removing conditionals

coq/ExpressionSemantics.v

@@ -90,6 +90,7 @@ Inductive eval_expr (E:env)
     eval_expr E Gamma DeltaMap f1 v1 m1 ->
     eval_expr (updEnv x v1 E) Gamma DeltaMap f2 v m2 ->
     eval_expr E Gamma DeltaMap (Let m1 x f1 f2) v m
+              (*
 | Cond_then m1 m2 m3 m f1 f2 f3 v1 v delta:
     Gamma (Cond f1 f2 f3) = Some m ->
     DeltaMap (Cond f1 f2 f3) m = Some delta ->
@@ -107,6 +108,7 @@ Inductive eval_expr (E:env)
     eval_expr E Gamma DeltaMap f1 0 m1 ->
     eval_expr E Gamma DeltaMap f3 v m3 ->
     eval_expr E Gamma DeltaMap (Cond f1 f2 f3) v m
+*)
 .
 
 Definition DeltaMapR: expr R -> mType -> option R := (fun x m => Some 0).
@@ -252,8 +254,10 @@ Proof.
     destruct m; try congruence; auto.
   - auto.
   - cbn in H3. congruence.
+    (*
   - cbn in H2. congruence.
   - cbn in H2. congruence.
+*)
 Qed.
 
 (**
@@ -317,6 +321,7 @@ Proof.
     destruct m4; try discriminate.
     subst.
     eapply IHf2; eauto.
+    (*
   - inversion ev1; inversion ev2; subst.
     + assert (m2 = REAL) by (eapply toRTMap_eval_REAL; eauto).
       assert (m4 = REAL) by (eapply toRTMap_eval_REAL; eauto).
@@ -334,6 +339,7 @@ Proof.
       assert (m5 = REAL) by (eapply toRTMap_eval_REAL; eauto).
       subst.
       eapply IHf3; eauto.
+*)
 Qed.
 
 (**
@@ -470,6 +476,7 @@ Proof.
         apply beq_nat_true in Heqy. subst. now rewrite Heqx.
       * intros ?. apply no_usedVar. set_tac.
         right. apply beq_nat_false in Heqx. auto.
+        (*
   - eapply Cond_then; eauto;
       [ eapply IHe1 | eapply IHe2];
       eauto;
@@ -480,6 +487,7 @@ Proof.
       eauto;
       hnf; intros; eapply no_usedVar;
       set_tac.
+*)
 Qed.
 
 Lemma eval_expr_det_ignore_bind2 e:
@@ -524,6 +532,7 @@ Proof.
         apply beq_nat_true in Heqy. subst. now rewrite Heqx.
       * intros ?. apply no_usedVar. set_tac.
         right. apply beq_nat_false in Heqx. auto.
+        (*
   - eapply Cond_then; eauto;
       [ eapply IHe1 | eapply IHe2];
       eauto;
@@ -534,6 +543,7 @@ Proof.
       eauto;
       hnf; intros; eapply no_usedVar;
       set_tac.
+*)
 Qed.
 
 Lemma swap_Gamma_eval_expr e E vR m Gamma1 Gamma2 DeltaMap:
@@ -552,8 +562,8 @@ Proof.
         | eapply Fma_dist'
         | eapply Downcast_dist'
         | eapply Let_dist
-        | eapply Cond_then
-        | eapply Cond_else ]; try eauto;
+        (* | eapply Cond_then
+        | eapply Cond_else *) ]; try eauto;
           rewrite <- Gamma_eq; auto.
 Qed.
 
@@ -598,11 +608,13 @@ Proof.
     replace v0 with v3 in * by (eapply IHe1; eauto).
     assert (m2 = m4) by (eapply Gamma_det; eauto); subst.
     eapply IHe2; eauto.
+    (*
   - inversion Heval1; inversion Heval2; subst.
     + eapply IHe2; erewrite Gamma_det; eauto.
     + exfalso. apply H6. eapply IHe1; eauto. erewrite Gamma_det; eauto.
     + exfalso. apply H17. eapply IHe1; eauto. erewrite Gamma_det; eauto.
     + eapply IHe3; erewrite Gamma_det; eauto.
+*)
 Qed.
 
