From 2ee7552c01a9e42754f9e3c99881b9399958cdda Mon Sep 17 00:00:00 2001
From: xleroy <xleroy@fca1b0fc-160b-0410-b1d3-a4f43f01ea2e>
Date: Tue, 16 Aug 2011 11:52:56 +0000
Subject: New backend pass "RRE": optimize (somewhat) redundant reloads
 introduced by the Reload pass.

git-svn-id: https://yquem.inria.fr/compcert/svn/compcert/trunk@1713 fca1b0fc-160b-0410-b1d3-a4f43f01ea2e
---
 backend/Locations.v | 35 +++++++++++++++--------------------
 1 file changed, 15 insertions(+), 20 deletions(-)

(limited to 'backend/Locations.v')

diff --git a/backend/Locations.v b/backend/Locations.v
index 8a0b5ea..0b538fd 100644
--- a/backend/Locations.v
+++ b/backend/Locations.v
@@ -301,22 +301,26 @@ Module Loc.
     | l1 :: ls => diff l l1 /\ notin l ls
     end.
 
+  Lemma notin_iff:
+    forall l ll, notin l ll <-> (forall l', In l' ll -> Loc.diff l l').
+  Proof.
+    induction ll; simpl. 
+    tauto.
+    rewrite IHll. intuition. subst a. auto. 
+  Qed.
+
   Lemma notin_not_in:
     forall l ll, notin l ll -> ~(In l ll).
   Proof.
-    unfold not; induction ll; simpl; intros.
-    auto.
-    elim H; intros. elim H0; intro. 
-    subst l. exact (same_not_diff a H1).
-    auto.
+    intros; red; intros. rewrite notin_iff in H.
+    elim (diff_not_eq l l); auto.
   Qed.
 
   Lemma reg_notin:
     forall r ll, ~(In (R r) ll) -> notin (R r) ll.
   Proof.
-    induction ll; simpl; intros. auto. 
-    split. destruct a; auto. intuition congruence.
-    apply IHll. intuition.
+    intros. rewrite notin_iff; intros. 
+    destruct l'; simpl. congruence. auto.
   Qed.
 
 (** [Loc.disjoint l1 l2] is true if the locations in list [l1]
@@ -347,29 +351,20 @@ Module Loc.
   Lemma in_notin_diff:
     forall l1 l2 ll, notin l1 ll -> In l2 ll -> diff l1 l2.
   Proof.
-    induction ll; simpl; intros.
-    elim H0.
-    elim H0; intro. subst a. tauto. apply IHll; tauto.
+    intros. rewrite notin_iff in H. auto. 
   Qed.
 
   Lemma notin_disjoint:
     forall l1 l2,
     (forall x, In x l1 -> notin x l2) -> disjoint l1 l2.
   Proof.
-    unfold disjoint; induction l1; intros.
-    elim H0. 
-    elim H0; intro.
-    subst x1. eapply in_notin_diff. apply H. auto with coqlib. auto.
-    eapply IHl1; eauto. intros. apply H. auto with coqlib.
+    intros; red; intros. exploit H; eauto. rewrite notin_iff; intros. auto. 
   Qed.
 
   Lemma disjoint_notin:
     forall l1 l2 x, disjoint l1 l2 -> In x l1 -> notin x l2.
   Proof.
-    unfold disjoint; induction l2; simpl; intros.
-    auto.
-    split. apply H. auto. tauto.
-    apply IHl2. intros. apply H. auto. tauto. auto.
+    intros; rewrite notin_iff; intros. red in H. auto. 
   Qed.
 
 (** [Loc.norepet ll] holds if the locations in list [ll] are pairwise
-- 
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