Add equality on booleans for expressions

coq/Expressions.v

 (**
 Formalization of the base expression language for the daisy framework
  **)
-Require Import Coq.Reals.Reals Coq.micromega.Psatz.
+Require Import Coq.Reals.Reals Coq.micromega.Psatz Coq.QArith.QArith.
 Require Import Daisy.Infra.RealSimps Daisy.Infra.Abbrevs.
 Set Implicit Arguments.
 (**
@@ -9,6 +9,15 @@ Set Implicit Arguments.
   Define them first
 **)
 Inductive binop : Type := Plus | Sub | Mult | Div.
+
+Definition binop_eq_bool (b1:binop) (b2:binop) :=
+  match b1 with
+    Plus => match b2 with Plus => true |_ => false end
+  | Sub => match b2 with Sub => true |_ => false end
+  | Mult => match b2 with Mult => true |_ => false end
+  | Div => match b2 with Div => true |_ => false end
+  end.
+
 (**
   Next define an evaluation function for binary operators on reals.
   Errors are added on the expression evaluation level later.
@@ -33,6 +42,30 @@ Inductive exp (V:Type): Type :=
 | Const: V -> exp V
 | Binop: binop -> exp V -> exp V -> exp V.
 
+
+Fixpoint exp_eq_bool (e1:exp Q) (e2:exp Q) :=
+  match e1 with
+  |Var _ v1 =>
+   match e2 with
+   |Var _ v2 => v1 =? v2
+   | _=> false
+   end
+  |Param _ v1 =>
+   match e2 with
+   |Param _ v2 => v1 =? v2
+   | _=> false
+   end
+  |Const n1 =>
+   match e2 with
+   |Const n2 => Qeq_bool n1 n2
+   | _=> false
+   end
+  |Binop b1 e11 e12 =>
+   match e2 with
+   |Binop b2 e21 e22 => andb (binop_eq_bool b1 b2) (andb (exp_eq_bool e11 e21) (exp_eq_bool e12 e22))
+   |_ => false
+   end
+  end.
 (**
   Define a perturbation function to ease writing of basic definitions
 **)