module dep where

data Nat : Set where
  zero : Nat
  suc  : Nat → Nat

data L (A : Set) : Set where
  []   : L A
  _::_ : A → L A → L A

data Vect (A : Set) : Nat → Set where
  vnil  : Vect A zero
  vcons : {n : Nat} → A → Vect A n → Vect A (suc n)

infix 2 _+_
infix 3 _*_

_+_ : Nat → Nat → Nat
n + zero = n
n + suc m = suc (n + m)

_*_ : Nat -> Nat -> Nat
n * zero = zero
n * suc m = n * m + n

inner : {n : Nat} → Vect Nat n → Vect Nat n → Nat
inner vnil vnil = zero
inner (vcons x xs) (vcons y ys) = x * y + inner xs ys