(** * Agreement between location sets and Mach states *)

(** Agreement with Mach register states *)

Definition agree_regs (j: meminj) (ls: locset) (rs: regset) : Prop :=
  forall r, Val.inject j (ls (R r)) (rs r).(** Agreement over locations *)

Record agree_locs (ls ls0: locset) : Prop :=
  mk_agree_locs {

    (** Unused registers have the same value as in the caller *)
    agree_unused_reg:
       forall r, ~(mreg_within_bounds b r) -> ls (R r) = ls0 (R r);

    (** Incoming stack slots have the same value as the
        corresponding Outgoing stack slots in the caller *)
    agree_incoming:
       forall ofs ty,
       In (S Incoming ofs ty) (regs_of_rpairs (loc_parameters f.(Linear.fn_sig))) ->
       ls (S Incoming ofs ty) = ls0 (S Outgoing ofs ty)
}.(** Agreement over locations *)

Record agree_locs (ls ls0: locset) : Prop :=
  mk_agree_locs {

    (** Unused registers have the same value as in the caller *)
    agree_unused_reg:
       forall r, ~(mreg_within_bounds b r) -> ls (R r) = ls0 (R r);

    (** Incoming stack slots have the same value as the
        corresponding Outgoing stack slots in the caller *)
    agree_incoming:
       forall ofs ty,
       In (S Incoming ofs ty) (regs_of_rpairs (loc_parameters f.(Linear.fn_sig))) ->
       ls (S Incoming ofs ty) = ls0 (S Outgoing ofs ty)
}.(** Agreement over locations *)

Record agree_locs (ls ls0: locset) : Prop :=
  mk_agree_locs {

    (** Unused registers have the same value as in the caller *)
    agree_unused_reg:
       forall r, ~(mreg_within_bounds b r) -> ls (R r) = ls0 (R r);

    (** Incoming stack slots have the same value as the
        corresponding Outgoing stack slots in the caller *)
    agree_incoming:
       forall ofs ty,
       In (S Incoming ofs ty) (regs_of_rpairs (loc_parameters f.(Linear.fn_sig))) ->
       ls (S Incoming ofs ty) = ls0 (S Outgoing ofs ty)
}.(** Agreement over locations *)

Record agree_locs (ls ls0: locset) : Prop :=
  mk_agree_locs {

    (** Unused registers have the same value as in the caller *)
    agree_unused_reg:
       forall r, ~(mreg_within_bounds b r) -> ls (R r) = ls0 (R r);

    (** Incoming stack slots have the same value as the
        corresponding Outgoing stack slots in the caller *)
    agree_incoming:
       forall ofs ty,
       In (S Incoming ofs ty) (regs_of_rpairs (loc_parameters f.(Linear.fn_sig))) ->
       ls (S Incoming ofs ty) = ls0 (S Outgoing ofs ty)
}.

Lemma agree_locs_undef_locs: forall ls0 regs ls, agree_locs ls ls0 -> existsb is_callee_save regs = false -> agree_locs (LTL.undef_regs regs ls) ls0.