  induction l.
+  - intros. simpl. apply list_norepet_nil.
+  - destruct a. intros. simpl. apply list_norepet_cons.
+    inv H0. apply transl_notin. apply H. simplify; auto.
+    intros. apply H. destruct (peq p0 p); subst; simplify; auto.
+    assumption. apply IHl. intros. apply H. destruct (peq p0 p); subst; simplify; auto.
+    simplify. inv H0. assumption.
+Qed.
+
 Section CORRECTNESS.
 
   Variable prog: HTL.program.
@@ -59,6 +152,52 @@ Section CORRECTNESS.
 
   Hypothesis TRANSL : match_prog prog tprog.
 
+  Lemma transl_list_correct :
+  forall l v ev f asr asa asrn asan asr' asa' asrn' asan',
+    (forall p0, In p0 (List.map fst l) -> 0 <= Z.pos p0 <= Int.max_unsigned) ->
+    list_norepet (List.map fst l) ->
+    asr!ev = Some v ->
+    (forall p s,
+      In (p, s) l ->
+      v = posToValue p ->
+      stmnt_runp f
+                 {| assoc_blocking := asr; assoc_nonblocking := asrn |}
+                 {| assoc_blocking := asa; assoc_nonblocking := asan |}
+                 s
+                 {| assoc_blocking := asr'; assoc_nonblocking := asrn' |}
+                 {| assoc_blocking := asa'; assoc_nonblocking := asan' |} ->
+      stmnt_runp f
+                 {| assoc_blocking := asr; assoc_nonblocking := asrn |}
+                 {| assoc_blocking := asa; assoc_nonblocking := asan |}
+                 (Vcase (Vvar ev) (transl_list l) (Some Vskip))
+                 {| assoc_blocking := asr'; assoc_nonblocking := asrn' |}
+                 {| assoc_blocking := asa'; assoc_nonblocking := asan' |}).
+  Proof.
+    induction l as [| a l IHl].
+    - contradiction.
+    - intros v ev f asr asa asrn asan asr' asa' asrn' asan' BOUND NOREP ASSOC p s IN EQ SRUN.
+      destruct a as [p' s']. simplify.
+      destruct (peq p p'); subst. eapply stmnt_runp_Vcase_match.
+      constructor. simplify. unfold AssocMap.find_assocmap, AssocMapExt.get_default.
+      rewrite ASSOC. trivial. constructor. auto.
+      inversion IN as [INV | INV]. inversion INV as [INV2]; subst. assumption.
+      inv NOREP. eapply in_map with (f := fst) in INV. contradiction.
+
+      eapply stmnt_runp_Vcase_nomatch. constructor. simplify.
+      unfold AssocMap.find_assocmap, AssocMapExt.get_default. rewrite ASSOC.
+      trivial. constructor. unfold not. intros. apply n. apply posToValue_inj.
+      apply BOUND. right. inv IN. inv H0; contradiction. eapply in_map with (f := fst) in H0. auto.
+      apply BOUND; auto. auto.
+
+      eapply IHl. auto. inv NOREP. auto. eassumption. inv IN. inv H. contradiction. apply H.
+      trivial. assumption.
+  Qed.
+
+  Lemma mis_stepp_decl :
+    forall l asr asa f,
+      mis_stepp f asr asa l asr asa.
+  Admitted.
+
   Let ge : HTL.genv := Globalenvs.Genv.globalenv prog.
   Let tge : genv := Globalenvs.Genv.globalenv tprog.
 
@@ -69,10 +208,45 @@ Section CORRECTNESS.
         match_states S1 R1 ->
         exists R2, Smallstep.plus step tge R1 t R2 /\ match_states S2 R2.
   Proof.
-(*    induction 1; intros R1 MSTATE; inv MSTATE; econstructor; split.
-    - apply Smallstep.plus_one. econstructor. eassumption. trivial.
-      * econstructor. econstructor.*)
-    Admitted.
+    induction 1; intros R1 MSTATE; inv MSTATE.
+    - econstructor; split. apply Smallstep.plus_one. econstructor.
+      assumption. assumption. eassumption. trivial.
+      econstructor. econstructor. eapply stmnt_runp_Vcond_false. econstructor. econstructor.
+      simpl. unfold find_assocmap. unfold AssocMapExt.get_default.
+      rewrite H. trivial.
+
+      econstructor. simpl. auto. auto.
+
+      eapply transl_list_correct.
+      assert (forall p0 : positive, In p0 (map fst (Maps.PTree.elements (HTL.mod_controllogic m)))
+                                    -> 0 <= Z.pos p0 <= Int.max_unsigned) by admit; auto.
+      apply Maps.PTree.elements_keys_norepet. eassumption.
+      2: { apply valueToPos_inj. assert (0 < Int.unsigned ist) by admit; auto.
+      admit. rewrite valueToPos_posToValue.  trivial. admit. }
+      apply Maps.PTree.elements_correct. eassumption. eassumption.
+
+      econstructor. econstructor.
+
+      eapply transl_list_correct.
+      assert (forall p0 : positive, In p0 (map fst (Maps.PTree.elements (HTL.mod_datapath m)))
+                                    -> 0 <= Z.pos p0 <= Int.max_unsigned) by admit; auto.
+      apply Maps.PTree.elements_keys_norepet. eassumption.
+      2: { apply valueToPos_inj. assert (0 < Int.unsigned ist) by admit; auto.
+      admit. rewrite valueToPos_posToValue.  trivial. admit. }
+      apply Maps.PTree.elements_correct. eassumption. eassumption.
+
+      apply mis_stepp_decl. trivial. trivial. simpl. eassumption. auto.
+      constructor; assumption.
+
+    - econstructor; split. apply Smallstep.plus_one. apply step_finish. assumption. eassumption.
+      constructor; assumption.
+    - econstructor; split. apply Smallstep.plus_one. constructor.
+
+      constructor. constructor.
+    - inv H3. econstructor; split. apply Smallstep.plus_one. constructor. trivial.
+
+      apply match_state. assumption.
+  Admitted.
 
   Theorem transf_program_correct:
     forward_simulation (HTL.semantics prog) (Verilog.semantics tprog).