Prove existential rewriting lemma for evaluations

coq/Expressions.v

@@ -93,6 +93,29 @@ Proof.
   rewrite (IHe2 v3 v5); auto.
 Qed.
 
+Lemma existential_rewriting (b:binop) (e1:exp R) (e2:exp R) (eps:R) (cenv:env_ty) (v:R):
+  (eval_exp eps cenv (Binop b e1 e2) v <->
+   exists v1 v2,
+     eval_exp eps cenv e1 v1 /\
+     eval_exp eps cenv e2 v2 /\
+     eval_exp eps (updEnv 1 v1 (updEnv 2 v2 cenv)) (Binop b (Var R 1) (Var R 2)) v).
+Proof.
+  split.
+  - intros eval_bin.
+    inversion eval_bin; subst.
+    exists v1, v2.
+    repeat split; try auto.
+    constructor; try auto.
+    constructor; auto.
+    constructor; auto.
+  - intros exists_val.
+    destruct exists_val as [v1 [v2 [eval_e1 [eval_e2 eval_e_env]]]].
+    inversion eval_e_env; subst.
+    inversion H4; inversion H5; subst.
+    unfold updEnv in *; simpl in *.
+    constructor; auto.
+Qed.
+
 (**
   Using the parametric expressions, define boolean expressions for conditionals
 **)

coq/Infra/ExpressionAbbrevs.v

+Require Import Coq.QArith.QArith.
+
+Require Export Daisy.Infra.Abbrevs Daisy.Expressions.
+
+Definition analysisResult :Type := exp Q -> intv * error.
\ No newline at end of file

coq/Infra/RealSimps.v

 Require Import Coq.Reals.Reals Coq.micromega.Psatz Coq.Setoids.Setoid.
+Require Import Daisy.Infra.RealConstruction.
 
 (**
   TODO REORDER AND DOCUMENT
@@ -75,4 +76,9 @@ Proof.
   apply Rsqr_eq_asb_1 in Rabs_eq.
   rewrite Rsqr_0 in Rabs_eq.
   apply Rsqr_0_uniq in Rabs_eq; assumption.
-Qed.
+Qed.
\ No newline at end of file
+(**
+  Define the machine epsilon for floating point operations.
+  Current value: 2^(-53)
+ **)
+Definition machineEpsilon:R := realFromNum 1 1 53.
\ No newline at end of file