(** * Operations over memory stores *)

(** The initial store *)

Program Definition empty: mem :=
  mkmem (PMap.init (ZMap.init Undef))
        (PMap.init (fun ofs k => None))
        1%positive _ _ _.(** Allocation of a fresh block with the given bounds.  Return an updated
  memory state and the address of the fresh block, which initially contains
  undefined cells.  Note that allocation never fails: we model an
  infinite memory. *)

Program Definition alloc (m: mem) (lo hi: Z) :=
  (mkmem (PMap.set m.(nextblock)
                   (ZMap.init Undef)
                   m.(mem_contents))
         (PMap.set m.(nextblock)
                   (fun ofs k => if zle lo ofs && zlt ofs hi then Some Freeable else None)
                   m.(mem_access))
         (Pos.succ m.(nextblock))
         _ _ _,
   m.(nextblock)).Definition free (m: mem) (b: block) (lo hi: Z): option mem :=
  if range_perm_dec m b lo hi Cur Freeable
  then Some(unchecked_free m b lo hi)
  else None.Fixpoint free_list (m: mem) (l: list (block * Z * Z)) {struct l}: option mem :=
  match l with
  | nil => Some m
  | (b, lo, hi) :: l' =>
      match free m b lo hi with
      | None => None
      | Some m' => free_list m' l'
      end
  end.(** Memory reads. *)

(** Reading N adjacent bytes in a block content. *)

Fixpoint getN (n: nat) (p: Z) (c: ZMap.t memval) {struct n}: list memval :=
  match n with
  | O => nil
  | S n' => ZMap.get p c :: getN n' (p + 1) c
  end.(** [loadv chunk m addr] is similar, but the address and offset are given
  as a single value [addr], which must be a pointer value. *)

Definition loadv (chunk: memory_chunk) (m: mem) (addr: val) : option val :=
  match addr with
  | Vptr b ofs => load chunk m b (Ptrofs.unsigned ofs)
  | _ => None
  end.(** Memory stores. *)

(** Writing N adjacent bytes in a block content. *)

Fixpoint setN (vl: list memval) (p: Z) (c: ZMap.t memval) {struct vl}: ZMap.t memval :=
  match vl with
  | nil => c
  | v :: vl' => setN vl' (p + 1) (ZMap.set p v c)
  end.Remark setN_other:
  forall vl c p q,
  (forall r, p <= r < p + Z.of_nat (length vl) -> r <> q) ->
  ZMap.get q (setN vl p c) = ZMap.get q c.Remark setN_outside:
  forall vl c p q,
  q < p \/ q >= p + Z.of_nat (length vl) ->
  ZMap.get q (setN vl p c) = ZMap.get q c.Remark getN_setN_same:
  forall vl p c,
  getN (length vl) p (setN vl p c) = vl.Remark getN_exten:
  forall c1 c2 n p,
  (forall i, p <= i < p + Z.of_nat n -> ZMap.get i c1 = ZMap.get i c2) ->
  getN n p c1 = getN n p c2.Remark getN_setN_disjoint:
  forall vl q c n p,
  Intv.disjoint (p, p + Z.of_nat n) (q, q + Z.of_nat (length vl)) ->
  getN n p (setN vl q c) = getN n p c.Remark getN_setN_outside:
  forall vl q c n p,
  p + Z.of_nat n <= q \/ q + Z.of_nat (length vl) <= p ->
  getN n p (setN vl q c) = getN n p c.Remark setN_default:
  forall vl q c, fst (setN vl q c) = fst c.(** [storev chunk m addr v] is similar, but the address and offset are given
  as a single value [addr], which must be a pointer value. *)

Definition storev (chunk: memory_chunk) (m: mem) (addr v: val) : option mem :=
  match addr with
  | Vptr b ofs => store chunk m b (Ptrofs.unsigned ofs) v
  | _ => None
  end.

Theorem store_valid_access_3: valid_access m1 chunk b ofs Writable.