open import Level
open import Function

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

open import Chapter2.Logic

open import Chapter5.IDesc
open import Chapter5.IDesc.Fixpoint
open import Chapter5.IDesc.InitialAlgebra

open import Chapter8.Ornament

module Chapter8.Ornament.Algebra 
           {ℓ k : Level}
           {I K : Set k}
           {D : func ℓ K K}
           {u : I → K}
           (o : orn D u u) where

open import Chapter8.Ornament.CartesianMorphism o

ornAlgebra : Alg ⟦ o ⟧orn (μ D ∘ u)
ornAlgebra xs = ⟨ forgetNat xs ⟩ 

forgetOrnament : {i : I} → μ ⟦ o ⟧orn i → μ D (u i)
forgetOrnament = fold ⟦ o ⟧orn ornAlgebra