Definition binary_constructor_correct
(make: expr -> type -> expr -> type -> res expr)
(sem: val -> type -> val -> type -> option val): Prop :=
forall a tya b tyb c va vb v e le m,
sem va tya vb tyb = Some v ->
make a tya b tyb = OK c ->
eval_expr ge e le m a va ->
eval_expr ge e le m b vb ->
eval_expr ge e le m c v.
Section MAKE_BIN.
Variable sem_int: signedness -> int -> int -> option val.
Variable sem_long: signedness -> int64 -> int64 -> option val.
Variable sem_float: float -> float -> option val.
Variables iop iopu fop lop lopu: binary_operation.
Hypothesis iop_ok:
forall x y m, eval_binop iop (Vint x) (Vint y) m = sem_int Signed x y.
Hypothesis iopu_ok:
forall x y m, eval_binop iopu (Vint x) (Vint y) m = sem_int Unsigned x y.
Hypothesis lop_ok:
forall x y m, eval_binop lop (Vlong x) (Vlong y) m = sem_long Signed x y.
Hypothesis lopu_ok:
forall x y m, eval_binop lopu (Vlong x) (Vlong y) m = sem_long Unsigned x y.
Hypothesis fop_ok:
forall x y m, eval_binop fop (Vfloat x) (Vfloat y) m = sem_float x y.

(* Specifications: *)
Lemma make_binarith_correct:
binary_constructor_correct
(make_binarith iop iopu fop lop lopu)
(sem_binarith sem_int sem_long sem_float).
Lemma make_binarith_int_correct:
binary_constructor_correct
(make_binarith_int iop iopu lop lopu)
(sem_binarith sem_int sem_long (fun x y => None)).