Definition poly_BC (p : pol) : BC :=
plusl_e (fst p) (map (poly_BC_mon (fst p)) (snd p)).

(* Specifications: *)
Lemma poly_BC_arities :
forall p, pWF p -> arities (poly_BC p) = ok_arities (parity p) 0.
Lemma poly_BC_correct :
forall p nl, pWF p ->
length (sem (poly_BC p) nl nil) = peval p (map (@length _) nl).