Tentative proofs in ErrorValidation

coq/ErrorValidation.v

@@ -21,7 +21,7 @@ Fixpoint validErrorbound (e:exp Q) (typeMap:exp Q -> option mType) (absenv:analy
     if (Qleb 0 err)
     then
       match e with
-      |Var _ _ v =>
+      |Var _ v =>
        if (NatSet.mem v dVars)
        then true
        else (Qleb (maxAbs intv * (meps m)) err)
@@ -69,7 +69,7 @@ Fixpoint validErrorbound (e:exp Q) (typeMap:exp Q -> option mType) (absenv:analy
 Fixpoint validErrorboundCmd (f:cmd Q) (typeMap:exp Q -> option mType) (env:analysisResult) (dVars:NatSet.t) {struct f} : bool :=
   match f with
   |Let m x e g =>
-   if ((validErrorbound e typeMap env dVars) && (Qeq_bool (snd (env e)) (snd (env (Var Q m x)))))
+   if ((validErrorbound e typeMap env dVars) && (Qeq_bool (snd (env e)) (snd (env (Var Q x)))))
    then validErrorboundCmd g typeMap env (NatSet.add x dVars)
    else false
   |Ret e => validErrorbound e typeMap env dVars
@@ -90,7 +90,7 @@ Proof.
     rewrite <- absenv_e in validErrorbound_e; simpl in *.
   - case_eq (Qleb 0 err); intros; auto; rewrite H in validErrorbound_e.
     + apply Qle_bool_iff,Qle_Rle in H; rewrite Q2R0_is_0 in H; auto.
-    + destruct (tmap (Var Q m n)); inversion validErrorbound_e.
+    + destruct (tmap (Var Q n)); inversion validErrorbound_e.
   - case_eq (Qleb 0 err); intros; auto; rewrite H in validErrorbound_e.
     + apply Qle_bool_iff,Qle_Rle in H; rewrite Q2R0_is_0 in H; auto.
     + destruct (tmap (Const m q)); inversion validErrorbound_e.
@@ -107,22 +107,21 @@ Qed.
 
 
 Lemma validErrorboundCorrectVariable:
-  forall E1 E2 absenv (v:nat) nR nF e nlo nhi P fVars dVars m Gamma,
-    validType Gamma (Var Q m v) m ->
+  forall E1 E2 absenv (v:nat) nR nF e nlo nhi P fVars dVars m Gamma defVars,
+    typeCheck (Var Q v) defVars Gamma = true -> 
     approxEnv E1 absenv fVars dVars E2 ->
-    eval_exp E1 (toREval (toRExp (Var Q m v))) nR M0 ->
-    eval_exp E2 (toRExp (Var Q m v)) nF m ->
-    validIntervalbounds (Var Q m v) absenv P dVars = true ->
-    validErrorbound (Var Q m v) Gamma absenv dVars = true ->
-    (forall v1 m1,
+    eval_exp E1 defVars (toREval (toRExp (Var Q v))) nR M0 ->
+    eval_exp E2 defVars (toRExp (Var Q v)) nF m ->
+    validIntervalbounds (Var Q v) absenv P dVars = true ->
+    validErrorbound (Var Q v) Gamma absenv dVars = true ->
+    (forall v1,
         NatSet.mem v1 dVars = true ->
-        exists r mv1,
-          E1 v1 = Some (r, M0) /\ Gamma (Var Q mv1 v1) = Some m1 /\
-          (Q2R (fst (fst (absenv (Var Q m1 v1)))) <= r <= Q2R (snd (fst (absenv (Var Q m1 v1)))))%R) ->
+        exists r, E1 v1 = Some (r, M0) /\ 
+             (Q2R (fst (fst (absenv (Var Q v1)))) <= r <= Q2R (snd (fst (absenv (Var Q v1)))))%R) ->
     (forall v1, NatSet.mem v1 fVars= true ->
           exists r, E1 v1 = Some (r, M0) /\
                 (Q2R (fst (P v1)) <= r <= Q2R (snd (P v1)))%R) ->
-    absenv (Var Q m v) = ((nlo, nhi), e) ->
+    absenv (Var Q v) = ((nlo, nhi), e) ->
     (Rabs (nR - nF) <= (Q2R e))%R.
 Proof.
   intros * typing_ok approxCEnv eval_real eval_float bounds_valid error_valid dVars_sound P_valid absenv_var.