(** * Compatibility of evaluation functions with respect to memory injections. *)

Remark val_inject_val_of_bool:
  forall f b, Val.inject f (Val.of_bool b) (Val.of_bool b).Remark val_inject_val_of_optbool:
  forall f ob, Val.inject f (Val.of_optbool ob) (Val.of_optbool ob).Ltac TrivialExists :=
  match goal with
  | [ |- exists y, Some ?x = Some y /\ Val.inject _ _ _ ] =>
      exists x; split; [auto | try(econstructor; eauto)]
  | [ |- exists y, _ /\ Val.inject _ (Vint ?x) _ ] =>
      exists (Vint x); split; [eauto with evalexpr | constructor]
  | [ |- exists y, _ /\ Val.inject _ (Vfloat ?x) _ ] =>
      exists (Vfloat x); split; [eauto with evalexpr | constructor]
  | [ |- exists y, _ /\ Val.inject _ (Vlong ?x) _ ] =>
      exists (Vlong x); split; [eauto with evalexpr | constructor]
  | _ => idtac
  end.

(* Specifications: *)
Lemma eval_unop_compat: forall f op v1 tv1 v, eval_unop op v1 = Some v -> Val.inject f v1 tv1 -> exists tv, eval_unop op tv1 = Some tv /\ Val.inject f v tv.
Lemma eval_binop_compat: forall f op v1 tv1 v2 tv2 v m tm, eval_binop op v1 v2 m = Some v -> Val.inject f v1 tv1 -> Val.inject f v2 tv2 -> Mem.inject f m tm -> exists tv, eval_binop op tv1 tv2 tm = Some tv /\ Val.inject f v tv.
Lemma var_addr_correct: forall cenv id f tf e le te sp lo hi m cs tm b, match_callstack f m tm (Frame cenv tf e le te sp lo hi :: cs) (Mem.nextblock m) (Mem.nextblock tm) -> eval_var_addr ge e id b -> exists tv, eval_expr tge (Vptr sp Ptrofs.zero) te tm (var_addr cenv id) tv /\ Val.inject f (Vptr b Ptrofs.zero) tv.