Instance CompSpecs : compspecs. make_compspecs prog. Defined.
Definition Vprog : varspecs. mk_varspecs prog. Defined.
Definition putchar_spec := DECLARE _putchar putchar_spec.
Definition getchar_spec := DECLARE _getchar getchar_spec.
Definition getchar_blocking_spec :=
DECLARE _getchar_blocking
WITH k : byte -> IO_itree
PRE [ ]
PROP ()
LOCAL ()
SEP (ITREE (r <- read stdin;; k r))
POST [ tint ]
EX i : byte,
PROP ()
LOCAL (temp ret_temp (Vubyte i))
SEP (ITREE (k i)).
Definition putchar_blocking_spec :=
DECLARE _putchar_blocking
WITH c : byte, k : IO_itree
PRE [ _c OF tint ]
PROP ()
LOCAL (temp _c (Vubyte c))
SEP (ITREE (r <- write stdout c ;; k))
POST [ tint ]
PROP ()
LOCAL (temp ret_temp (Vubyte c))
SEP (ITREE k).
Program Fixpoint chars_of_Z (n : Z) { measure (Z.to_nat n) } : list byte :=
let n' := n / 10 in
match n' <=? 0 with true => [Byte.repr (n + char0)] | false => chars_of_Z n' ++ [Byte.repr (n mod 10 + char0)] end.
Next Obligation.
Opaque Nat.div Nat.modulo.

Lemma read_sum_eq : forall n d, read_sum n d ≈
(if zlt n 1000 then if zlt d 10 then
write_list stdout (chars_of_Z (n + d));; write stdout (Byte.repr newline);;
c <- read stdin;; read_sum (n + d) (Byte.unsigned c - char0)
else Ret tt else Ret tt).