Inductive quantity : Type := Q32 | Q64.
Definition quantity_eq (q1 q2: quantity) : {q1 = q2} + {q1 <> q2}.
(** * Memory values *)
(** A ``memory value'' is a byte-sized quantity that describes the current content of a memory cell.  It can be either: - a concrete 8-bit integer; - a byte-sized fragment of an opaque value; - the special constant [Undef] that represents uninitialized memory. *)
(** Values stored in memory cells. *)
Inductive memval: Type :=
| Undef: memval
| Byte: byte -> memval
| Fragment: val -> quantity -> nat -> memval.
(** * Encoding and decoding integers *)
(** We define functions to convert between integers and lists of bytes of a given length *)
Fixpoint bytes_of_int (n: nat) (x: Z) {struct n}: list byte :=
match n with
| O => nil
| S m => Byte.repr x :: bytes_of_int m (x / 256)
end.
Fixpoint int_of_bytes (l: list byte): Z :=
match l with
| nil => 0
| b :: l' => Byte.unsigned b + int_of_bytes l' * 256
end.
Definition rev_if_be (l: list byte) : list byte :=
if Archi.big_endian then List.rev l else l.
Definition encode_int (sz: nat) (x: Z) : list byte :=
rev_if_be (bytes_of_int sz x).
Definition decode_int (b: list byte) : Z :=
int_of_bytes (rev_if_be b).
(** Length properties *)

(* Specifications: *)
Lemma length_bytes_of_int:
forall n x, length (bytes_of_int n x) = n.
Lemma rev_if_be_length:
forall l, length (rev_if_be l) = length l.
Lemma encode_int_length:
forall sz x, length(encode_int sz x) = sz.
Lemma length_bytes_of_int:
forall n x, length (bytes_of_int n x) = n.
Lemma rev_if_be_length:
forall l, length (rev_if_be l) = length l.
Lemma encode_int_length:
forall sz x, length(encode_int sz x) = sz.