Define type erasure for Q exps in IV validation file, needed to obtain soundness properties

coq/IntervalValidation.v

@@ -78,17 +78,26 @@ Fixpoint validIntervalboundsCmd (f:cmd Q) (absenv:analysisResult) (P:precond) (v
    validIntervalbounds e absenv P validVars
   end.
 
+Fixpoint erasure (e:exp Q) :exp Q :=
+  match e with
+  |Var _ m x => Var Q M0 x
+  |Unop u e => Unop u (erasure e)
+  |Binop b e1 e2 => Binop b (erasure e1) (erasure e2)
+  |Downcast _ e => Downcast M0 (erasure e)
+  |_ => e
+  end.
+
 Theorem ivbounds_approximatesPrecond_sound f absenv P V:
-  validIntervalbounds f absenv P V = true ->
+  validIntervalbounds (erasure f) absenv P V = true ->
   forall v, NatSet.In v (NatSet.diff (Expressions.usedVars f) V) ->
-       Is_true(isSupersetIntv (P v) (fst (absenv (Var Q v)))).
+       Is_true(isSupersetIntv (P v) (fst (absenv (Var Q M0 v)))).
 Proof.
   induction f; unfold validIntervalbounds.
-  - intros approx_true v v_in_fV; simpl in *.
+  - simpl. intros approx_true v v_in_fV; simpl in *.
     rewrite NatSet.diff_spec in v_in_fV.
     rewrite NatSet.singleton_spec in v_in_fV;
       destruct v_in_fV; subst.
-    destruct (absenv (Var Q n)); simpl in *.
+    destruct (absenv (Var Q M0 n)); simpl in *.
     case_eq (NatSet.mem n V); intros case_mem;
       rewrite case_mem in approx_true; simpl in *.
     + rewrite NatSet.mem_spec in case_mem.
@@ -101,7 +110,8 @@ Proof.
   - intros approx_unary_true v v_in_fV.
     unfold usedVars in v_in_fV.
     apply Is_true_eq_left in approx_unary_true.
-    destruct (absenv (Unop u f)); destruct (absenv f); simpl in *.
+    simpl in *.
+    destruct (absenv (Unop u (erasure f))); destruct (absenv (erasure f)); simpl in *.
     apply andb_prop_elim in approx_unary_true.
     destruct approx_unary_true.
     apply IHf; try auto.
@@ -112,7 +122,9 @@ Proof.
     destruct v_in_fV as [ v_in_fV v_not_in_V].
     rewrite NatSet.union_spec in v_in_fV.
     apply Is_true_eq_left in approx_bin_true.
-    destruct (absenv (Binop b f1 f2)); destruct (absenv f1); destruct (absenv f2); simpl in *.
+    simpl in *.
+    destruct (absenv (Binop b (erasure f1) (erasure f2))); destruct (absenv (erasure f1));
+      destruct (absenv (erasure f2)); simpl in *.
     apply andb_prop_elim in approx_bin_true.
     destruct approx_bin_true.
     apply andb_prop_elim in H.
@@ -124,7 +136,8 @@ Proof.
     + apply IHf2; auto.
       apply Is_true_eq_true; auto.
       rewrite NatSet.diff_spec; split; auto.
-Qed.
+  - admit.
+Admitted.
 
 Corollary Q2R_max4 a b c d:
   Q2R (IntervalArithQ.max4 a b c d) = max4 (Q2R a) (Q2R b) (Q2R c) (Q2R d).