(*exists e',*) alloc_variablesT g e mm l e' mm' T).  Section EXPR_T. (** Extends Clight.eval_expr etc with event traces. *)
Variable e: env.
Variable le: temp_env.
Variable m: mem.
Inductive eval_exprT: expr -> val -> list mem_event-> Prop :=
| evalT_Econst_int:   forall i ty,
eval_exprT (Econst_int i ty) (Vint i) nil
| evalT_Econst_float:   forall f ty,
eval_exprT (Econst_float f ty) (Vfloat f) nil
| evalT_Econst_single:   forall f ty,
eval_exprT (Econst_single f ty) (Vsingle f) nil
| evalT_Econst_long:   forall i ty,
eval_exprT (Econst_long i ty) (Vlong i) nil
| evalT_Etempvar:  forall id ty v,
le!id = Some v ->
eval_exprT (Etempvar id ty) v nil
| evalT_Eaddrof: forall a ty loc ofs T,
eval_lvalueT a loc ofs T ->
eval_exprT (Eaddrof a ty) (Vptr loc ofs) T
| evalT_Eunop:  forall op a ty v1 v T,
eval_exprT a v1 T ->
sem_unary_operation op v1 (typeof a) m = Some v ->
(*unops at most check weak_valid_ptr, so don't create a trace event*)
eval_exprT (Eunop op a ty) v T
| evalT_Ebinop: forall op a1 a2 ty v1 v2 v T1 T2,
eval_exprT a1 v1 T1 ->
eval_exprT a2 v2 T2 ->
sem_binary_operation g op v1 (typeof a1) v2 (typeof a2) m = Some v ->
(*binops at most check weak_valid_ptr or cast, so don't create a trace event*)
eval_exprT (Ebinop op a1 a2 ty) v (T1++T2)
| evalT_Ecast:   forall a ty v1 v T,
eval_exprT a v1 T ->
sem_cast v1 (typeof a) ty m = Some v ->
eval_exprT (Ecast a ty) v T
| evalT_Esizeof: forall ty1 ty,
eval_exprT (Esizeof ty1 ty) (Vptrofs (Ptrofs.repr (@sizeof g ty1))) nil
| evalT_Ealignof: forall ty1 ty,
eval_exprT (Ealignof ty1 ty) (Vptrofs (Ptrofs.repr (@alignof g ty1))) nil
| evalT_Elvalue: forall a loc ofs v T1 T2 T,
eval_lvalueT a loc ofs T1 ->
deref_locT (typeof a) m loc ofs v T2 -> T=(T1 ++ T2) ->
eval_exprT a v T
with eval_lvalueT: expr -> block -> ptrofs -> list mem_event-> Prop :=
| evalT_Evar_local:   forall id l ty,
e!id = Some(l, ty) ->
eval_lvalueT (Evar id ty) l Ptrofs.zero nil
| evalT_Evar_global: forall id l ty,
e!id = None ->
Genv.find_symbol g id = Some l ->
eval_lvalueT (Evar id ty) l Ptrofs.zero nil
| evalT_Ederef: forall a ty l ofs T,
eval_exprT a (Vptr l ofs) T ->
eval_lvalueT (Ederef a ty) l ofs T
| evalT_Efield_struct:   forall a i ty l ofs id co att delta T,
eval_exprT a (Vptr l ofs) T ->
typeof a = Tstruct id att ->
g.(genv_cenv)!id = Some co ->
field_offset g i (co_members co) = Errors.OK delta ->
eval_lvalueT (Efield a i ty) l (Ptrofs.add ofs (Ptrofs.repr delta)) T
| evalT_Efield_union:   forall a i ty l ofs id co att T,
eval_exprT a (Vptr l ofs) T ->
typeof a = Tunion id att ->
g.(genv_cenv)!id = Some co ->
eval_lvalueT (Efield a i ty) l ofs T.
Scheme eval_exprT_ind2 := Minimality for eval_exprT Sort Prop
with eval_lvalueT_ind2 := Minimality for eval_lvalueT Sort Prop.
Combined Scheme eval_exprT_lvalue_ind from eval_exprT_ind2, eval_lvalueT_ind2.
Inductive eval_exprTlist: list expr -> typelist -> list val -> list mem_event-> Prop :=
| eval_ETnil:
eval_exprTlist nil Tnil nil nil
| eval_ETcons:   forall a bl ty tyl v1 v2 vl T1 T2,
eval_exprT a v1 T1 ->
sem_cast v1 (typeof a) ty m = Some v2 ->
eval_exprTlist bl tyl vl T2 ->
eval_exprTlist (a :: bl) (Tcons ty tyl) (v2 :: vl) (T1++T2).

(* Specifications: *)
Lemma eval_exprT_ax1: forall a v T, eval_exprT a v T -> eval_expr g e le m a v
with eval_lvalueT_ax1: forall a b z T, eval_lvalueT a b z T -> eval_lvalue g e le m a b z.
Lemma eval_exprT_ax2: forall a v, eval_expr g e le m a v -> exists T, eval_exprT a v T
with eval_lvalueT_ax2: forall a b z, eval_lvalue g e le m a b z -> exists T, eval_lvalueT a b z T.
Lemma eval_exprT_lvalueT_fun:
(forall a v1 T1 v2 T2, eval_exprT a v1 T1 -> eval_exprT a v2 T2 -> (v1,T1)=(v2,T2)) /\
(forall a b1 b2 i1 i2 T1 T2, eval_lvalueT a b1 i1 T1 -> eval_lvalueT a b2 i2 T2 ->
(b1,i1,T1)=(b2,i2,T2)).
Lemma eval_exprT_fun a v1 T1 v2 T2: eval_exprT a v1 T1 -> eval_exprT a v2 T2 -> (v1,T1)=(v2,T2).
Lemma eval_exprTlist_ax2: forall es ts vs (E:eval_exprlist g e le m es ts vs),
exists T, eval_exprTlist es ts vs T.
Lemma eval_exprTlist_fun: forall es ts vs1 T1 (E1:eval_exprTlist es ts vs1 T1)
vs2 T2 (E2:eval_exprTlist es ts vs2 T2), (vs1,T1)=(vs2,T2).