Certificate Checker port is straightforward

coq/CertificateChecker.v

@@ -6,7 +6,7 @@
 **)
 Require Import Coq.Reals.Reals Coq.QArith.Qreals.
 Require Import Daisy.Infra.RealSimps Daisy.Infra.RationalSimps Daisy.Infra.RealRationalProps Daisy.Infra.Ltacs.
-Require Import Daisy.IntervalValidation Daisy.ErrorValidation Daisy.Environments.
+Require Import Daisy.IntervalValidation Daisy.ErrorValidation Daisy.Environments Daisy.Typing.
 
 Require Export Coq.QArith.QArith.
 Require Export Daisy.Infra.ExpressionAbbrevs.
@@ -14,7 +14,7 @@ Require Export Daisy.Infra.ExpressionAbbrevs.
 (** Certificate checking function **)
 Definition CertificateChecker (e:exp Q) (absenv:analysisResult) (P:precond) :=
   if (validIntervalbounds e absenv P NatSet.empty)
-  then (validErrorbound e absenv NatSet.empty)
+  then (validErrorbound e (typeExpression e) absenv NatSet.empty)
   else false.
 
 (**
@@ -23,14 +23,14 @@ Definition CertificateChecker (e:exp Q) (absenv:analysisResult) (P:precond) :=
    the real valued execution respects the precondition.
 **)
 Theorem Certificate_checking_is_sound (e:exp Q) (absenv:analysisResult) P:
-  forall (E1 E2:env) (vR:R) (vF:R) fVars,
+  forall (E1 E2:env) (vR:R) (vF:R) fVars m,
     approxEnv E1 absenv fVars NatSet.empty E2 ->
     (forall v, NatSet.mem v fVars = true ->
-          exists vR, E1 v = Some vR /\
+          exists vR, E1 v = Some (vR, M0) /\
                 (Q2R (fst (P v)) <= vR <= Q2R (snd (P v)))%R) ->
-    NatSet.Subset (Expressions.freeVars e) fVars ->
-    eval_exp 0%R E1 (toRExp e) vR ->
-    eval_exp (Q2R machineEpsilon) E2 (toRExp e) vF ->
+    NatSet.Subset (Expressions.usedVars e) fVars ->
+    eval_exp E1  (toREval (toRExp e)) vR M0 ->
+    eval_exp E2 (toRExp e) vF m ->
     CertificateChecker e absenv P = true ->
     (Rabs (vR - vF) <= Q2R (snd (absenv e)))%R.
 (**
@@ -38,8 +38,7 @@ Theorem Certificate_checking_is_sound (e:exp Q) (absenv:analysisResult) P:
    validator and the error bound validator.
 **)
 Proof.
-  intros E1 E2 vR vF fVars approxE1E2 P_valid fVars_subset eval_real eval_float
-         certificate_valid.
+  intros * approxE1E2 P_valid fVars_subset eval_real eval_float certificate_valid.
   unfold CertificateChecker in certificate_valid.
   rewrite <- andb_lazy_alt in certificate_valid.
   andb_to_prop certificate_valid.
@@ -48,11 +47,13 @@ Proof.
   destruct iv as [ivlo ivhi].
   rewrite absenv_eq; simpl.
   eapply validErrorbound_sound; eauto.
+  - eapply typeExpressionIsSound; eauto.
   - hnf. intros a in_diff.
     rewrite NatSet.diff_spec in in_diff.
     apply fVars_subset.
     destruct in_diff; auto.
-  - intros v v_in_empty.
+  - apply stupid; rewrite expEqBool_refl; auto.
+  - intros e0 v m0 v_in_empty.
     rewrite NatSet.mem_spec in v_in_empty.
     inversion v_in_empty.
 Qed.
@@ -63,15 +64,15 @@ Definition CertificateCheckerCmd (f:cmd Q) (absenv:analysisResult) (P:precond) :
   else false.
 
 Theorem Certificate_checking_cmds_is_sound (f:cmd Q) (absenv:analysisResult) P:
-  forall (E1 E2:env) outVars vR vF fVars,
+  forall (E1 E2:env) outVars vR vF fVars m,
     approxEnv E1 absenv fVars NatSet.empty E2 ->
     (forall v, NatSet.mem v fVars= true ->
-          exists vR, E1 v = Some vR /\
+          exists vR, E1 v = Some (vR, M0) /\
                 (Q2R (fst (P v)) <= vR <= Q2R (snd (P v)))%R) ->
     NatSet.Subset (Commands.freeVars f) fVars ->
     ssaPrg f fVars outVars ->
-    bstep (toRCmd f) E1 0 vR ->
-    bstep (toRCmd f) E2 (Q2R machineEpsilon) vF ->
+    bstep (toREvalCmd (toRCmd f)) E1 vR M0 ->
+    bstep (toRCmd f) E2 vF m ->
     CertificateCheckerCmd f absenv P = true ->
     (Rabs (vR - vF) <= Q2R (snd (absenv (getRetExp f))))%R.
 (**
@@ -79,7 +80,7 @@ Theorem Certificate_checking_cmds_is_sound (f:cmd Q) (absenv:analysisResult) P:
    validator and the error bound validator.
 **)
 Proof.
-  intros E1 E2 outVars vR vF fVars approxE1E2 P_valid fVars_subset ssa_f eval_real eval_float
+  intros * approxE1E2 P_valid fVars_subset ssa_f eval_real eval_float
          certificate_valid.
   unfold CertificateCheckerCmd in certificate_valid.
   rewrite <- andb_lazy_alt in certificate_valid.
@@ -101,7 +102,7 @@ Proof.
     rewrite NatSet.diff_spec in in_diff.
     destruct in_diff.
     apply fVars_subset; auto.
-  - intros v v_in_empty.
+  - intros v m1 v_in_empty.
     rewrite NatSet.mem_spec in v_in_empty.
     inversion v_in_empty.
 Qed.
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