redefining type precond

coq/CertificateChecker.v

@@ -61,10 +61,10 @@ Proof.
   assert (dVars_range_valid NatSet.empty E1 absenv).
   { unfold dVars_range_valid.
     intros; set_tac. }
-  assert (affine_dVars_range_valid NatSet.empty E1 absenv 1 (FloverMap.empty _) (fun _ => None))
+  (* assert (affine_dVars_range_valid NatSet.empty E1 absenv 1 (FloverMap.empty _) (fun _ => None))
     as affine_dvars_valid.
   { unfold affine_dVars_range_valid.
-    intros; set_tac. }
+    intros; set_tac. } *)
   assert (NatSet.Subset (usedVars e -- NatSet.empty) (Expressions.usedVars e)).
   { hnf; intros a in_empty.
     set_tac. }
@@ -145,8 +145,8 @@ Proof.
     as freeVars_contained by set_tac.
   assert (validRangesCmd f absenv E1 (toRTMap (toRExpMap Gamma))) as valid_f.
   { eapply (RangeValidatorCmd_sound _ (fVars:=preVars P)); eauto; intuition.
-    unfold affine_dVars_range_valid; intros.
-    set_tac. }
+    (* unfold affine_dVars_range_valid; intros.
+    set_tac. *) }
   pose proof (validRangesCmd_single _ _ _ _ valid_f) as valid_single.
   destruct valid_single as [iv [ err [vR [map_f [eval_real bounded_real_f]]]]].
   destruct iv as [f_lo f_hi].

coq/IEEE_connection.v

@@ -1191,10 +1191,10 @@ Proof.
   assert (dVars_range_valid NatSet.empty E1 A).
   { unfold dVars_range_valid.
     intros; set_tac. }
-  assert (AffineValidation.affine_dVars_range_valid NatSet.empty E1 A 1 (FloverMap.empty _) (fun _ => None))
+  (* assert (AffineValidation.affine_dVars_range_valid NatSet.empty E1 A 1 (FloverMap.empty _) (fun _ => None))
     as affine_dvars_valid.
   { unfold AffineValidation.affine_dVars_range_valid.
-    intros; set_tac. }
+    intros; set_tac. } *)
   assert (NatSet.Subset (usedVars (B2Qexpr e) -- NatSet.empty) (Expressions.usedVars (B2Qexpr e))).
   { hnf; intros a in_empty.
     set_tac. }
@@ -1270,8 +1270,8 @@ Proof.
     - eapply (ssa_equal_set (inVars:=preVars P)); eauto.
       apply NatSetProps.empty_union_2. set_tac.
     - unfold RealRangeArith.dVars_range_valid. intros; set_tac.
-    - unfold AffineValidation.affine_dVars_range_valid; intros.
-      set_tac.
+    (* - unfold AffineValidation.affine_dVars_range_valid; intros.
+      set_tac. *)
     - eapply validSSA_checks_freeVars; eauto. }
   pose proof (validRangesCmd_single _ _ _ _ valid_f) as valid_single.
   destruct valid_single as [iv [ err [vR [map_f [eval_real bounded_real_f]]]]].

coq/Infra/Abbrevs.v

@@ -35,12 +35,6 @@ Arguments mkIntv _ _/.
 Arguments ivlo _ /.
 Arguments ivhi _ /.
 
-(**
-  Later we will argue about program preconditions.
-  Define a precondition to be a function mapping numbers (resp. variables) to intervals.
-**)
-Definition precond :Type := nat -> intv.
-
 (**
   Abbreviation for the type of a variable environment, which should be a partial function
  **)

coq/Infra/ExpressionAbbrevs.v

@@ -170,6 +170,12 @@ Module FloverMapFacts := OrdProperties (FloverMap).
 Definition analysisResult :Type := FloverMap.t (intv * error).
 Definition expressionsAffine: Type := FloverMap.t (affine_form Q).
 
+(**
+  Later we will argue about program preconditions.
+  Define a precondition to be a function mapping numbers (resp. variables) to intervals.
+**)
+Definition precond : Type := FloverMap.t intv.
+
 Definition contained_flover_map V expmap1 expmap2 :=
   forall (e: expr Q) (v: V), FloverMap.find e expmap1 = Some v -> FloverMap.find e expmap2 = Some v.
 

coq/RealRangeArith.v

@@ -13,12 +13,6 @@ Definition dVars_range_valid (dVars:NatSet.t) (E:env) (A:analysisResult) :Prop :
          FloverMap.find (Var Q v) A = Some (iv, err) /\
          (Q2R (fst iv) <= vR <= Q2R (snd iv))%R.
 