 Lemma real_eval_expr_ignores_delta_map (f:expr R) (E:env) Gamma:
@@ -653,6 +665,7 @@ Proof.
   - inversion ev1; subst.
     destruct m2; try discriminate.
     econstructor; eauto. rewrite Rabs_R0. cbn. lra.
+    (*
   - inversion ev1; subst.
     + assert (m1 = REAL) by (eapply toRTMap_eval_REAL; eauto).
       assert (m2 = REAL) by (eapply toRTMap_eval_REAL; eauto).
@@ -664,4 +677,5 @@ Proof.
       subst.
       eapply Cond_else; eauto.
       cbn. rewrite Rabs_R0. lra.
+*)
 Qed.

coq/Expressions.v

@@ -114,8 +114,8 @@ Inductive expr (V:Type): Type :=
 | Fma: expr V -> expr V -> expr V -> expr V
 | Downcast: mType -> expr V -> expr V
 (* TODO: do we need mType in let-exprs? *)
-| Let: mType -> nat -> expr V -> expr V -> expr V
-| Cond: expr V -> expr V -> expr V -> expr V.
+| Let: mType -> nat -> expr V -> expr V -> expr V.
+(* | Cond: expr V -> expr V -> expr V -> expr V.*)
 
 Fixpoint toRExp (e:expr Q) :=
   match e with
@@ -126,7 +126,7 @@ Fixpoint toRExp (e:expr Q) :=
   | Fma e1 e2 e3 => Fma (toRExp e1) (toRExp e2) (toRExp e3)
   | Downcast m e1 => Downcast m (toRExp e1)
   | Let m v e1 e2 => Let m v (toRExp e1) (toRExp e2)
-  | Cond e1 e2 e3 => Cond (toRExp e1) (toRExp e2) (toRExp e3)
+  (* | Cond e1 e2 e3 => Cond (toRExp e1) (toRExp e2) (toRExp e3)*)
   end.
 
 Fixpoint toREval (e:expr R) :=
@@ -138,7 +138,7 @@ Fixpoint toREval (e:expr R) :=
   | Fma e1 e2 e3 => Fma (toREval e1) (toREval e2) (toREval e3)
   | Downcast _ e1 =>   Downcast REAL (toREval e1)
   | Let _ v e1 e2 => Let REAL v (toREval e1) (toREval e2)
-  | Cond e1 e2 e3 => Cond (toREval e1) (toREval e2) (toREval e3)
+ (* | Cond e1 e2 e3 => Cond (toREval e1) (toREval e2) (toREval e3) *)
   end.
 
 Definition toRMap (d:expr R -> option mType) (e: expr R) :=
@@ -176,7 +176,7 @@ Fixpoint freeVars (V:Type) (e:expr V) :NatSet.t :=
   | Fma e1 e2 e3 => NatSet.union (freeVars e1) (NatSet.union (freeVars e2) (freeVars e3))
   | Downcast _ e1 => freeVars e1
   | Let _ x e1 e2 => freeVars e1 ∪ NatSet.remove x (freeVars e2)
-  | Cond e1 e2 e3 => freeVars e1 ∪ freeVars e2 ∪ freeVars e3
+(*  | Cond e1 e2 e3 => freeVars e1 ∪ freeVars e2 ∪ freeVars e3 *)
   end.
 
 Module Type OrderType := Coq.Structures.Orders.OrderedType.
@@ -310,6 +310,7 @@ Module ExprOrderedType (V_ordered:OrderType) <: OrderType.
     | Let _ _ _ _, Downcast _ _ => Gt
     | Let _ _ _ _, Binop _ _ _ => Gt
     | Let _ _ _ _, Fma _ _ _ => Gt
+    (*
     | Let _ _ _ _, _ => Lt
     | Cond e11 e12 e13, Cond e21 e22 e23 =>
       match exprCompare e11 e21 with
@@ -320,6 +321,7 @@ Module ExprOrderedType (V_ordered:OrderType) <: OrderType.
       | r => r
       end
     | Cond _ _ _, _ => Gt
+     *)
     end.
 
   Lemma exprCompare_refl e: exprCompare e e = Eq.
@@ -332,7 +334,7 @@ Module ExprOrderedType (V_ordered:OrderType) <: OrderType.
     - now rewrite IHe1, IHe2, IHe3.
     - rewrite mTypeEq_refl; auto.
     - now rewrite mTypeEq_refl, Nat.compare_refl, IHe1, IHe2.
-    - now rewrite IHe1, IHe2, IHe3.
+    (* - now rewrite IHe1, IHe2, IHe3. *)
   Qed.
 
