Finish IEE validator soundness in Coq

coq/ErrorValidation.v

@@ -2256,13 +2256,14 @@ Proof.
     + rename R into valid_rec.
       rewrite (typingSoundnessExp _ _  L0 eval_float_e) in *;
         simpl in *.
+      destruct (Gamma (Var Q n)) eqn:?; try congruence.
       match goal with
       | [ H: _ && _ = true |- _] => andb_to_prop H
       end.
       type_conv.
       destruct (IHf absenv (updEnv n v E1) (updEnv n vF E2) outVars fVars
                     (NatSet.add n dVars) vR elo ehi err P Gamma
-                    (updDefVars n m defVars))
+                    (updDefVars n m0 defVars))
         as [vF_res [m_res step_res]];
         eauto.
       { eapply ssa_equal_set; eauto.
@@ -2381,13 +2382,14 @@ Proof.
     rename R into valid_rec.
     rewrite (typingSoundnessExp _ _  L0 eval_float_e) in *;
       simpl in *.
+    destruct (Gamma (Var Q n)); try congruence.
     match goal with
     | [ H: _ && _ = true |- _] => andb_to_prop H
     end.
     type_conv.
     apply (IHf absenv (updEnv n v E1) (updEnv n v0 E2) outVars fVars
                (NatSet.add n dVars) vR vF mF elo ehi err P Gamma
-               (updDefVars n m defVars));
+               (updDefVars n m0 defVars));
       eauto.
     + eapply approxUpdBound; try auto.
       simpl in *.

coq/IEEE_connection.v

-Require Import Coq.Reals.Reals Coq.QArith.QArith Coq.micromega.Psatz
+Require Import Coq.Reals.Reals Coq.QArith.QArith Coq.QArith.Qabs Coq.micromega.Psatz
         Coq.QArith.Qreals.
 Require Import Daisy.Expressions Daisy.Infra.RationalSimps
         Daisy.Infra.RealRationalProps.

coq/Typing.v

@@ -101,9 +101,10 @@ Fixpoint typeCheckCmd (c:cmd Q) (Gamma:nat -> option mType) (tMap:exp Q -> optio
   match c with
   | Let m x e g => if typeCheck e Gamma tMap
                   then
-                    match tMap e with
-                    | Some me =>  mTypeEq me m && typeCheckCmd g (updDefVars x me Gamma) tMap
-                    | _ => false
+                    match tMap e, tMap (Var Q x) with
+                    | Some me, Some mx =>  mTypeEq me m && mTypeEq m mx
+                                          && typeCheckCmd g (updDefVars x me Gamma) tMap
+                    | _, _ => false
                     end
                   else
                     false
@@ -260,6 +261,7 @@ Proof.
     specialize (IHc (updDefVars n m0 Gamma) (updEnv n v0 E)).
     simpl.
     rewrite e_type_m0 in R.
+    destruct (expTypes (Var Q n)) eqn:?; try congruence.
     andb_to_prop R.
     apply IHc; auto.
   - simpl in *.

hol4/TypingScript.sml

@@ -48,7 +48,7 @@ val typeCmd_def = Define `
 val typeMapCmd_def = Define `
   typeMapCmd (Gamma: num -> mType option) (f: real cmd) (f': real exp) : mType option =
     case f of
-      | Let m n e c => if f' = (Var n) then
+      | Let m n e c => if f' = (Var n) then (*FIXME: This may fail because n not in Gamma... *)
                            (case Gamma n of
                               | SOME m' => if isMorePrecise m m' then SOME m else NONE
                               | NONE => NONE)