From a8c744000247af207b489d3cdd4e3d3cf60f72e1 Mon Sep 17 00:00:00 2001
From: blazy <blazy@fca1b0fc-160b-0410-b1d3-a4f43f01ea2e>
Date: Fri, 8 Jan 2010 07:53:02 +0000
Subject: ajout branche allocation de registres

git-svn-id: https://yquem.inria.fr/compcert/svn/compcert/trunk@1220 fca1b0fc-160b-0410-b1d3-a4f43f01ea2e
---
 backend/OrderedOption.v | 96 +++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 96 insertions(+)
 create mode 100755 backend/OrderedOption.v

(limited to 'backend/OrderedOption.v')

diff --git a/backend/OrderedOption.v b/backend/OrderedOption.v
new file mode 100755
index 00000000..b2cebe2b
--- /dev/null
+++ b/backend/OrderedOption.v
@@ -0,0 +1,96 @@
+Require Import FSets.
+
+(* Definition of options types as ordered types,
+    in order to define weights *)
+
+Module OrderedOpt (O : OrderedType) <: OrderedType.
+
+Definition t := option O.t.
+
+Inductive eq_ : t -> t -> Prop :=
+|None_eq : eq_ None None
+|Some_eq : forall x y, O.eq x y -> eq_ (Some x) (Some y).
+
+Definition eq := eq_.
+
+Inductive lt_ : t -> t -> Prop := 
+|None_lt : forall o : O.t, lt_ None (Some o)
+|Some_lt : forall o o', O.lt o o' -> lt_ (Some o) (Some o').
+
+Definition lt := lt_.
+
+Lemma eq_refl : forall x : t, eq x x.
+
+Proof.
+unfold eq;intro x;destruct x;constructor;apply O.eq_refl.
+Qed.
+
+Lemma eq_sym : forall x y : t, eq x y -> eq y x.
+
+Proof.
+unfold eq;intros x y H;destruct x;destruct y.
+constructor;inversion H;apply O.eq_sym;assumption.
+inversion H.
+inversion H.
+assumption.
+Qed.
+
+Lemma eq_trans : forall x y z, eq x y -> eq y z -> eq x z.
+
+Proof.
+unfold eq;intros x y z H H0.
+inversion H;inversion H0.
+constructor.
+rewrite <-H2 in H4;inversion H4.
+rewrite <-H3 in H4;inversion H4.
+rewrite <-H3 in H5;inversion H5;subst.
+constructor;apply (O.eq_trans H1 H4).
+Qed.
+
+Lemma lt_trans : forall x y z, lt x y -> lt y z -> lt x z.
+
+Proof.
+unfold lt;intros x y z H H0.
+inversion H;inversion H0;constructor.
+rewrite <-H3 in H4;inversion H4.
+rewrite <-H3 in H5;inversion H5.
+subst.
+apply (O.lt_trans H1 H4).
+Qed.
+
+Lemma lt_not_eq : forall x y, lt x y -> ~eq x y.
+
+Proof.
+intros x y H.
+unfold eq;intro Heq.
+inversion H;inversion Heq.
+rewrite <-H3 in H1;inversion H1.
+rewrite <-H0 in H3;inversion H3.
+rewrite <-H1 in H3;inversion H3.
+subst;inversion H4;inversion H5;subst.
+elim (O.lt_not_eq H0 H3).
+Qed.
+
+Lemma compare : forall x y : t, Compare lt eq x y.
+
+Proof.
+intros x y.
+destruct x;destruct y.
+destruct (O.compare t0 t1);
+[apply LT;unfold lt|apply EQ;unfold eq|apply GT;unfold lt];constructor;assumption.
+apply GT;unfold lt;constructor.
+apply LT;unfold lt;constructor.
+apply EQ;unfold eq;constructor.
+Qed.
+
+Lemma eq_dec : forall x y, {eq x y}+{~eq x y}.
+
+Proof.
+intros x y.
+destruct (compare x y).
+right. apply lt_not_eq. assumption.
+left. assumption.
+right. intro H. generalize (eq_sym _ _ H). intro H0. elim (lt_not_eq _ _ l H0).
+Qed.
+
+End OrderedOpt.
\ No newline at end of file
-- 
cgit