(** * Properties of compile-time approximations of values *)

Definition val_match_approx (a: approx) (v: val) : Prop :=
  match a with
  | Int1 => v = Val.zero_ext 1 v
  | Int7 => v = Val.zero_ext 8 v /\ v = Val.sign_ext 8 v
  | Int8u => v = Val.zero_ext 8 v
  | Int8s => v = Val.sign_ext 8 v
  | Int15 => v = Val.zero_ext 16 v /\ v = Val.sign_ext 16 v
  | Int16u => v = Val.zero_ext 16 v
  | Int16s => v = Val.sign_ext 16 v
  | Float32 => v = Val.singleoffloat v
  | Any => True
  end.Remark undef_match_approx: forall a, val_match_approx a Vundef.

Lemma approx_unop_is_redundant_sound: forall op a v, Approx.unop_is_redundant op a = true -> val_match_approx a v -> eval_unop op v = Some v.