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+Inductive vector {A : Type} : nat -> Type :=
+| vnil : vector 0
+| vcons : A -> forall {n'}, vector n' -> vector (S n').
+
+Require Import Coq.Program.Program.
+
+Program Definition head {A : Type} {n : nat} (v : vector A (S n)) : vector A n :=
+ match v with
+ | vnil => !
+ | vcons a n' v' => v'
+ end.
+
+Fixpoint app {A : Type} {n m : nat} (v : vector A n) (w : vector A m) : vector A (n + m) :=
+ match v in vector _ n return vector A (n + m) with
+ | vnil => w
+ | vcons a n' v' => vcons a (app v' w)
+ end.