   Lemma exprCompare_eq_trans e1 :
@@ -447,11 +449,13 @@ Module ExprOrderedType (V_ordered:OrderType) <: OrderType.
           apply Ndec.Pcompare_Peqb in Heqc0;
             apply N.compare_eq in Heqc1.
             rewrite Pos.eqb_eq in *; subst; congruence.
+            (*
     - destruct (exprCompare e1_1 e2_1) eqn:?;
         destruct (exprCompare e2_1 e3_1) eqn:?;
       destruct (exprCompare e1_2 e2_2) eqn:?;
         destruct (exprCompare e2_2 e3_2) eqn:?;
       try congruence; try erewrite IHe1_1, IHe1_2; eauto.
+*)
   Qed.
 
   Lemma exprCompare_antisym e1:
@@ -568,12 +572,14 @@ Module ExprOrderedType (V_ordered:OrderType) <: OrderType.
           setoid_rewrite Pos.compare_antisym at 2.
           destruct (w ?= w0) eqn:?;
                    destruct (f ?= f0)%N eqn:?; simpl; auto.
+          (*
     - destruct (exprCompare e1_1 e2_1) eqn:first_comp;
       destruct (exprCompare e1_2 e2_2) eqn:second_comp;
       rewrite IHe1_1, IHe1_2 in *; simpl in *;
         rewrite CompOpp_iff in first_comp;
         rewrite CompOpp_iff in second_comp;
         rewrite first_comp, second_comp; simpl; try auto.
+*)
   Qed.
 
   Lemma exprCompare_eq_sym e1 e2:
@@ -708,6 +714,7 @@ Module ExprOrderedType (V_ordered:OrderType) <: OrderType.
           apply Ndec.Pcompare_Peqb in Heqc;
             apply N.compare_eq in Heqc0;
             rewrite Pos.eqb_eq in *; subst; congruence.
+        (*
     - destruct (exprCompare e1_1 e2_1) eqn:?;
         destruct (exprCompare e2_1 e3_1) eqn:?;
         try congruence;
@@ -718,6 +725,7 @@ Module ExprOrderedType (V_ordered:OrderType) <: OrderType.
         try congruence;
         try (erewrite IHe1_2; eauto; fail "");
         try erewrite exprCompare_eq_trans; eauto.
+*)
   Qed.
 
   Lemma exprCompare_eq_lt_is_lt e1:
@@ -834,6 +842,7 @@ Module ExprOrderedType (V_ordered:OrderType) <: OrderType.
           apply Ndec.Pcompare_Peqb in Heqc;
             apply N.compare_eq in Heqc0;
             rewrite Pos.eqb_eq in *; subst; congruence.
+        (*
     - destruct (exprCompare e1_1 e2_1) eqn:?;
         destruct (exprCompare e2_1 e3_1) eqn:?;
         try congruence;
@@ -844,6 +853,7 @@ Module ExprOrderedType (V_ordered:OrderType) <: OrderType.
         try congruence;
         try (erewrite IHe1_2; eauto; fail "");
         try erewrite exprCompare_eq_trans; eauto.
+*)
   Qed.
 
   Definition eq e1 e2 :=
@@ -874,9 +884,11 @@ Module ExprOrderedType (V_ordered:OrderType) <: OrderType.
         rewrite Nat.compare_refl in *.
         destruct (exprCompare x1 x1) eqn:?;
                  destruct (exprCompare x2 x2) eqn:?; congruence.
+        (*
       + destruct (exprCompare x1 x1) eqn:?;
                  destruct (exprCompare x2 x2) eqn:?;
                  destruct (exprCompare x3 x3) eqn:?; congruence.
+*)
     - unfold Transitive.
       intros e1. unfold lt.
       induction e1; intros * lt_e1_e2 lt_e2_e3;
@@ -1179,6 +1191,7 @@ Module ExprOrderedType (V_ordered:OrderType) <: OrderType.
                         eapply Pos.lt_trans; eauto);
                 rewrite G; auto. }
 *)
+        (* case for Cond
       + destruct (exprCompare e1_1 y1) eqn:?; try congruence;
           destruct (exprCompare y1 z1) eqn:?; try congruence;
           try (erewrite exprCompare_eq_lt_is_lt; eauto; fail);
@@ -1192,6 +1205,7 @@ Module ExprOrderedType (V_ordered:OrderType) <: OrderType.
           try (erewrite exprCompare_eq_lt_is_lt; eauto; fail);
           try (erewrite exprCompare_lt_eq_is_lt; eauto; fail);
           try (erewrite IHe1_2; eauto).
+*)
   Qed.
 