-Definition fVars_P_sound (fVars:NatSet.t) (E:env) (P:precond) :Prop :=
-  forall v,
-    NatSet.In v fVars ->
-    exists vR, E v = Some vR /\
-          (Q2R (fst (P v)) <= vR <= Q2R (snd (P v)))%R.
-
 Ltac kill_trivial_exists :=
   match goal with
   | [ |- exists iv err v, Some (?i,?e) = Some (iv, err) /\ _ ] => exists i, e

coq/RealRangeValidator.v

@@ -8,8 +8,10 @@ From Flover
 From Coq Require Export QArith.QArith.
 
 From Flover
-     Require Export IntervalValidation AffineValidation SMTArith SMTValidation RealRangeArith
+     Require Export IntervalValidation SMTArith SMTValidation RealRangeArith
      Infra.ExpressionAbbrevs Commands.
+(* TODO: add AffineValidation again to the export part after it is
+   adjusted to the new precond type *) 
 
 Definition RangeValidator e A P Qmap dVars :=
   if
@@ -23,11 +25,11 @@ Definition RangeValidator e A P Qmap dVars :=
        end.
 *)
 
-Theorem RangeValidator_sound (e : expr Q) (A : analysisResult) (P : FloverMap.t intv)
+Theorem RangeValidator_sound (e : expr Q) (A : analysisResult) (P : precond)
         Qmap dVars (E : env) (Gamma : FloverMap.t mType):
   RangeValidator e A P Qmap dVars = true ->
   dVars_range_valid dVars E A ->
-  affine_dVars_range_valid dVars E A 1 (FloverMap.empty (affine_form Q)) (fun _: nat => None) ->
+  (* affine_dVars_range_valid dVars E A 1 (FloverMap.empty (affine_form Q)) (fun _: nat => None) -> *)
   validTypes e Gamma ->
   eval_precond E P ->
   unsat_queries E Qmap ->
@@ -81,13 +83,13 @@ Definition RangeValidatorCmd e A P Qmap dVars:=
        end.
 *)
 
-Theorem RangeValidatorCmd_sound (f : cmd Q) (A : analysisResult) (P : FloverMap.t intv)
-        (Qmap: FloverMap.t (SMTLogic * SMTLogic)) dVars
+Theorem RangeValidatorCmd_sound (f : cmd Q) (A : analysisResult) (P : precond)
+        (Qmap: usedQueries) dVars
         (E : env) Gamma fVars outVars:
   RangeValidatorCmd f A P Qmap dVars = true ->
   ssa f (NatSet.union fVars dVars) outVars ->
   dVars_range_valid dVars E A ->
-  affine_dVars_range_valid dVars E A 1 (FloverMap.empty (affine_form Q)) (fun _: nat => None) ->
+  (* affine_dVars_range_valid dVars E A 1 (FloverMap.empty (affine_form Q)) (fun _: nat => None) -> *)
   eval_precond E P ->
   NatSet.Subset (preVars P) fVars ->
   NatSet.Subset (freeVars f -- dVars) fVars ->

coq/SMTArith.v

@@ -42,6 +42,8 @@ Inductive SMTLogic :=
 
 Definition FalseQ := NotQ TrueQ.
 
+Definition usedQueries : Type := FloverMap.t (SMTLogic * SMTLogic).
+
 Definition getPrecond q :=
   match q with
   | AndQ p _ => Some p
@@ -252,7 +254,7 @@ Definition unsat_queries E qMap :=
   forall e ql qh, FloverMap.find e qMap = Some (ql, qh) -> ~ eval_smt_logic E ql /\ ~ eval_smt_logic E qh.
 
 (*
-Definition eval_precond E (P: FloverMap.t intv) :=
+Definition eval_precond E (P: precond) :=
   forall x iv, FloverMap.find (Var Q x) P = Some iv
              -> exists vR: R, E x = Some vR /\ Q2R (fst iv) <= vR <= Q2R (snd iv).
 *)
@@ -274,7 +276,7 @@ Proof.
   apply eqb_var in Heq. cbn in *. now subst.
 Qed.
 
