(** [Loc.no_overlap l1 l2] holds if elements of [l1] never overlap partially
  with elements of [l2]. *)

  Definition no_overlap (l1 l2 : list loc) :=
   forall r, In r l1 -> forall s, In s l2 ->  r = s \/ Loc.diff r s.Definition t := loc -> val.Definition init (x: val) : t := fun (_: loc) => x.Definition get (l: loc) (m: t) : val := m l.(** The [set] operation over location mappings reflects the overlapping
      properties of locations: changing the value of a location [l]
      invalidates (sets to [Vundef]) the locations that partially overlap
      with [l].  In other terms, the result of [set l v m]
      maps location [l] to value [v], locations that overlap with [l]
      to [Vundef], and locations that are different (and non-overlapping)
      from [l] to their previous values in [m].  This is apparent in the
      ``good variables'' properties [Locmap.gss] and [Locmap.gso].

      Additionally, the [set] operation also anticipates the fact that
      abstract stack slots are mapped to concrete memory locations
      in the [Stacking] phase.  Hence, values stored in stack slots
      are normalized according to the type of the slot. *)

  Definition set (l: loc) (v: val) (m: t) : t :=
    fun (p: loc) =>
      if Loc.eq l p then
        match l with R r => v | S sl ofs ty => Val.load_result (chunk_of_type ty) v end
      else if Loc.diff_dec l p then
        m p
      else Vundef.

Lemma gss_reg: forall r v m, (set (R r) v m) (R r) = v.