forallb

forallb.v

(** Recall the function [forallb], from the exercise
    [forall_exists_challenge] in chapter [Poly]: *)

Fixpoint forallb {X : Type} (test : X -> bool) (l : list X) : bool :=
  match l with
    | [] => true
    | x :: l' => andb (test x) (forallb test l')
  end.

(** Using the property [all], write down a specification for [forallb],
    and prove that it satisfies the specification. Try to make your 
    specification as precise as possible. *)