-Definition eval_precond E (P: FloverMap.t intv) :=
+Definition eval_precond E (P: precond) :=
   forall x iv, List.In (Var Q x, iv) (FloverMap.elements P) ->
           exists vR: R, E x = Some vR /\ Q2R (fst iv) <= vR <= Q2R (snd iv).
 
@@ -284,7 +286,7 @@ Definition addVar2Set (elt: (expr Q * intv)) s :=
   | _ => s
   end.
 
-Definition preVars (P: FloverMap.t intv) :=
+Definition preVars (P: precond) :=
   List.fold_right addVar2Set NatSet.empty (FloverMap.elements P).
 
 Lemma preVars_sound P x iv :
@@ -329,7 +331,7 @@ Definition addVarConstraint (el: expr Q * intv) q :=
   | _ => q
   end.
 
-Definition precond2SMT (P: FloverMap.t intv) :=
+Definition precond2SMT (P: precond) :=
   List.fold_right addVarConstraint TrueQ (FloverMap.elements P).
 
 (*

coq/SMTValidation.v

@@ -28,7 +28,7 @@ Definition tightenUpperBound (e: expr Q) (hi: Q) (q: SMTLogic) P :=
   | _ => hi
   end.
 
-Definition tightenBounds (e: expr Q) (iv: intv) (qMap: FloverMap.t (SMTLogic * SMTLogic)) P :=
+Definition tightenBounds (e: expr Q) (iv: intv) (qMap: usedQueries) P :=
   match FloverMap.find e qMap with
   | None => iv
   | Some (loQ, hiQ) => (tightenLowerBound e (fst iv) loQ P, tightenUpperBound e (snd iv) hiQ P)
@@ -107,8 +107,8 @@ Lemma Rle_trans2 a b x y z :
   (a <= x)%R -> (z <= b)%R -> (x <= y <= z)%R -> (a <= y <= b)%R.
 Proof. lra. Qed.
 
-Fixpoint validSMTIntervalbounds (e: expr Q) (A: analysisResult) (P: FloverMap.t intv)
-         (Q: FloverMap.t (SMTLogic * SMTLogic)) (validVars: NatSet.t) : bool :=
+Fixpoint validSMTIntervalbounds (e: expr Q) (A: analysisResult) (P: precond)
+         (Q: usedQueries) (validVars: NatSet.t) : bool :=
   match FloverMap.find e A with
   | None => false
   | Some (intv, _) =>
@@ -195,8 +195,8 @@ Fixpoint validSMTIntervalbounds (e: expr Q) (A: analysisResult) (P: FloverMap.t
        end
   end.
 
-Fixpoint validSMTIntervalboundsCmd (f:cmd Q) (A:analysisResult) (P: FloverMap.t intv)
-         (Q: FloverMap.t (SMTLogic * SMTLogic)) (validVars:NatSet.t) : bool :=
+Fixpoint validSMTIntervalboundsCmd (f:cmd Q) (A:analysisResult) (P: precond)
+         (Q: usedQueries) (validVars:NatSet.t) : bool :=
   match f with
   | Let m x e g => false
     (*
@@ -214,8 +214,8 @@ Fixpoint validSMTIntervalboundsCmd (f:cmd Q) (A:analysisResult) (P: FloverMap.t
    validSMTIntervalbounds e A P Q validVars
   end.
 
-Theorem validSMTIntervalbounds_sound (f: expr Q) (A: analysisResult) (P: FloverMap.t intv)
-        (Q: FloverMap.t (SMTLogic * SMTLogic)) fVars dVars (E: env) Gamma :
+Theorem validSMTIntervalbounds_sound (f: expr Q) (A: analysisResult) (P: precond)
+        (Q: usedQueries) fVars dVars (E: env) Gamma :
   unsat_queries E Q ->
   validSMTIntervalbounds f A P Q dVars = true ->
   dVars_range_valid dVars E A ->
@@ -435,7 +435,7 @@ Proof.
 Qed.
 
 Theorem validSMTIntervalboundsCmd_sound (f:cmd Q) (A:analysisResult)
-        (Q: FloverMap.t (SMTLogic * SMTLogic)):
+        (Q: usedQueries):
   forall Gamma E fVars dVars outVars P,
     ssa f (NatSet.union fVars dVars) outVars ->
     dVars_range_valid dVars E A ->