   Instance eq_compat: Proper (eq ==> eq ==> iff) eq.
@@ -1328,6 +1342,7 @@ Module ExprOrderedType (V_ordered:OrderType) <: OrderType.
            destruct (w ?= w0) eqn:c1; destruct (f ?= f0)%N eqn:c2; try congruence;
              apply Ndec.Pcompare_Peqb in c1; apply N.compare_eq in c2;
                rewrite Pos.eqb_eq in *; subst; congruence.
+         (*
     - try (split; auto; fail);
         destruct (exprCompare e1_1 e2_1) eqn:?;
                  destruct (exprCompare e3_1 e4_1) eqn:?;
@@ -1354,6 +1369,7 @@ Module ExprOrderedType (V_ordered:OrderType) <: OrderType.
         erewrite exprCompare_eq_trans; eauto;
         rewrite exprCompare_antisym;
         now (try rewrite e3_eq_e4; try rewrite e1_eq_e2).
+*)
   Qed.
 
   Instance lt_compat: Proper (eq ==> eq ==> iff) lt.
@@ -1522,6 +1538,7 @@ Module ExprOrderedType (V_ordered:OrderType) <: OrderType.
            destruct (w ?= w0) eqn:c1; destruct (f ?= f0)%N eqn:c2; try congruence;
              apply Ndec.Pcompare_Peqb in c1; apply N.compare_eq in c2;
                rewrite Pos.eqb_eq in *; subst; congruence.
+         (*
     - pose proof eq_compat as eq_comp. unfold Proper, eq in eq_comp.
       destruct (exprCompare e1_1 e2_1) eqn:?;
                destruct (exprCompare e3_1 e4_1) eqn:?;
@@ -1554,6 +1571,7 @@ Module ExprOrderedType (V_ordered:OrderType) <: OrderType.
       + rewrite exprCompare_eq_sym in e3_eq_e4;
         apply (exprCompare_lt_eq_is_lt _ _ _ H) in e3_eq_e4;
         now apply (exprCompare_eq_lt_is_lt _ _ _ e1_eq_e2).
+*)
   Qed.
 
   Lemma compare_spec : forall x y, CompSpec eq lt x y (exprCompare x y).

coq/Infra/ExpressionAbbrevs.v

@@ -107,11 +107,13 @@ Proof.
   - rewrite e7; auto.
   - rewrite e7; auto.
   - rewrite e7; auto.
+    (*
   - rewrite <- IHc, <- IHc0, e3, e4; auto.
   - rewrite <- IHc, <- IHc0, e3, e4; auto.
   - rewrite <- IHc, <- IHc0, e3, e4; auto.
   - rewrite <- IHc, e3; auto.
   - rewrite <- IHc, e3; auto.
+*)
 Qed.
 
 (* Lemma QcompareExp_toREvalcompare e1 e2: *)
@@ -190,6 +192,7 @@ Proof.
     rewrite N.eqb_compare in e3.
     rewrite Heq, e7 in e3.
     discriminate.
+    (*
   - specialize (IHc e3).
     specialize (IHc0 e4).
     specialize (IHc1 Heq).
@@ -198,6 +201,7 @@ Proof.
     apply NatSet.eq_leibniz in IHc1.
     simpl.
     now rewrite IHc, IHc0, IHc1.
+*)
 Qed.
 
 Lemma freeVars_toREval_toRExp_compat e:
@@ -207,7 +211,7 @@ Proof.
   - now rewrite IHe1, IHe2.
   - now rewrite IHe1, IHe2, IHe3.
   - now rewrite IHe1, IHe2.
-  - now rewrite IHe1, IHe2, IHe3.
+  (* - now rewrite IHe1, IHe2, IHe3. *)
 Qed.
 
 Lemma freeVars_toRExp_compat e:
@@ -217,7 +221,7 @@ Proof.
   - now rewrite IHe1, IHe2.
   - now rewrite IHe1, IHe2, IHe3.
   - now rewrite IHe1, IHe2.
-  - now rewrite IHe1, IHe2, IHe3.
+  (* - now rewrite IHe1, IHe2, IHe3. *)
 Qed.
 
 Module FloverMap := FMapAVL.Make(legacy_OrderedQExps).
@@ -470,7 +474,7 @@ Proof.
     rewrite N.eqb_compare in e3.
     rewrite H, e7 in e3.
     discriminate.
-  - rewrite IHc, IHc0; auto.
+  (* - rewrite IHc, IHc0; auto. *)
 Qed.
 
 Lemma no_cycle_unop e: