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Inductive vector {A : Type} : nat -> Type :=
| vnil : vector 0
| vcons : A -> forall {n'}, vector n' -> vector (S n').
Implicit Arguments vector [].
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.
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