module Chapter5.Brady.Vec 
         (A : Set)
       where

open import Function

open import Data.Unit
open import Data.Nat
open import Data.Fin
open import Data.Product

open import Relation.Binary.PropositionalEquality

open import Chapter1.Logic

open import Chapter2.IDesc.Fixpoint
open import Chapter2.IDesc.Examples.Vec

open import Chapter5.Ornament

VecO : orn (Constraint.VecD A) id id
VecO = orn.mk λ { zero  deleteΣ zero 
                                 (deleteΣ refl `1) 
                ; (suc n)  deleteΣ (suc zero) 
                                    ( λ _  
                                      deleteΣ n 
                                              (deleteΣ refl 
                                                       (`var (inv n)  `1))) }

Vec' :   Set
Vec' = μ  VecO ⟧orn 

vnil : Vec' 0
vnil =  tt 

vcons : ∀{n}  A  Vec' n  Vec' (suc n)
vcons a vs =  a , vs , tt