Definition binary_constructor_correct
    (make: expr -> type -> expr -> type -> res expr)
    (sem: val -> type -> val -> type -> mem -> option val): Prop :=
  forall a tya b tyb c va vb v e le m,
  sem va tya vb tyb m = 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.Definition shift_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.

Lemma make_add_correct: binary_constructor_correct (make_add cunit.(prog_comp_env)) (sem_add prog.(prog_comp_env)).