> data Vect : Nat -> Type -> Type where
>      Nil : Vect Z a
>      (::) : a -> Vect k a -> Vect (S k) a

> %name Vect xs, ys, zs

> my_cong : forall f . (x : a) -> (y : a) -> x = y -> f x = f y

> my_curry : ((a, b) -> c) -> a -> b -> c

> my_uncurry : (a -> b -> c) -> (a, b) -> c

> append : Vect n a -> Vect m a -> Vect (n + m) a

> lappend : (1 xs : List a) -> (1 ys : List a) -> List a

> zipWith : (a -> b -> c) -> Vect n a -> Vect n b -> Vect n c

> data Env : Vect n Type -> Type where
>      ENil : Env []
>      ECons : a -> Env xs -> Env (a :: xs)

> %name Env es

> data Elem : a -> Vect n a -> Type where
>      Here : Elem x (x :: xs)
>      There : (p : Elem x xs) -> Elem x (y :: xs)

> lookup : Elem ty vs -> Env vs -> ty
