module Chapter10.AlgebraicOrnament.Examples.Vec 
         (A : Set)
       where

open import Level hiding (zero ; suc)
open import Function

open import Data.Unit
open import Data.Nat
open import Data.Fin hiding (lift)
open import Data.Product

open import Relation.Binary.PropositionalEquality

open import Chapter6.IDesc
open import Chapter6.IDesc.Fixpoint
open import Chapter6.IDesc.InitialAlgebra
open import Chapter6.IDesc.Examples.Nat

open import Chapter10.Ornament
open import Chapter10.Ornament.Examples.List

open import Chapter10.Ornament.Algebra (ListO A)
import Chapter10.AlgebraicOrnament
open Chapter10.AlgebraicOrnament.Func ( ListO A ⟧orn) ornAlgebra

Vec : Nat  Set
Vec n = μ algOrnD (tt , n)

vnil : Vec ze
vnil =  (zero , lift tt) , refl , lift tt 

vcons : ∀{n}  A  Vec n  Vec (su n)
vcons {n} a xs =  (suc zero , a , n , lift tt) , 
                   refl , xs , lift tt