From 5787da9e4d024dc3a3190bff0fe29385abbcece9 Mon Sep 17 00:00:00 2001
From: David Monniaux <david.monniaux@univ-grenoble-alpes.fr>
Date: Thu, 9 Jan 2020 07:47:27 +0100
Subject: some more proof

---
 backend/ForwardMovesproof.v | 56 ++++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 53 insertions(+), 3 deletions(-)

(limited to 'backend/ForwardMovesproof.v')

diff --git a/backend/ForwardMovesproof.v b/backend/ForwardMovesproof.v
index 3db67ed6..99b546c7 100644
--- a/backend/ForwardMovesproof.v
+++ b/backend/ForwardMovesproof.v
@@ -298,7 +298,25 @@ Proof.
   rewrite subst_args_ok; assumption.
   constructor; auto.
 
-  admit.
+  simpl in *.
+  unfold fmap_sem in *.
+  destruct (forward_map _) as [map |] eqn:MAP in *; trivial.
+  destruct (map # pc) as [mpc |] eqn:MPC in *; try contradiction.
+  apply get_rb_sem_ge with (rb2 := Some (kill dst mpc)).
+  {
+    replace (Some (kill dst mpc)) with (apply_instr' (fn_code f) pc (map # pc)).
+    {
+      eapply DS.fixpoint_solution with (code := fn_code f) (successors := successors_instr); try eassumption.
+      2: apply apply_instr'_bot.
+      simpl. tauto.
+    }
+    unfold apply_instr'.
+    rewrite H.
+    rewrite MPC.
+    reflexivity.
+  }
+  apply kill_ok.
+  assumption.
   
 - (* load notrap2 *)
   econstructor; split.
@@ -308,7 +326,25 @@ Proof.
   rewrite subst_args_ok; assumption.
   constructor; auto.
 
-  admit.
+  simpl in *.
+  unfold fmap_sem in *.
+  destruct (forward_map _) as [map |] eqn:MAP in *; trivial.
+  destruct (map # pc) as [mpc |] eqn:MPC in *; try contradiction.
+  apply get_rb_sem_ge with (rb2 := Some (kill dst mpc)).
+  {
+    replace (Some (kill dst mpc)) with (apply_instr' (fn_code f) pc (map # pc)).
+    {
+      eapply DS.fixpoint_solution with (code := fn_code f) (successors := successors_instr); try eassumption.
+      2: apply apply_instr'_bot.
+      simpl. tauto.
+    }
+    unfold apply_instr'.
+    rewrite H.
+    rewrite MPC.
+    reflexivity.
+  }
+  apply kill_ok.
+  assumption.
   
 - (* store *)
   econstructor; split.
@@ -318,7 +354,21 @@ Proof.
   rewrite subst_args_ok; assumption.
   constructor; auto.
 
-  admit.
+  simpl in *.
+  unfold fmap_sem in *.
+  destruct (forward_map _) as [map |] eqn:MAP in *; trivial.
+  apply get_rb_sem_ge with (rb2 := map # pc); trivial.
+  replace (map # pc) with (apply_instr' (fn_code f) pc (map # pc)).
+  {
+    eapply DS.fixpoint_solution with (code := fn_code f) (successors := successors_instr); try eassumption.
+    2: apply apply_instr'_bot.
+    simpl. tauto.
+  }
+  unfold apply_instr'.
+  unfold get_rb_sem in *.
+  destruct (map # pc) in *; try contradiction.
+  rewrite H.
+  reflexivity.
   
 (* call *)
 - econstructor; split.
-- 
cgit